Bonferroni correction
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The question is what is the Bonferroni correction? When is it used? What is the principle of the Bonferroni correction?
What are planned comparisons? Why do researchers making planned comparisons need to make the Bonferroni correction? If a researcher is making four planned comparisons using the .05 significance level, what would be the Bonferroni corrected significance level?
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Solution Summary
The solution provides details about the Bonferroni correction in relation to hypothesis testing. Two references are included for further research on the topic.
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The ANOVA uses the F test to determine whether there exists a significant difference among treatment means or interactions. In this sense it is a preliminary test that informs us if we should continue the investigation of the data at hand. If the null hypothesis (no difference among treatments or interactions) is accepted, there is an implication that no relation exists between the factor levels and the response. There is not much we can learn, and we are finished with the analysis. When the F test rejects the null hypothesis, we usually want to undertake a thorough analysis of the nature of the factor-level effects.
When processes are compared and the null hypothesis of equality (or homogeneity) is rejected, all we know at that point is that there is no equality amongst them. But we do not know the form of the inequality. Post hoc comparisons are generally performed after obtaining a significant omnibus F. Then we look at all possible pairwise or all possible pairwise and otherwise comparisons. Here, we are focusing on the largest difference between levels of the IV, but you are still sifting through the data in hopes of finding something significant.
The ANOVA calculations test the null hypothesis that all groups of data really are sampled from ...
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