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	Multiple comparisons - Wikipedia, the free encyclopedia
		In statistics, the multiple comparisons problem tests null hypotheses stating that the averages of several disjoint populations are equal to each other (homogeneous).
		Multiple comparison procedures are commonly used after obtaining a significant ANOVA F-test.
		For large-scale multiple testing (for example, as is very common in genomics when using technologies such as DNA microarrays) one controls the false discovery rate (FDR), defined to be the proportion of false positives among all significant tests.
	en.wikipedia.org /wiki/Multiple_comparisons (565 words)

	Multiple Comparisons (Site not responding. Last check: 2007-10-22)
		A common question concerns the use of multiple comparison techniques when the variable in question is a repeated measures variable.
		The Sethi and Seligman (1993) paper on optimism and religious fundamentalism involves both a one-way analysis of variance and multiple comparisons.
		The example on the sampling distribution of F allows you to change the means of the populations (and especially the spacing of those means within the range from lowest to highest) and note the effects on multiple comparison tests.
	www.uvm.edu /~dhowell/StatPages/More_Stuff/MultComp/MultComp.html (335 words)

	Multiple Comparisons
		The goal in multiple comparisons is to compare the average effects of three or more "treatments" (for example, drugs, groups of subjects) to decide which treatments are better, which ones are worse, and by how much, while controlling the probability of making an incorrect decision.
		Multiple comparison procedures can be categorized in two ways: by the comparisons they make and by the strength of inference they provide.
		When you interpret multiple comparisons, remember that failure to reject the hypothesis that two or more means are equal should not lead you to conclude that the population means are, in fact, equal.
	v8doc.sas.com /sashtml/stat/chap30/sect35.htm (3608 words)

	[No title]
		Statisticians have developed many "multiple comparison procedures" to let us proceed when there are many tests to be performed or comparisons to be made.
		Provided the nonsimultaneous statistician [one who never adjusts for multiple comparisons] and his client are well aware of their error rates for groups of statements, and feel the group rates are either satisfactory or unimportant, the author has no quarrel with them.
		Some computer programs perform multiple comparison procedures for unequal sample sizes by pretending that the sample sizes are equal to their harmonic mean.
	www.tufts.edu /~gdallal/mc.htm (3993 words)

	obswww23: Closed Multiple Testing Procedures and PROC MULTTEST (Site not responding. Last check: 2007-10-22)
		Multiple comparisons and multiple testing problems arise frequently in statistical data analysis, and it is important to address them appropriately.
		In this article, "multiple comparisons" typically refers to comparisons among mean values of different groups (for example, A vs B, A vs. C, B vs. C).
		This is very similar to the case where you perform multiple comparisons of means when one has a very large sample size, and an extremely different variance: pooling the variances across all groups means that the estimated standard errors will be grossly inaccurate for certain contrasts.
	support.sas.com /documentation/periodicals/obs/obswww23 (5854 words)

	Multiple Comparisons
		There are six such comparisons: 1 with 2, 1 with 3, 1 with 4, 2 with 3, 2 with 4 and 3 with 4.
		Bonferroni: The Bonferroni multiple comparison test is a conservative test, that is, the FWE is not exactly equal to ALPHA, but is less than ALPHA in most situations.
		In SAS multiple comparisons tests can be easily obtained, without additional programming, only in the case when all pairwise comparisons among all combinations of the levels of variables involved in the interaction or only pairwise comparisons with a control are of interest.
	www.uky.edu /ComputingCenter/SSTARS/MultipleComparisons_3.htm (3343 words)

	multiple comparisons (Site not responding. Last check: 2007-10-22)
		Be cautious whenever you test multiple hypotheses, also called making "multiple comparisons." Suppose you gather performance data on 15 systems, and you wish to test the hypothesis that no two of these systems differ in their mean performance.
		Suppose that unknown to you the systems perform equally, that is, all the performance data are drawn from the same population, so their population means are equal.
		is the probability of "heads," which corresponds to the spurious result that the samples in the comparison are drawn from different populations.
	eksl-www.cs.umass.edu /eis/pages/warnings/multiple-comparisons.html (216 words)

	multiple comparisons (Site not responding. Last check: 2007-10-22)
		Furthermore, a researcher may want to make additional comparisons that are not simply of one group to another-for example, an average of three groups compared to a fourth (perhaps the first three are different types of experimental groups and the fourth is a control group).
		In post hoc comparisons, all possible comparisons have to be taken into account when figuring the overall chance of any one of them turning out significant.
		These are comparisons the investigator decides to make after inspection of the data, and may be suggested by such inspection.
	www.chsbs.cmich.edu /k_han/psy511/postmul.htm (691 words)

	Multiple Comparisons (Site not responding. Last check: 2007-10-22)
		Pre-planned comparisons that are linearly independent of one another, hence involving no more contrasts than the appropriate degrees of freedom, can be made using either t-tests or F tests (although it should be noted that this does not, of itself address the issue of multiple comparisons).
		Multiple comparison tests are characterised by considering the number of tests that could be made.
		If we did not have this as a pre-planned comparison, but rather after our analysis we noted this difference and wanted to know if it was significant we should be using a multiple comparison test, e.g.
	animsci.agrenv.mcgill.ca /servers/anbreed/statisticsII/mcomp (1210 words)

