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The secret of the family-wise error rate: How to ensure the accuracy of multiple hypothesis testing?
In today's data-driven society, hypothesis testing is particularly important in scientific research. However, with the popularity of multiple hypothesis testing, the family-wise error rate (FWER) has become an important concept that scholars need to have a deeper understanding of. The family-wise error rate is the probability of falsely rejecting a true null hypothesis at least once when performing multiple hypothesis tests. This means that if researchers conduct multiple independent tests, there is a chance that they could make a mistake in one or more of them.
"Understanding the family-wise error rate is critical for any researcher conducting multiple hypothesis testing."
The control of family-wise error rate involves a variety of statistical procedures, some of which are widely used and show good results. This article will focus on different control procedures and explore why they can ensure the accuracy of hypothesis testing.
Difference between family-wise and experimental error rates
The family-wise error rate was first proposed by John Tukey in 1953 as the probability of a type I error occurring in a particular set of tests. The associated experimental error rate refers to the probability of a Type I error occurring throughout the experiment. The main difference between the two is that the experimental error rate includes all assays performed, not just a specific family. Therefore, control of family-wise error rate is considered more important in multiple testing.
Income and Results of Multiple Hypothesis Testing
Each time multiple hypothesis testing is performed, researchers test all hypotheses (such as H1, H2, etc.) and decide whether to reject these hypotheses based on the P values obtained. The results of the test may include true rejections, false rejections, and true acceptances and false acceptances. In this case, the type I error rate is the family-wise error rate.
Methods for controlling family-wise error rate
There are various techniques for controlling family-wise error rates, including:
- Bonferroni procedure: This is a simple control procedure that requires that the P value of each test must be less than or equal to
α/m, wheremis The total number of assumptions. - Sidak procedure: Similar to the Bonferroni procedure, but with a slightly higher intensity test that can provide more detection power in certain situations.
- Holm's procedure: This is a descending method that decides which hypotheses to reject based on the order of P values.
Resampling procedures such as bootstrapping and permutation are another effective way to control the family-wise error rate. These methods adjust the error rate by simulating and estimating the results of hypothesis tests so that the statistical results can be accurately controlled in the presence of dependence. The power of these procedures is particularly evident when the sample dependence is known.
“The application of the resampling procedure can significantly improve the detection resolution and reduce the risk of type 1 errors.”
Balance effectiveness and control error rate
Controlling family-wise error rate is an essential part of scientific research, but this control also requires researchers to find a balance between effectiveness and error control. Some methods such as false positive rate control procedures increase the strength of detection but may also increase the risk of false rejections. Therefore, the selection of appropriate control procedures is crucial to maintaining the credibility of the study.
Thinking about the future direction
With the advancement of statistical techniques, how to more effectively control the family-wise error rate in multiple hypothesis testing will be a major challenge in the future. New methods and technologies not only require further research, but also their effectiveness and applicability in practical research must be considered. Ultimately, whether the effectiveness of hypothesis testing and error rate control can be balanced in a better way will affect the future development of scientific research.
Against this backdrop, how do you see the role of family-wise error rate control in promoting scientific accuracy?
