Familywise Type 1 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
Familywise Error Rate Anova
the probability of making one or more false discoveries, or type familywise error rate calculator I errors, among all the hypotheses when performing multiple hypotheses tests. Contents 1 History 2 Background 2.1
Experiment Wise Error Rate
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 procedure (1979) 4.5 family wise error calculator 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 the statistical framework, there per comparison error rate 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 hypotheses. Suppose we have a number m of mu
the simple question posed by an analysis of variance - do at least two treatment means differ? It may be that embedded in a group of treatments there is only one "control" treatment to which every other treatment should be compared,
Family Wise Error Rate Post Hoc
and comparisons among the non-control treatments may be uninteresting. One may also, after performing an analysis comparison wise error rate of variance and rejecting the null hypothesis of equality of treatment means want to know exactly which treatments or groups of treatments differ.
Familywise Non Coverage Error Rate
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 https://en.wikipedia.org/wiki/Family-wise_error_rate Type I error rate acceptable for the group of hypotheses as a whole. Comparisons or Contrasts If we let represent a treatment mean and ci a weight associated with the ith treatment mean then a comparison or contrast can be represented as: , where It can be seen that this contrast is a linear combination of treatment means (other contrasts such as quadratic and cubic are also possible). All of the following are possible comparisons: http://online.sfsu.edu/efc/classes/biol458/multcomp/multcomp.htm because they are weighted linear combinations of treatment means and the weights sum to zero. For example, previously we have performed comparisons between two treatment means using the t - statistic: with (n1 + n2) - 2 degrees of freedom. This statistic is a "contrast." The numerator of this expression follows the general form of the contrast outlined above with the weights c1 and c2 equal to 1 and -1, respectively: However, we also see that this contrast is divided by the pooled within cell or within group variation. So, a contrast is actually the ratio of a linear combination of weighted means to an estimate of the pooled within cell or error variation in the experiment: with degrees of freedom. For a non - directional null hypothesis t could be replaced by F: with 1, and degrees of freedom. In general, a contrast is the ratio of a linear combination of weighted means to the mean square within cells times the sum of the squares of the weights assigned to each mean divided by the sample size within cells: where the cI' s are the weights assigned to each treatment mean,, ni is the number of observations in each cell and MSerror is the within cell variation pooled from the entire experiment (the within cell m
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or more absolutely true null hypotheses in a family of several absolutely true null hypotheses. Rejecting an absolutely true null hypothesis is known as a "Type One Error." It is important to keep in mind that one cannot make a Type I error unless one tests an absolutely true null hypothesis. Accordingly, if absolutely true null hypotheses are unlikely to be encountered, then the unconditional probability of making a Type I error will be quite small. Psychologists and some others act as if they think they will burn in hell for an eternity if they ever make even a single Type I error -- that is, if they ever reject a null hypothesis when, in fact, that hypothesis is absolutely true. I and many others are of the opinion that the unconditional probability of making a Type I error is close to zero, since it is highly unlikely that one will ever test a null hypothesis that is absolutely true. Why worry so much about making an error that is almost impossible to make? There exists a variety of techniques for capping familywise alpha at some value, usually .05. Why .05? Maybe .05 is, sometimes, a reasonable criterion for statistical significance when making a single comparison, but is it really reasonable to cap familywise alpha at .05? Even if it is, what reasonably constitutes the family for which one should cap familywise alpha at .05? Is it the family of hypotheses that I am testing for this particular outcome variable in this particular research project? I am testing for all comparisons make in this particular research project? I am testing this month, this year, or during my lifetime? All psychologists are testing this month, this year, or whenever? Many times I have asked this question about what reasonably constitutes a family of comparisons for which alpha should be capped at .05. I have never been satisfied with any answer I have received. Controlling Familywise Alpha When Making Multiple Comparisons Among Means The context in which the term "familywise alpha" is most likely to arise is when making multiple comparisons among means or groups of means. Suppose one has four means and wishes to compare each mean with each other mean. That is six comparisons. If all four means were absolutely equal in the populations of interest, that would be six absolutely true null hypotheses being tested. Those obsessed with familywise alpha are likely to use a technique like Tukey or Bonferroni or Scheffe to cap the familywise alpha when making those