236:
there were other factors they would like to test. They said there were, but that making added runs would exceed their budget. Christer showed them how they could test two additional factors "for free" – without increasing the number of runs and without reducing the accuracy of their estimate of the cage effect. In this arrangement, called a 2×2×2 factorial design, each of the three factors would be run at two levels and all the eight possible combinations included. The various combinations can conveniently be shown as the vertices of a cube ... " "In each case, the standard condition is indicated by a minus sign and the modified condition by a plus sign. The factors changed were heat treatment, outer ring osculation, and cage design. The numbers show the relative lengths of lives of the bearings. If you look at , you can see that the choice of cage design did not make a lot of difference. … But, if you average the pairs of numbers for cage design, you get the , which shows what the two other factors did. … It led to the extraordinary discovery that, in this particular application, the life of a bearing can be increased fivefold if the two factor(s) outer ring osculation and inner ring heat treatments are increased together."
3130:
of factor A depends on the level of factor C, and vice versa. Factor A (temperature) has very little effect on filtration rate when factor C is at the + level. But Factor A has a large effect on filtration rate when factor C (formaldehyde) is at the − level. The combination of A at the + level and C at the − level gives the highest filtration rate. This observation indicates how one-factor-at-a-time analyses can miss important interactions. Only by varying both factors A and C at the same time could the engineer discover that the effect of factor A depends on the level of factor C.
2938:
6853:
4542:
3112:
229:
2950:
42:
3134:
141:"No aphorism is more frequently repeated in connection with field trials, than that we must ask Nature few questions, or, ideally, one question, at a time. The writer is convinced that this view is wholly mistaken. Nature, he suggests, will best respond to a logical and carefully thought out questionnaire; indeed, if we ask her a single question, she will often refuse to answer until some other topic has been discussed."
6839:
299:
6877:
6865:
2532:
difficult. In these cases, it is common to only run a single replicate of the design, and to assume that factor interactions of more than a certain order (say, between three or more factors) are negligible. Under this assumption, estimates of such high order interactions are estimates of an exact zero, thus really an estimate of experimental error.
3129:
The coefficients for A, C, and D are all positive in the ANOVA, which would suggest running the process with all three variables set to the high value. However, the main effect of each variable is the average over the levels of the other variables. The A:C interaction plot above shows that the effect
2550:
Factorial experiments can be used when there are more than two levels of each factor. However, the number of experimental runs required for three-level (or more) factorial designs will be considerably greater than for their two-level counterparts. Factorial designs are therefore less attractive if a
522:
If these values represent "low" and "high" settings of a treatment, then it is natural to have 1 represent "high", whether using 0 and 1 or −1 and 1. This is illustrated in the accompanying table for a 2×2 experiment. If the factor levels are simply categories, the correspondence might be different;
2630:
used in the process. Previous attempts to reduce the formaldehyde have lowered the filtration rate. The current filtration rate is 75 gallons per hour. Four factors are considered: temperature (A), pressure (B), formaldehyde concentration (C), and stirring rate (D). Each of the four factors will be
224:
gives many examples of the benefits of factorial experiments. Here is one. Engineers at the bearing manufacturer SKF wanted to know if changing to a less expensive "cage" design would affect bearing life. The engineers asked
Christer Hellstrand, a statistician, for help in designing the experiment.
3141:
The best filtration rate is seen when A and D are at the high level, and C is at the low level. This result also satisfies the objective of reducing formaldehyde (factor C). Because B does not appear to be important, it can be dropped from the model. Performing the ANOVA using factors A, C, and D,
2507:
For more than two factors, a 2 factorial experiment can usually be recursively designed from a 2 factorial experiment by replicating the 2 experiment, assigning the first replicate to the first (or low) level of the new factor, and the second replicate to the second (or high) level. This framework
318:
Factorial experiments are described by two things: the number of factors, and the number of levels of each factor. For example, a 2×3 factorial experiment has two factors, the first at 2 levels and the second at 3 levels. Such an experiment has 2×3=6 treatment combinations or cells. Similarly, a
290:
The simplest factorial experiment contains two levels for each of two factors. Suppose an engineer wishes to study the total power used by each of two different motors, A and B, running at each of two different speeds, 2000 or 3000 RPM. The factorial experiment would consist of four experimental
235:
Box reports the following. "The results were assessed by an accelerated life test. … The runs were expensive because they needed to be made on an actual production line and the experimenters were planning to make four runs with the standard cage and four with the modified cage. Christer asked if
2531:
can often be exploited. Replication is more common for small experiments and is a very reliable way of assessing experimental error. When the number of factors is large (typically more than about 5 factors, but this does vary by application), replication of the design can become operationally
278:"Remembering that bearings like this one have been made for decades, it is at first surprising that it could take so long to discover so important an improvement. A likely explanation is that, because most engineers have, until recently, employed only one factor at a time experimentation,
2535:
When there are many factors, many experimental runs will be necessary, even without replication. For example, experimenting with 10 factors at two levels each produces 2=1024 combinations. At some point this becomes infeasible due to high cost or insufficient resources. In this case,
2343:, the number 1 may be replaced by any constant, because the resulting columns will still be contrast vectors. For example, it is common to use the number 1/4 in 2 × 2 × 2 experiments to define each main effect or interaction, and to declare, for example, that the contrast
2576:. To compute the main effect of a factor "A" in a 2-level experiment, subtract the average response of all experimental runs for which A was at its low (or first) level from the average response of all experimental runs for which A was at its high (or second) level.
2949:
2490:
2960:
The non-parallel lines in the A:C interaction plot indicate that the effect of factor A depends on the level of factor C. A similar results holds for the A:D interaction. The graphs indicate that factor B has little effect on filtration rate. The
145:
A factorial design allows the effect of several factors and even interactions between them to be determined with the same number of trials as are necessary to determine any one of the effects by itself with the same degree of accuracy.
428:. In the aquaculture experiment, the ordered triple (25, 80, 10) represents the treatment combination having the lowest level of each factor. In a general 2×3 experiment the ordered pair (2, 1) would indicate the cell in which factor
1829:
This will have 1 degree of freedom for every main effect and interaction. For example, a two-factor interaction will have (2-1)(2-1) = 1 degree of freedom. Thus just a single column is needed to specify each of the seven effects.
80:
For the vast majority of factorial experiments, each factor has only two levels. For example, with two factors each taking two levels, a factorial experiment would have four treatment combinations in total, and is usually called a
195:
The main disadvantage of the full factorial design is its sample size requirement, which grows exponentially with the number of factors or inputs considered. Alternative strategies with improved computational efficiency include
309:
This can be conducted with or without replication, depending on its intended purpose and available resources. It will provide the effects of the three independent variables on the dependent variable and possible interactions.
1359:
The formula for more than two factors follows this pattern. In the 2 × 3 example above, the degrees of freedom for the two main effects and the interaction — the number of columns for each — are 1, 2 and 2, respectively.
804:
362:
at 10%, 25% and 40%. In many cases, though, the factor levels are simply categories, and the coding of levels is somewhat arbitrary. For example, the levels of an 6-level factor might simply be denoted 1, 2, ..., 6.
294:
This experiment is an example of a 2 (or 2×2) factorial experiment, so named because it considers two levels (the base) for each of two factors (the power or superscript), or #levels, producing 2=4 factorial points.
3321:
This choice gives the correspondence 01 ←→ +−, the opposite of that given in the table. There are also algebraic reasons for doing this. The choice of coding via + and − is not important "as long as the labeling is
3613:
Hellstrand, C.; Oosterhoorn, A. D.; Sherwin, D. J.; Gerson, M. (24 February 1989). "The
Necessity of Modern Quality Improvement and Some Experience with its Implementation in the Manufacture of Rolling Bearings ".
2937:
984:
918:
350:
There are various traditions to denote the levels of each factor. If a factor already has natural units, then those are used. For example, a shrimp aquaculture experiment might have factors
306:
Designs can involve many independent variables. As a further example, the effects of three input variables can be evaluated in eight experimental conditions shown as the corners of a cube.
523:
for example, it is natural to represent "control" and "experimental" conditions by coding "control" as 0 if using 0 and 1, and as 1 if using 1 and −1. An example of the latter is given
3137:
Cube plot for the ANOVA using factors A, C, and D, and the interaction terms A:C and A:D. The plot aids in visualizing the result and shows that the best combination is A+, D+, and C−.
2349:
184:
When the effect of one factor is different for different levels of another factor, it cannot be detected by an OFAT experiment design. Factorial designs are required to detect such
191:
Factorial designs allow the effects of a factor to be estimated at several levels of the other factors, yielding conclusions that are valid over a range of experimental conditions.
706:
181:
Factorial designs are more efficient than OFAT experiments. They provide more information at similar or lower cost. They can find optimal conditions faster than OFAT experiments.
3411:
1864:
291:
units: motor A at 2000 RPM, motor B at 2000 RPM, motor A at 3000 RPM, and motor B at 3000 RPM. Each combination of a single level selected from every factor is present once.
662:
of cell means in which the coefficients sum to 0. Contrasts are of interest in themselves, and are the building blocks by which main effects and interactions are defined.
85:. In such a design, the interaction between the variables is often the most important. This applies even to scenarios where a main effect and an interaction are present.
1483:
1408:
1090:
3126:
cannot be calculated for this model. The coefficient values and the graphs suggest that the important factors are A, C, and D, and the interaction terms A:C and A:D.
1368:
In the tables in the following examples, the entries in the "cell" column are treatment combinations: The first component of each combination is the level of factor
5974:
2032:
2005:
1981:
1957:
6479:
4116:
1933:
1912:
1891:
1456:
1435:
1063:
1042:
831:
2325:
column represents the three-factor interaction: its entries depend on the levels of all three factors, and it is orthogonal to the other six contrast vectors.
2259:
represent the corresponding main effects, as the entries in each column depend only on the level of the corresponding factor. For example, the entries in the
6629:
6253:
4084:
4894:
2332:
give an alternate notation, mentioned above, for the treatment combinations (cells) in this experiment: cell 000 corresponds to +++, 001 to ++−, etc.
4441:
6027:
6466:
3142:
and the interaction terms A:C and A:D, gives the result shown in the following table, in which all the terms are significant (p-value < 0.05).
2955:
Plot of the interaction effects showing the mean filtration rate at each of the four possible combinations of levels for a given pair of factors.
717:
4067:
3966:
3943:
3924:
3902:
3856:
3540:
3509:
3456:
6908:
4889:
4589:
2965:(ANOVA) including all 4 factors and all possible interaction terms between them yields the coefficient estimates shown in the table below.
1000:) if these expressions equal 0. Additivity may be viewed as a kind of parallelism between factors, as illustrated in the Analysis section
711:
is a contrast that compares the mean responses of the treatment combinations 11 and 12. (The coefficients here are 1 and –1.) The contrast
5493:
4641:
4465:
137:
argued in 1926 that "complex" designs (such as factorial designs) were more efficient than studying one factor at a time. Fisher wrote,
6881:
4046:
4027:
6276:
6168:
4516:
4354:
4109:
4004:
3985:
2543:
As with any statistical experiment, the experimental runs in a factorial experiment should be randomized to reduce the impact that
339:
is the number of factors. Thus a 2 experiment has 5 factors, each at 2 levels. Experiments that are not fixed-level are said to be
6454:
6328:
2626:
An engineer would like to increase the filtration rate (output) of a process to produce a chemical, and to reduce the amount of
319:
2×2×3 experiment has three factors, two at 2 levels and one at 3, for a total of 12 treatment combinations. If every factor has
6512:
6173:
5918:
5289:
4879:
4529:
4237:
4223:
128:
5503:
1808:
interaction, as their entries depend on the values of both factors, and as all four columns are orthogonal to the columns for
188:. Use of OFAT when interactions are present can lead to serious misunderstanding of how the response changes with the factors.
