Talk:Type I and type II errors

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121.6 km/h. Thus, at this speed, 95% of drivers fined should have indeed exceeded the speed limit. And 5% will have not - but would still be fined. The fundamental point missing here is that many cars will be well in excess of 121.6 km/h, and nearly 100% of these will be rightly fined, with very few falsely fined. Thus, based on this, the rate of false positives should not be equal to alpha: rather it should be equal to OR LESS THAN alpha. Hardly any text that I have come across address this problem. Rather oddly, as the precision of the measurement improve the PROPORTION of false positives does not seem to change, but the total number of false positives increases. This is because many of those drivers that would not have been fined with a less precise measurement are now fined - because the critical speed has been brought closer to 120 km/h. This increases the number of people in the potential false-positive group. So improving the experiment leads to a greater number of people being falsely accused of driving above the speed limit, and at the same time it reduces the number of drivers that get away without a fine.

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to be negative and the test return positive. A false negative is the converse (known to be true, test returns false). In contrast, type I error is the probability of incorrectly rejecting the null hypothesis and making a wrong claim. Whereas type II error we fail to reject the null hypothesis even though the alternative hypothesis is true. BTW: Other term you may want to add include: The sensitivity of of a test is the P(test positive|has condition), and the sensitivity is P(test negative|without condition). The predictive value positive (which is most likely the piece of information physicians and patients actually want) is the P(has condition|positive test) and the predictive negative value is the P(without condition|negative test). --Dan (Daniels W.W, Biostatistics: A Foundation for Analysis in the Health Sciences 8th Ed,p74-5,217, Wiley:New York)

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undesirable outcomes. However, unlike many other forms of testing and measurement, the purpose of the security screening is, ostensibly, to reduce the incidence of Type II errors to zero or as close to zero as possible. Consequently, the rate of Type I error is of secondary importance. The only time this would be of primary relevance would be if you were comparing two or more different screening protocols, all of which identical Type II error rates, but each of which had a different Type I error rate. The protocol that had the lowest incidence of Type I error would obviously be preferable under these circumstances, but of course this assumes complete equivalence among all of the measured protocols in eliminating Type II errors to begin with.

5027:"speculative" hypothesis that is being compared to the null hypothesis.) 2. True and False have little place in science,(but unfortunately statistics is midway between science and math, and these terms have STATISTICAL meaning different from their common one). 3.Signficance has a fairly well defined meaning in Statistics. It should not be confused with error (but a discussion of these concepts is far too involved to go into here.) Your use of the term is wrong here - specifically a result can be significant whether or not it confirms or contradicts ANY hypothesis and equally confirmation or negatation of ANY hypothesis can be "not significant". 4664:

That is not Type I error. Also an "error of credulity" could go either way - too much or too little. There is no good way to fix these sentences using the same words because they can be interpreted different ways. What is an "error of skepticism"? Was one too skeptical? Not skeptical enough? Skeptical when they should have been credulous? Finally I cannot see why anyone would want to rely on an "Encyclopedia of Pseudoscience" for a definition of a statistical concept. I could find ten other good definitions in statistical references. I don't think that we want pseudoscience but rather science.

901:. The reason they were not included in this "original" article is due to the fact that the present article, as it stands, is a comprehensive rearrangement and reordering of information, and an amalgamation of already existing Wiki-articles that, in my view, should never have been existing separately in the first place, given that (a) each needed to be understood in the context of the others, and (b) the way each was written did not encourage the reader to visit any of the other associated articles. (In other words, there is no reason not to do what you suggest). 1259:. Hope your wrist is better soon. I have followed the links you provide. The articles you have displayed certainly do separate the "references" from the "footnotes"; however, as I understood from your original request, you were well aware that Wiki articles did not have "pages" (in the same way that the articles you have offered as samples have individual pages) -- and, therefore, you were aware that it was impossible for the "footnotes" to appear at the bottom of each page (whilst the "references" appeared at the absolute end of the article). 2912:

psychology. For example:Schernhammer et al state, “Findings from this study indicate that job stress is not related to any increase in breast cancer risk”. In fact their trial contained many serious flaws and so demonstrated nothing. A claim of rejection as a null hypothesis is predicated on a complete and flawless study which is very often not the case. Schernhammer, ES, Hankinson, SE, Rosner, B, Kroenke, CH, Willett, WC, Colditz, GA, Kawachi, I. Job Stress and Breast Cancer Risk. Am J Epidemiol, 2004 160(11):1079-1086

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in" one or another kind of "population" (the term "population" has a technical meaning in statistics and is not synonymous with "statistical sample"). However, my real problem is that I simply don't understand three out of five sentences in this paragraph (I do understand sentences #1 and #3). There are some "differences between two populations" that random samples are supposed to be "averaging out." What are then the differences that persist "post treatment"? (While we're at it, what is this "treatment," enclosed in

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x-axis being labelled P(FP), FPR), and the 2x2 table in the upper right. The caption only describes the top diagram, and there is no explanation whatsoever for the bottom diagram, nor for the 2x2 table in the upper right. I think the diagram should be split up into 3 separate diagrams (upper diagram, lower diagram, and 2x2 table), each being described by a well-written caption. This would be in the spirit of answering the criticism that "This article may be too technical for most readers to understand."

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work created by our predecessors, until we have evidence to do otherwise, and most of these derived texts tend to be more accessible to the non-statistician. However I agree that, when writing for e.g. Knowledge, it is certainly useful to differentiate between 'correct' and 'common' usage, particularly when the latter is rather misleading. This is why your contribution intrigued me so -- I look forward to reading around this and getting back to you soon -- many thanks for your swift reply! --

1112:. I would say I agree with what you have done, but not how you have done it. I much preffered the old style of linking when references were by numbers, rather than the new inline scheme which you now employ. I didn't do the changes myself since I am not sure of how to do them, but what I would have liked had been two separate numbering schemes, one for the footnotes and one for the references. I've done some research on the proper style for wikipedia, but I can't figure it out properly, see ( 174: 153: 2979:?) I find the whole second sentence (the one beginning with "The argument is") very confusing. And finally, what is the point of this paragraph? Is it simply to warn that Type-I errors are always possible? Or is it that Type-II errors are always possible? In either case, it's too trivial a point to deserve a paragraph. If the intention is to say something else, then the whole paragraph should definitely be re-written by someone who understands what this something else is supposed to be. 31: 4206:(6) That historical aspects be reduced to one such brief paragraph, rather than as an alternative parallel development of the fundamentals; (Every chemist mentions its origin with Kekule when teaching about benzene's aromaticity; no one spends any more than a line or two on it, because our understanding of the concept is all the deeper for the passed time, and because the target audience for his writing is not like current audiences in any way; and 1944:

Suppose the test indicates that the disease condition exists or that the illegal drugs were taken. Then, if the patient is disease-free, or the drugs were not taken, this is a "false positive" in the usual meaning of the term. If for example under the null hypothesis, 5% of the subjects nonetheless test positive, then it is usually said that "the type I error rate is 0.05." That is, 5% of the subjects have falsely tested positive.

1207:(1) If you still feel that the "references" should be (a) separate from the "footnotes", and (b) not in the article's text -- and, as I have said, I have no aesthetic or intellectual objections to such a move -- then maybe you should request "HELP ME" and seek the advice and guidance of a Wiki "higher up" (because there may be some "higher level" of programming or formatting that will allow you to achieve what you are seeking). 1450:. I'm not sure if it is the best name, but I would like a major heading, with "Neyman and Pearson","Type I and type II errors","False negative rate","False positive rate" and "The null hypothesis" as subheadings. "Bayes' theorem" is probably also best treated under this heading. I think some rearangement could be done under this chapter too, perhaps reducing the number of subheadings, and introduce a subchapter "definitions"? 1026:. I'm not sure if it is the best name, but I would like a major heading, with "Neyman and Pearson","Type I and type II errors","False negative rate","False positive rate" and "The null hypothesis" as subheadings. "Bayes' theorem" is probably also best treated under this heading. I think some rearangement could be done under this chapter too, perhaps reducing the number of subheadings, and introduce a subchapter "definitions"? 446:

you want to explain someone what a false postive is in the case of an anti-virus check and you point him to this site. He will see all the math talk and run - but that is not necessary: the concept of a false positive can be understood even if you have no clue about statistics. e.g. here is an explanation which has nothing to do with statistics, but is perfectly understandable for people who are not mathematically inclined:

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single case is not altogether different from the apple example, and if many such people make many such choices, the error becomes statistically significant. Maybe I should mention that while single case examples can help illustrate the Types, that they do not become statistically relevant until there is a group of them. Otherwise, what do you think of the current lead as I updated it yesterday?

3309:. When talking of an experiment to determine whether a taster can successfully discriminate whether milk or tea was added first to a cup, Fisher defines his null hypothesis as "that the judgements given are in no way influenced by the order in which the ingredients have been added ... Every experiment may be said to exist only in order to give the facts a chance of disproving the null hypothesis." 1084:. Upon reflection your views are correct here. They are two entirely different sorts of "additional information". I will do my best to correct things so that everything now matches your design -- except that, I now think that the piece in note 8 ("O" not zero, etc) should appear in the text (simply on the basis that most of those prone to make the mistake will probably not look at the footnote). 278: 916:(d) a description of practical instances of each of the terms' application -- and, wherever possible, the examples of the usages are contrasted such that, depending upon the real-life applications you might be describing, you might finish up describing "true negative" contrasted with "false positive" in one situation, and "true negative" contrasted with "true positive" in another, 262: 4646:

choosing for credulity, i.e. choosing a reliable investigator, who only cries "wolf" when he is pretty sure there is one. If we want to use the words credulity and skepticism in connection with the types of error, we may say: as a consequence of the "credulity" an error of type I is sometimes made, and as a consequence of the "skepticism" an error of type II is sometimes made.

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the case (by contrast with "scientists" who generally couch their research question in terms of what they actually believe to be the case) is something that someone like you could far better describe than myself -- and, also, I believe that it would be extremely informative to the more general reader. All the best in your editing. If you have any queries, contact me again pls.

2930:) I suggest that it would be far better to choose a domain other than pregnancy for the example; because it could well be construed that, rather than testing for the presence/absence of a pregnancy (i.e., the presence of a foetus within the woman's uterus), it was actually testing for the presence/absence of a "false pregnancy" (viz., pseudocyesis with no foetus present). 22: 4203:(5) That all other extraneous subject matter be limited or eliminated, e.g., in taking the reader from standard Type I/II thinking to the current state of the statistical art (what most statisticians believe and apply, right now), rather than listing encyclopedically every additional proposed error type, even the humorous -- one short insight-filled paragraph (please!); 363:

bringing them back around home to what are Type I and Type II errors shown. While I follow the example easily, I don't yet completely trust my mapping of the example to the error types, which I am left to do on my own, in part because the text in the initial definition of the types is confusing, appearing to rely on double negatives for the definition. But I'm not sure.)

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written in such a way that it's not always clear what one should consider the null hypothesis. Thus, when discussing computer identity authenticitation, I've presumed that a positive test results corresponds with identifying the subject logging in as authentic, whereas a negative result corresponds with identifying the subject as an imposter. Please check my work.

1432:. I'm not familiar with this term, but for certain it should not be introduced in subchapter x.y.z.t etc. This need to be promoted somehow. I'm not sure of how, but either we could use spam filtering as the case study (No need to be conservative about the screening if not necessary), or we could make spam filtering the only case study. Other sugestions are welcome. 1008:. I'm not familiar with this term, but for certain it should not be introduced in subchapter x.y.z.t etc. This need to be promoted somehow. I'm not sure of how, but either we could use spam filtering as the case study (No need to be conservative about the screening if not necessary), or we could make spam filtering the only case study. Other sugestions are welcome. 2155:, and perhaps that could be expanded to take in (positive and negative) likelihood ratios as well, or alternatively split off into a separate article. To be honest, Knowledge's coverage of theis topic seems in need of some major reorganisation, so if you want to contribute it would be much appreciated. (Registering a user name might be a good start). Regards, 3560:

basis is more a "preponderance of doubt". It could also be argued that the de facto situation in a kangaroo court uses a "not innocent" null hypothesis, but in that case I don't beleive it's consistent with a hypothesis test either since the "truth" is not what they're after. I never heard of someone being found "not innocent" by even a kangaroo court.

1096:. Forgot to mention that, overall, the article looking much better with your input. Also far more informative. Hope that what I have done with the references now meets your approval. If it doesn't, can you please explain why (as I have done what I think you are asking). Also, I hope that you agree that the "O"/zero bit should appear 3231:

many conversations with professional mathematicians and statisticians and none of them had any idea where the notion of Type I and type II errors came from and, as a consequence, I would not be at all surprised to find that the majority of mathematicians and statisticians had no idea of the origins and meaning of "null" hypothesis.

1072:. They should be separated in order to make a clear distinction between them. A typical reader (at least me) would typically read the footnotes, but only look up the references if they were of special interest to me. Having too many notes makes the text flow badly, while adding many references are usually not a big problem IMHO. 2014:, hence I concluded without checking into the matter that the interchange was vandalism. Upon investigating your claims, I agree that they have substance. There is a list of work that has to be done to this article, so I will put it on the todo list, however if you had been able to do it yourself, nothing would be better. 2048:. First off, I would like to thank you for your edits. I have two tips about form which I would like to bring to your attention. You forgot to use an edit summary, upon doing such a major edit, it is especially important, since it could easily be considered vandalism or its like. I would have used an edit summary such as 1048:. Away for a couple of days. Will respond more fully then. All seems ok with what you have written, except for bit on footnotes. Can you please explain (at some length because I don't understand what you have written at all) what you mean in relation to the remarks on footnotes and references? Back in 2 days. Best to you 3795:: they are used in completely different disciplinary domains, and are used to denote entirely different entities as their respective referents. A merge would simply encourage an unproductive and misleading sloppiness of speech and thought in those who are less better informed and who come to Knowledge to be set straight. 3602:

very confusing. A false positive doesn't "indicate" anything; a false positive is a statistical mistake - a misreading of the auguries, if you will. I've also taken out the Winnie-the-Pooh capitalization and inserted "actually" to make it clear that the false positive (or negative) stands in contradiction to reality.

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Obviously, life isn't as simple. There is little chance that one will pick random samples that result in significantly same populations. Even if they are the same populations, we can't be sure whether the results that we are seeing are just one time (or rare) events or actually significant (regularly occurring) events.

