Familywise error rate

Definition

The familywise error rate (FWER) is the probability of making one or more Type I errors when performing multiple hypothesis tests simultaneously. It reflects the risk of incorrectly rejecting at least one null hypothesis across a family of tests, which can inflate the overall error rate as the number of comparisons increases. Controlling for the FWER is essential in statistical analyses involving multiple comparisons to maintain the integrity and validity of the findings.

5 Must Know Facts For Your Next Test

1. The familywise error rate increases as more hypotheses are tested, which is why controlling it is crucial for accurate statistical inference.
2. Common methods to control FWER include the Bonferroni correction and Holm's sequentially rejective method.
3. FWER is often set at a threshold (e.g., 0.05), meaning that researchers aim to keep the probability of making at least one Type I error below this level.
4. Ignoring FWER in multiple testing can lead to misleading conclusions, as researchers may falsely conclude that there are significant effects when there are none.
5. Familywise error rate control is particularly important in fields such as medical research, where false positives can lead to incorrect treatment decisions.

Review Questions

• How does performing multiple hypothesis tests affect the familywise error rate, and what implications does this have for researchers?
  • Performing multiple hypothesis tests increases the likelihood of encountering at least one Type I error, thus raising the familywise error rate. This inflation means that researchers need to be cautious when interpreting results from multiple tests because even if individual tests appear significant, the overall risk of false positives increases. Consequently, researchers must implement appropriate adjustments to control for FWER and ensure their conclusions are valid.
• What are some common methods used to control for familywise error rate, and how do they differ in their approach?
  • Common methods for controlling familywise error rate include the Bonferroni correction and Holm's sequentially rejective method. The Bonferroni correction adjusts the significance level by dividing the alpha level by the number of tests, which can be quite conservative, especially with many comparisons. In contrast, Holm's method is less conservative and sequentially adjusts p-values while keeping track of their ranks, allowing for more power in detecting true effects while still controlling FWER.
• Evaluate the importance of controlling the familywise error rate in different research fields, particularly those involving clinical trials or public health studies.
  • Controlling the familywise error rate is critically important in fields such as clinical trials and public health studies where decisions based on statistical findings can have significant real-world implications. In these settings, a Type I error could lead to erroneous conclusions about treatment efficacy or safety, resulting in potential harm to patients or misallocation of resources. Therefore, employing methods to control FWER not only enhances the credibility of research findings but also safeguards public health by ensuring that only truly effective interventions are pursued.

Related terms

Type I Error: A Type I error occurs when a true null hypothesis is incorrectly rejected, leading to a false positive result.

Bonferroni Correction: A statistical method used to control the familywise error rate by adjusting the significance level based on the number of comparisons being made.

False Discovery Rate: The false discovery rate (FDR) is the expected proportion of false positives among all rejected hypotheses, providing a different approach to controlling errors in multiple testing scenarios.