6903:
6563:
5775:
5582:
5471:
5429:
4534:
923:
857:
4668:
1289:
Similar definitions hold for interactions of more than two factors. In the 2 × 3 example, for instance, the pattern of the
6806:
5765:
2528:
5815:
57:
is an experiment whose design consists of two or more factors, each with discrete possible values or "levels", and whose
6357:
6306:
6291:
6281:
6150:
6022:
5989:
5770:
5600:
4435:
4400:
4332:
4188:
4102:
4089:
2635:
Onwards, the minus (−) and plus (+) signs will indicate whether the factor is run at a low or high level, respectively.
2611:
2537:
6426:
5727:
6701:
6502:
5481:
5150:
4614:
4556:
4505:
4417:
1274:
197:
174:
89:
6586:
6553:
3292:
6558:
6301:
6060:
5966:
5946:
5854:
5565:
5383:
4866:
4738:
4313:
5732:
5498:
5356:
1007:
Since it is the coefficients of these contrasts that carry the essential information, they are often displayed as
6318:
6086:
5807:
5661:
5590:
5510:
5368:
5349:
5057:
4778:
3532:
161:
6431:
3331:
This choice of factor levels facilitates the use of algebra to handle certain issues of experimental design. If
6801:
6568:
6116:
6081:
6045:
5830:
5272:
5181:
5140:
5052:
4743:
4582:
4491:
4486:
4451:
4335:
4253:
4208:
4203:
3365:
2607:
2584:
2485:{\displaystyle (\mu _{000}+\mu _{001}+\mu _{010}+\mu _{011})/4-(\mu _{100}+\mu _{101}+\mu _{110}+\mu _{111})/4}
848:
279:
205:
201:
185:
74:
5838:
5822:
3448:
45:
Designed experiments with full factorial design (left), response surface with second-degree polynomial (right)
6710:
6323:
6263:
6200:
5560:
5422:
5412:
5262:
5176:
4459:
2943:
Plot of the main effects showing the filtration rates for the low (−) and high (+) settings for each factor.
2592:
6471:
6408:
4446:
6748:
6678:
6163:
6050:
5047:
4944:
4851:
4730:
4629:
4422:
4366:
4308:
3802:
1008:
6869:
5747:
671:
6773:
6715:
6658:
6484:
6377:
6286:
6012:
5896:
5755:
5637:
5629:
5444:
5340:
5318:
5277:
5242:
5209:
5155:
5130:
5085:
5024:
4984:
4786:
4609:
4551:
4395:
4295:
4269:
4248:
4228:
4165:
4148:
4125:
3282:
1781:
column is the same as the pattern of the first component of "cell". (If necessary, sorting the table on
104:
6852:
5742:
4541:
1837:
6696:
6271:
6220:
6196:
6158:
6076:
6055:
6007:
5886:
5864:
5833:
5619:
5570:
5488:
5461:
5417:
5373:
4911:
4791:
4349:
4343:
3277:
2962:
1309:
124:
3807:
88:
If the number of combinations in a full factorial design is too high to be logistically feasible, a
6843:
6768:
6691:
6372:
6136:
6129:
6091:
5999:
5979:
5951:
5684:
5550:
5545:
5535:
5527:
5345:
5306:
5196:
5186:
5095:
4874:
4830:
4748:
4673:
4575:
4511:
4476:
4385:
3958:
3840:
3133:
3122:
Because there are 16 observations and 16 coefficients (intercept, main effects, and interactions),
2573:
648:
6418:
159:
The term "factorial" may not have been used in print before 1935, when Fisher used it in his book
6857:
6668:
6522:
6367:
6243:
6140:
6124:
6101:
5878:
5612:
5595:
5555:
5466:
5361:
5323:
5294:
5254:
5214:
5160:
5077:
4763:
4758:
4546:
4153:
3862:
3631:
2603:
2520:
659:
539:
2547:
could have on the experimental results. In practice, this can be a large operational challenge.
1766:
interaction. This accounts for the number of columns for each effect in the accompanying table.
1380:. The entries in each of the other columns sum to 0, so that each column is a contrast vector.
2263:
column follow the same pattern as the middle component of "cell", as can be seen by sorting on
1462:
1387:
1069:
6763:
6733:
6725:
6545:
6536:
6461:
6392:
6248:
6233:
6208:
6096:
6037:
5903:
5891:
5517:
5434:
5378:
5301:
5145:
5067:
4846:
4720:
4303:
4290:
4280:
4193:
4170:
4162:
4158:
4133:
4063:
4057:
4042:
4023:
4000:
3981:
3962:
3939:
3920:
3898:
3852:
3595:
3591:
3536:
3505:
3501:
3302:
3111:
120:
70:
58:
41:
851:
between factors, and is also expressed by contrasts. In the 2 × 3 experiment, the contrasts
508:
To denote factor levels in 2 experiments, three particular systems appear in the literature:
92:
may be done, in which some of the possible combinations (usually at least half) are omitted.
6788:
6743:
6507:
6494:
6387:
6362:
6296:
6228:
6106:
5714:
5607:
5540:
5453:
5400:
5219:
5090:
4884:
4683:
4650:
4481:
4175:
3912:
3890:
3874:
3844:
3812:
3623:
3565:
3424:
3287:
1237:
228:
221:
6705:
6449:
6311:
6238:
5913:
5787:
5760:
5737:
5706:
5333:
5328:
5282:
5012:
4663:
4497:
4427:
4380:
3583:
3297:
2524:
31:
3895:
Statistics for
Experimenters: An Introduction to Design, Data Analysis and Model Building
2606:
effect is expected for a factor, a more complicated experiment should be used, such as a
2598:
When the factors are continuous, two-level factorial designs assume that the effects are
2282:
represent the corresponding two-factor interactions. For example, (i) the entries in the
2011:
1987:
1963:
1939:
6654:
6649:
5112:
5042:
4688:
4183:
3402:
2563:
1918:
1897:
1876:
1441:
1420:
1048:
1027:
816:
634:
153:
69:. Such an experiment allows the investigator to study the effect of each factor on the
6897:
6811:
6778:
6641:
6602:
6413:
6382:
5846:
5800:
5405:
5107:
4934:
4698:
4693:
4321:
4263:
4198:
3866:
3635:
3444:
3420:
2544:
173:
Many people examine the effect of only a single factor or variable. Compared to such
134:
4964:
3687:, p. 73). Hocking and others use the term "population mean" for expected value.
6753:
6686:
6663:
6578:
5908:
5204:
5102:
5037:
4979:
4901:
4856:
4471:
3336:
3115:
2627:
2610:. Optimization of factors that could have quadratic effects is the primary goal of
2588:
436:
at level 1. The parentheses are often dropped, as shown in the accompanying table.
61:
take on all possible combinations of these levels across all such factors. A full
6796:
6758:
6441:
6342:
6204:
6017:
5984:
5476:
5393:
5388:
5032:
4989:
4969:
4949:
4939:
4708:
4327:
4258:
4243:
4213:
4019:
3398:
3352:
2580:
1817:
538:−1 are often used to denote factor levels. These are the values of the integers
424:
Treatment combinations are denoted by ordered pairs or, more generally, ordered
152:
made significant contributions, particularly in the analysis of designs, by the
149:
17:
3569:
1754:
Here we expect 3-1 = 2 degrees of freedom each for the main effects of factors
298:
5642:
5122:
4822:
4753:
4703:
4678:
4598:
4143:
3848:
2622:
Montgomery gives the following example of analysis of a factorial experiment:.
1797:, namely the second component of "cell", so they belong to the main effect of
50:
4039:
Design of
Experiments: Statistical Principles of Research Design and Analysis
5795:
5647:
5267:
5062:
4974:
4959:
4954:
4919:
4275:
3526:
35:
3877:, R. C. (1947). "Mathematical theory of the symmetrical factorial design".
3627:
3429:
3406:
799:{\displaystyle \mu _{11}+\mu _{12}+\mu _{13}-\mu _{21}-\mu _{22}-\mu _{23}}
3793:
Cohen, J (1968). "Multiple regression as a general data-analytic system".
3556:
Tong, C. (2006). "Refinement strategies for stratified sampling methods".
2579:
Other useful exploratory analysis tools for factorial experiments include
5311:
4929:
4806:
4801:
4796:
4768:
1277:(perpendicular) to the contrast vectors representing the main effects of
4094:
3335:
is a power of a prime, the levels may be denoted by the elements of the
1248:
if the values of its components depend only on the level of that factor.
6816:
6517:
3599:
3123:
1785:
will show this.) Thus these two vectors belong to the main effect of
1221:: their components add up to 0. Each effect is determined by both the
227:
6738:
5719:
5693:
5673:
4924:
4715:
4090:
GOV.UK Factorial randomised controlled trials (Public Health
England)
3816:
2599:
3368:, namely the space of all contrast vectors belonging to that effect.
3475:
1265:, if (i) the values of its components depend only on the levels of
177:(OFAT) experiments, factorial experiments offer several advantages
3464:. London, England: Ministry of Agriculture and Fisheries: 503–513.
3132:
3110:
2569:
425:
297:
3936:
Theory of
Factorial Design: Single- and Multi-Stratum Experiments
1777:. This can be seen by noting that the pattern of entries in each
95:
Other terms for "treatment combinations" are often used, such as
30:
This article is about factorial design. For factor loadings, see
4658:
651:.) This notation is illustrated here for the 2 × 3 experiment.
527:. That example illustrates another use of the coding +1 and −1.
6627:
6194:
5941:
5240:
5010:
4627:
4571:
4098:
3917:
1376:, and the third (in the 2 × 2 × 2 example) the level of factor
4567:
3476:"Earliest Known Uses of Some of the Words of Mathematics (F)"
1011:. For the example above, such a table might look like this:
3118:
showing the relative magnitude of the factor coefficients.
1236:
of these columns reflect the general definitions given by
813:
as it contrasts the responses to the "1" level of factor
665:
In the 2 × 3 experiment illustrated here, the expression
515:
the values 1 and −1, often simply abbreviated by + and −;
4085:
Factorial
Designs (California State University, Fresno)
3457:
Journal of the
Ministry of Agriculture of Great Britain
979:{\displaystyle \mu _{11}-\mu _{13}-\mu _{21}+\mu _{23}}
913:{\displaystyle \mu _{11}-\mu _{12}-\mu _{21}+\mu _{22}}
3980:(3rd ed.). New York: Holt, Rinehart and Winston.
2512:, designing three replicates for three level factors,
643:, usually denoted using the Greek letter μ. (The term
3953:
Dean, Angela; Voss, Daniel; Draguljić, Danel (2017).
3364:
The degrees of freedom for an effect is actually the
2352:
2014:
1990:
1966:
1942:
1921:
1900:
1879:
1840:
1465:
1444:
1423:
1390:
1072:
1051:
1030:
926:
860:
819:
720:
674:
169:
Advantages and disadvantages of factorial experiments
6480:
Autoregressive conditional heteroskedasticity (ARCH)
4056:
Wu, C. F. Jeff; Hamada, Michael S. (30 March 2021).
3528:
A First Course in Design and
Analysis of Experiments
3412:
Biographical Memoirs of Fellows of the Royal Society
2551:
researcher wishes to consider more than two levels.