1906: 1247:. Except for the Trier article, they all use the same style. The Trier article has an interesting alternative style. FYI, I will probably not be doing so much editing for a while, since I have broken my wrist this weekend, and using the keyboard with one hand is not that easy. (Training is bad for the body ;-) ) 3015:

any alternative terms that have been proposed in the literature? This would make an important topic to include in the article, if this sort of thing has gone on. It seems there may be a parallel here between this sort of thing and what has happened in other areas of mathematics, such as where the use of

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So far so good. But what about the terms (excessive) "skepticism" and "credulity". Normally a test is skeptical, i.e. one only beliefs there is a wolf if one sees one. Because of this skepticism a type I error is not made easily. As a consequence a type II error is at hand, and may only be avoided by

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What makes an apple healthy and unhealthy? If you don't buy it, you won't know until someone else make a bad decision. It's a selfish decision example. It takes an objective outsider to help. Four cases for the individual, extra cases to get the statistical errors. The simple single event example

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I moved this from the Lead. The 4-option matrix is helpful (there's actually a chart of this in the body of the article, maybe it should go there. It probably doesn't belong in the lead, since there are already examples, but let's discuss that. Also, whether type I or type II error is more harmful

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I suggest removing this example table. I'm not clear on what legal system abjectly uses a test for "innocence" where the presumption (null hypothesis) is on "not innocent". It could be argued that civil law uses this; however, there it's not really consistent with a hypothesis test at all since the

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article, I will more drastically change the paragraph that suggests that, for a one-tailed test, it is possible to have a null hypothesis "that sample A is drawn from a population whose mean is lower than the mean of the population from which sample B is drawn". As I had previously suspected, this is

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Later, Fisher talks about fair testing, namely in ensuring that other possible causes of differentiation (between the cups of tea, in this case) are held fixed or are randomised, to ensure that they are not confounds. By doing this, Fisher explains that every possible cause of differentiation is thus

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Finally, and this comment is not meant to be a criticism of anyone in particular, simply an observation, I came across something in social science literature that mentioned a "type 2 error" about two years ago. It took me nearly 12 months to track down the source to Neyman and Pearson's papers. I had

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Once again, the truth table got changed to an invalid state. The problem is obviously that True and False are used here in two different senses (i.e. the name of the actual condition and the validity of the test result); and so some people look at the intersection of the False column and the Negative

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you will also find that the smart and innovative system used -- which allows distinctions to be made between "NOTES" and "CITATIONS" within the text of the main article -- also allows the use of (digit) "footnotes" within the (alphabet) "NOTES" section that direct the reader to the "CITATION" that is

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which -- as far as I can tell (and I stress "as far as I can tell") -- has a number of participants advocating a position that what they term "references" and what they term "footnotes" should be processed in such a way that they appear in separate lists (a distinction which, I think, matches the two

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I personally do not agree about the section called : Consequences. Where the article discusses NASA. You guys wrote: "For example, NASA engineers would prefer to throw out an electronic circuit that is really fine (null hypothesis H0: not broken; reality: not broken; action: thrown out; error: type

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The reference given does not say that Type I error is an "error of credulity." It discusses these terms in the extremes: "believe everything!" and "believe nothing!" The phrase "Type I error is an error of credulity" is vague - does it mean that one makes an error by believing that the null is true?

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In case 1 and 4 you made no mistake your decision was correct. But in case 3 and 4 there is error. Error in case 2 is more harmful, it effect you more because you have purchased unhealthy apple. So this is TYPE II error. Where as error of case 3 is not so crucial, is not so harmful. because you have

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I've changed the two "In other words" lines that try to put the false negative and false positive hypotheses in layman's terms, in order to clarify them a bit. In their previous form they said "In other words, a false positive indicates a Positive Inference is False." This is both poor grammar and

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I'm not entirely certain, But I have a feeling that Fisher's work -- which I cited as "Fisher (1935, p.19)", and that reference would be accurate -- was an elaboration and extension of the work of Neyman and Pearson (and, as I recall, Fisher completely understood the it was an oh, rather than a zero

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The consistent application by statisticians of Neyman and Pearson's convention of representing "the hypothesis to be tested" (or "the hypothesis to be nullified") with the expression Ho -- associated with an increasing tendency to incorrectly read the expression's subscript as a zero, rather than an

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I have heard many statisticians complain about how "type I" and "type II" error are bad names for statistical terminology, because they are easily confused, and the names themselves carry no explanatory meaning. Has anyone encountered a published source making a statement to this effect? Are there

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At this point one might have wanted to, say, provide a better segue into this paragraph, getting rid of the awkward "Associated section" lead in. One might also have corrected the fourth sentence (the one beginning with "There is little chance"), which makes it sound as if random samples can "result

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One last concern I have is that the whole thing with the medical examples is not helping to understand the statistical elements underlying the two types of errors. It's like we are no longer dealing with conditional probabilities, and instead we are finding simple frecuencies and classifying them in

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As the original contributor, I have written a new introduction, and have moved the previous introduction down the page. I think that, as I have written it, most of the "complaints" about the technical complexity of the article will stop -- given that we can now say that the other stuff is connected

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So, though rarely would I say this, I feel less solidly informed on this subject (honestly, feeling more confused) after perusing the wiki article than I did when first coming to the site (after having looked at 2-4 min YouTube videos to see state of that pedagogic art). Here, one is left with the

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I believe that it might be helpful to make some sort of comment to the effect that when statisticians work -- rather than scientists, that is -- they set up a question that is couched in very particular terms and then try to disprove it (and, if it can not be disproved, the proposition stands, more

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I'd agree that i'd prefer "fail to reject the null" to "accept the null" (and i see it's been changed now). However I think the term "false negative" *is* appropriate as the situation in medical testing is pretty much analagous - a negative test result means e.g. "the test produced no evidence that

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Despite the Knowledge guideline to be bold, I'm posting this to the talk page rather than making a correction to the article itself, in part because my knowledge of statistics isn't all that deep and there may well be further subtleties here that I'm missing. (In other words, I'd rather risk a type

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I think that the right way to approach this in the main article is to point out (and link to) the connection to decision theory, perhaps using this example as a springboard. But since this article is explaining only Type I/II errors, it isn't the place to give a full explication of decision theory.

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I hear what you're saying and indeed the double negative bothers me as well. The problem is that according to standard (frequentist) hypothesis testing theory, one never "accepts" the null hypothesis; one only "fails to reject" it. I haven't been able to think of a good way around this that is both

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Hi, First time making a comment so forgive me if this is in the wrong place. The article gives the impression that false positive and type I errors are the same and false negative and type II error are the same. This is common, but incorrect. A false positive results is when true status is known

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What do others think about this merger? I wanted to point a friend to an article about "false positives". Even though the information in the article is statistically correct, it makes little sense if you talk about false positives in the context off e-mail spam filters or anti-virus checks. Imagine

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I thought the definitions are the following: Type I error is: rejecting the null hypothesis when it is really true. Type II error: accepting the null hypothesis when it is really not true. Null Hypothesis: the hypothesis a researcher is testing is not true, there is no statistical significance.

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redirect, hoping for some basic explanation of what a false positive is and what the significance of them is. Instead I get something about a "Type I error" and an "error of the first kind" that just makes my brain hurt trying to understand what it is saying - and I've taken an undergraduate-level

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While there are portions of great substance in this article, overall it leaves this reader -- who has seen many presentations of this subject over the years, and three further today -- with the impression of a flailing about with the subject, or perhaps experimenting with it. It is like a teacher

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As far as I remember, the null hypothesis in database searches is that documents are NOT relevant unless proven otherwise. This is thus exactly the opposite of what is said in the article. I tend to remove the whole section, but I think I will wait for some time to see whether citations for one or

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The way that the notion of just precisely how the issue of a "null hypothesis" is contemplated by "statisticians" and the way that this (to common ordinary people counter-intuitive notion) of, essentially, couching one's research question as the polar opposite of what one actually believes to be

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First of all, you are quite right to talk of the null hypothesis as the 'original hypothesis' -- that is, the hypothesis that we are trying to nullify. However Neyman & Pearson do in fact use a zero (rather than a letter 'O') as the subscript to denote a null hypothesis. In this way, they show

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As a general comment, I think it entirely acceptable for people working in a subject, or writing a subject-specific text book / course to read texts more geared towards their own flavour of science, rather than the originals. After all, science is built upon the principle that we trust much of the

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Now I know the trouble with stats in empirical science is that everyone is always feeling their way to some extent -- it's an inexact science that tries to bring sharp definition to the real world! But I'm really intrigued to know what you're basing this statement on -- I'm one of those people who

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A parent is worried that his teenage daughter has been lying to him. She said to him: "last night I went to Amanda's house". The father suspects that she went to a party instead. If he checks with Amanda (his daughter's friend) whether she was there indeed, there is some chance that she lies to

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Reading the article more carefully, I find that it is inconsistent even within itself about "false negative" and "false positive". Whereas the lead-in (incorrectly) identifies a false negative as "rejecting a null hypothesis that should have been accepted", later on in the article, in the "medical

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The further work, to some extent, needs someone with a higher level of statistical understanding than I possess. However, I am certain that, now I have supplied all of the "historical" information, supported by the appropriate references, that the statistical descriptions and merging will be a far

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I've been doing some minor edits on the diagram caption, namely defining the acronyms. Now I realize that the diagram is really 3 diagrams - the "upper diagram" (with the overlapping blue TN bell curve and red TP bell curve), the "lower diagram" (with the y-axis being labelled P(TP), TPR, and the

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You wrote:"Null Hypothesis: the hypothesis a researcher is testing is not true, there is no statistical significance." This is just plain wrong but the NASA example has been removed.. 1. a researcher could be testing the null hypothesis. (But (as of August, 2015) the article explains that it is a

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I agree that it's not a great example. Although, the single simple event is implied to have scale effects; for example, a common type II error, and one used in the article is a legal case, is where the court lets a guilty man go free to avoid the type I error of convicting an innocent one. That

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on what the null hypothesis is. Sometimes being too conservative is ok (walking along a cliff), but sometimes being too conservative is very harmful (not pulling the trigger enough). Sometimes being too open is ok (meeting new friends) but sometimes being too open is very dangerous (falling for

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It isn't quite true that one normally tries to make the Type I and Type II error rates equal. Usually one tries to balance the two against each other, i.e., choosing a test that will have an appropriate Type I error rate, and then picking other factors (e.g., the number of cases tested) that will

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This makes the order of "condition positive" and "condition negative" columns more consistent with all the Knowledge pages that contain the confusion matrix information. I believe this version of the table makes the concepts more easily mentally connected with both hypothesis testing and machine

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I think that there is a fundamental error when stating that the probability of a type I error is equal to alpha. I don't think this is correct. I refer you to the discussion in the article about the calculation of the average speed of a car. At alpha = 0.05 it is stated that the critical speed is

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Rework the introduction, again, to be less confusing, especially eliminating the possible misinterpretation of double negatives. (I find some of the examples useful, like the tradeoff about the risk in airport security between false negatives and false positives. What's missing in the examples is

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The moral of The Boy Who Cried Wolf is that if you abuse peoples trust they wont trust you when it matters. It is about deliberate deciet not being mistaken (i.e. an error!). It's not intuitive and it's a terrible metaphor. It really doesn't help make it clearer. Why not use an example which is

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If this is a vote, I agree with Qwfp and Frederic Y Bois--the terms Type I and Type II errors are widely used in statistics and (at least) the social sciences. Were a student to look up Type I errors and be redirected to Sensitivity, she would be enormously confused, since the concepts are only

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Unfortunately, I do not have these papers at hand and, so, I can not tell you precisely which of these papers was the source of this statement; but I can assure you that the statement was made on the basis of reading all three papers. From memory, I recall that they were quite specific in their

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Yeah, I sometimes forget the edit summary and after I sent it off I had a "Doh!" moment. The only problem with repeated indents is that after a while it gets out of hand; so I was using the alternative convention where the original person doesn't indent. I've seen this frequently. But since you

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is saying... it depends on how you define your positive test result. If a positive test indicates an intruder (which would be my intuition for a computer security test), then the example is correct. If a positive test indicates a user, then the example is reverse. I've actually seen "positive"

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accept the null. You either reject the null (i.e. accept the alternative) or you refrain from rejecting the null. So the above sentence incorrectly defines "type II error". However, a "false negative" can indeed refer to a situation where an assertive declaration is made, e.g. "You do not have

2563:

That said, it is still the case that in decision problems, the Type I/II error rates are part, but not all of the problem. For one thing, Type I/II error rates assume that the null/alternative hypothesis is correct, and take no account of the probability that the null/alternative hypothesis is

2075:

I look forward to your having a chance to check my edits. I do think that the article needs a lot of work, even now. For example, a preamble identifying examples of null hypotheses and positive/negative test results, at the very beginning, would help. As it is, the initial definitions are very

2034:

Hi, I've made the changes I am aware of that should be made. There was also some confusion on sensitivity and power which I've also fixed. However, as this was done in one grand edit, I may have missed some things or incorrectly changed some others. Part of the confusion is that the article is

1943:

In my experience, the usual notion of false positive is in situations such as this: One is testing to see if a patient has a disease, or if a person has taken illegal drugs. The null hypothesis is that no disease exists, or no drugs were taken. A test is administered, and a result is obtained.

2911:

To assert a type 2 null hypothesis deductively implies that the experiment is "complete", in other words, the methodology was perfect, the measuring instruments were 100% accurate, every confounding factor was fully accounted for. In many areas of research we can not say this, particularly in

2968:

Associated section - Statistics derives its power from random sampling. The argument is that random sampling will average out the differences between two populations and the differences between the populations seen post "treatment" could be easily traceable as a result of the treatment only.

4717:

Talk here would essentially be recapitulating them. Concisely, The edits removed unnecessary anecdotes, unreferenced claims for alternative names, and focussed on clear examples (as requested in the heading, noting that the article is current;y unapproachable. No substantive content removed

3363:

I will tone down the paragraph about original vs. nil hypotheses: the subscript is actually a zero, but it is entirely correct that the hypothesis should not be read as a "nil hypothesis" -- I agree that it is important to emphasise that the null hypothesis is that one that we are trying to

2533:

Comment: I am not sure if "positive predictive value" is an appropriate method of measurement of security screening measures, because Type I and Type II errors are not of equal importance in this context. Traditional analysis of error rates assumes that Type I and Type II errors are equally

4483:

A type I error (or error of the first kind) happens when a statistician mistakenly suggests a new cause and effect relationship. The correct conclusion in such as situation should have been to accept the "null hypothesis" (ie the hypothesis that the relationship observed by predecessors is

3689:

I agree with Frederic. Many people in the health sciences need to learn about sensitivity and specificity but do not need to learn about Type I and Type II errors and would be confused by that nomenclature (which is pretty awful, IMHO, but its far too entrenched to change it). Although the

3324:

Finally, Fisher emphasises that "the null hypothesis must be exact, that is free from vagueness and ambiguity, because it must supply the basis of the 'problem of distribution,' of which the test of significance is the solution". He gives an example of a hypothesis that can never be a null

4343:

I rewrote the introduction, firstly because the term "false positive" and "false negative" come from other test areas, and are not specifically used in statistical test situations. And secondly the example that was given, could hardly be understood as an example in a statistical test.

4524:

with the imprecise catachrestical extension of the technical terms (by people that are too lazy to create their own) into these other areas in which, it seems, it is not desirable to speak in direct plain English, and that one must be as distant, obscure, and as jargon-laden as possible.

4216:

Note: The only thing I did editorially was to remove as tangential the reference to types of error in science, because that section begged the question of the relation of those types to this articles' Types I and II error, where connection (explanatory text) was completely missing. (!)

3248:

Thanks for the references, Lindsay658 -- I'll dig them out, and have a bit of a chat with my more statsy colleagues here, and will let you know what we reckon. I do agree that it's somewhat non-ideal that such a tenet of experimental design is described rather differently in a range of

2260:

I am a judge in a court, there is a suspect of murder and he is trying to prove his alibi. What would be the null hypothesis? Lets assume I have no evidence that the suspect is guilty, but still: can I reject the validity of his alibi? If I do so, does it turns him innocent? does it

1931:

above, the false negatives becomes the sum of the offdiagonal column elements belonging to the respective hypothesis, while the false positives becomes the sum of the offdiagonal row elements. The true positives becomes the ondiagonal element, while true negative makes little sense.

