Calculating Family Wise Error Rate
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may be challenged and removed. (June 2016) (Learn how and when to remove this template message) In statistics, family-wise error rate (FWER) is the probability of making one or more false
Family Wise Error Rate Post Hoc
discoveries, or type I errors, among all the hypotheses when performing multiple hypotheses family wise error rate r tests. Contents 1 History 2 Background 2.1 Classification of multiple hypothesis tests 3 Definition 4 Controlling procedures 4.1 The
Family Wise Error Rate Definition
Bonferroni procedure 4.2 The Šidák procedure 4.3 Tukey's procedure 4.4 Holm's step-down procedure (1979) 4.5 Hochberg's step-up procedure 4.6 Dunnett's correction 4.7 Scheffé's method 4.8 Resampling procedures 5 Alternative approaches 6 familywise error rate calculator References History[edit] Tukey coined the terms experimentwise error rate and "error rate per-experiment" to indicate error rates that the researcher could use as a control level in a multiple hypothesis experiment.[citation needed] Background[edit] Within the statistical framework, there are several definitions for the term "family": Hochberg & Tamhane defined "family" in 1987 as "any collection of inferences for which it is meaningful familywise error rate anova to take into account some combined measure of error".[1][pageneeded] According to Cox in 1982, a set of inferences should be regarded a family:[citation needed] To take into account the selection effect due to data dredging To ensure simultaneous correctness of a set of inferences as to guarantee a correct overall decision To summarize, a family could best be defined by the potential selective inference that is being faced: A family is the smallest set of items of inference in an analysis, interchangeable about their meaning for the goal of research, from which selection of results for action, presentation or highlighting could be made (Yoav Benjamini).[citation needed] Classification of multiple hypothesis tests[edit] Main article: Classification of multiple hypothesis tests The following table defines various errors committed when testing multiple null hypotheses. Suppose we have a number m of multiple null hypotheses, denoted by: H1,H2,...,Hm. Using a statistical test, we reject the null hypothesis if the test is declared significant. We do not reject the null hypothesis if the test is non-significant. Summing the test results over Hi will give us the following table and related random variab
the experimentwise error rate is: where αew https://en.wikipedia.org/wiki/Family-wise_error_rate is experimentwise error rate αpc is the per-comparison error rate, and c is the number of comparisons. For example, if 5 independent comparisons http://davidmlane.com/hyperstat/A43646.html were each to be done at the .05 level, then the probability that at least one of them would result in a Type I error is: 1 - (1 - .05)5 = 0.226. If the comparisons are not independent then the experimentwise error rate is less than . Finally, regardless of whether the comparisons are independent, αew ≤ (c)(αpc) For this example, .226 < (5)(.05) = 0.25.
Counseling and Clinical Psychology. The subjects were 45 rape victims who were randomly assigned to one of four groups. The four groups were 1) Stress Inoculation Therapy (SIT), in which subjects were taught a variety of coping skills; 2) Prolonged https://www.uvm.edu/~dhowell/gradstat/psych340/Lectures/Anova/anova3.html Exposure (PE), in which subjects went over the rape in their mind repeatedly for seven sessions; 3) Supportive Counseling (SC), which was a standard therapy control group; and 4) a Waiting List (WL) control. In the actually study pre- and post-treatment measures were taken on a number of variables. For our purposes we will only look at post-treatment data on PTSD Severity, which was the total number of symptoms endorsed by the subject. The descriptive statistics and error rate the summary table for the analysis of variance follows. This is what we saw last time. Obviously there are significant differences, but we don't know where they lie. My personal guess would be that the two control groups are different from the experimental groups, but I don't know whether the latter differ from each other or not. Multiple Comparisons Error rates There are two kinds of error rates that we care about: Error rate per comparison This wise error rate is the probability that any particular comparison will yield a Type I error. We don’t care about any other comparisons when we are talking about this, but only about the comparison in question. If we ran a bunch of t tests at a = .05, then the per comparison error rate would be .05. Error rate familywise This is the probability that a particular set of comparisons will contain at least one Type I error. (It could contain 8 Type I errors for all we care, just so long as it contained at least 1.) It should be apparent that the more tests we run, the more opportunity we will have to make an error, unless we somehow adjust our test to prevent this from happening. If we ran several tests, each at a , the probability of at least one error is no greater than ca , where c is the number of comparisons, or tests. In general, multiple comparison procedures are established to control the familywise error rate in some way. Different procedures do this in different ways. What are multiple comparison procedures all about? When I looked at what I had planned to say in this class, I realized that I had left out the forest for the trees. The overall point is that all of the procedures that I will talk about are based on very
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