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of hypotheses. Of particular interest is how to simultaneously control the overall error rate, preserve statistical power, and incorporate the dependence between tests into the adjustment. These issues are especially relevant when the number of simultaneous tests can be very large, as is
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are generally of a different flavor; according to John Tukey, "difficulties in identifying problems have delayed statistics far more than difficulties in solving problems." A list of "one or two open problems" (in fact 22 of them) was given by
23:
571:
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is often used to estimate the common mean of two normal populations with unknown and possibly unequal variances. Though this estimator is generally unbiased, its
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Pal, Nabendu; Lim, Wooi K. (1997). "A note on second-order admissibility of the
Graybill-Deal estimator of a common mean of several normal populations".
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Cox, D. R. (1984). "Present
Position and Potential Developments: Some Personal Views: Design of Experiments and Regression".
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for the difference of two means when the variances are unknown and possibly unequal. That is, there is no
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460:"Fermat, Schubert, Einstein, and Behrens–Fisher: The Probable Difference Between Two Means When σ
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and may never be able to satisfy particular standards for completeness. You can help by
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147:: There are various ways to adjust p-values to compensate for the simultaneous or
131:) that is also the most powerful for all values of the variances (which are thus
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Tukey, John W. (1954). "Unsolved
Problems of Experimental Statistics".
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203:: How is a probability updated when there is unanticipated new data?
123:(meaning that, if the means are in fact equal, one that rejects the
164:: A list of open problems in Bayesian statistics has been proposed.
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given only an estimate of the total number of humans born so far?
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99:, techniques are still being developed to handle the case of
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Journal of the Royal
Statistical Society. Series A (General)
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could have immediate applicability to experimental design.
135:). Though there are many approximate solutions (such as
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for which a solution has still not yet been found. The
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Zabell, S. L. (1992). "Predicting the unpredictable".
377:"What are the open problems in Bayesian statistics?"
152:increasingly the case in the analysis of data from
343:"Studentization and deriving accurate p-values"
246:Journal of the American Statistical Association
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472:Journal of Modern Applied Statistical Methods
441:Statistical Problems with Nuisance Parameters
316:Journal of Statistical Planning and Inference
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193:Problems of a more philosophical nature
341:Fraser, D.A.S.; Rousseau, J. (2008).
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68:are large (a situation Tukey termed
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443:. American Mathematical Society.
628:Unsolved problems in mathematics
115:showed in 1966 that there is no
35:unsolved problems in mathematics
64:, especially in sciences where
458:Sawilowsky, Shlomo S. (2002).
58:How to detect and correct for
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328:10.1016/S0378-3758(96)00202-9
39:notable unsolved problems in
117:uniformly most powerful test
33:There are many longstanding
200:Sampling of species problem
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618:Lists of unsolved problems
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532:
485:10.22237/jmasm/1036109940
185:problems in Latin squares
623:Statistics-related lists
178:is a cornerstone in the
77:Graybill–Deal estimator
439:Linnik, Jurii (1968).
375:Jordan, M. I. (2011).
213:probabilistic argument
108:Behrens–Fisher problem
95:can be combined using
362:10.1093/biomet/asm093
180:design of experiments
129:probability exactly α
91:: Though independent
70:uncomfortable science
53:Inference and testing
144:Multiple comparisons
83:remains to be shown.
24:adding missing items
211:: How valid is the
169:Experimental design
161:Bayesian statistics
133:nuisance parameters
572:Information theory
415:10.1007/bf00485351
149:sequential testing
101:dependent p-values
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525:unsolved problems
384:The ISBA Bulletin
208:Doomsday argument
174:As the theory of
61:systematic errors
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28:reliable sources
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20:dynamic list
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577:Mathematics
523:Well-known
113:Yuri Linnik
612:Categories
597:Statistics
567:Geoscience
433:References
409:(2): 205.
350:Biometrika
225:human race
121:exact test
41:statistics
18:This is a
557:Economics
547:Chemistry
537:Astronomy
390:(1): 1–5.
322:: 71–78.
47:David Cox
582:Medicine
403:Synthese
356:: 1–16.
93:p-values
592:Physics
542:Biology
423:9416747
301:2981685
266:2281535
217:predict
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221:future
478:(2).
419:S2CID
380:(PDF)
346:(PDF)
297:JSTOR
262:JSTOR
232:Notes
127:with
26:with
445:ISBN
219:the
75:The
480:doi
464:≠ σ
411:doi
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324:doi
289:doi
285:147
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