1200:

I have not the slightest "personal" problem with your suggestion, which seems just as logical (if not more logical) as having them all combined; but it does seem that, according to the current Wiki convention, the "references" must be either in the "text" of the article, or in the

4956:

I, false positive) than to use one on a spacecraft that is actually broken (null hypothesis H0: not broken; reality: broken; action: use it; error: type II, false negative). In that situation a type I error raises the budget, but a type II error would risk the entire mission."

2393:

So, in sum, my suggestion is to state these errors as being "consistent with the data" or "inconsistent with the data", instead of the "accepting" and "rejecting" terminology. See Arnold Zellner's chapter in the "Handbook of econometrics" of Elsevier for a reliable source on

2307:

hypothesis are not independent, and one should be careful to always state both the null and the alternative together. Otherwise, a reader might think that the corresponding null of "H1: the guy is innocent" was "H0: the guy is guilty", which is not the case! Lets see another

1262:

Thus, the focus of my response was at the possibility of having both "footnotes" and "references" (a) in different locations at the end of the article, and (b) indicated in a different way (so that one could easily say "this indicates a footnote" or "this indicates a

3320:

is "that the death-rates of two groups of animal are equal, without specifying what those death-rates actually are. In such cases it is evidently the equality rather than any particular values of the death-rates that the experiment is designed to test, and possibly to

3127:"O" (for "original") -- has led to circumstances where many understand the term "the null hypothesis" as meaning "the nil hypothesis". That is, they incorrectly understand it to mean "there is no phenomenon", and that the results in question have arisen through chance. 2052:. Another less important thing is how you reply on this discussion page, you should really use indentation with an apropriate amount of ":". In large discussions it makes it easier to follow branches. I'll try to find time to verify your actual edits some time later. 1303:

The special case in this article is the amount of footnotes and how we make references. This boils down to my original problem, references are good, footnotes too, but only in limited numbers. The amount of notes is so large that we should perhaps do something about

4111:, which would clearly link (also using aforementioned table) often confused, but related terms such as type I and II errors, false negative, positive, alpha, beta, sensitivity, specificity, false positive and negative rate etc - this should of course not appear in 2962:

on 10 December 2006 (19:27 edit). The second paragraph, starting with the lead-in "Associated section," was (at the time I deleted it) substantially the same as in that original contribution. To help the discussion, here is the deleted paragraph in its entirety:

4887:

For those experiencing difficulty correctly identifying the two error types, the following mnemonic is based on the fact that (a) an "error" is false, and (b) the Initial letters of "Positive" and "Negative" are written with a different number of vertical lines:

4379:

I've noticed that "false positive" and 'false negative" directs to this article. This means this either article should clearly treat all the terms and the different context they refer to, or a separate article should treat "false positive" and 'false negative".

4093:

discusses issues arrising in the application of statistical methods to fields such as medicine, physics and "airport security check science". I have edited the summary accordingly, also adding (a little clumsy) "about" template redirecting "applied" readers to

4248:

I also find the article confusing (as most of statistic textbooks). The hypothesis is a set of parameters, and the probabilities \alpha and \beta depend hence on the parameter. I think \alpha and \beta should be bounds of the probabilities, not probabilities.

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sense of the results of gulping large mouthfuls and swallowing with only brief chewing -- which gets the job done, but is not great in terms of nutrition (or avoiding GI discomfort). I ascribe the impression as likely being due to the polyglot authorship.

1972:

Therefore, I seriously propose that the article be edited to reflect properly the usual uses of these terms. As it stands, any Freshman statistics student would be immediately confused when comparing this article to what his statistics textbook states.

4194:(2) That the individual do that major edit by first distilling the article down to the best available single pedagogic approach to presenting the T-1/T-2 definitions and fundamentals, **including standard graphics/tables the best teachers use** (!); 4399:

In the section "Understanding Type I and Type II errors," the last sentence includes "3.4 parts per million (0.00002941 %)," in which the parenthetical percentage seems to be in error. If you calculate 3.4/1000000, the answer is 3.4E-6, or 0.00034%.

3139:

I'm a cognitive psychologist rather than a statistician, so I'm entirely prepared to accept that this may be a common misconception, but was wondering whether you could point me towards some decent reference sources that try to clear this up, if so!

559:

It seems like the following proposed rearrangement of The Table of Error Types would be more consistent with the TP/FP/FN/TN graphic in the Error Rate section and be more consistent with the location of TP/FP/FN/TN and Type I and II errors in the

4200:(4) That next provided might be **limited**, clear, authoritative set examples, with focus on standard examples appearing in at least one major source text, which can then be cited so that deeper discussion and understanding can be pursued; 435:

Also, I am certain that, once the articles are merged, and once all of the statistical discussions have become symmetrical in form and content, that the average reader will find the Wiki far more helpful than it is at present. My best to you

4197:(3) Expanding to add a second standard but alternative (textbook-worthy) approach to the explanation, but one clearly tied to the first approach so that readers get two different attempts ("angles") at explaining the fundamental concepts; 1151:

method is now, essentially, obsolete (for reasons connected with its overall inflexibilty in relation to it not being able to continue to match other completely unrelated, but inter-connected technical changes that might be made in overall

1372:. From a readers POV this is exactly what I'm looking for. From an editors POV, there are some drawbacks I think, namely the lack of auto-numbering and sorting at the end. I think this is as close as we may reasonably get to my vision. If 1210:(2) Otherwise, I am more than happy to set about changing things back to how they were, with one exception: upon reflection I am most certain that the piece about the difference between the "O" and ZERO subscript should remain in the text. 1635: 3675:- Sensitivity and Specificity are also used to characterize the performance of physical or biological tests. In that case nobody calls them type-I or type-II errors, which is statistical jargon. I think we should leave them separate. 925:(g) (in my view, the most important of all), is it the case that these terms (and the concepts they represent) were derived from, and first used to contrast with, "false negative" and "false positive", or was it the other way around? 2724: 677:'s comment below except that this recognizes that the above table is written from the perspective of H0 rather than H1 as it probably should be. Alternately, the whole table could be represented in the context of both H0 and H1: 930:

My view is that, if those simple points can be covered in your changes, the impact, importance and information value of the present article will be very greatly embellished by such a valuable inclusion. Best to you and your work

3038:

I'd agree that "Type I" and "Type II" isn't great terminology. I see little wrong with "false negative" and "false positive" as alternative more descriptive names myself and i've seen them used in medical statistics literature.

2775:

There seem to be some inconsistant use of capitalization of the word type in this article. It seems there is confusion on the web too. Does any one know if 'type' should be capitalized if appearing in the middle of a sentence?

394:

The best and most helpful analogy for I/II errors I've ever heard is the courtroom analogy, where a type I error is represented by a wrongfully convicted innocent, and a type II error by a wrongfully acquitted criminal.

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row and think the cell should contain "False Negative". I've tried to make this blatantly clear, though some will think this solution is belabored. If you can think of a better way to get this idea across, please leap in.

2873:

I've made some minor tweaks to the section on null hypotheses. If anyone wants to check out the background to these changes (it necessitated a bit of head scratching and a visit to a library!), there are comments over at

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is moving towards being, at least strongly non-recommended, if not it being the obligatory practice not to use it (and, once again, it seems that this is so on the grounds of flexibility in the face of other programming

1983:

screening" section, rejecting a null hypothesis that should have been accepted (i.e., deciding that the individual being screened has the condition when he does not -- the null hypothesis being that the individual does

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at the beginning of this article, and explain each term with a reference to the matrix. I'm going to do the linkup when I finish writing this. If no opposition is uttered before Tuesday, I will do the proposed changes.

3132:

has always understood the null hypothesis to be a statement of null effect. I've just dug out my old undergrad notes on this, and that's certainly what I was taught at Cambridge; and it's also what my stats reference (

3053:

I completely agree, Type I and Type II are merely legacy terminology, are easily confused, and are really meaningless. "false negative" and and "false positive" are to the point. I see no benefit for any other term.

1231:, the inline use of (Snikklefritz 1994), will do that; but it looks quite forbidding to readers who aren't used to it. (Some editors like it for that reason; they think it adds tone.). There's even a set of templates. 3235:

in the subscript). Sorry I can't be of any more help. The collection that contains the reprints of Neyman and Pearson's papers and the book by Fisher should be fairly easy for you to find in most university libraries.

1306:

I wonder if it is time to involve more people in this discussion. In particular to let them review the problem of separation in light of this? If more people agree, we might also need to involve developers. Thoughts?

4049:"A false positive in hiring job candidates would mean turning down a good candidate which performed poorly in an interview, while a false negative means hiring a bad candidate that performs well in an interview." 2606:

I removed the statement that size is equal to power. This is wrong; in fact size is the maximum probability of Type I error; that is, the smallest level of significance of a test. In many cases, size is equal to

4686:

It never is good practice to make much edits at the same time, as it is rather difficult to see which ones are acceptable and which not. So, make suggestions here on the talk page, before changing the article.

2284:"H0: the guy remains a suspect", vs "H1: the guy is no longer a suspect". Error type I would be not to believe the alibi when it was a true one. Error type II would be to believe the alibi when it was not true. 1298:. Got a lighter cast now, so it is now possible to write with both hands. Makes things a bit easier :) . (BTW, this discussion is becoming quite large now.). The links were in response to your point (b) above. 4426:

course in philosophical logic in the past and have been told on several occasions I have above average comprehension. Knowledge is a general encyclopaedia not an encyclopaedia for professional statisticians.

4124:

Stressing that talking about type I and type II errors is meaningless without knowing "the real state of things" (we need a clear term for this one too) and clear relation to null hypothesis; as well as that

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hypothesis: that a subject can make some discrimination between two different sorts of object. This cannot be a null hypothesis, as it is inexact, and could relate to an infinity of possible exact scenarios.

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now i) randomised; ii) a consequence of the treatment itself (order of pouring milk & tea), "of which on the null hypothesis there will be none, by definition"; or iii) an effect "supervening by chance".

1926:

theory however, there is no such preference among the alternative hypothesis, the notion of false positive and false negative becomes connected to the hypothesis one is currently discussing. Refering to the

4212:

These are my suggestions as a teacher and writer and as a knowledgable outsider on this, and is prompted by my inability to suggest the article, as is, to young people needing to understand these errors.

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of making a particular decision, given the probability that the state of nature is what it is (e.g., terrorist, innocuous traveller) has to be taken into account. None of these has anything to do with the

4914:

Nice. Of course this would be unnecessary if everybody used "false positive" and "false negative" instead of the stupid and dull labels "I" and "II". Anybody in favor of making this article a redirect to

4316:"A statistical test can either reject (prove false) or fail to reject (fail to prove false) a null hypothesis, but never prove it true (i.e., failing to reject a null hypothesis does not prove it true)" 2024:

HI, thanks for the feedback. I've been a bit busy of late, but if I can find the time I'll go at it. Some of the later stuff is fine, but the introduction and some of the earlier stuff needs to be fixed.

4157:

Removing "false positive rate", "false negative rate", "null hypothesis", "Bayes' theorem" and "error in science" from their respective paragraphs and putting them into "definitions" in another, proper

3069:

I struggled with remembering which way round these are when I was doing courses in psychology, and discovered a mnemonic to help in this which I've added to the page. I hope they meet others' approval.

3537:

section is clear to me because it fits my intuition, but perhaps can be made a little clear for those to whom it is counter-intuitive. If no one wants to try to modify it, I'll take a stab at it soon.

4441:

Totally agree with Thurduulf. I came here using the same search terms and was dismayed by the hyper-technicality of the article. For the lay reader it is, IMO, mostly rubbish. (anon, 15, June 2012)

3270:

OK, I've now had a read of the references that you mentioned, as well as some others that seemed relevant. Thanks again for giving me these citations -- they were really helpful. This is what I found:

910:(b) a coherent story is included which clearly describes why these two (being "true") are considered to be in the same sort of domain as those already mentioned in the current article (being "false"), 3136:, by David C. Howell) seems to suggest. In addition, whenever I've been an examiner for public exams, the markscheme has tended to state the definition of a null as being a statement of null effect. 2439:": the error not rejecting a null hypothesis that is not the true state of nature. In other words, this is the error of failing to accept an alternative hypothesis when you don't have adequate power. 1408:

promote to case study. Medical screening is one of the oldest uses of statistics. Explanations could be done with respect to the case study. Expand and elaborate. Move this so it becomes chapter 1.

984:

promote to case study. Medical screening is one of the oldest uses of statistics. Explanations could be done with respect to the case study. Expand and elaborate. Move this so it becomes chapter 1.

135: 2826:

Type II error, also known as an "error of the second kind", a β error, or a "false negative": the error of accepting a null hypothesis when the alternative hypothesis is the true state of nature.

3391:(where we may be looking to see whether the value of a particular measured variable significantly differs from that of a prediction), and in this case the concept of "no effect" has no meaning. 3172:

Neyman, J. & Pearson, E.S., "On the Use and Interpretation of Certain Test Criteria for Purposes of Statistical Inference, Part I", reprinted at pp.1-66 in Neyman, J. & Pearson, E.S.,

2119:, but i think it gets rather confusing to try to discuss their wider use in testing in general, such as diagnostic testing, within the same article. I recently proposed a series of mergers of 1456:. There are far to many footnotes. Is there an easy way to distinguish between footnotes and references? The specific references should be treated as specific references and not as footnotes. 1032:. There are far to many footnotes. Is there an easy way to distinguish between footnotes and references? The specific references should be treated as specific references and not as footnotes. 841:

states that the True positive is the power of the test (i.e. 1 - beta) which is not what is in the table. Could you please check and / or clarify what is meant here ? - Date: 28 March 2018

240: 2177:

Hello everyone, I want to comment several things. First of all, in order to understand the meaning of error types, we need to understand when a hypothesis is eligible to be used as a "Null

3376:

actively incorrect: such a hypothesis is numerically inexact. The null hypothesis, in the case described, remains "that sample A is drawn from a population with the same mean as sample B".

2343:

The father in this story can make two kinds of mistakes i) if he doesn't trust Amanda when she was saying the truth, or ii) if he trusts Amanda when she is in fact lying. The null here is:

1969:. Usually this is the "default" hypothesis that one is trying to reject, e.g., that the accused is innocent, that the patient is disease-free, that the athlete is not using illegal drugs. 1227:

I have seen books which distinguish between footnotes (substantive) and endnotes (pure citations); but WP doesn't envisage anything that long. If you really want to make this distinction,

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Apparition starts with an "A", as does "alpha, which is another term for Type I error. An apparition is a ghost, i.e. you're seeing something (a defect or a difference) that isn't there.

4364:

I've the impression that big parts of the article treats type I and type II errors as synonymous with false positives and false negatives. Imo they belong to different fields of research.

3919:

Consider your self in a market and you want to buy an apple. Now seeing an apple at fruit shop you have to take decision whether apple is Healthy or Unhealthy? There will be four cases:

5649: 3579:

I'm going to be studying this article, and in the process will clean up a few minor things. The references to a "person" getting pregnant are silly, for example. Check the wiki page on

2512:

In my opinion, your "the error of not rejecting a null hypothesis when the alternative hypothesis is the true state of nature" has solved everything. Congratulations on a clear mind.

2853:

you have cancer". It's a good analogy when the test result is really continuous (e.g. a chemical concentration) and is dichotomised at some cut-off that should be chosen with care.