	Multiple Comparisons (Site not responding. Last check: 2007-10-22)
		Dunn uses c instead of J. c is the actual number of comparisons and must equal J(J-1)/4 or less.
		For simple comparisons, N-K is more powerful than Tukey, but it also has a higher Type I error rate.
		Multiple t and Duncan have alpha values that are unacceptably high.
	carbon.cudenver.edu /~lsherry/rem/mcp.html (440 words)

	Multiple Comparisons
		To answer these kinds of questions requires careful consideration of the hypotheses of interest both before and after an experiment is conducted, the Type I error rate selected for each hypothesis, the power of each hypothesis test, and the Type I error rate acceptable for the group of hypotheses as a whole.
		The comparison - wise error rate is the probability of a Type I error set by the experimentor for evaluating each comparison.
		When comparisons are performed after the data have been examined (a posteriori) or subjected to an analysis of variance then controlling the experiment - wise error rate requires an even larger penalty.
	userwww.sfsu.edu /~efc/classes/biol458/multcomp/multcomp.htm (1048 words)

	Multiple-comparison procedures for steady-state simulations, Marvin K. Nakayama
		We consider the problem of running independent, single-stage simulations to make multiple comparisons of the steady-state means of the different systems.
		We derive asymptotically valid (as the run lengths of the simulations of the systems tend to infinity) simultaneous confidence intervals for each of the following problems: all pairwise comparisons of means, all contrasts, multiple comparisons with a control and multiple comparisons with the best.
		TAMHANE, A. A comparison of procedures for multiple comparisons of means with unequal variances.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.aos/1030741080 (787 words)

	7.4.7. How can we make multiple comparisons?
		This is because the overall significance level is not as specified for a single pair comparison.
		These types of investigations should be done on combinations of factors that were determined in advance of observing the experimental results, or else the confidence levels are not as specified by the procedure.
		However, there are also several powerful multiple comparison procedures we can use after observing the experimental results.
	www.itl.nist.gov /div898/handbook/prc/section4/prc47.htm (522 words)

	Intuitive Biostatistics:Interpreting Nonsignificant P values
		Interpreting multiple P values, therefore, is similar to interpreting multiple coincidences.
		But with three comparisons, the chance that any one (or more) of them will be significant is far higher than 5%.
		Beware of analyses of multiple subgroups as you are very likely to encounter small P values, even if all null hypotheses are true.
	www.graphpad.com /www/Book/mulcomp.htm (3385 words)

	Multiple Comparisons with the Best Using Common Random Numbers for Steady-State Simulations - Nakayama (ResearchIndex) (Site not responding. Last check: 2007-10-22)
		We consider the problem of running a singlestage simulation using common random numbers to construct simultaneous confidence intervals for ¯ i \Gamma max j 6=i ¯ j, i = 1; 2; : : : ; k.
		This is known as multiple comparisons with the best (MCB).
		Multiple comparisons with the best using common random numbers in steady-state simulations.
	citeseer.ist.psu.edu /1555.html (575 words)

	Bonferroni correction online. Adjustment for multiple comparisons.
		The number of comparisons, a positive integer number without decimals, is given in the second box.
		This is the case, for example, if we want to compare three religious groups on their attitudes towards alcohol use, or four groups of medical specialists on their usage of pain relief strategy after surgery.
		Most of the methods to adjust for multiple comparisons in k-means are based on the assumption that you want to compare any mean with any other mean, so, these methods mostly presume that you want to do c=k(k-1)/2 comparisons* in k means.
	home.clara.net /sisa/bonhlp.htm (1785 words)

	lecture notes multiple comparisons (Site not responding. Last check: 2007-10-22)
		Multiple Comparison Tests of Treatment Means – by hand and using SAS
		Once an ANOVA has been carried out and has identified that there are some differences between the treatment means, it is necessary to identify which treatments are different from each other.
		Because of the element of chance and uncertainty involved in any statistical test, in a situation where a large number of similar tests are carried out there is a potential to find significant differences simply by chance.
	www.ens.gu.edu.au /stats/aes2291/lectures/multiple.htm (546 words)

	Multiple comparisons: philosophies and illustrations -- Curran-Everett 279 (1): 1 -- AJP - Regulatory, Integrative and ...
		In many of the studies tallied in Table 1, a multiple comparison procedure was used to analyze several groups of observations
		is a multiple range test that compares the underlying population means of r experimental groups.
		Although it is not a multiple comparison procedure per se, the Bonferroni inequality can be used for multiple comparison problems.
	ajpregu.physiology.org /cgi/content/full/279/1/R1 (3132 words)

