Familywise error rate

Definition

The familywise error rate (FWER) is the probability of making one or more Type I errors when conducting multiple hypothesis tests. In simpler terms, it reflects the likelihood of incorrectly rejecting at least one true null hypothesis across a set of comparisons. This concept is crucial when performing multiple comparisons, as it helps to control the overall error rate and reduce the risk of finding false positives.

5 Must Know Facts For Your Next Test

1. The familywise error rate increases as the number of comparisons made increases, meaning that the more tests you run, the greater your chance of encountering at least one Type I error.
2. Controlling the familywise error rate is essential in studies where multiple hypotheses are tested simultaneously, as it helps maintain the integrity of statistical conclusions.
3. Common methods to control the familywise error rate include the Bonferroni correction and Holm's sequential method, which adjust p-values based on the number of comparisons.
4. In practical applications, researchers often face a trade-off between increasing power (sensitivity to detect true effects) and controlling the familywise error rate.
5. The familywise error rate can be contrasted with other approaches like controlling the false discovery rate, which may allow for a higher overall error rate in favor of discovering more true positives.

Review Questions

• How does increasing the number of hypothesis tests affect the familywise error rate, and what implications does this have for statistical analysis?
  • As the number of hypothesis tests increases, so does the familywise error rate, which signifies a higher likelihood of incorrectly rejecting at least one true null hypothesis. This rise in error rate can lead to more false positives in research findings, potentially misguiding conclusions and leading to incorrect interpretations. Therefore, it is vital for researchers to implement strategies to control this rate when conducting multiple comparisons.
• Discuss how the Bonferroni correction works and its role in controlling the familywise error rate during multiple testing.
  • The Bonferroni correction adjusts the significance threshold for each individual hypothesis test by dividing the desired alpha level (e.g., 0.05) by the number of tests being conducted. This means that each test is held to a stricter standard for significance in order to control the overall familywise error rate. While effective in reducing Type I errors, this method can also lead to decreased power and an increased risk of Type II errors, especially when many comparisons are made.
• Evaluate the balance between controlling the familywise error rate and maintaining statistical power in research studies involving multiple comparisons.
  • Controlling the familywise error rate is crucial for ensuring that researchers do not mistakenly claim significant effects that are actually due to chance. However, this control often comes at the cost of statistical power, which is the ability to detect true effects. In many cases, stricter corrections like Bonferroni may be overly conservative, leading to missed opportunities for discovering real differences. Thus, researchers must carefully consider their objectives and choose appropriate methods that balance these two aspects effectively based on their study design and context.

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 adjust the significance levels when performing multiple comparisons, aiming to control the familywise error rate.

False Discovery Rate: The proportion of false positives among all positive findings, which contrasts with the familywise error rate that focuses on the overall probability of making any false discoveries.