4235:

Thanks for your insightful comments. One key point. Knowledge functions as a reference encyclopedia not a pedagogic tool. We include all relevant aspects and do not do so in a

2181:

hypothesis" within a statistical standpoint. For example, if I'm interested in proving that "my eyes are brown", some may argue that the null hypothesis can be stated like this:

4497:

A type II error (or error of the second kind) is the failure to recognise a new relationship. In such a situation the null hypothesis was wrongly accepted by the statistician.

1957:

The article attempts to account for this by mentioning ambiguity of testing for innocence versus testing for guilt; while there is some rationale for this (especially under a

4089:. Consensus (look: Merge proposal) seems to be that thay should stay separate. This article takes care of technical side of things (formulas, alternative definitions), while 2804:

This article, currently, is very math and statistics heavy and is not useful as a cross reference from other articles that talk about false negatives and false positives.—

837:

The Table of Error Types is inconsistent with the text and with other wikipedia pages. In particular the True Positive and True Negative appear to be reversed. This page:

3179:

Neyman, J. & Pearson, E.S., "The testing of statistical hypotheses in relation to probabilities a priori", reprinted at pp.186-202 in Neyman, J. & Pearson, E.S.,

1901:{\displaystyle {\rm {false\ positive\ rate}}={\frac {\rm {number\ of\ false\ positives}}{\rm {number\ of\ negative\ instances}}}={\frac {9.990}{989.010+9.990}}=0.01=1\%} 2625: 2560:

guarantee a desired Type II error rate. I'm not aware that anyone slavishly decides that a study will be designed so that Type I and Type II error rates will be equal.

5639: 4574: 1477:

perspective. I am considering making up an example where we look at the hypothesis testing as a two class Bayesian classification problem. Does that sound reasonable?

4639: 4609: 4209:(7) That referencing and notes be reviewed for focus, relevance, and scholarly value; e.g., the citation of the high school AP stats prep website should probably go. 3118:, I've been canvassing for opinions on a change that I plan to make regarding the formulation of a null hypothesis. However I've just noticed your excellent edits on 913:(c) a clear identification of who was the first to use each of the terms, when, and to what purpose (and, also, whether they were first used separately or as a pair), 2993:

In qualitity control applications, this is also known as producer's risk (the risk of rejecting a good item) and consumer's risk (the risk of accepting a bad item)

4897: 4794:

Blind starts with a "B", as does beta, which is another term for Type II error. Blind means you're not seeing something (a defect or a difference) that is there.

4239:. You can help us improve specific examples and phrasing if you like, but please take note of the difference between this approach and a teaching guide. Cheers, 520:

Lindsay658's plans for that improvement seem reasonable. Lindsay, if you could use some assistance, especially in straightening out double redirects, let me know.

5654: 5416: 5412: 5398: 5308: 5304: 5290: 5158: 5154: 5140: 3871:

I agree. It's garbage. And in any case this specific example of an application of type I/type II errors etc adds nothing of value to the article. Remove the lot.

2744: 2645: 359:

Adding a more rigorous mathematical foundation to the formula sections. Rice - Mathematical Statistics and Data Analysis sets up such a framework. See pp 16, 300.

4312:

In the section "Type II error", under the section "Statistical test theory", rejecting the null hypothesis is equated with proving it false. This is inaccurate:

2573:

of what is a Type I/II error. They are important considerations that have to be considered when one is making a decision, but they don't reflect directly on the

2538:

I have moved the comment here because comments don't belong on the main page. The editor here has some justice behind his comments. Indeed, this is a problem of

4894:

With this, you need to remember that a false positive means rejecting a true null hypothesis and a false negative is failing to reject a false null hypothesis.

2902:

I have a major issue with the definitions of "Null Hypothesis" on this page and, less so, on the null hypothesis page. There are two types of null hypothesis:

3743:

suggestion of a merger. In epidemiology and diagnostic testing, the issue is Sensitivity and Specificity, and type I and type II errors are barely mentioned.

2111:

I'd agree that the article is a bit confusing at present. In particular the terms "False positive" and "false negative" are used in a wider context than just

1352:

Once again, it seems that this mechanism would match your expressed needs 100%. If you agree, I will attempt to appply this system to this article. Thoughts?

5664: 1167:; and this system also allows multiple textual footnotes citing the same page of the same reference to be listed as a single footnote in the "NOTES" section. 125: 35: 2650: 5679: 5118: 3409:

Thanks again for your comments on this. I will hold back on my edits for a little longer, in case you have any further comments that you would like to add!

3224:

It seems that it is yet one more case of people citing citations that are also citing a citation in someone else's work, rather than reading the originals.

230: 3770:

Both are jargon, and are essentially the same thing, but one takes a positive view (how good the test is) and the other negative (how bad the test is). --

944:. I admit to not reading the entire article, just shimming. I've done a reread of the article upon reading your comments. I'll try to cover your points: 3218:

And, as I recall, Fisher was adamant that whatever it was to be examined was the NULL hypothesis, because it was the hypothesis that was to be NULLIFIED.

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So what is the right answer? Well, neither of them is valid because the question is not suited for the kind of analysis that requires the testing of a

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I was totally confused by this section of the article. Please inform me If I am wrong, or maybe I didn't understand what you meant by this section.

4788:

A few years ago, I came up with a mnemonic device to help people remember what Type I and Type II errors are. Just remember "apparition" and "blind".

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converting their lecture notes into a textbook after the first time teaching through a course, rather than after teaching the subject for many years.

2564:

actually the state of nature. This is something that is only reflected in a Bayesian context, through the prior. Secondly, as I point out above, the

1144:(I've gone "inwards" a little, so that our discussion, if it continues, as it well might, does not finish up being comprised of single word columns). 907:(a) very clear distinctions are made between the terms "true negative" and "true positive" (i.e., how are they the same and how are they different?), 425:

The reason that I have suggested the merge is that each of these three pieces desperately need to be understood within the context of the other two.

5669: 2940:

Yes, good point. Somebody added that example long ago, and it seemed clear enough at the time, but something else would be better. I've changed it.

872: 5599:

Then, "Type I" and "Type II" would have more semantic utility, of being a that "Type I" is about "positives", and "Type II" is about "negatives".

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find the style appealing, you have my blessing to go ahed and implement it. I'm going to hold off on the other edits untill we resolve this issue.

5644: 3227:

The second point to make is that the passage you cite from my contribution was 100% based on the literature (and, in fact, the original articles).

3143: 4891:

A Type I error is a false POSITIVE; and P has a single vertical line. A Type II error is a false NEGATIVE; and N has two vertical lines.

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Both my "first version" (all in "notes") and my "second version" (half in text and half in "notes") are symmetrical with the conventions of the

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You leave the apple thinking it is is Unhealthy and it turns out to be Healthy. Again your decision was wrong. Other kind of error in decision.

206: 5674: 1990:

This is going to take a lot of care to edit to make the whole article consistent with both usual terminology and to make it self-consistent.

101: 5246: 3926:

You purchased apple thinking that apple is Healthy and it turns out to be Unhealthy. Your decision was wrong. One kind of error in decision.

5659: 5519: 4449: 2010:. I feel a little bit guilty of negligence here, there was an anonymous user doing such edits the 31st of July, he was quickly reverted by 453: 4448:

Agree... Can something be done about the triple negative in the opening sentence please "incorrect rejection of a true null hypothesis."

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Here is a suggested rewording. Because I am a statistician I may be kidding myself that this is simpler for lay people, but here goes...

4323: 3857: 3836: 951:(c)-(e) I do not know of these terms are the most commonly used, but they are easily understood by most practicioners in the context of 856: 5606: 5034: 5011: 4137:

Accomodation of true positives and true negatives (false/true negatives/positives all redirect here, maybe 'trues' should redirect to

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that applies, since the loss on detaining a harmless passenger is much less than the loss on allowing a terrorist passenger on board.

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confirms this). As, I said before, I would be quite happy to change the text back to what it was, if that was what you thought best.

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When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

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This scenario provided by User 174.21.120.17 is an excellent example of (so to speak) "perfect choice" consequent upon a "flawed"

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Defining statistical errors has nothing to do with their relative "harmfulness". We seem to have (too) many good examples already.

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the higher the significance level, the less likely it is that the phenomena in question could have been produced by chance alone.

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You purchased apple thinking that apple is Healthy and it turns out to be Healthy. Your decision was right. No error in decision.

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In my opinion, the article as currently written systematically reverses the usual meanings of false negative and false positive.

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https://stats.stackexchange.com/questions/1610/is-there-a-way-to-remember-the-definitions-of-type-i-and-type-ii-errors/1620#1620

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You left apple thinking that apple is Unhealthy and it turns out to be Unhealthy. Your decision was right. No error in decision.

5629: 3885: 3757: 965:(g) From what I have already stated, I think it is pretty clear that these concepts are understood by being the complements of 4810: 4138: 3690:

mathematical definitions are closely related the contexts are quite different, so it's less confusing to keep them separate.

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to this article. They are however not explained here, so they need to be added. I think it would be a good thing to create a

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On the basis that there is a well-established medical/physiological/psychological condition known as "false pregnancy" (see

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Pearson, E.S. & Neyman, J., "On the Problem of Two Samples", reprinted at pp.99-115 in Neyman, J. & Pearson, E.S.,

2588:, for example, but it is also appropriate to use the security checking example as one that describes what Type I/II errors 471:

This article was proposed for deletion on the basis of qualms about its name. I agree that it should be moved, and suggest

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Subsequent comments should be made on the appropriate discussion page. No further edits should be made to this discussion.

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Sensitivity and Specificity are essentially measures of type-I and type-II error - I think the articles could be merged.

1335:. Maybe it is using some sort of non-recommended Wiki-manipulation, but it certainly seems to meet your needs. Thoughts? 1331:. On the basis of all of the above, which asserts that what you desire is 100% impossible, I wonder if you could look at 5459: 5119:

https://web.archive.org/20060909224540/http://www.publichealth.pitt.edu/supercourse/SupercoursePPT/18011-19001/18951.ppt

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Wouldn't it be better to create an article about "false postives" and let it point to this article for further details?

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I will tone down my original suggestion slightly: A null hypothesis isn't a "statement of no effect" per se, but in an

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is connected with the rate of falsely "discovering" effects that are solely due to chance under the null hypothesis.

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I copied the article improvement suggestions here to separate them from the very lengthy discussion about footnotes.

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It seems that this suggestion was rejected; and it seems that there were, essentially, two grounds to the objection:

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https://web.archive.org/20050328035901/http://www.the-atlantic-paranormal-society.com:80/images/tapspics/index.html

3383:(where we are manipulating an independent variable), it logically follows that the null hypothesis states that the 1193:(b) none of the "objecting" participants had ever seen such a thing in their lives in any book or journal article. 5368: 5218: 5080: 4831: 3680: 3607: 3534: 3475: 3341: 3119: 2952: 2140: 2136: 500: 472: 318: 5415:

to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the

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https://web.archive.org/web/20050328035901/http://the-atlantic-paranormal-society.com/images/tapspics/index.html

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to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the

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to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the

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Expansion of the table under type II error to include "true positive" and "true negative" under "right decision"

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Furthermore, Fisher explains that a null hypothesis may contain "arbitrary elements" -- e.g. in the case where H

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II error than a type I error. ;-) If you can affirm, qualify, or refute what I've said here, please do. Thanks.

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testing and I don't think they should redirect to this article. I think the article is correct about their use

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for zero). Also, from memory, I am certain that the first use of the notion of a "null" hypothesis comes from:

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I have done what I can to make the "matrix" which the combined three will inhabit as clear as I possibly can.

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cons). Any example must make clear that context matters. I'll see if I can incorporate this into the body.

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Agreed, definitely no merging. While the concepts are similar they are applied to very different situations.

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In one of the elaborations of the presence or absence of errors, the example of pregnancy testing is given.

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Thus, I think that it's appropriate to mention this issue briefly with links to the appropriate articles on

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the alternative hypothesis. When the article is edited to remove these problems, this should also be fixed.

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terminology is being replaced by more descriptive terms, such as "of the first category" being replaced by

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this article is being re-titled and re-organized in a way that far better represents the overall situation.

5062: 3603: 2362:"H0: it is PLAUSIBLE that the daughter went to the party", vs "H1: the daughter couldn't go to the party". 2101: 1919: 512: 504: 496: 5247:

http://web.archive.org/web/20060908135857/http://www.nlm.nih.gov:80/medlineplus/news/fullstory_34471.html

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If you have discovered URLs which were erroneously considered dead by the bot, you can report them with

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If you have discovered URLs which were erroneously considered dead by the bot, you can report them with

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If you have discovered URLs which were erroneously considered dead by the bot, you can report them with

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I've just seen this on Stack Overflow, and thought it was a good way to remember which error was which;

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Notice that one can replace H1 by this one: "H1: the guy is innocent". Phrasing it like this shows that

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context, it wouldn't be an issue, but as long as we're considering standard hypothesis testing, it is.

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article but it says hardly anything on the statistics. In fact there's already an overview of these at

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I note in passing that under frequentist theory, one never "accepts" the null hypothesis. Rather, one

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As you mentioned, Fisher introduced the term null hypothesis, and defines this a number of times in

959:, as they explain the two remainig boxes of in the confusion matrix of a two-class decision problem. 288: 21: 5512:") and the link to simple.wikipedia is missing (even though wikidata has the correct information) 4822:

Thanks, that is a good mnemonic device, maybe it could be added to the <<Memory formulas: -->

4802: 4723: 4431: 4298: 4191:(1) Agree to have one significant and authoritative contributor take on the task of a major edit; 3971: 3879: 3751: 3592: 3394:

I'll add in the relevant citations, as these really do help to resolve this issue once and for all!

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After reading the article, I also propose that the article is reorganization in the following way:

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For ease of learning and symmetry of terminology, there has to also exist typification of truths.

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Type II error: Electronic circuit is not broken, when its really broken.Accepting Null hypothesis

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hypothesis. Let me show a couple of examples that DO require us to make use of hypothesis testing:

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I am currently contemplating how this could best be done, an example should be useful both from a

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on Knowledge. If you would like to participate, please visit the project page, where you can join

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on Knowledge. If you would like to participate, please visit the project page, where you can join

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Type I error: Electronic circuit is broken, when its really not broken.Rejecting Null hypothesis

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before doing mass systematic removals. This message is updated dynamically through the template

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before doing mass systematic removals. This message is updated dynamically through the template

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before doing mass systematic removals. This message is updated dynamically through the template

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Type I error: Electronic circuit is good, when its really not good. Rejecting Null hypothesis.

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Type II error: electronic circuit is not good, when its really good. Accepting Null Hypothesis

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Basically the section about NASA could have been interpreted with two scenarios, for instance:

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the type I and type II definition are totally wrong according to more books and otherwebsites

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Just a note to say that I have finally had the chance to sit down and word some changes to the

2475:"the error IN not rejecting a null hypothesis". (I suspect it should be the first; i.e., "of"). 1961:

interpretation, where all hypotheses are treated the same), it is not usually the situation in

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http://web.archive.org/web/20070108070702/http://www.nlm.nih.gov:80/medlineplus/news/fullstory

5228: 5090: 5058: 4919:? Which of those labels is actually more common, the sensible one or the unimaginative one? -- 4281: 4225: 3775: 3724: 3665: 2593: 2551: 2501: 2077: 2036: 2026: 2011: 1998: 1974: 827: 538: 508: 5342: 5192: 4920: 4771: 4742: 4692: 4651: 4385: 4369: 4349: 4236: 3994: 3952: 3028: 2959: 2809: 2610: 2399: 2135:

and feel free to add your thoughts. I notice now that we also have two separate articles on

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In medicine one often dicsuss the possibility of large scale medical screening (see below).