1308:
for the effect, and is an essential quantity in the
6787:
6724:
6677:
6640:
6595:
6577:
6544:
6535:
6493:
6440:
6401:
6350:
6341:
6262:
6219:
6149:
6115:
6069:
6036:
5998:
5965:
5877:
5786:
5705:
5660:
5628:
5581:
5526:
5452:
5443:
5253:
5195:
5169:
5121:
5076:
5023:
4910:
4865:
4839:
4821:
4777:
4729:
4649:
4640:
4394:
4289:
4222:
4132:
1293:column follows the pattern of the levels of factor
119:Factorial designs were used in the 19th century by
3999:. Pacific Grove, CA: Wadsworth & Brooks/Cole.
2484:
2026:
1999:
1975:
1951:
1927:
1906:
1885:
1858:
1477:
1450:
1429:
1402:
1084:
1057:
1036:
978:
912:
833:with those for the "2" level. The main effect of
825:
798:
700:
4059:Experiments: Planning, Analysis, and Optimization
3978:Fundamental Concepts in the Design of Experiments
1297:, indicated by the first component of each cell.
1246:belongs to the main effect of a particular factor
2519:A factorial experiment allows for estimation of
2318:, as can be verified by computing dot products.
1762:, and (3-1)(3-1) = 4 degrees of freedom for the
331:design), the experiment is typically denoted by
111:(arising as intersections of rows and columns).
6028:Multivariate adaptive regression splines (MARS)
4041:(2nd ed.). Pacific Grove,CA: Brooks/Cole.
3780:
3672:
3616:Philosophical Transactions of the Royal Society
139:
2499:, a numerical quantity that can be estimated.
212:Example of advantages of factorial experiments
4583:
4110:
3351:Orthogonality is determined by computing the
2568:A factorial experiment can be analyzed using
639:to a given treatment combination is called a
518:A lower-case letter with the exponent 0 or 1.
8:
3491:
3489:
2639:Design matrix and resulting filtration rate
3588:Improving Almost Anything: Ideas and Essays
3558:Reliability Engineering & System Safety
1804:The last four column vectors belong to the
558:Cell means in a 2 × 3 factorial experiment
218:Improving Almost Anything: Ideas and Essays
6637:
6624:
6541:
6347:
6216:
6191:
5962:
5938:
5666:
5449:
5250:
5237:
5020:
5007:
4646:
4637:
4624:
4590:
4576:
4568:
4117:
4103:
4095:
3997:Theory and Application of the Linear Model
3144:
2967:
2637:
2302:) component, as can be seen by sorting on
1832:
1789:. Similarly, the two contrast vectors for
1382:
1013:
77:between factors on the response variable.
3806:
3590:(Revised ed.). Hoboken, New Jersey:
3428:
2474:
2465:
2452:
2439:
2426:
2408:
2399:
2386:
2373:
2360:
2351:
2013:
1989:
1965:
1941:
1920:
1899:
1878:
1839:
1464:
1443:
1422:
1389:
1255:belongs to the interaction of two factors
1071:
1050:
1029:
970:
957:
944:
931:
925:
904:
891:
878:
865:
859:
847:in a factorial experiment is the lack of
818:
790:
777:
764:
751:
738:
725:
719:
692:
679:
673:
3696:
1816:. The latter can be verified by taking
556:
553:Contrasts, main effects and interactions
438:
365:
238:
40:
3915:; Hunter, W. G.; Hunter, J. S. (2005).
3893:; Hunter, W. G.; Hunter, J. S. (1978).
3684:
3390:
3314:
2933:
2286:column depend on the second and third (
1217:The columns of such a table are called
6554:Kaplan–Meier estimator (product limit)
3449:"The Arrangement of Field Experiments"
2328:Combined and read row-by-row, columns
3768:
3756:
3744:
3720:
3708:
3660:
3648:
3500:(8th ed.). Hoboken, New Jersey:
1304:needed to specify each effect is the
1001:
811:belong to the main effect of factor A
534:) experiments, the values 0, 1, ...,
240:Bearing life vs. heat and osculation
7:
6864:
6564:Accelerated failure time (AFT) model
3732:
2298:, and are independent of the first (
1327:The interaction of two factors with
6876:
6159:Analysis of variance (ANOVA, anova)
4466:Generalized randomized block design
3957:(2nd ed.). Cham, Switzerland:
3531:(Revised ed.). New York City:
2523:in two ways. The experiment can be
1793:depend only on the level of factor
1773:depend only on the level of factor
701:{\displaystyle \mu _{11}-\mu _{12}}
358:at 80 or 160 shrimp/40 liters, and
6254:Cochran–Mantel–Haenszel statistics
4880:Pearson product-moment correlation
3955:Design and Analysis of Experiments
3938:. Boca Raton, Florida: CRC Press.
3498:Design and Analysis of Experiments
440:Cell notation in a 2×2 experiment
34:. For factorial numbers (n!), see
25:
4517:Sequential probability ratio test
1859:{\displaystyle 2\times 2\times 2}
27:Experimental design in statistics
6875:
6863:
6851:
6838:
6837:
4540:
4442:Polynomial and rational modeling
2948:
2936:
2310:column is orthogonal to columns
1316:A main effect for a factor with
367:The cells in a 2 × 3 experiment
206:quasi-random sampling techniques
6513:Least-squares spectral analysis
3496:Montgomery, Douglas C. (2013).
2495:is "the" main effect of factor
990:belong to the A × B interaction
302:Cube plot for factorial design
129:Rothamsted Experimental Station
5494:Mean-unbiased minimum-variance
4209:Replication versus subsampling
3976:Graybill, Franklin A. (1976).
3781:Box, Hunter & Hunter (2005
3673:Box, Hunter & Hunter (1978
2471:
2419:
2405:
2353:
1:
6807:Geographic information system
6023:Simultaneous equations models
4016:The Analysis of Linear Models
2529:sparsity-of-effects principle
1769:The two contrast vectors for
1312:. The formula is as follows:
841:if this expression equals 0.
524:
103:(viewing the combinations as
5990:Coefficient of determination
5601:Uniformly most powerful test
4436:Response surface methodology
4344:Analysis of variance (Anova)
2612:response surface methodology
2538:fractional factorial designs
647:is borrowed from its use in
198:fractional factorial designs
73:, as well as the effects of
6909:Statistical process control
6559:Proportional hazards models
6503:Spectral density estimation
6485:Vector autoregression (VAR)
5919:Maximum posterior estimator
5151:Randomized controlled trial
4506:Randomized controlled trial
4014:Hocking, Ronald R. (1985).
3366:dimension of a vector space
1341:levels, respectively, has (
1017:2 × 3 factorial experiment
282:effects have been missed."
90:fractional factorial design
6925:
6319:Multivariate distributions
4739:Average absolute deviation
3995:Hicks, Charles R. (1982).
3934:Cheng, Ching-Shui (2019).
3570:10.1016/j.ress.2005.11.027
2595:of the estimated effects.
2561:
29:
6833:
6636:
6623:
6307:Structural equation model
6215:
6190:
5961:
5937:
5669:
5643:Score/Lagrange multiplier
5249:
5236:
5058:Sample size determination
5019:
5006:
4636:
4623:
4605:
4525:
4062:. John Wiley & Sons.
4037:Kuehl, Robert O. (2000).
3849:10.1007/978-3-031-08176-7
3533:W. H. Freeman and Company
3377:And 1/2 in 2 experiments.
1478:{\displaystyle A\times B}
1459:
1438:
1417:
1403:{\displaystyle 3\times 3}
1085:{\displaystyle A\times B}
1066:
1045:
1015:Contrast vectors for the
432:is at level 2 and factor
162:The Design of Experiments
6802:Environmental statistics
6324:Elliptical distributions
6117:Generalized linear model
6046:Simple linear regression
5816:Hodges–Lehmann estimator
5273:Probability distribution
5182:Stochastic approximation
4744:Coefficient of variation
4492:Repeated measures design
4204:Restricted randomization
3837:Linear Models and Design
2608:central composite design
1372:, the second for factor
202:Latin hypercube sampling
6462:Cross-correlation (XCF)
6070:Non-standard predictors
5504:Lehmann–Scheffé theorem
5177:Adaptive clinical trial
3919:(2nd ed.). Wiley.
2593:normal probability plot
2508:can be generalized to,
1827:A 2 × 2 × 2 experiment:
1355:−1) degrees of freedom.
1225:in its columns and the
530:For other fixed-level (
6858:Mathematics portal
6679:Engineering statistics
6587:Nelson–Aalen estimator
6164:Analysis of covariance
6051:Ordinary least squares
5975:Pearson product-moment
5379:Statistical functional
5290:Empirical distribution
5123:Controlled experiments
4852:Frequency distribution
4630:Descriptive statistics
4547:Mathematics portal
4309:Ordinary least squares
3835:Beder, Jay H. (2022).
3795:Psychological Bulletin
3628:10.1098/rsta.1989.0008
3525:Oehlert, Gary (2000).
3430:10.1098/rsbm.1963.0006
3407:"Ronald Aylmer Fisher"
3293:Plackett–Burman design
3138:
3119:
2633:
2486:
2028:
2001:
1977:
1953:
1929:
1908:
1887:
1860:
1834:Contrast vectors in a
1479:
1452:
1431:
1404:
1384:Contrast vectors in a
1324:−1 degrees of freedom.
1234:patterns of components
1086:
1059:
1038:
980:
914:
827:
800:
702:
656:contrast in cell means
303:
232:
143:
46:
6904:Design of experiments
6774:Population statistics
6716:System identification
6450:Autocorrelation (ACF)
6378:Exponential smoothing
6292:Discriminant analysis
6287:Canonical correlation
6151:Partition of variance
6013:Regression validation
5857:(Jonckheere–Terpstra)
5756:Likelihood-ratio test
5445:Frequentist inference
5357:Location–scale family
5278:Sampling distribution
5243:Statistical inference
5210:Cross-sectional study
5197:Observational studies
5156:Randomized experiment
4985:Stem-and-leaf display
4787:Central limit theorem
4144:Scientific experiment
4126:Design of experiments
4018:. Pacific Grove, CA:
3839:. Cham, Switzerland:
3309:Explanatory footnotes
3283:Design of experiments
3136:
3114:
2631:tested at two levels.
2624:
2487:
2029:
2002:
1978:
1954:
1930:
1909:
1888:
1861:
1480:
1453:
1432:
1405:
1223:pattern of components
1087:
1060:
1039:
981:
915:
828:
801:
703:
301:
231:
65:may also be called a
44:
6697:Probabilistic design
6282:Principal components
6125:Exponential families
6077:Nonlinear regression
6056:General linear model
6018:Mixed effects models
6008:Errors and residuals
5985:Confounding variable
5887:Bayesian probability
5865:Van der Waerden test
5855:Ordered alternative
5620:Multiple comparisons
5499:Rao–Blackwellization
5462:Estimating equations
5418:Statistical distance
5136:Factorial experiment
4669:Arithmetic-Geometric
4418:Fractional factorial
3564:(10–11): 1257–1265.
3342:for the same reason.
