![]() It just requires simple arithmetic.įor an experimenter who is most concerned with controlling error rate familywise, the Bonferroni correction is a good choice. The Bonferroni correction is easy to apply.The Bonferroni correction can be used with planned comparisons and with post hoc comparisons.The experimenter sets the significance level for a family of hypothesis tests,Īnd the Bonferroni correction specifies the right significance level for each individual hypothesis test. The Bonferroni correction does a great job of controlling error rate familywise. ![]() There are several things to like about the Bonferroni correction, including the following: In some situations, the F ratio is a good technique for testing the statistical significance of multiple comparisons. The desired error rate familywise of 0.05. ![]() With the Bonferroni correction, the chances of making at least one Type I error are approximately equal to The experimenter specifies a significance level for each individual comparison of 0.05/4 or 0.125.Īnd the probability of making at least one Type I error is: ![]() However, what happens if the experimenter uses the Bonferroni correction? The probability of making at least one Type I error is: The probability of incorrectly rejecting at least one null hypothesis is greater than 0.05,īecause there are four chances go wrong. What happens if the experimenter tests four true, independent null hypotheses, using a significance level of 0.05 for each test? Suppose an experimenter wants to set the error rate familywise at 0.05. Α is the significance level for a single hypothesis test,Īnd C is the number of orthogonal comparisons being tested. (i.e., ERF is the error rate familywise), Where ERF is the probability of making at least one Type I error when testing C orthogonal hypotheses Incorrectly rejecting at least one null hypothesis is easily calculated as: When comparisons in the family are orthogonal, the probability of If the experiment included four comparisons to be tested, the significance level to test each individual comparison Use the value from Step 2 as the significance level to test individual comparisons.įor example, suppose an experimenter set the error rate familywise at 0.05. Divide the significance level by the number of comparisons to be tested. Set a significance level for the error rate familywise. This lesson explains how to use an F ratio with analysis of variance to test statistical hypotheses represented by planned comparisons.īonferroni's correction is an adjustment to the significance level used to evaluate the statistical significance of an individual comparison. This lesson describes how the probability of committing a Type I error is affected by the number of comparisons tested. It explains how to represent a statistical hypothesis mathematically by a comparison.Īnd it explains how to compute the sum of squares for a comparison. This lesson defines an ordinary comparison. If you don't know these things, review the following lessons: Type I error is affected by the number of comparisons tested.Īnd you should know how to use an F ratio to test multiple comparisons. You should understand how the probability of committing a You should be able to compute the sum of squares associated with a comparison. You should know how to represent a statistical hypothesis mathematically by a comparison. Prerequisites: This lesson assumes familiarity with multiple comparisons for follow-testing in ANOVA. The lesson is all about the Bonferroni correction - what it is, why it is needed, when to use it, and how to implement it. The Bonferroni correction (aka, Bonferroni adjustment, Bonferroni test, Bonferroni method) is way to control error rate familywise with experiments that test multiple comparisons.
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