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Hypothesis in each case. To clarify that it should def. be added in front like "Type-1 = H

4753: 4617: 4587: 4525: 4166: 4067: 4029: 3796: 3706: 3538: 3471: 3458: 3372: 3345: 3236: 3151: 3112: 3095: 3073: 2931: 2790: 2581: 2539: 2513: 2497: 2480: 2148: 1966: 1915: 1438:. I would propose adding a more rigorous mathematical foundation to the formula sections. 1353: 1336: 1271: 1232: 1219: 1101: 1085: 1049: 1014:. I would propose adding a more rigorous mathematical foundation to the formula sections. 932: 546: 542: 521: 476: 437: 4707:

Can you please have a look at those edits and tell me which ones you think are incorrect?

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learning contexts. This version of the table also puts the table in the context of BOTH

922:(f) whether all of those that use the two technical terms use them in the same way, and, 5401:, "External links modified" talk page sections are no longer generated or monitored by 5293:, "External links modified" talk page sections are no longer generated or monitored by 5143:, "External links modified" talk page sections are no longer generated or monitored by 4834:. It seems totally confusing if you look at the table and read off the intersections (H 4719: 4504: 4427: 3967: 3873: 3745: 3695: 3646: 3519: 3044: 3016: 2941: 2858: 2762: 2719:{\displaystyle \operatorname {sup} \{\operatorname {Pr} \left:\theta \in \Theta _{0}\}} 2160: 5614: 5561: 5527: 5498: 5464: 5441:

If you found an error with any archives or the URLs themselves, you can fix them with

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If you found an error with any archives or the URLs themselves, you can fix them with

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If you found an error with any archives or the URLs themselves, you can fix them with

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By contrast, a type I or type II error would be one that is consequent upon a flawed

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They are each also, I think, easily revertable one by one with reasons, rather than

3478:. Do shout and/or make changes if you think my changes are misleading/confusing! -- 3340:

So, where does that leave us? I propose to make the following slight changes to the

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that the null hypothesis is merely the original in a range of possible hypotheses: H

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There seems to be no reason to capitalize 'type'. Let's proceed with small letters.

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There are two articles discussing related, but non-synonymous terms: this one and

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having a continuous distribution and point null hypothesis), but in general it is

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Also, it seems that "the error not rejecting a null hypothesis" should either be:

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http://www.publichealth.pitt.edu/supercourse/SupercoursePPT/18011-19001/18951.ppt

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since not only must the Type I/II error rate be taken into account, but also the

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technically correct and easy to understand. Any help here would be appreciated.

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Corrected wrong use of false positive/false negative + some minor stuff, see talk

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The style I'm talking about is the one I know from most scientific journals. Eg.

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which is really the only context for which Type I and II errors are meaningful.

5408: 5300: 5150: 4871: 4767: 4738: 4688: 4647: 4381: 4365: 4345: 4240: 3990: 3948: 3024: 2805: 2747: 2395: 1962: 1064:, you will notice a difference in nature between eg. note 3-7, which are really 919:(e) an indication of the sorts of people that might use the two technical terms, 202: 3196:

written text and in their choice of mathematical symbols to stress that it was

3190:, Cambridge University Press, (Cambridge), 1967 (originally published in 1930). 3183:, Cambridge University Press, (Cambridge), 1967 (originally published in 1933). 3176:, Cambridge University Press, (Cambridge), 1967 (originally published in 1928). 2076:

abstract, which may have caused the confusion in the first place. Best wishes!

1177:

There is a very long and very convoluted and very hard-to-follow discussion at

5407:. No special action is required regarding these talk page notices, other than 5299:. No special action is required regarding these talk page notices, other than 5149:. No special action is required regarding these talk page notices, other than 3898: 3897:

Removed section for reasons stated above since no one has disputed in a year.

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the text, rather than in the footnote. Best to you for the rest of your task.

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Promote case study. Medical screening is one of the oldest uses of statistics.

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neglects the multi event rates required to define Type I and Type II errors.

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the error of accepting a null hypothesis that is not the true state of nature

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matrices like that is all is needed to understand hypotheses and their tests.

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http://service1.symantec.com/sarc/sarc.nsf/info/html/what.false.positive.html

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Anyways: I think there is a real issue with the <<Memory formulas: -->

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true but rejected it", or changed completely. What do others think? best --

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So a type II error and a false negative aren't necessarily the same thing.

2143:, which I think it would be sensible to merge into a single article. Maybe 1266:

It seems that this is impossible (and, it seems that the note, above, from

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Type 2 H0 defined as: there is no correlation between the two parameters.

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What you are suggesting sounds a very positive step to me, provided that:

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Merge False negative, false positive, and type III error into this article

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Under frequentist theory one would always refer to one hypothesis as the

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Give a hypothetical idealized screening situation the following is true:

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The following is a draft proposal for a case study, meant to come before

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after the link to keep me from modifying it. Alternatively, you can add

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after the link to keep me from modifying it. Alternatively, you can add

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This discussion has become more and more about footnotes. To summarize:

1190:(a) none of the available "style manuals" suggested such a practice, and 495:

was a mistake, as there is material here that should be retained in an

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the source of the information contained within each individual "NOTE".

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Graphs are unavailable due to technical issues. There is more info on

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http://the-atlantic-paranormal-society.com/images/tapspics/index.html

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http://the-atlantic-paranormal-society.com/images/tapspics/index.html

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indicating both definitions in this domain. The example given in the

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The section "Understanding Type I and Type II Errors" was created by

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theory, where one hypothesis is usually distinguished as the obvious

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There has been editing over and over about the example of the wolf.

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In the section on "Statistical significance", it currently reads:

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to keep me off the page altogether. I made the following changes:

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to keep me off the page altogether. I made the following changes:

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of these could even be merged into one article? There's already a

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have the condition), is correctly identified as a false positive.

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which is the Type 1 error, but in the formula it says: "Type-1 =

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has no effect. However null hypotheses are equally useful in an

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different sorts of thing that you have very clearly identified).

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I wouldn't know how to reject one edit and accept a later one.

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that was made from a (so to speak) "perfect" selection process.

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I thought that the following should appear here (originally at

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article. Conversation with the primary author (on my talk page

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Researcher hypothesis: there is a statistical significance.

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So, I'd suggest that the wiki group that's created this page:

1416:. This is basically a listing of different uses. Rename it to 992:. This is basically a listing of different uses. Rename it to 300: 272: 256: 15: 2951:

Removing the paragraph "Associated section" from the section

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I am certain that it could easily be re-written in the form:

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This observation is contrary to how the article is written.

962:(f) I can not see how anyone could use them in any other way. 875:. I think it would be most appropriate to link the two terms 5266:

When you have finished reviewing my changes, please set the

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http://www.nlm.nih.gov/medlineplus/news/fullstory_34471.html

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When you have finished reviewing my changes, please set the

1420:. Demote it so that it becomes the very last chapter before 1344:

Aditional note: When you carefully examine the structure of

996:. Demote it so that it becomes the very last chapter before 4150:

Shortening of "Examples" (they should be more prominent in

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for additional information. I made the following changes:

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Hopefully the parts you are referring to are now correct.

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Rewriting of "Statistical error" in a non-textbook manner

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Sjb90 . . . There are three papers by Neyman and Pearson:

3122:. In particular, in the null hypothesis section you say: 2818:

Distinguishing between type II errors and false negatives

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and some may think it is more appropiate to use this one:

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I have just added archive links to 2 external links on

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I have just added archive links to 2 external links on

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Also, x, X, Y, and Ŷ are not defined in the caption.

2452:(b) null hypothesis is NOT "the true state of nature", 2153:

Binary classification#Evaluation of binary classifiers

4971:Electronic circuit Is good: researcher hypothesis. 4784:

Mnemonic Device to remember Type I and Type II Errors

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Type 1 H0 defined as: the experiment is inconclusive

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It's my understanding that in a hypothesis test, you

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Capitalization of the terms type I and type II errors

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The link to de.wikipedia is a wrong one (should be "

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Electronic circuit is broken: researcher hypotheis.

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Subsequent comments should be made in a new section.

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request it, I will follow the other convention here.

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https://en.wikipedia.org/Sensitivity_and_specificity

201:, a collaborative effort to improve the coverage of 96:, a collaborative effort to improve the coverage of 5411:using the archive tool instructions below. Editors 5303:using the archive tool instructions below. Editors 5153:using the archive tool instructions below. Editors 4147:

Merging of "Consequences" paragraph with "Examples"

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Talk:Null hypothesis#Formulation of null hypotheses