3278:Combinatorial design
2963:analysis of variance
2350:
2012:
1988:
1964:
1940:
1919:
1898:
1877:
1838:
1463:
1442:
1421:
1388:
1310:analysis of variance
1070:
1049:
1028:
924:
858:
817:
718:
672:
323:levels (a so-called
175:one-factor-at-a-time
125:Joseph Henry Gilbert
99:(of an experiment),
83:2×2 factorial design
67:fully crossed design
55:factorial experiment
6769:Official statistics
6692:Methods engineering
6373:Seasonal adjustment
6141:Poisson regressions
6061:Bayesian regression
6000:Regression analysis
5980:Partial correlation
5952:Regression analysis
5551:Prediction interval
5546:Likelihood interval
5536:Confidence interval
5528:Interval estimation
5489:Unbiased estimators
5307:Model specification
5187:Up-and-down designs
4875:Partial correlation
4831:Index of dispersion
4749:Interquartile range
4552:Statistical outline
4512:Sequential analysis
4477:Graeco-Latin square
4386:Multiple comparison
4333:Hierarchical model:
3735:, pp. 110–111)
3651:, pp. 200–205)
3419:. London, England:
3248:9.4 × 10
3231:5.9 × 10
3214:1.2 × 10
3197:1.9 × 10
3180:2.3 × 10
3147:
2970:
2640:
2574:regression analysis
2027:{\displaystyle ABC}
1867:
1752:A 3 × 3 experiment:
1411:
1018:
559:
512:The values 1 and 0;
441:
368:
241:
105:vertices of a graph
6789:Spatial statistics
6669:Medical statistics
6569:First hitting time
6523:Whittle likelihood
6174:Degrees of freedom
6169:Multivariate ANOVA
6102:Heteroscedasticity
5914:Bayesian estimator
5879:Bayesian inference
5728:Kolmogorov–Smirnov
5613:Randomization test
5583:Testing hypotheses
5556:Tolerance interval
5467:Maximum likelihood
5362:Exponential family
5295:Density estimation
5255:Statistical theory
5215:Natural experiment
5161:Scientific control
5078:Survey methodology
4764:Standard deviation
4557:Statistical topics
4149:Statistical design
3699:, p. 559-560)
3480:jeff560.tripod.com
3145:
3139:
3120:
2968:
2638:
2521:experimental error
2482:
2024:
2000:{\displaystyle BC}
1997:
1976:{\displaystyle AC}
1973:
1952:{\displaystyle AB}
1949:
1925:
1904:
1883:
1856:
1833:
1475:
1448:
1427:
1400:
1383:
1306:degrees of freedom
1253:A contrast vector
1244:A contrast vector
1082:
1055:
1034:
1014:
992:; interaction is
976:
920: and
910:
823:
796:
698:
660:linear combination
557:
439:
366:
354:at 25°C and 35°C,
304:
239:
233:
59:experimental units
47:
6891:
6890:
6829:
6828:
6825:
6824:
6764:National accounts
6734:Actuarial science
6726:Social statistics
6619:
6618:
6615:
6614:
6611:
6610:
6546:Survival function
6531:
6530:
6393:Granger causality
6234:Contingency table
6209:Survival analysis
6186:
6185:
6182:
6181:
6038:Linear regression
5933:
5932:
5929:
5928:
5904:Credible interval
5873:
5872:
5656:
5655:
5472:Method of moments
5341:Parametric family
5302:Statistical model
5232:
5231:
5228:
5227:
5146:Random assignment
5068:Statistical power
5002:
5001:
4998:
4997:
4847:Contingency table
4817:
4816:
4684:Generalized/power
4565:
4564:
4452:Central composite
4350:Cochran's theorem
4304:Linear regression
4281:Nuisance variable
4194:Random assignment
4171:Experimental unit
4069:978-1-119-47010-6
3968:978-3-319-52250-0
3945:978-0-367-37898-1
3926:978-0-471-71813-0
3904:978-0-471-09315-2
3858:978-3-031-08175-0
3711:, pp. 29–30)
3622:(1596): 529–537.
3542:978-0-7167-3510-6
3511:978-1-119-32093-7
3269:
3268:
3265:2 × 10
3109:
3108:
2932:
2931:
2585:interaction plots
2245:
2244:
1928:{\displaystyle C}
1907:{\displaystyle B}
1886:{\displaystyle A}
1749:
1748:
1451:{\displaystyle B}
1430:{\displaystyle A}
1302:number of columns
1273:, and (ii) it is
1227:number of columns
1215:
1214:
1058:{\displaystyle B}
1037:{\displaystyle A}
826:{\displaystyle A}
636:expected response
631:
630:
506:
505:
422:
421:
276:
275:
121:John Bennet Lawes
71:response variable
16:(Redirected from
6916:
6879:
6878:
6867:
6866:
6856:
6855:
6841:
6840:
6744:Crime statistics
6638:
6625:
6542:
6508:Fourier analysis
6495:Frequency domain
6475:
6422:
6388:Structural break
6348:
6297:Cluster analysis
6244:Log-linear model
6217:
6192:
6133:
6107:Homoscedasticity
5963:
5939:
5858:
5850:
5842:
5841:(Kruskal–Wallis)
5826:
5811:
5766:Cross validation
5751:
5733:Anderson–Darling
5680:
5667:
5638:Likelihood-ratio
5630:Parametric tests
5608:Permutation test
5591:1- & 2-tails
5482:Minimum distance
5454:Point estimation
5450:
5401:Optimal decision
5352:
5251:
5238:
5220:Quasi-experiment
5170:Adaptive designs
5021:
5008:
4885:Rank correlation
4647:
4638:
4625:
4592:
4585:
4578:
4569:
4545:
4544:
4482:Orthogonal array
4119:
4112:
4105:
4096:
4073:
4052:
4033:
4010:
3991:
3972:
3949:
3930:
3908:
3886:
3870:
3821:
3820:
3817:10.1037/h0026714
3810:
3790:
3784:
3778:
3772:
3766:
3760:
3754:
3748:
3742:
3736:
3730:
3724:
3718:
3712:
3706:
3700:
3694:
3688:
3682:
3676:
3670:
3664:
3658:
3652:
3646:
3640:
3639:
3610:
3604:
3603:
3584:George E.P., Box
3580:
3574:
3573:
3553:
3547:
3546:
3522:
3516:
3515:
3493:
3484:
3483:
3472:
3466:
3465:
3453:
3441:
3435:
3434:
3432:
3395:
3378:
3375:
3369:
3362:
3356:
3349:
3343:
3329:
3323:
3319:
3288:Orthogonal array
3148:
2971:
2952:
2940:
2656:Filtration rate
2641:
2618:Analysis example
2491:
2489:
2488:
2483:
2478:
2470:
2469:
2457:
2456:
2444:
2443:
2431:
2430:
2412:
2404:
2403:
2391:
2390:
2378:
2377:
2365:
2364:
2294:) components of
2270:The columns for
2247:The columns for
2033:
2031:
2030:
2025:
2006:
2004:
2003:
1998:
1982:
1980:
1979:
1974:
1958:
1956:
1955:
1950:
1934:
1932:
1931:
1926:
1913:
1911:
1910:
1905:
1892:
1890:
1889:
1884:
1868:
1865:
1863:
1862:
1857:
1484:
1482:
1481:
1476:
1457:
1455:
1454:
1449:
1436:
1434:
1433:
1428:
1412:
1409:
1407:
1406:
1401:
1219:contrast vectors
1091:
1089:
1088:
1083:
1064:
1062:
1061:
1056:
1043:
1041:
1040:
1035:
1019:
985:
983:
982:
977:
975:
974:
962:
961:
949:
948:
936:
935:
919:
917:
916:
911:
909:
908:
896:
895:
883:
882:
870:
869:
832:
830:
829:
824:
805:
803:
802:
797:
795:
794:
782:
781:
769:
768:
756:
755:
743:
742:
730:
729:
707:
705:
704:
699:
697:
696:
684:
683:
560:
442:
369:
242:
63:factorial design
21:
18:Factorial design
6924:
6923:
6919:
6918:
6917:
6915:
6914:
6913:
6894:
6893:
6892:
6887:
6850:
6821:
6783:
6720:
6706:quality control
6673:
6655:Clinical trials
6632:
6607:
6591:
6579:Hazard function
6573:
6527:
6489:
6473:
6436:
6432:Breusch–Godfrey
6420:
6397:
6337:
6312:Factor analysis
6258:
6239:Graphical model
6211:
6178:
6145:
6131:
6111:
6065:
6032:
5994:
5957:
5956:
5925:
5869:
5856:
5848:
5840:
5824:
5809:
5788:Rank statistics
5782:
5761:Model selection
5749:
5707:Goodness of fit
5701:
5678:
5652:
5624:
5577:
5522:
5511:Median unbiased
5439:
5350:
5283:Order statistic
5245:
5224:
5191:
5165:
5117:
5072:
5015:
5013:Data collection
4994:
4906:
4861:
4835:
4813:
4773:
4725:
4642:Continuous data
4632:
4619:
4601:
4596:
4566:
4561:
4539:
4521:
4498:Crossover study
4489:
4487:Latin hypercube
4423:Plackett–Burman
4402:
4399:
4398:
4390:
4293:
4285:
4226:
4218:
4135:
4128:
4123:
4081:
4076:
4070:
4055:
4049:
4036:
4030:
4013:
4007:
3994:
3988:
3975:
3969:
3952:
3946:
3933:
3927:
3911:
3905:
3889:
3873:
3859:
3834:
3830:
3825:
3824:
3808:10.1.1.476.6180
3792:
3791:
3787:
3779:
3775:
3767:
3763:
3755:
3751:
3743:
3739:
3731:
3727:
3723:, Example 5.21)
3719:
3715:
3707:
3703:
3695:
3691:
3683:
3679:
3671:
3667:
3659:
3655:
3647:
3643:
3612:
3611:
3607:
3582:
3581:
3577:
3555:
3554:
3550:
3543:
3524:
3523:
3519:
3512:
3495:
3494:
3487:
3474:
3473:
3469:
3451:
3443:
3442:
3438:
3403:Mather, Kenneth
3397:
3396:
3392:
3387:
3382:
3381:
3376:
3372:
3363:
3359:
3350:
3346:
3330:
3326:
3320:
3316:
3311:
3298:Taguchi methods
3274:
3157:Standard error
2956:
2953:
2944:
2941:
2620:
2566:
2560:
2554:
2505:
2493:
2461:
2448:
2435:
2422:
2395:
2382:
2369:
2356:
2348:
2347:
2306:; and (ii) the
2010:
2009:
1986:
1985:
1962:
1961:
1938:
1937:
1917:
1916:
1896:
1895:
1875:
1874:
1836:
1835:
1823:
1461:
1460:
1440:
1439:
1419:
1418:
1386:
1385:
1366:
1354:
