Family Wise Error Rate Anova
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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) familywise error rate anova is the probability of making one or more false discoveries, or family wise error rate post hoc type I errors, among all the hypotheses when performing multiple hypotheses tests. Contents 1 History 2
Family Wise Error Rate R
Background 2.1 Classification of multiple hypothesis tests 3 Definition 4 Controlling procedures 4.1 The Bonferroni procedure 4.2 The Šidák procedure 4.3 Tukey's procedure 4.4 Holm's step-down
How To Calculate Family Wise Error Rate
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 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 family wise error rate formula 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 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 hypo
describe a number of different ways of testing which means are different Before describing the tests, it is necessary to consider two different ways of thinking about error and how they are
Family Wise Error Rate Definition
relevant to doing multiple comparisons Error Rate per Comparison (PC) This is simply the Type family wise error rate correction I error that we have talked about all along. So far, we have been simply setting its value at .05, a 5% chance family wise error calculator of making an error Familywise Error Rate (FW) Often, after an ANOVA, we want to do a number of comparisons, not just one The collection of comparisons we do is described as the "family" The familywise error https://en.wikipedia.org/wiki/Family-wise_error_rate rate is the probability that at least one of these comparisons will include a type I error Assuming that a ¢ is the per comparison error rate, then: The per comparison error: a = a ¢ but, the familywise error: a = 1 - (1-a ¢ )c Thus, if we do two comparisons, but keep a ¢ at 0.05, the FWerror will really be: a = 1 - (1 - 0.05)2 =1 - (0.95)2 http://www.psych.utoronto.ca/courses/c1/chap12/chap12.html = 1 - 0.9025 = 0.0975 Thus, there is almost a 10% chance of one of the comparisons being significant when we do two comparisons, even when the nulls are true. The basic problem then, is that if we are doing many comparisons, we want to somehow control our familywise error so that we don’t end up concluding that differences are there, when they really are not The various tests we will talk about differ in terms of how they do this They will also be categorized as being either "A priori" or "post hoc" A priori: A priori tests are comparisons that the experimenter clearly intended to test before collecting any data Post hoc: Post hoc tests are comparisons the experimenter has decided to test after collecting the data, looking at the means, and noting which means "seem" different. The probability of making a type I error is smaller for A priori tests because, when doing post hoc tests, you are essentially doing all possible comparisons before deciding which to test in a formal statistical manner Steve: Significant F issue An example for context See page 351 for a very complete description of the Morphine Tolerance study .. Seigel (1975) Highlights: paw lick latency as a measure of pain resistance tolerance to morphine develops quickly notion of a compensatory mecha
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 https://www.uvm.edu/~dhowell/gradstat/psych340/Lectures/Anova/anova3.html variety of coping skills; 2) Prolonged 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 wise error total number of symptoms endorsed by the subject. The descriptive statistics and 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 family wise error Error rates There are two kinds of error rates that we care about: Error rate per comparison This 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
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