2550:Perhaps this can be added to the list of "to-dos". 2529:An anonyomous editor noted on the main page that: 4992:Electronic circuit is not broken: Null hypothesis 4633: 4603: 4568: 2738: 2718: 2639: 2619: 2472:"the error OF not rejecting a null hypothesis", or 1900: 5261:http://www.nlm.nih.gov/medlineplus/news/fullstory 3514:I don't see anything backward about them myself. 4974:Electronic circuit is not good: Null hypothesis 4101:I would like to discuss following improvements: 2133:Talk:Sensitivity_and_specificity#Merger_proposal 1440:Rice - Mathematical Statistics and Data Analysis 1215:PLease let met know your thinking in due course. 1016:Rice - Mathematical Statistics and Data Analysis 673:I believe this is consistent with the spirit of 5650:Knowledge level-5 vital articles in Mathematics 4766:You're the one who wants to change some parts. 3437:I agree with your changes. As you can see from 2592:, which is of course the point of the article. 5397:This message was posted before February 2018. 5289:This message was posted before February 2018. 5139:This message was posted before February 2018. 2577:of the terms being described by this article. 1936:Confusion of false negative and false positive 5510:https://de.wikipedia.org/Fehler_1._und_2._Art 3634:A summary of the conclusions reached follows. 3476:Type_I_and_type_II_errors#The_null_hypothesis 8: 2989:Alternate terms for Type I and Type II Error 2713: 2660: 1204:Perhaps, this is the way we should proceed: 3448:] I really didn't have a lot to work with. 507:) suggests he/she intends to improve it. — 390:Regarding the simplification of the article 5600: 5534:Diagram is Really Three Separate Diagrams! 5513: 5367:I have just modified one external link on 5028: 4611:is rejected and there is actually no wolf. 1163:Thus, the currently recommended system is 842: 505:User talk:Arthur Rubin#Four types of error 396: 147: 58: 4858:it". This seems to be talking about the H 4625: 4619: 4595: 4589: 4557: 4551: 4098:. The rest of the article should follow. 3221:I hope that is of some assistance to you. 2731: 2707: 2652: 2632: 2612: 2265:makes him guilty? my null here has to be: 1865: 1777: 1703: 1701: 1640: 1639: 1637: 1442:sets up such a framework. See pp 16, 300. 1018:sets up such a framework. See pp 16, 300. 4580:Is rejected when some-one cries "wolf'. 873:Knowledge:Requested_articles/Mathematics 679: 566: 5640:Knowledge vital articles in Mathematics 4109:Creation of new paragraph "Definitions" 2953:Understanding Type I and Type II Errors 2445:Given that you seem to be saying that: 2226:"H0: the color of my eyes is not brown" 1488:Various proposals for further extension 371:) 23:41, 10 August 2019 (UTC)AugustMohr 149: 60: 19: 3856:the other interpretation can be given. 3213:, Oliver & Boyd (Edinburgh), 1935. 5655:B-Class vital articles in Mathematics 5278:to let others know (documentation at 3937:left apple. So this is TYPE I error. 1617:From this we may read the following: 1060:. If you take a look at the notes in 682: 569: 7: 4641:is not rejected but there is a wolf. 4115:, where application has the priority 3625:The following discussion is closed. 2880:User_talk:Lindsay658#Null_hypotheses 2449:(a) null hypothesis is NOT rejected. 195:This article is within the scope of 90:This article is within the scope of 5665:High-importance Statistics articles 4917:False positives and false negatives 4866:false, but accept it" , "Type-2 = H 3829:Is home testing for aids accurate 2196:"H0: the color of my eyes is brown" 537:Heeding the advice and guidance of 49:It is of interest to the following 5680:High-priority mathematics articles 3134:Statistical Methods for Psychology 2704: 1895: 1856: 1853: 1850: 1847: 1844: 1841: 1838: 1835: 1832: 1827: 1824: 1821: 1818: 1815: 1812: 1809: 1806: 1801: 1798: 1793: 1790: 1787: 1784: 1781: 1778: 1773: 1770: 1767: 1764: 1761: 1758: 1755: 1752: 1749: 1744: 1741: 1738: 1735: 1732: 1727: 1724: 1719: 1716: 1713: 1710: 1707: 1704: 1693: 1690: 1687: 1684: 1679: 1676: 1673: 1670: 1667: 1664: 1661: 1658: 1653: 1650: 1647: 1644: 1641: 14: 5371:. Please take a moment to review 5221:. Please take a moment to review 5083:. Please take a moment to review 4752:Then you edit and stop reverting. 4127:null hypothesis is never accepted 1510:The total population is 1.000.000 1413:False negative vs. false positive 1244:with more, for some examples see 989:False negative vs. false positive 475:, but I see no reason to delete. 215:Knowledge:WikiProject Mathematics 5685:Knowledge pages with to-do lists 5635:Knowledge level-5 vital articles 5055:actually about making an error? 4951:Consequences section about NASA. 4129:, one can only fail to reject it 3816:The discussion above is closed. 1516:The occurrence of illness is 1 ‰ 1147:To the best of my knowledge the 308: 276: 260: 218:Template:WikiProject Mathematics 182: 172: 151: 110:Knowledge:WikiProject Statistics 83: 62: 29: 20: 5670:WikiProject Statistics articles 4967:Scenario 1:alternative scenario 4119:Clean-up of "Further extension" 1520:From these data, we can form a 555:True negative and true positive 235:This article has been rated as 130:This article has been rated as 113:Template:WikiProject Statistics 5645:B-Class level-5 vital articles 4929:17:42, 30 September 2018 (UTC) 4909:09:42, 30 September 2018 (UTC) 4776:05:48, 12 September 2012 (UTC) 4762:00:44, 11 September 2012 (UTC) 4419:I got to this article via the 4139:Statistical hypothesis testing 4121:- some examples are anecdotal 4043:I have removed the following: 2627:(for example a test statistic 1471:hypothesis testing perspective 1: 5465:13:18, 30 December 2016 (UTC) 5205:14:23, 18 February 2016 (UTC) 4747:07:56, 6 September 2012 (UTC) 4728:11:25, 5 September 2012 (UTC) 4697:07:04, 5 September 2012 (UTC) 4534:00:48, 21 December 2011 (UTC) 4390:20:28, 14 November 2011 (UTC) 4374:11:15, 14 November 2011 (UTC) 4265:this concept is totally wrong 4259:22:49, 20 November 2023 (UTC) 3612:13:41, 29 November 2010 (UTC) 3495:Are the 2 examples under the 3104:21:21, 22 February 2008 (UTC) 2900:04:14, 14 February 2014 (UTC) 2766:05:19, 13 December 2006 (UTC) 1499:Case study: Medical screening 1424:and the rest of the endnotes. 1000:and the rest of the endnotes. 948:(a),(b) Should be no problem. 209:and see a list of open tasks. 104:and see a list of open tasks. 5675:B-Class mathematics articles 5562:21:25, 24 October 2021 (UTC) 5528:12:26, 22 October 2018 (UTC) 5067:17:05, 25 October 2013 (UTC) 4880:14:32, 7 November 2015 (UTC) 4436:13:11, 9 December 2011 (UTC) 4410:15:06, 21 October 2011 (UTC) 4354:09:15, 13 October 2011 (UTC) 4332:12:36, 9 November 2012 (UTC) 4307:06:56, 13 October 2011 (UTC) 4176:Problematic article, overall 3907:21:38, 7 December 2010 (UTC) 3893:09:49, 9 December 2009 (UTC) 3866:08:43, 9 December 2009 (UTC) 3805:01:09, 9 November 2008 (UTC) 3780:17:39, 8 November 2008 (UTC) 3765:11:03, 3 November 2008 (UTC) 3729:05:01, 3 November 2008 (UTC) 3715:02:26, 15 October 2008 (UTC) 3700:23:07, 14 October 2008 (UTC) 3685:12:53, 14 October 2008 (UTC) 3670:14:43, 10 October 2008 (UTC) 3651:08:52, 9 November 2008 (UTC) 3049:12:45, 21 January 2008 (UTC) 3033:18:57, 7 December 2007 (UTC) 2984:05:25, 14 October 2007 (UTC) 2863:12:30, 21 January 2008 (UTC) 2751:22:11, 3 November 2006 (UTC) 5660:B-Class Statistics articles 4815:08:38, 6 October 2012 (UTC) 4614:Type II error is made when 4152:specificity and sensitivity 4113:specificity and sensitivity 4096:Sensitivity and specificity 4091:Sensitivity and specificity 4087:Sensitivity and specificity 3597:01:50, 25 August 2008 (UTC) 3474:article and the section on 3082:21:03, 6 October 2009 (UTC) 2597:01:47, 22 August 2006 (UTC) 2555:23:55, 21 August 2006 (UTC) 2517:21:44, 18 August 2006 (UTC) 2505:11:36, 18 August 2006 (UTC) 2484:03:05, 18 August 2006 (UTC) 2081:13:10, 15 August 2006 (UTC) 2057:07:02, 15 August 2006 (UTC) 2040:21:47, 14 August 2006 (UTC) 2030:13:59, 14 August 2006 (UTC) 2019:07:36, 14 August 2006 (UTC) 2002:23:44, 11 August 2006 (UTC) 1978:02:03, 11 August 2006 (UTC) 1494:13:36, 18 August 2006 (UTC) 1068:, and eg. 14-16, which are 5701: 5486:the significance level ... 5428:(last update: 5 June 2024) 5364:Hello fellow Wikipedians, 5320:(last update: 5 June 2024) 5239:|deny=InternetArchiveBot}} 5214:Hello fellow Wikipedians, 5170:(last update: 5 June 2024) 5101:|deny=InternetArchiveBot}} 5076:Hello fellow Wikipedians, 5043:18:12, 2 August 2015 (UTC) 4674:19:23, 12 April 2012 (UTC) 4656:07:58, 12 April 2012 (UTC) 4584:Type I error is made when 4171:17:47, 13 April 2011 (UTC) 4076:22:32, 27 March 2011 (UTC) 4034:15:49, 13 April 2011 (UTC) 3999:12:45, 20 March 2011 (UTC) 3976:07:37, 20 March 2011 (UTC) 3957:21:36, 18 March 2011 (UTC) 3851:computer database searches 3570:19:41, 22 March 2009 (UTC) 2945:03:18, 2 August 2007 (UTC) 2935:01:13, 2 August 2007 (UTC) 2915:Phaedrus273 - Paul Wilson 2813:20:45, 12 March 2007 (UTC) 2795:15:41, 13 April 2011 (UTC) 2165:15:33, 11 March 2008 (UTC) 2117:in this particular context 2106:13:42, 11 March 2008 (UTC) 1482:13:07, 7 August 2006 (UTC) 1400:12:14, 7 August 2006 (UTC) 1381:12:19, 7 August 2006 (UTC) 1357:00:07, 7 August 2006 (UTC) 1340:02:03, 4 August 2006 (UTC) 1218:Best to you and your work 861:09:18, 28 March 2018 (UTC) 832:20:45, 16 March 2020 (UTC) 5568:Type I and type II truths 5369:Type I and type II errors 5355:03:10, 1 March 2016 (UTC) 5219:Type I and type II errors 5081:Type I and type II errors 5020:22:26, 3 April 2013 (UTC) 4943:18:13, 26 July 2024 (UTC) 4290:10:05, 15 July 2011 (UTC) 3845:23:15, 30 July 2009 (UTC) 3705:similar, not identical.-- 3524:18:06, 2 April 2008 (UTC) 3509:14:15, 2 April 2008 (UTC) 3483:11:33, 14 June 2007 (UTC) 3342:Type I and type II errors 3307:The Design of Experiments 3211:The Design of Experiments 3120:Type I and type II errors 3064:14:09, 2 April 2008 (UTC) 3009:13:48, 29 July 2010 (UTC) 2887:11:35, 14 June 2007 (UTC) 2781:10:40, 8 March 2007 (UTC) 2141:negative predictive value 2137:positive predictive value 1950:Similarly, the notion of 1513:The symmetric error is 1% 1312:14:39, 31 July 2006 (UTC) 1275:00:22, 26 July 2006 (UTC) 1252:14:24, 24 July 2006 (UTC) 1236:15:46, 22 July 2006 (UTC) 1223:23:29, 21 July 2006 (UTC) 1129:14:31, 21 July 2006 (UTC) 1105:01:46, 20 July 2006 (UTC) 1089:01:25, 20 July 2006 (UTC) 1077:18:24, 18 July 2006 (UTC) 1053:05:14, 18 July 2006 (UTC) 1037:11:06, 17 July 2006 (UTC) 936:19:45, 16 July 2006 (UTC) 893:15:18, 16 July 2006 (UTC) 707: 685: 594: 572: 533:Reorganization of article 501:Type I and Type II errors 473:Type I and Type II errors 441:22:01, 23 June 2006 (UTC) 319:Type I and type II errors 234: 167: 129: 78: 57: 5615:00:24, 9 June 2022 (UTC) 5499:07:47, 9 July 2017 (UTC) 5480:I think that should be: 4985:Scenario 2:Your scenario 4509:14:42, 1 July 2013 (UTC) 4458:11:42, 1 July 2013 (UTC) 4244:02:35, 9 June 2011 (UTC) 4230:00:45, 9 June 2011 (UTC) 3818:Please do not modify it. 3628:Please do not modify it. 3547:23:20, 28 May 2008 (UTC) 3462:21:49, 17 May 2007 (UTC) 3427:17:33, 17 May 2007 (UTC) 3258:07:39, 17 May 2007 (UTC) 3240:22:37, 16 May 2007 (UTC) 3188:Joint Statistical Papers 3181:Joint Statistical Papers 3174:Joint Statistical Papers 3160:11:07, 16 May 2007 (UTC) 2429:error of the second kind 1460:11:06, 17 July 2006 (UTC 1179:Wikipedia_talk:Footnote3 1066:very specific references 550:22:45, 3 July 2006 (UTC) 525:12:56, 3 July 2006 (UTC) 516:12:17, 3 July 2006 (UTC) 480:21:32, 2 July 2006 (UTC) 415:22:30, 21 May 2020 (UTC) 241:project's priority scale 5360:External links modified 5210:External links modified 5072:External links modified 3555:Innocent / Not Innocent 3094:for the ease of others. 2847:16:40, 4 May 2007 (UTC) 2746:is the critical value. 2620:{\displaystyle \alpha } 2404:21:19, 5 May 2008 (UTC) 1475:Bayesian classification 1429:Critical false positive 1005:Critical false positive 462:15:40, 4 May 2009 (UTC) 198:WikiProject Mathematics 5630:B-Class vital articles 4635: 4605: 4570: 4569:{\displaystyle H_{0}:} 3200:for original (and not 3129: 2869:Null hypothesis tweaks 2740: 2720: 2641: 2621: 2326:cover the whole thing. 2113:statistical hypothesis 1920:alternative hypothesis 1918:, and the other as an 1902: 1621:True negative: 989.010 687:Alternate hypothesis ( 93:WikiProject Statistics 4636: 4634:{\displaystyle H_{0}} 4606: 4604:{\displaystyle H_{0}} 4571: 4395:3.4 Parts Per Million 3146:comment was added by 3124: 2756:Truth table confusion 2741: 2721: 2642: 2622: 1903: 1627:False positive: 9.990 1447:Statistical treatment 1023:Statistical treatment 683:Table of error types 570:Table of error types 36:level-5 vital article 5409:regular verification 5301:regular verification 5225:. If necessary, add 5151:regular verification 5136:to let others know. 5087:. If necessary, add 5050:The Wolf Thing Again 4832:Table of error types 4618: 4588: 4550: 3587:get pregnant. Etc.. 3453:or less by default). 