1347:
1340:
1333:
1068:
1067:
1047:
1046:
1026:
1025:
1016:
996:(additivity is
987:
966:
953:
940:
927:
922:
921:
900:
887:
874:
861:
856:
855:
815:
814:
807:
786:
773:
760:
747:
734:
721:
716:
715:
709:
688:
675:
670:
669:
627:
621:
615:
604:
598:
592:
572:
567:
555:
381:
376:
316:
288:
220:, statistician
214:
171:
117:
39:
32:Factor analysis
28:
23:
22:
15:
12:
11:
5:
6922:
6920:
6912:
6911:
6906:
6896:
6895:
6889:
6888:
6886:
6885:
6873:
6861:
6847:
6834:
6831:
6830:
6827:
6826:
6823:
6822:
6820:
6819:
6814:
6809:
6804:
6799:
6793:
6791:
6785:
6784:
6782:
6781:
6776:
6771:
6766:
6761:
6756:
6751:
6746:
6741:
6736:
6730:
6728:
6722:
6721:
6719:
6718:
6713:
6708:
6699:
6694:
6689:
6683:
6681:
6675:
6674:
6672:
6671:
6666:
6661:
6652:
6650:Bioinformatics
6646:
6644:
6634:
6633:
6628:
6621:
6620:
6617:
6616:
6613:
6612:
6609:
6608:
6606:
6605:
6599:
6597:
6593:
6592:
6590:
6589:
6583:
6581:
6575:
6574:
6572:
6571:
6566:
6561:
6556:
6550:
6548:
6539:
6533:
6532:
6529:
6528:
6526:
6525:
6520:
6515:
6510:
6505:
6499:
6497:
6491:
6490:
6488:
6487:
6482:
6477:
6469:
6464:
6459:
6458:
6457:
6455:partial (PACF)
6446:
6444:
6438:
6437:
6435:
6434:
6429:
6424:
6416:
6411:
6405:
6403:
6402:Specific tests
6399:
6398:
6396:
6395:
6390:
6385:
6380:
6375:
6370:
6365:
6360:
6354:
6352:
6345:
6339:
6338:
6336:
6335:
6334:
6333:
6332:
6331:
6316:
6315:
6314:
6304:
6302:Classification
6299:
6294:
6289:
6284:
6279:
6274:
6268:
6266:
6260:
6259:
6257:
6256:
6251:
6249:McNemar's test
6246:
6241:
6236:
6231:
6225:
6223:
6213:
6212:
6195:
6188:
6187:
6184:
6183:
6180:
6179:
6177:
6176:
6171:
6166:
6161:
6155:
6153:
6147:
6146:
6144:
6143:
6127:
6121:
6119:
6113:
6112:
6110:
6109:
6104:
6099:
6094:
6089:
6087:Semiparametric
6084:
6079:
6073:
6071:
6067:
6066:
6064:
6063:
6058:
6053:
6048:
6042:
6040:
6034:
6033:
6031:
6030:
6025:
6020:
6015:
6010:
6004:
6002:
5996:
5995:
5993:
5992:
5987:
5982:
5977:
5971:
5969:
5959:
5958:
5955:
5954:
5949:
5943:
5942:
5935:
5934:
5931:
5930:
5927:
5926:
5924:
5923:
5922:
5921:
5911:
5906:
5901:
5900:
5899:
5894:
5883:
5881:
5875:
5874:
5871:
5870:
5868:
5867:
5862:
5861:
5860:
5852:
5844:
5828:
5825:(Mann–Whitney)
5820:
5819:
5818:
5805:
5804:
5803:
5792:
5790:
5784:
5783:
5781:
5780:
5779:
5778:
5773:
5768:
5758:
5753:
5750:(Shapiro–Wilk)
5745:
5740:
5735:
5730:
5725:
5717:
5711:
5709:
5703:
5702:
5700:
5699:
5691:
5682:
5670:
5664:
5662:Specific tests
5658:
5657:
5654:
5653:
5651:
5650:
5645:
5640:
5634:
5632:
5626:
5625:
5623:
5622:
5617:
5616:
5615:
5605:
5604:
5603:
5593:
5587:
5585:
5579:
5578:
5576:
5575:
5574:
5573:
5568:
5558:
5553:
5548:
5543:
5538:
5532:
5530:
5524:
5523:
5521:
5520:
5515:
5514:
5513:
5508:
5507:
5506:
5501:
5486:
5485:
5484:
5479:
5474:
5469:
5458:
5456:
5447:
5441:
5440:
5438:
5437:
5432:
5427:
5426:
5425:
5415:
5410:
5409:
5408:
5398:
5397:
5396:
5391:
5386:
5376:
5371:
5366:
5365:
5364:
5359:
5354:
5338:
5337:
5336:
5331:
5326:
5316:
5315:
5314:
5309:
5299:
5298:
5297:
5287:
5286:
5285:
5275:
5270:
5265:
5259:
5257:
5247:
5246:
5241:
5234:
5233:
5230:
5229:
5226:
5225:
5223:
5222:
5217:
5212:
5207:
5201:
5199:
5193:
5192:
5190:
5189:
5184:
5179:
5173:
5171:
5167:
5166:
5164:
5163:
5158:
5153:
5148:
5143:
5138:
5133:
5127:
5125:
5119:
5118:
5116:
5115:
5113:Standard error
5110:
5105:
5100:
5099:
5098:
5093:
5082:
5080:
5074:
5073:
5071:
5070:
5065:
5060:
5055:
5050:
5045:
5043:Optimal design
5040:
5035:
5029:
5027:
5017:
5016:
5011:
5004:
5003:
5000:
4999:
4996:
4995:
4993:
4992:
4987:
4982:
4977:
4972:
4967:
4962:
4957:
4952:
4947:
4942:
4937:
4932:
4927:
4922:
4916:
4914:
4908:
4907:
4905:
4904:
4899:
4898:
4897:
4892:
4882:
4877:
4871:
4869:
4863:
4862:
4860:
4859:
4854:
4849:
4843:
4841:
4840:Summary tables
4837:
4836:
4834:
4833:
4827:
4825:
4819:
4818:
4815:
4814:
4812:
4811:
4810:
4809:
4804:
4799:
4789:
4783:
4781:
4775:
4774:
4772:
4771:
4766:
4761:
4756:
4751:
4746:
4741:
4735:
4733:
4727:
4726:
4724:
4723:
4718:
4713:
4712:
4711:
4706:
4701:
4696:
4691:
4686:
4681:
4676:
4674:Contraharmonic
4671:
4666:
4655:
4653:
4644:
4634:
4633:
4628:
4621:
4620:
4618:
4617:
4612:
4606:
4603:
4602:
4597:
4595:
4594:
4587:
4580:
4572:
4563:
4562:
4560:
4559:
4554:
4549:
4537:
4532:
4526:
4523:
4522:
4520:
4519:
4514:
4509:
4501:
4500:
4495:
4484:
4479:
4474:
4469:
4463:
4455:
4454:
4449:
4444:
4439:
4431:
4430:
4425:
4420:
4415:
4407:
4405:
4392:
4391:
4389:
4388:
4383:
4377:
4376:
4364:
4352:
4347:
4339:
4338:
4330:
4325:
4317:
4316:
4311:
4306:
4300:
4298:
4287:
4286:
4284:
4283:
4278:
4273:
4266:
4261:
4256:
4251:
4246:
4241:
4233:
4231:
4220:
4219:
4217:
4216:
4211:
4206:
4201:
4196:
4191:
4184:Optimal design
4179:
4178:
4173:
4168:
4156:
4151:
4146:
4140:
4138:
4130:
4129:
4124:
4122:
4121:
4114:
4107:
4099:
4093:
4092:
4087:
4080:
4079:External links
4077:
4075:
4074:
4068:
4053:
4048:978-0534368340
4047:
4034:
4029:978-0534036188
4028:
4011:
4005:
3992:
3986:
3973:
3967:
3950:
3944:
3931:
3925:
3909:
3903:
3887:
3871:
3857:
3831:
3829:
3826:
3823:
3822:
3801:(6): 426–443.
3785:
3783:, p. 180)
3773:
3761:
3759:, p. 202)
3749:
3737:
3725:
3713:
3701:
3697:Graybill (1976
3689:
3677:
3675:, p. 307)
3665:
3653:
3641:
3605:
3575:
3548:
3541:
3517:
3510:
3485:
3467:
3445:Fisher, Ronald
3436:
3389:
3388:
3386:
3383:
3380:
3379:
3370:
3357:
3344:
3324:
3313:
3312:
3310:
3307:
3306:
3305:
3303:Welch's t-test
3300:
3295:
3290:
3285:
3280:
3273:
3270:
3267:
3266:
3263:
3260:
3257:
3254:
3250:
3249:
3246:
3243:
3240:
3237:
3233:
3232:
3229:
3226:
3223:
3220:
3216:
3215:
3212:
3209:
3206:
3203:
3199:
3198:
3195:
3192:
3189:
3186:
3182:
3181:
3178:
3175:
3172:
3169:
3165:
3164:
3161:
3158:
3155:
3152:
3146:ANOVA results
3107:
3106:
3103:
3099:
3098:
3095:
3091:
3090:
3087:
3083:
3082:
3079:
3075:
3074:
3071:
3067:
3066:
3063:
3059:
3058:
3055:
3051:
3050:
3047:
3043:
3042:
3039:
3035:
3034:
3031:
3027:
3026:
3023:
3019:
3018:
3015:
3011:
3010:
3007:
3003:
3002:
2999:
2995:
2994:
2991:
2987:
2986:
2983:
2979:
2978:
2975:
2969:ANOVA results
2958:
2957:
2954:
2947:
2945:
2942:
2935:
2930:
2929:
2926:
2923:
2920:
2917:
2913:
2912:
2909:
2906:
2903:
2900:
2896:
2895:
2892:
2889:
2886:
2883:
2879:
2878:
2875:
2872:
2869:
2866:
2862:
2861:
2858:
2855:
2852:
2849:
2845:
2844:
2841:
2838:
2835:
2832:
2828:
2827:
2824:
2821:
2818:
2815:
2811:
2810:
2807:
2804:
2801:
2798:
2794:
2793:
2790:
2787:
2784:
2781:
2777:
2776:
2773:
2770:
2767:
2764:
2760:
2759:
2756:
2753:
2750:
2747:
2743:
2742:
2739:
2736:
2733:
2730:
2726:
2725:
2722:
2719:
2716:
2713:
2709:
2708:
2705:
2702:
2699:
2696:
2692:
2691:
2688:
2685:
2682:
2679:
2675:
2674:
2671:
2668:
2665:
2662:
2658:
2657:
2654:
2651:
2648:
2645:
2619:
2616:
2564:Yates analysis
2562:Main article:
2559:
2556:
2504:
2503:Implementation
2501:
2481:
2477:
2473:
2468:
2464:
2460:
2455:
2451:
2447:
2442:
2438:
2434:
2429:
2425:
2421:
2418:
2415:
2411:
2407:
2402:
2398:
2394:
2389:
2385:
2381:
2376:
2372:
2368:
2363:
2359:
2355:
2345:
2243:
2242:
2239:
2236:
2233:
2230:
2227:
2224:
2221:
2217:
2216:
2213:
2210:
2207:
2204:
2201:
2198:
2195:
2191:
2190:
2187:
2184:
2181:
2178:
2175:
2172:
2169:
2165:
2164:
2161:
2158:
2155:
2152:
2149:
2146:
2143:
2139:
2138:
2135:
2132:
2129:
2126:
2123:
2120:
2117:
2113:
2112:
2109:
2106:
2103:
2100:
2097:
2094:
2091:
2087:
2086:
2083:
2080:
2077:
2074:
2071:
2068:
2065:
2061:
2060:
2057:
2054:
2051:
2048:
2045:
2042:
2039:
2035:
2034:
2023:
2020:
2017:
2007:
1996:
1993:
1983:
1972:
1969:
1959:
1948:
1945:
1935:
1924:
1914:
1903:
1893:
1882:
1872:
1855:
1852:
1849:
1846:
1843:
1747:
1746:
1743:
1740:
1737:
1734:
1731:
1728:
1725:
1722:
1718:
1717:
1714:
1711:
1708:
1705:
1702:
1699:
1696:
1693:
1689:
1688:
1685:
1682:
1679:
1676:
1673:
1670:
1667:
1664:
1660:
1659:
1656:
1653:
1650:
1647:
1644:
1641:
1638:
1635:
1631:
1630:
1627:
1624:
1621:
1618:
1615:
1612:
1609:
1606:
1602:
1601:
1598:
1595:
1592:
1589:
1586:
1583:
1580:
1577:
1573:
1572:
1569:
1566:
1563:
1560:
1557:
1554:
1551:
1548:
1544:
1543:
1540:
1537:
1534:
1531:
1528:
1525:
1522:
1519:
1515:
1514:
1511:
1508:
1505:
1502:
1499:
1496:
1493:
1490:
1486:
1485:
1474:
1471:
1468:
1458:
1447:
1437:
1426:
1416:
1399:
1396:
1393:
1365:
1362:
1357:
1356:
1352:
1345:
1338:
1331:
1325:
1287:
1286:
1250:
1249:
1213:
1212:
1209:
1206:
1203:
1200:
1197:
1193:
1192:
1189:
1186:
1183:
1180:
1177:
1173:
1172:
1169:
1166:
1163:
1160:
1157:
1153:
1152:
1149:
1146:
1143:
1140:
1137:
1133:
1132:
1129:
1126:
1123:
1120:
1117:
1113:
1112:
1109:
1106:
1103:
1100:
1097:
1093:
1092:
1081:
1078:
1075:
1065:
1054:
1044:
1033:
1023:
1009:column vectors
973:
969:
965:
960:
956:
952:
947:
943:
939:
934:
930:
907:
903:
899:
894:
890:
886:
881:
877:
873:
868:
864:
853:
837:is said to be
822:
793:
789:
785:
780:
776:
772:
767:
763:
759:
754:
750:
746:
741:
737:
733:
728:
724:
713:
695:
691:
687:
682:
678:
667:
649:tables of data
629:
628:
625:
622:
619:
616:
613:
610:
606:
605:
602:
599:
596:
593:
590:
587:
583:
582:
579:
576:
573:
568:
563:
554:
551:
520:
519:
516:
513:
504:
503:
500:
497:
494:
490:
489:
486:
483:
480:
473:
472:
469:
466:
463:
456:
455:
452:
449:
446:
420:
419:
416:
413:
410:
406:
405:
402:
399:
396:
392:
391:
388:
385:
382:
377:
372:
315:
312:
287:
284:
274:
273:
270:
267:
263:
262:
259:
256:
252:
251:
248:
245:
213:
210:
193:
192:
189:
182:
170:
167:
154:Yates analysis
116:
113:
26:
24:
14:
13:
10:
9:
6:
4:
3:
2:
6921:
6910:
6907:
6905:
6902:
6901:
6899:
6884:
6883:
6874:
6872:
6871:
6862:
6860:
6859:
6854:
6848:
6846:
6845:
6836:
6835:
6832:
6818:
6815:
6813:
6812:Geostatistics
6810:
6808:
6805:
6803:
6800:
6798:
6795:
6794:
6792:
6790:
6786:
6780:
6779:Psychometrics
6777:
6775:
6772:
6770:
6767:
6765:
6762:
6760:
6757:
6755:
6752:
6750:
6747:
6745:
6742:
6740:
6737:
6735:
6732:
6731:
6729:
6727:
6723:
6717:
6714:
6712:
6709:
6707:
6703:
6700:
6698:
6695:
6693:
6690:
6688:
6685:
6684:
6682:
6680:
6676:
6670:
6667:
6665:
6662:
6660:
6656:
6653:
6651:
6648:
6647:
6645:
6643:
6642:Biostatistics
6639:
6635:
6631:
6626:
6622:
6604:
6603:Log-rank test
6601:
6600:
6598:
6594:
6588:
6585:
6584:
6582:
6580:
6576:
6570:
6567:
6565:
6562:
6560:
6557:
6555:
6552:
6551:
6549:
6547:
6543:
6540:
6538:
6534:
6524:
6521:
6519:
6516:
6514:
6511:
6509:
6506:
6504:
6501:
6500:
6498:
6496:
6492:
6486:
6483:
6481:
6478:
6476:
6474:(Box–Jenkins)
6470:
6468:
6465:
6463:
6460:
6456:
6453:
6452:
6451:
6448:
6447:
6445:
6443:
6439:
6433:
6430:
6428:
6427:Durbin–Watson
6425:
6423:
6417:
6415:
6412:
6410:
6409:Dickey–Fuller
6407:
6406:
6404:
6400:
6394:
6391:
6389:
6386:
6384:
6383:Cointegration
6381:
6379:
6376:
6374:
6371:
6369:
6366:
6364:
6361:
6359:
6358:Decomposition
6356:
6355:
6353:
6349:
6346:
6344:
6340:
6330:
6327:
6326:
6325:
6322:
6321:
6320:
6317:
6313:
6310:
6309:
6308:
6305:
6303:
6300:
6298:
6295:
6293:
6290:
6288:
6285:
6283:
6280:
6278:
6275:
6273:
6270:
6269:
6267:
6265:
6261:
6255:
6252:
6250:
6247:
6245:
6242:
6240:
6237:
6235:
6232:
6230:
6229:Cohen's kappa
6227:
6226:
6224:
6222:
6218:
6214:
6210:
6206:
6202:
6198:
6193:
6189:
6175:
6172:
6170:
6167:
6165:
6162:
6160:
6157:
6156:
6154:
6152:
6148:
6142:
6138:
6134:
6128:
6126:
6123:
6122:
6120:
6118:
6114:
6108:
6105:
6103:
6100:
6098:
6095:
6093:
6090:
6088:
6085:
6083:
6082:Nonparametric
6080:
6078:
6075:
6074:
6072:
6068:
6062:
6059:
6057:
6054:
6052:
6049:
6047:
6044:
6043:
6041:
6039:
6035:
6029:
6026:
6024:
6021:
6019:
6016:
6014:
6011:
6009:
6006:
6005:
6003:
6001:
5997:
5991:
5988:
5986:
5983:
5981:
5978:
5976:
5973:
5972:
5970:
5968:
5964:
5960:
5953:
5950:
5948:
5945:
5944:
5940:
5936:
5920:
5917:
5916:
5915:
5912:
5910:
5907:
5905:
5902:
5898:
5895:
5893:
5890:
5889:
5888:
5885:
5884:
5882:
5880:
5876:
5866:
5863:
5859:
5853:
5851:
5845:
5843:
5837:
5836:
5835:
5832:
5831:Nonparametric
5829:
5827:
5821:
5817:
5814:
5813:
5812:
5806:
5802:
5801:Sample median
5799:
5798:
5797:
5794:
5793:
5791:
5789:
5785:
5777:
5774:
5772:
5769:
5767:
5764:
5763:
5762:
5759:
5757:
5754:
5752:
5746:
5744:
5741:
5739:
5736:
5734:
5731:
5729:
5726:
5724:
5722:
5718:
5716:
5713:
5712:
5710:
5708:
5704:
5698:
5696:
5692:
5690:
5688:
5683:
5681:
5676:
5672:
5671:
5668:
5665:
5663:
5659:
5649:
5646:
5644:
5641:
5639:
5636:
5635:
5633:
5631:
5627:
5621:
5618:
5614:
5611:
5610:
5609:
5606:
5602:
5599:
5598:
5597:
5594:
5592:
5589:
5588:
5586:
5584:
5580:
5572:
5569:
5567:
5564:
5563:
5562:
5559:
5557:
5554:
5552:
5549:
5547:
5544:
5542:
5539:
5537:
5534:
5533:
5531:
5529:
5525:
5519:
5516:
5512:
5509:
5505:
5502:
5500:
5497:
5496:
5495:
5492:
5491:
5490:
5487:
5483:
5480:
5478:
5475:
5473:
5470:
5468:
5465:
5464:
5463:
5460:
5459:
5457:
5455:
5451:
5448:
5446:
5442:
5436:
5433:
5431:
5428:
5424:
5421:
5420:
5419:
5416:
5414:
5411:
5407:
5406:loss function
5404:
5403:
5402:
5399:
5395:
5392:
5390:
5387:
5385:
5382:
5381:
5380:
5377:
5375:
5372:
5370:
5367:
5363:
5360:
5358:
5355:
5353:
5347:
5344:
5343:
5342:
5339:
5335:
5332:
5330:
5327:
5325:
5322:
5321:
5320:
5317:
5313:
5310:
5308:
5305:
5304:
5303:
5300:
5296:
5293:
5292:
5291:
5288:
5284:
5281:
5280:
5279:
5276:
5274:
5271:
5269:
5266:
5264:
5261:
5260:
5258:
5256:
5252:
5248:
5244:
5239:
5235:
5221:
5218:
5216:
5213:
5211:
5208:
5206:
5203:
5202:
5200:
5198:
5194:
5188:
5185:
5183:
5180:
5178:
5175:
5174:
5172:
5168:
5162:
5159:
5157:
5154:
5152:
5149:
5147:
5144:
5142:
5139:
5137:
5134:
5132:
5129:
5128:
5126:
5124:
5120:
5114:
5111:
5109:
5108:Questionnaire
5106:
5104:
5101:
5097:
5094:
5092:
5089:
5088:
5087:
5084:
5083:
5081:
5079:
5075:
5069:
5066:
5064:
5061:
5059:
5056:
5054:
5051:
5049:
5046:
5044:
5041:
5039:
5036:
5034:
5031:
5030:
5028:
5026:
5022:
5018:
5014:
5009:
5005:
4991:
4988:
4986:
4983:
4981:
4978:
4976:
4973:
4971:
4968:
4966:
4963:
4961:
4958:
4956:
4953:
4951:
4948:
4946:
4943:
4941:
4938:
4936:
4935:Control chart
4933:
4931:
4928:
4926:
4923:
4921:
4918:
4917:
4915:
4913:
4909:
4903:
4900:
4896:
4893:
4891:
4888:
4887:
4886:
4883:
4881:
4878:
4876:
4873:
4872:
4870:
4868:
4864:
4858:
4855:
4853:
4850:
4848:
4845:
4844:
4842:
4838:
4832:
4829:
4828:
4826:
4824:
4820:
4808:
4805:
4803:
4800:
4798:
4795:
4794:
4793:
4790:
4788:
4785:
4784:
4782:
4780:
4776:
4770:
4767:
4765:
4762:
4760:
4757:
4755:
4752:
4750:
4747:
4745:
4742:
4740:
4737:
4736:
4734:
4732:
4728:
4722:
4719:
4717:
4714:
4710:
4707:
4705:
4702:
4700:
4697:
4695:
4692:
4690:
4687:
4685:
4682:
4680:
4677:
4675:
4672:
4670:
4667:
4665:
4662:
4661:
4660:
4657:
4656:
4654:
4652:
4648:
4645:
4643:
4639:
4635:
4631:
4626:
4622:
4616:
4613:
4611:
4608:
4607:
4604:
4600:
4593:
4588:
4586:
4581:
4579:
4574:
4573:
4570:
4558:
4555:
4553:
4550:
4548:
4543:
4538:
4536:
4533:
4531:
4528:
4527:
4524:
4518:
4515:
4513:
4510:
4508:
4507:
4503:
4502:
4499:
4496:
4494:
4493:
4488:
4485:
4483:
4480:
4478:
4475:
4473:
4470:
4467:
4464:
4462:
4461:
4457:
4456:
4453:
4450:
4448:
4445:
4443:
4440:
4438:
4437:
4433:
4432:
4429:
4426:
4424:
4421:
4419:
4416:
4414:
4413:
4409:
4408:
4406:
4404:
4397:
4393:
4387:
4384:
4382:
4381:Compare means
4379:
4378:
4375:
4373:
4369:
4365:
4363:
4361:
4357:
4353:
4351:
4348:
4346:
4345:
4341:
4340:
4337:
4334:
4331:
4329:
4326:
4324:
4323:
4322:Random effect
4319:
4318:
4315:
4312:
4310:
4307:
4305:
4302:
4301:
4299:
4297:
4292:
4288:
4282:
4279:
4277:
4274:
4272:
4271:
4267:
4265:
4264:Orthogonality
4262:
4260:
4257:
4255:
4252:
4250:
4247:
4245:
4242:
4240:
4239:
4235:
4234:
4232:
4230:
4225:
4221:
4215:
4212:
4210:
4207:
4205:
4202:
4200:
4199:Randomization
4197:
4195:
4192:
4190:
4186:
4185:
4181:
4180:
4177:
4174:
4172:
4169:
4167:
4164:
4160:
4157:
4155:
4152:
4150:
4147:
4145:
4142:
4141:
4139:
4137:
4131:
4127:
4120:
4115:
4113:
4108:
4106:
4101:
4100:
4097:
4091:
4088:
4086:
4083:
4082:
4078:
4071:
4065:
4061:
4060:
4054:
4050:
4044:
4040:
4035:
4031:
4025:
4021:
4017:
4012:
4008:
4006:0-87872-108-8
4002:
3998:
3993:
3989:
3987:0-03-061706-5
3983:
3979:
3974:
3970:
3964:
3960:
3956:
3951:
3947:
3941:
3937:
3932:
3928:
3922:
3918:
3914:
3910:
3906:
3900:
3896:
3892:
3888:
3884:
3880:
3876:
3872:
3868:
3864:
3860:
3854:
3850:
3846:
3842:
3838:
3833:
3832:
3827:
3818:
3814:
3809:
3804:
3800:
3796:
3789:
3786:
3782:
3777:
3774:
3771:, p. 78)
3770:
3765:
3762:
3758:
3753:
3750:
3747:, p. 77)
3746:
3741:
3738:
3734:
3729:
3726:
3722:
3717:
3714:
3710:
3705:
3702:
3698:
3693:
3690:
3686:
3685:Hocking (1985
3681:
3678:
3674:
3669:
3666:
3663:, Remark 8.1)
3662:
3657:
3654:
3650:
3645:
3642:
3637:
3633:
3629:
3625:
3621:
3617:
3609:
3606:
3601:
3597:
3593:
3589:
3585:
3579:
3576:
3571:
3567:
3563:
3559:
3552:
3549:
3544:
3538:
3534:
3530:
3529:
3521:
3518:
3513:
3507:
3503:
3499:
3492:
3490:
3486:
3481:
3477:
3471:
3468:
3463:
3459:
3458:
3450:
3446:
3440:
3437:
3431:
3426:
3422:
3421:Royal Society
3418:
3414:
3413:
3408:
3404:
3400:
3394:
3391:
3384:
3374:
3371:
3367:
3361:
3358:
3354:
3348:
3345:
3341:
3338:
3334:
3328:
3325:
3318:
3315:
3308:
3304:
3301:
3299:
3296:
3294:
3291:
3289:
3286:
3284:
3281:
3279:
3276:
3275:
3271:
3264:
3261:
3258:
3255:
3252:
3251:
3247:
3244:
3241:
3238:
3235:
3234:
3230:
3227:
3224:
3221:
3218:
3217:
3213:
3210:
3207:
3204:
3201:
3200:
3196:
3193:
3190:
3187:
3184:
3183:
3179:
3176:
3173:
3170:
3167:
3166:
3162:
3159:
3156:
3153:
3150:
3149:
3143:
3135:
3131:
3127:
3125:
3117:
3113:
3104:
3101:
3100:
3096:
3093:
3092:
3088:
3085:
3084:
3080:
3077:
3076:
3072:
3069:
3068:
3064:
3061:
3060:
3056:
3053:
3052:
3048:
3045:
3044:
3040:
3037:
3036:
3032:
3029:
3028:
3024:
3021:
3020:
3016:
3013:
3012:
3008:
3005:
3004:
3000:
2997:
2996:
2992:
2989:
2988:
2984:
2981:
2980:
2976:
2974:Coefficients
2973:
2972:
2966:
2964:
2951:
2946:
2939:
2934:
2927:
2924:
2921:
2918:
2915:
2914:
2910:
2907:
2904:
2901:
2898:
2897:
2893:
2890:
2887:
2884:
2881:
2880:
2876:
2873:
2870:
2867:
2864:
2863:
2859:
2856:
2853:
2850:
2847:
2846:
2842:
2839:
2836:
2833:
2830:
2829:
2825:
2822:
2819:
2816:
2813:
2812:
2808:
2805:
2802:
2799:
2796:
2795:
2791:
2788:
2785:
2782:
2779:
2778:
2774:
2771:
2768:
2765:
2762:
2761:
2757:
2754:
2751:
2748:
2745:
2744:
2740:
2737:
2734:
2731:
2728:
2727:
2723:
2720:
2717:
2714:
2711:
2710:
2706:
2703:
2700:
2697:
2694:
2693:
2689:
2686:
2683:
2680:
2677:
2676:
2672:
2669:
2666:
2663:
2660:
2659:
2655:
2652:
2649:
2646:
2643:
2642:
2636:
2632:
2629:
2623:
2617:
2615:
2613:
2609:
2605:
2601:
2596:
2594:
2590:
2586:
2582:
2577:
2575:
2571:
2565:
2557:
2555:
2552:
2548:
2546:
2541:
2540:may be used.
2539:
2533:
2530:
2526:
2522:
2517:
2515:
2511:
2502:
2500:
2498:
2492:
2479:
2475:
2466:
2462:
2458:
2453:
2449:
2445:
2440:
2436:
2432:
2427:
2423:
2416:
2413:
2409:
2400:
2396:
2392:
2387:
2383:
2379:
2374:
2370:
2366:
2361:
2357:
2344:
2342:
2338:
2333:
2331:
2326:
2324:
2321:Finally, the
2319:
2317:
2313:
2309:
2305:
2301:
2297:
2293:
2289:
2285:
2281:
2277:
2273:
2268:
2266:
2262:
2258:
2254:
2250:
2240:
2237:
2234:
2231:
2228:
2225:
2222:
2219:
2218:
2214:
2211:
2208:
2205:
2202:
2199:
2196:
2193:
2192:
2188:
2185:
2182:
2179:
2176:
2173:
2170:
2167:
2166:
2162:
2159:
2156:
2153:
2150:
2147:
2144:
2141:
2140:
2136:
2133:
2130:
2127:
2124:
2121:
2118:
2115:
2114:
2110:
2107:
2104:
2101:
2098:
2095:
2092:
2089:
2088:
2084:
2081:
2078:
2075:
2072:
2069:
2066:
2063:
2062:
2058:
2055:
2052:
2049:
2046:
2043:
2040:
2037:
2036:
2021:
2018:
2015:
2008:
1994:
1991:
1984:
1970:
1967:
1960:
1946:
1943:
1936:
1922:
1915:
1901:
1894:
1880:
1873:
1870:
1869:
1853:
1850:
1847:
1844:
1841:
1831:
1828:
1824:
1821:
1819:
1815:
1811:
1807:
1802:
1800:
1796:
1792:
1788:
1784:
1780:
1776:
1772:
1767:
1765:
1761:
1757:
1753:
1744:
1741:
1738:
1735:
1732:
1729:
1726:
1723:
1720:
1719:
1715:
1712:
1709:
1706:
1703:
1700:
1697:
1694:
1691:
1690:
1686:
1683:
1680:
1677:
1674:
1671:
1668:
1665:
1662:
1661:
1657:
1654:
1651:
1648:
1645:
1642:
1639:
1636:
1633:
1632:
1628:
1625:
1622:
1619:
1616:
1613:
1610:
1607:
1604:
1603:
1599:
1596:
1593:
1590:
1587:
1584:
1581:
1578:
1575:
1574:
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250:Osculation +
249:
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216:In his book,
211:
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135:Ronald Fisher
132:
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6880:
6868:
6849:
6842:
6754:Econometrics
6704: /
6687:Chemometrics
6664:Epidemiology
6657: /
6630:Applications
6472:ARIMA model
6419:Q-statistic
6368:Stationarity
6264:Multivariate
6207: /
6203: /
6201:Multivariate
6199: /
6139: /
6135: /
5909:Bayes factor
5808:Signed rank
5720:
5694:
5686:
5674:
5369:Completeness
5205:Cohort study
5135:
5103:Opinion poll
5038:Missing data
5025:Study design
4980:Scatter plot
4902:Scatter plot
4895:Spearman's ρ
4857:Grouped data
4504:
4490:
4472:Latin square
4458:
4434:
4411:
4410:
4371:
4367:
4360:multivariate
4359:
4355:
4342:
4320:
4268:
4236:
4182:
4058:
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4015:
3996:
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3497:
3479:
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3461:
3455:
3439:
3416:
3410:
3399:Yates, Frank
3393:
3373:
3360:
3347:
3339:
3337:finite field
3332:
3327:
3322:consistent."
3317:
3151:Coefficient
3140:
3128:
3121:
2959:
2634:
2628:formaldehyde
2625:
2621:
2597:
2589:Pareto plots
2581:main effects
2578:
2567:
2553:
2549:
2542:
2534:
2518:
2513:
2509:
2506:
2496:
2494:
2346:
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2256:
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1826:
1825:
1822:
1818:dot products
1813:
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328:
324:
320:
317:
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305:
293:
289:
277:
247:Osculation −
234:
217:
215:
194:
186:interactions
172:
160:
158:
148:
144:
140:
133:
118:
108:
100:
96:
94:
87:
82:
79:
75:interactions
66:
62:
54:
48:
6882:WikiProject
6797:Cartography
6759:Jurimetrics
6711:Reliability
6442:Time domain
6421:(Ljung–Box)
6343:Time-series
6221:Categorical
6205:Time-series
6197:Categorical
6132:(Bernoulli)
5967:Correlation
5947:Correlation
5743:Jarque–Bera
5715:Chi-squared
5477:M-estimator
5430:Asymptotics
5374:Sufficiency
5141:Interaction
5053:Replication
5033:Effect size
4990:Violin plot
4970:Radar chart
4950:Forest plot
4940:Correlogram
4890:Kendall's τ
4447:Box–Behnken
4328:Mixed model
4259:Confounding
4254:Interaction
4244:Effect size
4214:Sample size
4020:Brooks/Cole
3769:Cheng (2019
3757:Kuehl (2000
3745:Cheng (2019
3721:Beder (2022
3709:Beder (2022
3661:Cheng (2019
3649:Kuehl (2000
3355:of vectors.
3353:dot product
3116:Pareto plot
2335:In columns
1866:experiment
1410:experiment
1320:levels has
845:Interaction
809:is said to
352:temperature
341:mixed-level
325:fixed-level
280:interaction
150:Frank Yates
6898:Categories
6749:Demography
6467:ARMA model
6272:Regression
5849:(Friedman)
5810:(Wilcoxon)
5748:Normality
5738:Lilliefors
5685:Student's
5561:Resampling
5435:Robustness
5423:divergence
5413:Efficiency
5351:(monotone)
5346:Likelihood
5263:Population
5096:Stratified
5048:Population
4867:Dependence
4823:Count data
4754:Percentile
4731:Dispersion
4664:Arithmetic
4599:Statistics
4403:randomized
4401:Completely
4372:covariance
4134:Scientific
3913:Box, G. E.
3891:Box, G. E.
3885:: 107–166.
3828:References
3733:Bose (1947
3600:B01FKSM9VY
3423:: 91–120.
3168:Intercept
2982:Intercept
2525:replicated
1275:orthogonal
849:additivity
549:is prime.
345:asymmetric
222:George Box
51:statistics
6130:Logistic
5897:posterior
5823:Rank sum
5571:Jackknife
5566:Bootstrap
5384:Bootstrap
5319:Parameter
5268:Statistic
5063:Statistic
4975:Run chart
4960:Pie chart
4955:Histogram
4945:Fan chart
4920:Bar chart
4802:L-moments
4689:Geometric
4412:Factorial
4296:inference
4276:Covariate
4238:Treatment
4224:Treatment
3897:. Wiley.
