How are multiple comparisons used in hypothesis testing?
In short, we use hypothesis testing to prove some hypothesis about our data. This is a fairly straightforward process until we want to test a set of hypotheses simultaneously. In this post, I’ll review the problems with making such multiple comparisons and how to address them accordingly.
How is α used in the multiple comparison problem?
Of these, α is perhaps most relevant to the multiple comparison problem. It is important to first have a thorough understanding of how α is used in hypothesis testing. If we find a difference in the mean pain scores across the two groups, does it actually mean anything?
Which is the best correction for multiple comparisons?
Below, I’ll provide a brief overview of available correction procedures for multiple comparisons. The most conservative of corrections, the Bonferroni correction is also perhaps the most straightforward in its approach. Simply divide α by the number of tests ( m ).
How to reduce the power of multiple comparisons?
Simply divide α by the number of tests ( m ). However, with many tests, α* will become very small. This reduces power, which means that we are very unlikely to make any true discoveries.
When to use the rejection rule for multiple hypothesis tests?
1.2 Multiple Hypotheses When conducting multiple hypothesis tests, if we follow the same rejection rule independently for each test, the resulting probability of making at least one Type I error is substantially higher than the nominal level used for each test, particularly when the number of total tests mis large.
What is the error rate for Type 1 hypothesis tests?
For a single hypothesis test at the α=0.05 level, the type 1 error rate is only 5%. There is only a 5% chance of erroneously rejecting the null hypothesis. For 2 hypothesis tests, however, the overall α becomes 0.10. The probability of erroneously rejecting at least 1 null hypothesis is 0.10.
What is the problem of multiple comparisons in statistics?
If many data series are compared, similarly convincing but coincidental data may be obtained. In statistics, the multiple comparisons, multiplicity or multiple testing problem occurs when one considers a set of statistical inferences simultaneously or infers a subset of parameters selected based on the observed values.