2730: 2651: 2631: 2611: 1952:false discovery rate 1636: 1391:Article improvements 497:Errors (statistical) 221:mathematics articles 5399:After February 2018 5291:After February 2018 5270:parameter below to 5141:After February 2018 5132:parameter below to 4081:Reorganization 2011 3528:I think I see what 2919:Misleading example? 2427:, also known as a " 2418:For the paragraph: 1229:Harvard referencing 1157:Knowledge:Footnote2 1155:It also seems that 1118:Knowledge:Footnote2 116:Statistics articles 5470:Significance Level 5453:InternetArchiveBot 5404:InternetArchiveBot 5296:InternetArchiveBot 5146:InternetArchiveBot 4631: 4601: 4566: 3638:The consensus was 3499:section backwards? 2822:From the article: 2736: 2716: 2637: 2617: 2525:Security Screening 2498:decision-theoretic 2125:specificity (test) 2121:sensitivity (test) 1898: 1630:True positive: 990 1624:False negative: 10 1436:Statistics formula 1152:Wiki-programming). 1012:Statistics formula 791:Correct inference 657:Correct inference 348:Updated 2021-11-21 190:Mathematics portal 45:content assessment 5617: 5605:comment added by 5548:comment added by 5530: 5518:comment added by 5429: 5353: 5321: 5203: 5171: 5045: 5033:comment added by 5010:comment added by 4818: 4801:comment added by 4322:comment added by 4293: 4276:comment added by 4057:selection process 3891: 3835:comment added by 3763: 3535:computer security 3497:Computer Security 3491:Computer Security 3163: 2999:comment added by 2739:{\displaystyle c} 2640:{\displaystyle T} 2108: 2096:comment added by 2012:User:Arthur Rubin 1881: 1860: 1831: 1805: 1797: 1748: 1731: 1723: 1683: 1657: 1613: 1612: 1570: 1569: 1465:Medical screening 1406:Medical screening 982:Medical screening 863: 847:comment added by 805: 804: 795:(probability = 1− 756:(false positive) 745:(probability = 1− 741:Correct inference 671: 670: 661:(probability = 1− 628:(false positive) 617:(probability = 1− 613:Correct inference 574:Null hypothesis ( 417: 401:comment added by 384: 383: 299: 298: 295: 294: 255: 254: 251: 250: 247: 246: 146: 145: 142: 141: 5692: 5564: 5463: 5454: 5427: 5426: 5405: 5349: 5348:Talk to my owner 5344: 5319: 5318: 5297: 5285: 5240: 5232: 5199: 5198:Talk to my owner 5194: 5169: 5168: 5147: 5102: 5094: 5022: 4817: 4795: 4640: 4638: 4637: 4632: 4630: 4629: 4610: 4608: 4607: 4602: 4600: 4599: 4575: 4573: 4572: 4567: 4562: 4561: 4519:New Introduction 4424: 4402:Gilmore.the.Lion 4334: 4292: 4270: 4064:selection choice 3872: 3847: 3744: 3630: 3604:Ivan Denisovitch 3141: 3011: 2800:Statistics Heavy 2745: 2743: 2742: 2737: 2725: 2723: 2722: 2717: 2712: 2711: 2693: 2689: 2646: 2644: 2643: 2638: 2626: 2624: 2623: 2618: 2129:test sensitivity 2091: 1929:confusion matrix 1907: 1905: 1904: 1899: 1882: 1880: 1866: 1861: 1859: 1830: 1804: 1796: 1776: 1747: 1730: 1722: 1702: 1697: 1696: 1682: 1656: 1576: 1549:Classified well 1528: 1522:confusion matrix 885:confusion matrix 871:is requested at 793:(true negative) 781:(false negative) 743:(true positive) 680: 659:(true negative) 647:(false negative) 615:(true positive) 567: 562:Confusion_matrix 494: 488: 485:Very well. The 349: 312: 311: 301: 280: 279: 273: 269:Daily page views 264: 257: 223: 222: 219: 216: 213: 192: 187: 186: 176: 169: 168: 163: 155: 148: 136:importance scale 118: 117: 114: 111: 108: 87: 80: 79: 74: 66: 59: 42: 33: 32: 25: 24: 16: 5700: 5699: 5695: 5694: 5693: 5691: 5690: 5689: 5620: 5619: 5584:Power of a test 5570: 5543: 5536: 5506: 5472: 5457: 5452: 5420: 5413:have permission 5403: 5377:this simple FaQ 5362: 5352: 5347: 5312: 5305:have permission 5295: 5279: 5234: 5226: 5212: 5202: 5197: 5162: 5155:have permission 5145: 5096: 5088: 5074: 5052: 5005: 4953: 4892: 4889: 4869: 4865: 4861: 4845: 4837: 4796: 4786: 4684: 4621: 4616: 4615: 4591: 4586: 4585: 4553: 4548: 4547: 4541: 4521: 4420: 4417: 4397: 4361: 4341: 4317: 4271: 4267: 4178: 4105:My introduction 4083: 4041: 3917: 3853: 3830: 3827: 3822: 3821: 3677:Frederic Y Bois 3658: 3626: 3619: 3577: 3557: 3493: 3472:Null hypothesis 3373:null hypothesis 3346:null hypothesis 3319: 3301: 3297: 3293: 3289: 3142:—The preceding 3113:null hypothesis 3089: 3087:Null hypotheses 2994: 2991: 2956: 2921: 2871: 2820: 2802: 2773: 2758: 2728: 2727: 2703: 2673: 2669: 2649: 2648: 2629: 2628: 2609: 2608: 2604: 2582:decision theory 2540:decision theory 2527: 2416: 2414:Double negative 2149:diagnostic test 1995:fails to reject 1967:null hypothesis 1938: 1916:null hypothesis 1870: 1634: 1633: 1602:False positive 1595:False negative 1560:Classified ill 1543: 1536: 1533:Correct well (H 1501: 1467: 1393: 1268:Septentrionalis 1233:Septentrionalis 821: 814: 783:(probability = 776: 758:(probability = 736: 728: 718: 693: 649:(probability = 630:(probability = 605: 580: 557: 543:Septentrionalis 535: 522:Septentrionalis 492: 486: 477:Septentrionalis 469: 423: 392: 380: 379: 323: 309: 277: 271: 220: 217: 214: 211: 210: 188: 181: 161: 132:High-importance 115: 112: 109: 106: 105: 73:High‑importance 72: 43:on Knowledge's 40: 30: 12: 11: 5: 5698: 5696: 5688: 5687: 5682: 5677: 5672: 5667: 5662: 5657: 5652: 5647: 5642: 5637: 5632: 5622: 5621: 5569: 5566: 5535: 5532: 5520:194.209.78.123 5505: 5502: 5491:Lasse Kliemann 5471: 5468: 5447: 5446: 5439: 5392: 5391: 5383:Added archive 5361: 5358: 5345: 5339: 5338: 5331: 5264: 5263: 5255:Added archive 5253: 5245:Added archive 5211: 5208: 5195: 5189: 5188: 5181: 5126: 5125: 5117:Added archive 5115: 5107:Added archive 5073: 5070: 5051: 5048: 5047: 5046: 5001: 4983: 4952: 4949: 4948: 4947: 4946: 4945: 4890: 4886: 4867: 4863: 4859: 4843: 4835: 4826: 4825: 4785: 4782: 4781: 4780: 4779: 4778: 4735: 4734: 4733: 4732: 4731: 4730: 4715: 4708: 4683: 4680: 4679: 4678: 4677: 4676: 4643: 4642: 4628: 4624: 4612: 4598: 4594: 4578: 4577: 4565: 4560: 4556: 4540: 4537: 4520: 4517: 4516: 4515: 4514: 4513: 4512: 4511: 4498: 4490: 4489: 4488: 4487: 4486: 4485: 4476: 4475: 4474: 4473: 4472: 4471: 4463: 4462: 4461: 4460: 4450:122.150.178.86 4443: 4442: 4422:false positive 4416: 4413: 4396: 4393: 4377: 4376: 4360: 4357: 4340: 4337: 4336: 4335: 4310: 4309: 4299:Kernel.package 4266: 4263: 4262: 4261: 4246: 4177: 4174: 4160: 4159: 4155: 4148: 4145: 4142: 4135: 4130: 4122: 4116: 4106: 4082: 4079: 4053: 4052: 4051: 4050: 4040: 4037: 4023: 4022: 4021: 4020: 4019: 4018: 4017: 4016: 4006: 4005: 4004: 4003: 4002: 4001: 3981: 3980: 3979: 3978: 3960: 3959: 3934: 3933: 3930: 3927: 3924: 3916: 3913: 3912: 3911: 3910: 3909: 3852: 3849: 3826: 3823: 3815: 3814: 3813: 3812: 3811: 3810: 3809: 3808: 3807: 3768: 3767: 3737: 3736: 3735: 3734: 3733: 3732: 3731: 3657: 3656: 3655: 3654: 3653: 3621: 3620: 3618: 3617:Merge proposal 3615: 3576: 3573: 3556: 3553: 3552: 3551: 3550: 3549: 3492: 3489: 3488: 3487: 3486: 3485: 3465: 3464: 3454: 3441: 3440: 3434: 3433: 3432: 3431: 3430: 3429: 3415: 3414: 3413: 3412: 3411: 3410: 3402: 3401: 3400: 3399: 3398: 3397: 3396: 3395: 3392: 3377: 3369: 3354: 3353: 3352: 3351: 3350: 3349: 3333: 3332: 3331: 3330: 3329: 3328: 3327: 3326: 3322: 3317: 3314: 3310: 3303: 3299: 3295: 3291: 3287: 3276: 3275: 3274: 3273: 3272: 3271: 3263: 3262: 3261: 3260: 3250: 3243: 3242: 3232: 3228: 3225: 3222: 3219: 3215: 3214: 3209:Fisher, R.A., 3206: 3205: 3192: 3191: 3184: 3177: 3169: 3168: 3088: 3085: 3067: 3066: 3051: 3017:baire category 2990: 2987: 2972: 2971: 2955: 2949: 2948: 2947: 2920: 2917: 2870: 2867: 2866: 2865: 2819: 2816: 2801: 2798: 2778:194.83.138.183 2772: 2769: 2757: 2754: 2735: 2715: 2710: 2706: 2702: 2699: 2696: 2692: 2688: 2685: 2682: 2679: 2676: 2672: 2668: 2665: 2662: 2659: 2656: 2636: 2616: 2603: 2600: 2536: 2535: 2526: 2523: 2522: 2521: 2520: 2519: 2477: 2476: 2473: 2466: 2465: 2454: 2453: 2450: 2443: 2442: 2441: 2440: 2437:false negative 2415: 2412: 2411: 2410: 2409: 2408: 2407: 2406: 2386: 2385: 2384: 2383: 2382: 2381: 2372: 2371: 2370: 2369: 2368: 2367: 2366: 2365: 2364: 2363: 2351: 2350: 2349: 2348: 2347: 2346: 2345: 2344: 2334: 2333: 2332: 2331: 2330: 2329: 2328: 2327: 2316: 2315: 2314: 2313: 2312: 2311: 2310: 2309: 2294: 2293: 2292: 2291: 2290: 2289: 2288: 2287: 2286: 2285: 2273: 2272: 2271: 2270: 2269: 2268: 2267: 2266: 2251: 2250: 2249: 2248: 2247: 2246: 2234: 2233: 2232: 2231: 2230: 2229: 2228: 2227: 2217: 2216: 2215: 2214: 2213: 2212: 2204: 2203: 2202: 2201: 2200: 2199: 2198: 2197: 2187: 2186: 2185: 2184: 2183: 2182: 2170: 2169: 2168: 2167: 2086: 2085: 2084: 2083: 2070: 2069: 2068: 2067: 2060: 2059: 2022: 2021: 1937: 1934: 1912: 1911: 1908: 1897: 1894: 1891: 1888: 1885: 1879: 1876: 1873: 1869: 1864: 1858: 1855: 1852: 1849: 1846: 1843: 1840: 1837: 1834: 1829: 1826: 1823: 1820: 1817: 1814: 1811: 1808: 1803: 1800: 1795: 1792: 1789: 1786: 1783: 1780: 1775: 1772: 1769: 1766: 1763: 1760: 1757: 1754: 1751: 1746: 1743: 1740: 1737: 1734: 1729: 1726: 1721: 1718: 1715: 1712: 1709: 1706: 1700: 1695: 1692: 1689: 1686: 1681: 1678: 1675: 1672: 1669: 1666: 1663: 1660: 1655: 1652: 1649: 1646: 1643: 1631: 1628: 1625: 1622: 1615: 1614: 1611: 1610: 1609:True positive 1607: 1604: 1603: 1600: 1597: 1596: 1593: 1590: 1589: 1588:True negative 1586: 1583: 1582: 1579: 1572: 1571: 1568: 1567: 1564: 1561: 1557: 1556: 1553: 1550: 1546: 1545: 1541: 1540:Correct ill (H 1538: 1534: 1531: 1518: 1517: 1514: 1511: 1500: 1497: 1466: 1463: 1462: 1461: 1451: 1443: 1433: 1425: 1418:Usage examples 1409: 1392: 1389: 1388: 1387: 1386: 1385: 1384: 1383: 1362: 1361: 1360: 1359: 1350: 1342: 1323: 1322: 1321: 1320: 1319: 1318: 1317: 1316: 1315: 1314: 1299: 1284: 1283: 1282: 1281: 1280: 1279: 1278: 1277: 1264: 1260: 1216: 1213: 1212: 1211: 1208: 1202: 1198: 1197: 1196: 1195: 1194: 1191: 1183: 1175: 1168: 1161: 1153: 1145: 1139: 1138: 1137: 1136: 1135: 1134: 1133: 1132: 1131: 1091: 1070:true footnotes 1040: 1039: 1027: 1019: 1009: 1001: 994:Usage examples 985: 975: 974: 971:false positive 967:false negative 963: 960: 957:false negative 953:false positive 949: 939: 938: 928: 927: 926: 923: 920: 917: 914: 911: 908: 902: 866: 836: 819: 812: 803: 802: 800: 792: 790: 788: 782: 780: 779:Type II error 777: 774: 769: 765: 764: 755: 752: 750: 742: 740: 738: 734: 729: 726: 720: 716: 711: 709: 705: 704: 701: 697: 696: 695: 691: 686: 684: 669: 668: 666: 658: 656: 654: 648: 646: 645:Type II error 643: 641: 637: 636: 627: 624: 622: 614: 612: 610: 607: 603: 598: 596: 592: 591: 588: 584: 583: 582: 578: 573: 571: 556: 553: 534: 531: 530: 529: 528: 527: 468: 465: 454:79.199.225.197 422: 419: 391: 388: 386: 382: 381: 375: 373: 372: 360: 357: 351: 306: 304: 297: 296: 293: 292: 281: 267: 265: 253: 252: 249: 248: 245: 244: 233: 227: 226: 224: 207:the discussion 194: 193: 177: 165: 164: 156: 144: 143: 140: 139: 128: 122: 121: 119: 102:the discussion 88: 76: 75: 67: 55: 54: 48: 26: 13: 10: 9: 6: 4: 3: 2: 5697: 5686: 5683: 5681: 5678: 5676: 5673: 5671: 5668: 5666: 5663: 5661: 5658: 5656: 5653: 5651: 5648: 5646: 5643: 5641: 5638: 5636: 5633: 5631: 5628: 5627: 5625: 5618: 5616: 5612: 5608: 5604: 5597: 5595: 5594:true negative 5591: 5590:Type II truth 5587: 5585: 5581: 5580:true positive 5577: 5573: 5567: 5565: 5563: 5559: 5555: 5551: 5547: 5540: 5533: 5531: 5529: 5525: 5521: 5517: 5511: 5503: 5501: 5500: 5496: 5492: 5488: 5487: 5485: 5478: 5477: 5469: 5467: 5466: 5461: 5456: 5455: 5444: 5440: 5437: 5433: 5432: 5431: 5424: 5418: 5414: 5410: 5406: 5400: 5395: 5390: 5386: 5382: 5381: 5380: 5378: 5374: 5370: 5365: 5359: 5357: 5356: 5350: 5343: 5336: 5332: 5329: 5325: 5324: 5323: 5316: 5310: 5306: 5302: 5298: 5292: 5287: 5283: 5277: 5273: 5269: 5262: 5258: 5254: 5252: 5248: 5244: 5243: 5242: 5238: 5230: 5224: 5220: 5215: 5209: 5207: 5206: 5200: 5193: 5186: 5182: 5179: 5175: 5174: 5173: 5166: 5160: 5156: 5152: 5148: 5142: 5137: 5135: 5131: 5124: 5120: 5116: 5114: 5110: 5106: 5105: 5104: 5100: 5092: 5086: 5082: 5077: 5071: 5069: 5068: 5064: 5060: 5056: 5049: 5044: 5040: 5036: 5032: 5025: 5024: 5023: 5021: 5017: 5013: 5009: 5002: 4999: 4996: 4993: 4990: 4987: 4986: 4981: 4978: 4975: 4972: 4969: 4968: 4964: 4961: 4957: 4950: 4944: 4940: 4936: 4932: 4931: 4930: 4926: 4922: 4918: 4913: 4912: 4911: 4910: 4906: 4902: 4899: 4895: 4885: 4882: 4881: 4877: 4873: 4857: 4853: 4849: 4841: 4833: 4821: 4820: 4819: 4816: 4812: 4808: 4804: 4800: 4792: 4789: 4783: 4777: 4773: 4769: 4765: 4764: 4763: 4759: 4755: 4751: 4750: 4749: 4748: 4744: 4740: 4729: 4725: 4721: 4716: 4713: 4709: 4706: 4705: 4703: 4702: 4701: 4700: 4699: 4698: 4694: 4690: 4681: 4675: 4671: 4667: 4662: 4661: 4660: 4659: 4658: 4657: 4653: 