3867:253542415
3803:CiteSeerX
3636:122252479
3154:Estimate
2977:Estimate
2604:quadratic
2527:, or the
2463:μ
2450:μ
2437:μ
2424:μ
2417:−
2397:μ
2384:μ
2371:μ
2358:μ
1851:×
1845:×
1470:×
1395:×
1077:×
968:μ
955:μ
951:−
942:μ
938:−
929:μ
902:μ
889:μ
885:−
876:μ
872:−
863:μ
788:μ
784:−
775:μ
771:−
762:μ
758:−
749:μ
736:μ
723:μ
690:μ
686:−
677:μ
641:cell mean
493:Both high
329:symmetric
53:, a full
36:Factorial
6844:Category
6537:Survival
6414:Johansen
6137:Binomial
6092:Isotonic
5679:(normal)
5324:location
5131:Blocking
5086:Sampling
4965:Q–Q plot
4930:Box plot
4912:Graphics
4807:Skewness
4797:Kurtosis
4769:Variance
4699:Heronian
4694:Harmonic
4535:Category
4530:Glossary
4336:Bayesian
4314:Bayesian
4270:Blocking
4249:Contrast
4229:blocking
4189:Bayesian
4176:Blinding
4166:validity
4163:external
4159:Internal
3959:Springer
3841:Springer
3586:(2006).
3447:(1926).
3405:(1963).
3272:See also
3163:p-value
3160:t value
3124:p-values
3102:A:B:C:D
2591:, and a
2558:Analysis
2339:through
1364:Examples
445:Both low
360:salinity
335:, where
314:Notation
6870:Commons
6817:Kriging
6702:Process
6659:studies
6518:Wavelet
6351:General
5518:Plug-in
5312:L space
5091:Cluster
4792:Moments
4610:Outline
4428:Taguchi
4396:Designs
4154:Control
3879:Sankhya
3245:−8.206
3239:−9.063
3188:10.812
3177:63.444
3171:70.062
3097:−1.313
3089:−0.813
3065:−0.563
3057:−0.188
3033:−9.063
2993:10.813
2985:70.063
2602:. If a
2583:plots,
2330:A, B, C
998:present
356:density
286:Example
266:Heat +
255:Heat −
127:of the
115:History
6739:Census
6329:Normal
6277:Manova
6097:Robust
5847:2-way
5839:1-way
5677:-test
5348:
4925:Biplot
4716:Median
4709:Lehmer
4651:Center
4468:(GRBD)
4368:Ancova
4356:Manova
4291:Models
4136:method
4066:
4045:
4026:
4003:
3984:
3965:
3942:
3923:
3901:
3865:
3855:
3805:
3634:
3598:
3539:
3508:
3262:7.527
3259:1.104
3256:8.312
3242:1.104
3228:6.622
3225:1.104
3222:7.313
3211:4.471
3208:1.104
3205:4.938
3194:9.791
3191:1.104
3174:1.104
3105:0.688
3094:B:C:D
3086:A:C:D
3081:2.063
3078:A:B:D
3073:0.938
3070:A:B:C
3049:8.313
3041:1.188
3025:0.063
3017:7.313
3009:4.938
3001:1.563
2600:linear
1257:, say
994:absent
839:absent
540:modulo
426:tuples
204:, and
107:, and
101:points
6363:Trend
5892:prior
5834:anova
5723:-test
5697:-test
5689:-test
5596:Power
5541:Pivot
5334:shape
5329:scale
4779:Shape
4759:Range
4704:Heinz
4679:Cubic
4615:Index
4460:Block
3863:S2CID
3632:S2CID
3592:Wiley
3502:Wiley
3452:(PDF)
3385:Notes
3340:GF(s)
2570:ANOVA
1806:A × B
1764:A × B
1002:below
658:is a
545:when
525:below
109:cells
6596:Test
5796:Sign
5648:Wald
4721:Mode
4659:Mean
4294:and
4227:and
4161:and
4064:ISBN
4043:ISBN
4024:ISBN
4001:ISBN
3982:ISBN
3963:ISBN
3940:ISBN
3921:ISBN
3899:ISBN
3875:Bose
3853:ISBN
3596:ASIN
3537:ISBN
3506:ISBN
3253:A:D
3236:A:C
3062:C:D
3054:B:D
3046:A:D
3038:B:C
3030:A:C
3022:A:B
2860:104
2826:100
2545:bias
2510:e.g.
2314:and
2296:cell
2290:and
2278:and
2255:and
1871:cell
1812:and
1758:and
1415:cell
1348:−1)(
1334:and
1300:The
1281:and
1269:and
1261:and
1238:Bose
1232:The
1022:cell
645:cell
633:The
454:(1)
272:106
123:and
97:runs
5776:BIC
5771:AIC
3845:doi
3813:doi
3624:doi
3620:327
3566:doi
3425:doi
2928:96
2911:70
2894:86
2877:75
2843:45
2809:43
2792:65
2775:80
2758:60
2741:68
2724:65
2707:48
2690:71
2673:45
2572:or
2514:etc
2467:111
2454:110
2441:101
2428:100
2401:011
2388:010
2375:001
2362:000
2341:ABC
2323:ABC
2241:−1
2220:111
2194:110
2168:101
2163:−1
2142:100
2116:011
2111:−1
2090:010
2085:−1
2064:001
2038:000
1687:-1
1571:-1
1285:.
1240::
1171:-1
1151:−1
502:ab
479:low
462:low
418:23
415:22
412:21
404:13
401:12
398:11
343:or
327:or
261:23
208:.
49:In
6900::
4187::
4022:.
3961:.
3881:.
3861:.
3851:.
3843:.
3811:.
3799:70
3797:.
3630:.
3618:.
3594:.
3562:91
3560:.
3535:.
3504:.
3488:^
3478:.
3462:33
3460:.
3454:.
3415:.
3409:.
3401:;
3219:D
3202:C
3185:A
3014:D
3006:C
2998:B
2990:A
2925:+
2922:+
2919:+
2916:+
2908:+
2905:+
2902:+
2899:−
2891:+
2888:+
2885:−
2882:+
2874:+
2871:+
2868:−
2865:−
2857:+
2854:−
2851:+
2848:+
2840:+
2837:−
2834:+
2831:−
2823:+
2820:−
2817:−
2814:+
2806:+
2803:−
2800:−
2797:−
2789:−
2786:+
2783:+
2780:+
2772:−
2769:+
2766:+
2763:−
2755:−
2752:+
2749:−
2746:+
2738:−
2735:+
2732:−
2729:−
2721:−
2718:−
2715:+
2712:+
2704:−
2701:−
2698:+
2695:−
2687:−
2684:−
2681:−
2678:+
2670:−
2667:−
2664:−
2661:−
2653:D
2650:C
2647:B
2644:A
2614:.
2587:,
2516:.
2308:BC
2304:BC
2284:BC
2280:BC
2276:AC
2274:,
2272:AB
2267:.
2251:,
2229:−1
2226:−1
2223:−1
2215:1
2212:−1
2209:−1
2200:−1
2197:−1
2189:1
2186:−1
2180:−1
2177:−1
2171:−1
2157:−1
2154:−1
2145:−1
2137:1
2131:−1
2128:−1
2125:−1
2122:−1
2108:−1
2102:−1
2096:−1
2082:−1
2079:−1
2073:−1
2059:1
1820:.
1801:.
1745:1
1733:-1
1727:-1
1721:22
1716:0
1701:-1
1698:-1
1692:21
1684:-1
1669:-1
1663:20
1658:0
1646:-1
1637:-1
1634:12
1629:0
1614:-1
1608:-1
1605:11
1600:0
1594:-1
1591:-1
1579:-1
1576:10
1565:-1
1559:-1
1547:02
1542:0
1539:-1
1533:-1
1527:-1
1518:01
1513:1
1489:00
1229:.
1211:1
1205:−1
1199:−1
1196:23
1191:0
1182:−1
1179:−1
1176:22
1168:−1
1159:−1
1156:21
1145:−1
1136:13
1131:0
1128:-1
1122:−1
1116:12
1111:1
1096:11
1004:.
972:23
959:21
946:13
933:11
906:22
893:21
880:12
867:11
792:23
779:22
766:21
753:13
740:12
727:11
694:12
681:11
654:A
626:23
620:22
614:21
609:2
603:13
597:12
591:11
586:1
581:3
578:2
575:1
499:++
496:11
488:b
485:+−
482:10
471:a
468:−+
465:01
451:−−
448:00
409:2
395:1
390:3
387:2
384:1
347:.
269:21
258:18
200:,
165:.
156:.
131:.
5721:G
5695:F
5687:t
5675:Z
5394:V
5389:U
4591:e
4584:t
4577:v
4374:)
4370:(
4362:)
4358:(
4118:e
4111:t
4104:v
4072:.
4051:.
4032:.
4009:.
3990:.
3971:.
3948:.
3929:.
3907:.
3883:8
3869:.
3847::
3819:.
3815::
3638:.
3626::
3602:.
3572:.
3568::
3545:.
3514:.
3482:.
3433:.
3427::
3417:9
3333:s
2497:A
2480:4
2476:/
2472:)
2459:+
2446:+
2433:+
2420:(
2414:4
2410:/
2406:)
2393:+
2380:+
2367:+
2354:(
2337:A
2316:C
2312:B
2300:A
2292:C
2288:B
2265:B
2261:B
2257:C
2253:B
2249:A
2238:1
2235:1
2232:1
2206:1
2203:1
2183:1
2174:1
2160:1
2151:1
2148:1
2134:1
2119:1
2105:1
2099:1
2093:1
2076:1
2070:1
2067:1
2056:1
2053:1
2050:1
2047:1
2044:1
2041:1
2022:C
2019:B
2016:A
1995:C
1992:B
1971:C
1968:A
1947:B
1944:A
1923:C
1902:B
1881:A
1854:2
1848:2
1842:2
1814:B
1810:A
1799:B
1795:B
1791:B
1787:A
1783:A
1779:A
1775:A
1771:A
1760:B
1756:A
1742:0
1739:0
1736:0
1730:0
1724:0
1713:1
1710:0
1707:0
1704:0
1695:0
1681:0
1678:0
1675:1
1672:1
1666:0
1655:0
1652:1
1649:0
1643:0
1640:0
1626:0
1623:0
1620:1
1617:0
1611:0
1597:0
1588:1
1585:1
1582:0
1568:0
1562:0
1556:0
1553:1
1550:1
1536:0
1530:0
1524:1
1521:1
1510:1
1507:1
1504:1
1501:1
1498:1
1495:1
1492:1
1473:B
1467:A
1446:B
1425:A
1398:3
1392:3
1378:C
1374:B
1370:A
1353:2
1350:s
1346:1
1343:s
1339:2
1336:s
1332:1
1329:s
1322:s
1318:s
1295:A
1291:A
1283:B
1279:A
1271:B
1267:A
1263:B
1259:A
1208:0
1202:0
1188:1
1185:1
1165:0
1162:1
1148:0
1142:0
1139:1
1125:1
1119:1
1108:1
1105:0
1102:1
1099:1
1080:B
1074:A
1053:B
1032:A
964:+
898:+
835:A
821:A
745:+
732:+
624:μ
618:μ
612:μ
601:μ
595:μ
589:μ
570:A
565:B
547:s
543:s
536:s
532:s
477:B
460:A
434:B
430:A
379:A
374:B
337:k
333:s
321:s
38:.
20:)
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