	Simultaneous comparison of multiple treatments: combining direct and indirect evidence -- Caldwell et al. 331 (7521): ... (Site not responding. Last check: 2007-10-22)
		Simultaneous comparison of multiple treatments: combining direct and indirect evidence -- Caldwell et al.
		Table 1 Evidence structure for comparison of multiple treatments used in two meta-analyses: number of randomised controlled trials directly comparing seven treatments for acute myocardial infarction.
		comparison analysis it clearly is (0.74, 0.61 to 0.89).
	bmj.bmjjournals.com /cgi/content/full/331/7521/897?ehom (2266 words)

	3. Multiple Comparisons of Treatment Means (Site not responding. Last check: 2007-10-22)
		When there are a lot of such comparisons, one or more may be significant simply by chance, and there is no way of knowing this.
		Multiple range tests such as SNK make such an allowance and provide a control across the whole set of comparisons.
		Comparisons across a span of 4 will occur for JL versus WP, for FD versus RR and for EB versus TTS; each of these will need to be 4.745 different to reach significance.
	www.ens.gu.edu.au /stats/aes2291/week3/multiple.htm (3171 words)

	Multiple Comparisons with Repeated Measures
		One of the commonly asked questions on listservs dealing with statistical issue is "How do I use SPSS (or whatever software is at hand) to run multiple comparisons among a set of repeated measures?" This page is a (longwinded) attempt to address that question.
		Virtually all the multiple comparison procedures can be computed using the lowly t test; either t test for independent means, or a t test for related means, whichever is appropriate.
		Remember, if you run multiple comparisons, such as the Tukey, between groups at each time, each set of comparisons is protected against an increase in the risk of Type I errors by the nature of the test.
	www.uvm.edu /~dhowell/StatPages/More_Stuff/RepMeasMultComp/RepMeasMultComp.html (5321 words)

	Multiple Comparisons
		The problem: When making multiple tests, the nominal significance level of the test may be an underestimate and one may reject the null hypothesis erroneously.
		Use when testing all possible comparisons in a set of means (not necessarily between pairs of means; e.g., when testing non-orthogonal contrasts).
		Comparison of methods example (see Repeated Measures handout).
	darkwing.uoregon.edu /~mauro/psy612/MULTCOMP.htm (419 words)

	Sample size computation for multiple comparisons (Site not responding. Last check: 2007-10-22)
		Traditional sample size computation based on "power" does not apply directly to multiple comparisons, because the power of a test of homogeneity includes the probability of an incorrect decision.
		Thus, the power of a test of homogeneity includes some probability of incorrect multiple comparison inference, which is undesirable.
		See Appendix C of Multiple Comparisons: Theory and Methods for a discussion of this concept and details of the computation.
	www.stat.ohio-state.edu /~jch/ssinput.html (394 words)

	Using proc multtest to perform multiple comparisons
		This procedure adjusts the p-values for multiple comparisons.
		The p-value given in proc multtest is the proportion of p-values from the n samples that were smaller than the raw p-value based on the original data.
		One of the desirable properties of the bootstrap method is that it explicitly incorporates all sources of correlation, from both the multiple contrasts and the multivariate structure.
	www.ats.ucla.edu /stat/SAS/library/multtest.htm (1859 words)

	Multiple Comparisons
		It requires the name of an Analysis of Variance (aov) model or Linear Model (lm) and specification of which effects are of interest.
		Select the model object on which to perform multiple comparisons.
		Select the type of comparisons to be made among the adjusted means.
	fas.sfu.ca /doc/help/guihelp/__hhelp/multiple_comparisons.htm (522 words)

	Multiple Comparisons
		half of them) to identify measurements that one believes may be significant, and then formulate a specific hypothesis that those are significant, that one can then test with the rest of the experiments and for which one can obtain a p-value without accounting for multiple comparisons, since there is only one hypothesis being tested.
		Calculate the p-value, without accounting for multiple comparisons, for the measurement whose multiple comparisons (MC)-corrected p-value we wish to obtain, i.e.
		For each of the other measurements, calculate, without accounting for multiple comparisons, the level of the measurement that constitutes the same p-value calculated in (1).
	www.cco.caltech.edu /~alex/MultipleComparisons.html (395 words)

	EEB 581: Multiple comparisons (Site not responding. Last check: 2007-10-22)
		Multiple Comparisons: Bonferroni, Sequential Bonferroni Corrections and False Discovery Rates
		Hochberg, Y. A sharper Bonferroni procedure for multiple tests of significance.
		Simes, J. An improved Bonferroni procedure for multiple tests of significance.
	nitro.biosci.arizona.edu /courses/EEB581-2004/topics/multiple.html (274 words)

	Amazon.com: Books: Multiple Comparisons: Theory and Methods (Site not responding. Last check: 2007-10-22)
		Multiple Comparison Procedures (Wiley Series in Probability and Statistics) by Yosef Hochberg
		Exposes abuses and misconceptions of statistical multiple comparison methods, and guides the reader to the correct method of analysis for each problem.
		This chapter discusses simultaneous statistical inference, that is, inference on several parameters at once, in a setting simpler than multiple comparisons inference, which is simultaneous inference on certain functions of the differences of the treatment effects.
	www.amazon.com /exec/obidos/tg/detail/-/0412982811?v=glance (679 words)

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