4649: 4626: 4622: 4613: 4596: 4592: 4583: 4582: 4581: 4563: 4558: 4554: 4546: 4545: 4544: 4538: 4536: 4535: 4531: 4527: 4518: 4510: 4506: 4502: 4499: 4496: 4495: 4494: 4493: 4492: 4491: 4482: 4481: 4480: 4479: 4478: 4477: 4469: 4468: 4467: 4466: 4465: 4464: 4459: 4455: 4451: 4447: 4446: 4445: 4444: 4440: 4439: 4438: 4437: 4433: 4429: 4423: 4415:Too technical 4414: 4412: 4411: 4407: 4403: 4394: 4392: 4391: 4387: 4383: 4375: 4371: 4367: 4363: 4362: 4359:Related terms 4358: 4356: 4355: 4351: 4347: 4338: 4333: 4329: 4325: 4324:97.251.38.192 4321: 4315: 4314: 4313: 4308: 4304: 4300: 4296: 4295: 4294: 4291: 4287: 4283: 4279: 4275: 4264: 4260: 4256: 4252: 4251:Sophia.Orthoi 4247: 4245: 4242: 4238: 4237:how-to format 4234: 4233: 4232: 4231: 4227: 4223: 4218: 4214: 4210: 4207: 4204: 4201: 4198: 4195: 4192: 4189: 4186: 4182: 4175: 4173: 4172: 4168: 4164: 4156: 4153: 4149: 4146: 4143: 4140: 4136: 4134: 4131: 4128: 4123: 4120: 4117: 4114: 4110: 4107: 4104: 4103: 4102: 4099: 4097: 4092: 4088: 4080: 4078: 4077: 4073: 4069: 4065: 4060: 4058: 4048: 4047: 4046: 4045: 4044: 4038: 4036: 4035: 4031: 4027: 4014: 4013: 4012: 4011: 4010: 4009: 4008: 4007: 4000: 3996: 3992: 3987: 3986: 3985: 3984: 3983: 3982: 3977: 3973: 3969: 3968:Zulu Papa 5 * 3964: 3963: 3962: 3961: 3958: 3954: 3950: 3945: 3940: 3939: 3938: 3931: 3928: 3925: 3922: 3921: 3920: 3915:Apple example 3914: 3908: 3904: 3900: 3896: 3895: 3894: 3889: 3888: 3883: 3882: 3877: 3876: 3870: 3869: 3868: 3867: 3863: 3859: 3858:194.94.96.194 3850: 3848: 3846: 3842: 3838: 3837:70.119.131.29 3834: 3824: 3819: 3806: 3802: 3798: 3794: 3790: 3789: 3788: 3787: 3786: 3785: 3784: 3783: 3782: 3781: 3777: 3773: 3766: 3761: 3760: 3755: 3754: 3749: 3748: 3742: 3738: 3730: 3726: 3722: 3718: 3717: 3716: 3712: 3708: 3703: 3702: 3701: 3697: 3693: 3688: 3687: 3686: 3682: 3678: 3674: 3673: 3672: 3671: 3667: 3663: 3652: 3648: 3644: 3641: 3637: 3636: 3635: 3632: 3629: 3623: 3622: 3616: 3614: 3613: 3609: 3605: 3599: 3598: 3594: 3590: 3586: 3582: 3574: 3572: 3571: 3567: 3563: 3554: 3548: 3544: 3540: 3536: 3531: 3527: 3526: 3525: 3521: 3517: 3513: 3512: 3511: 3510: 3506: 3502: 3498: 3490: 3484: 3481: 3477: 3473: 3469: 3468: 3467: 3466: 3463: 3460: 3455: 3451: 3450: 3449: 3447: 3445: 3443: 3438: 3436: 3435: 3428: 3425: 3421: 3420: 3419: 3418: 3417: 3416: 3408: 3407: 3406: 3405: 3404: 3403: 3393: 3390: 3386: 3382: 3378: 3374: 3370: 3367: 3362: 3361: 3360: 3359: 3358: 3357: 3356: 3355: 3347: 3344:page and the 3343: 3339: 3338: 3337: 3336: 3335: 3334: 3323: 3315: 3311: 3308: 3304: 3284: 3283: 3282: 3281: 3280: 3279: 3278: 3277: 3269: 3268: 3267: 3266: 3265: 3264: 3259: 3256: 3251: 3247: 3246: 3245: 3244: 3241: 3238: 3233: 3229: 3226: 3223: 3220: 3217: 3216: 3212: 3208: 3207: 3203: 3199: 3194: 3193: 3189: 3185: 3182: 3178: 3175: 3171: 3170: 3166: 3165: 3164: 3161: 3157: 3153: 3149: 3145: 3137: 3135: 3128: 3123: 3121: 3117: 3114: 3109: 3106: 3105: 3101: 3097: 3093: 3086: 3084: 3083: 3079: 3075: 3071: 3065: 3061: 3057: 3052: 3050: 3046: 3042: 3037: 3036: 3035: 3034: 3030: 3026: 3022: 3018: 3012: 3010: 3006: 3002: 2998: 2988: 2986: 2985: 2982: 2978: 2970: 2966: 2965: 2964: 2961: 2954: 2950: 2946: 2943: 2942:Trevor Hanson 2939: 2938: 2937: 2936: 2933: 2929: 2924: 2918: 2916: 2913: 2909: 2906: 2903: 2901: 2897: 2893: 2889: 2888: 2885: 2881: 2877: 2868: 2864: 2860: 2856: 2851: 2850: 2849: 2848: 2845: 2839: 2836: 2833: 2828: 2827: 2823: 2817: 2815: 2814: 2811: 2807: 2799: 2797: 2796: 2792: 2788: 2783: 2782: 2779: 2770: 2768: 2767: 2764: 2763:Trevor Hanson 2755: 2753: 2752: 2749: 2733: 2708: 2700: 2697: 2694: 2690: 2686: 2683: 2680: 2677: 2674: 2670: 2666: 2663: 2657: 2654: 2634: 2614: 2601: 2599: 2598: 2595: 2594:Bill Jefferys 2591: 2587: 2586:loss function 2583: 2578: 2576: 2572: 2567: 2561: 2557: 2556: 2553: 2552:Bill Jefferys 2547: 2545: 2544:loss function 2541: 2532: 2531: 2530: 2524: 2518: 2515: 2511: 2510: 2509: 2508: 2507: 2506: 2503: 2502:Bill Jefferys 2499: 2495: 2490: 2486: 2485: 2482: 2474: 2471: 2470: 2469: 2464: 2463: 2459: 2458: 2457: 2451: 2448: 2447: 2446: 2438: 2434: 2430: 2426: 2425:Type II error 2423: 2422: 2421: 2420: 2419: 2413: 2405: 2401: 2397: 2392: 2391: 2390: 2389: 2388: 2387: 2378: 2377: 2376: 2375: 2374: 2373: 2361: 2360: 2359: 2358: 2357: 2356: 2355: 2354: 2353: 2352: 2342: 2341: 2340: 2339: 2338: 2337: 2336: 2335: 2324: 2323: 2322: 2321: 2320: 2319: 2318: 2317: 2306: 2302: 2301: 2300: 2299: 2298: 2297: 2296: 2295: 2283: 2282: 2281: 2280: 2279: 2278: 2277: 2276: 2275: 2274: 2264: 2259: 2258: 2257: 2256: 2255: 2254: 2253: 2252: 2244: 2240: 2239: 2238: 2237: 2236: 2235: 2225: 2224: 2223: 2222: 2221: 2220: 2219: 2218: 2210: 2209: 2208: 2207: 2206: 2205: 2195: 2194: 2193: 2192: 2191: 2190: 2189: 2188: 2180: 2176: 2175: 2174: 2173: 2172: 2171: 2166: 2162: 2158: 2154: 2150: 2146: 2142: 2138: 2134: 2130: 2126: 2122: 2118: 2114: 2110: 2109: 2107: 2103: 2099: 2095: 2088: 2087: 2082: 2079: 2078:Bill Jefferys 2074: 2073: 2072: 2071: 2064: 2063: 2062: 2061: 2058: 2055: 2051: 2047: 2044: 2043: 2042: 2041: 2038: 2037:Bill Jefferys 2032: 2031: 2028: 2027:Bill Jefferys 2020: 2017: 2013: 2009: 2006: 2005: 2004: 2003: 2000: 1999:Bill Jefferys 1996: 1991: 1988: 1986: 1980: 1979: 1976: 1975:Bill Jefferys 1970: 1968: 1964: 1960: 1955: 1953: 1948: 1945: 1941: 1935: 1933: 1930: 1925: 1921: 1917: 1909: 1892: 1889: 1886: 1883: 1877: 1874: 1871: 1867: 1862: 1698: 1632: 1629: 1626: 1623: 1620: 1619: 1618: 1608: 1606: 1605: 1601: 1599: 1598: 1594: 1592: 1591: 1587: 1585: 1584: 1580: 1578: 1577: 1574: 1573: 1565: 1562: 1559: 1558: 1554: 1551: 1548: 1547: 1539: 1532: 1530: 1529: 1526: 1525: 1524: 1523: 1515: 1512: 1509: 1508: 1507: 1504: 1498: 1496: 1495: 1492: 1489: 1484: 1483: 1480: 1476: 1472: 1464: 1459: 1455: 1452: 1449: 1448: 1444: 1441: 1437: 1434: 1431: 1430: 1426: 1423: 1419: 1415: 1414: 1410: 1407: 1404: 1403: 1402: 1401: 1398: 1390: 1382: 1379: 1375: 1371: 1368: 1367: 1366: 1365: 1364: 1363: 1358: 1355: 1351: 1347: 1343: 1341: 1338: 1334: 1330: 1327: 1326: 1325: 1324: 1313: 1310: 1305: 1300: 1297: 1294: 1293: 1292: 1291: 1290: 1289: 1288: 1287: 1286: 1285: 1276: 1273: 1269: 1265: 1261: 1258: 1255: 1254: 1253: 1250: 1246: 1243: 1239: 1238: 1237: 1234: 1230: 1226: 1225: 1224: 1221: 1217: 1214: 1209: 1206: 1205: 1203: 1199: 1192: 1189: 1188: 1187: 1186: 1184: 1180: 1176: 1173: 1169: 1166: 1162: 1158: 1154: 1150: 1146: 1143: 1140: 1130: 1127: 1123: 1119: 1115: 1111: 1108: 1107: 1106: 1103: 1099: 1095: 1092: 1090: 1087: 1083: 1080: 1079: 1078: 1075: 1071: 1067: 1063: 1062:this revision 1059: 1056: 1055: 1054: 1051: 1047: 1044: 1043: 1042: 1041: 1038: 1035: 1031: 1028: 1025: 1024: 1020: 1017: 1013: 1010: 1007: 1006: 1002: 999: 995: 991: 990: 986: 983: 980: 979: 978: 972: 968: 964: 961: 958: 954: 950: 947: 946: 945: 943: 937: 934: 929: 924: 921: 918: 915: 912: 909: 906: 905: 903: 900: 897: 896: 895: 894: 891: 886: 882: 881:true positive 878: 877:true negative 874: 870: 869:true negative 864: 862: 858: 854: 850: 849:Xavier maxime 846: 840: 834: 833: 829: 825: 818: 811: 801: 798: 789: 786: 778: 773: 767: 766: 763: 761: 754:Type I error 753: 751: 748: 739: 733: 725: 721: 715: 706: 702: 699: 698: 690: 681: 678: 676: 675:Xavier maxime 667: 664: 655: 652: 644: 639: 638: 635: 633: 626:Type I error 625: 623: 620: 611: 608: 602: 593: 589: 586: 585: 577: 568: 565: 563: 554: 552: 551: 548: 544: 540: 532: 526: 523: 519: 518: 517: 514: 510: 506: 502: 498: 491: 484: 483: 482: 481: 478: 474: 466: 464: 463: 459: 455: 450: 449: 443: 442: 439: 433: 432:easier task. 429: 426: 420: 418: 416: 412: 408: 404: 400: 389: 387: 378: 370: 366: 361: 358: 355: 354: 353: 350: 347: 344: 341: 338: 335: 332: 329: 326: 322: 320: 316: 305: 303: 302: 290: 289:MediaWiki.org 286: 282: 275: 274: 270: 266: 263: 259: 258: 242: 238: 237:High-priority 232: 229: 228: 225: 208: 204: 200: 199: 191: 185: 180: 178: 175: 171: 170: 166: 162:High‑priority 160: 157: 154: 150: 137: 133: 127: 124: 123: 120: 103: 99: 95: 94: 89: 86: 82: 81: 77: 71: 68: 65: 61: 56: 52: 46: 38: 37: 27: 23: 18: 17: 5607:78.56.218.15 5601:— Preceding 5598: 5593: 5589: 5588: 5579: 5576:Type I truth 5575: 5574: 5571: 5544:— Preceding 5541: 5537: 5514:— Preceding 5507: 5489: 5483: 5481: 5479: 5475: 5473: 5451: 5448: 5423:source check 5402: 5396: 5393: 5366: 5363: 5340: 5315:source check 5294: 5288: 5275: 5271: 5267: 5265: 5216: 5213: 5190: 5165:source check 5144: 5138: 5133: 5129: 5127: 5078: 5075: 5059:Lucaswilkins 5057: 5053: 5035:216.96.77.80 5029:— Preceding 5012:67.80.92.202 5006:— Preceding 5003: 5000: 4997: 4994: 4991: 4988: 4984: 4982: 4979: 4976: 4973: 4970: 4966: 4965: 4962: 4958: 4954: 4896: 4893: 4883: 4855: 4851: 4847: 4839: 4827: 4797:— Preceding 4793: 4790: 4787: 4736: 4711: 4685: 4682:Recent edits 4644: 4579: 4542: 4522: 4418: 4398: 4378: 4342: 4318:— Preceding 4311: 4272:— Preceding 4268: 4219: 4215: 4211: 4208: 4205: 4202: 4199: 4196: 4193: 4190: 4187: 4183: 4179: 4161: 4132: 4126: 4118: 4108: 4100: 4084: 4063: 4061: 4056: 4054: 4042: 4024: 3943: 3935: 3918: 3886: 3880: 3874: 3854: 3828: 3825:aids testing 3817: 3792: 3769: 3758: 3752: 3746: 3740: 3659: 3640:not to merge 3639: 3633: 3627: 3624: 3600: 3584: 3578: 3558: 3496: 3494: 3442: 3388: 3384: 3380: 3365: 3306: 3210: 3201: 3197: 3187: 3180: 3173: 3138: 3133: 3130: 3125: 3111:Over on the 3110: 3107: 3090: 3072: 3068: 3013: 3001:70.168.79.54 2992: 2977:scare quotes 2973: 2967: 2957: 2928:pseudocyesis 2925: 2922: 2914: 2910: 2907: 2904: 2890: 2872: 2840: 2837: 2831: 2829: 2825: 2824: 2821: 2803: 2784: 2774: 2759: 2605: 2589: 2579: 2574: 2570: 2565: 2562: 2558: 2548: 2537: 2528: 2491: 2487: 2478: 2467: 2461: 2460: 2455: 2444: 2436: 2432: 2428: 2424: 2417: 2304: 2262: 2242: 2178: 2144: 2116: 2112: 2098:128.231.88.5 2049: 2045: 2033: 2023: 2007: 1994: 1992: 1989: 1984: 1981: 1971: 1956: 1949: 1946: 1942: 1939: 1913: 1616: 1519: 1505: 1502: 1487: 1485: 1474: 1470: 1468: 1453: 1446: 1445: 1439: 1435: 1428: 1427: 1421: 1417: 1412: 1411: 1405: 1394: 1373: 1369: 1346:Amda Seyon I 1333:Amda Seyon I 1328: 1302: 1295: 1267: 1256: 1201:"footnotes". 1172:WP:Footnotes 1165:WP:Footnotes 1149:WP:Footnote3 1141: 1122:WP:Footnote3 1114:WP:Footnotes 1109: 1097: 1093: 1081: 1069: 1065: 1057: 1045: 1029: 1022: 1021: 1015: 1011: 1004: 1003: 997: 993: 988: 987: 981: 976: 970: 966: 956: 952: 941: 940: 898: 880: 876: 868: 865: 843:— Preceding 835: 816: 809: 806: 796: 794: 784: 771: 759: 757: 746: 744: 731: 723: 713: 712:hypothesis ( 688: 672: 662: 660: 650: 631: 629: 618: 616: 600: 599:hypothesis ( 575: 558: 539:Arthur Rubin 536: 509:Arthur Rubin 470: 451: 444: 434: 430: 427: 424: 397:— Preceding 393: 385: 374: 352: 345: 339: 333: 327: 313: 307: 268: 236: 196: 131: 91: 51:WikiProjects 34: 5282:Sourcecheck 4921:Hob Gadling 4854:result but 4824:in the box? 3831:—Preceding 3575:Minor Edits 3389:observation 2995:—Preceding 2960:Varuag doos 2892:Phaedrus273 2092:—Preceding 1963:frequentist 1263:reference". 285:Phabricator 212:Mathematics 203:mathematics 159:Mathematics 5624:Categories 5592:being the 5578:being the 5460:Report bug 4935:Meltingpot 4901:Meltingpot 4840:Valid/True 4754:Curb Chain 4526:Lindsay658 4068:Lindsay658 3797:Lindsay658 3707:Anthon.Eff 3562:Garykempen 3539:WDavis1911 3459:Lindsay658 3381:experiment 3321:disprove." 3237:Lindsay658 3108:Hi there, 3096:Lindsay658 3074:Meltingpot 2932:Lindsay658 2575:definition 2571:definition 2514:Lindsay658 2481:Lindsay658 2243:hyphotesis 2179:hyphotesis 2131:... — see 1354:Lindsay658 1337:Lindsay658 1272:Lindsay658 1220:Lindsay658 1102:Lindsay658 1086:Lindsay658 1050:Lindsay658 933:Lindsay658 737:Accepted) 710:about null 597:about null 547:Lindsay658 438:Lindsay658 365:AugustMohr 315:To-do list 107:Statistics 98:statistics 70:Statistics 5504:Languages 5443:this tool 5436:this tool 5335:this tool 5328:this tool 5185:this tool 5178:this tool 4933:I agree. 4720:Tim bates 4576:"no wolf" 4428:Thryduulf 4339:New intro 4039:Interview 3875:SNALWIBMA 3791:Strongly 3747:SNALWIBMA 3739:Strongly 3581:pregnancy 3385:treatment 3116:talk page 2835:cancer." 1454:Footnotes 1160:changes). 1030:Footnotes 867:The term 39:is rated 5603:unsigned 5558:contribs 5546:unsigned 5516:unsigned 5449:Cheers.— 5341:Cheers.— 5229:cbignore 5191:Cheers.— 5091:cbignore 5031:unsigned 5008:unsigned 4811:contribs 4803:WaltGary 4799:unsigned 4712:en masse 4704:Dear N, 4666:Mathstat 4320:unsigned 4286:contribs 4274:unsigned 3887:contribs 3833:unsigned 3759:contribs 3530:Mingramh 3501:Mingramh 3156:contribs 3144:unsigned 3056:Mingramh 2997:unsigned 2494:Bayesian 2435:, or a " 2308:example: 2305:a set of 2094:unsigned 1959:Bayesian 1924:Bayesian 1922:. 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