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Experimental Error Rate vs. Family-Wide Error Rate: What's the Difference and Why Does It Matter?
Data analysis and statistics are an indispensable part of today's scientific research, especially in the process of hypothesis testing. However, when researchers conduct multiple hypothesis tests, controlling the proportion of errors becomes particularly important. At this point, we must understand the difference between the experimentwise error rate (EER) and the family-wise error rate (FWER), and why we should control one or both.
The family-wise error rate is the probability of making at least one type I error when performing a set of hypothesis tests.
The concept of family-wise error rate
The concept of family-wise error rate was proposed by statistician John Tukey in 1953. It is specifically targeted at a specific set of tests, namely a "family" of tests. In statistics, a Type I error occurs when you mistakenly reject a hypothesis that is actually true (i.e., null). This means that when multiple tests are performed, if any one test is wrong, the overall result will be affected.
The experimental error rate describes the probability of making at least one Type I error within a given experiment.
The significance of experimental error rate
The experimental error rate, meanwhile, focuses on testing for the entire experiment, which includes all the tests performed in an experiment. This setting means that when analyzing the results, if any one test is false, the overall result must be considered carefully.
Why is it important to distinguish between the two?
Understanding the difference between these two concepts is critical to correctly interpreting research results. Since FWER is an error control for a set of hypothesis tests, and EER focuses more on the repeatability and reliability of the entire experiment, this distinction can help academic researchers interpret and reflect on the results of hypothesis testing more accurately.
Strategies for controlling error rates
There are various ways to control these error rates, including the Bonferroni procedure, the Šidák procedure, and others.
These methods are designed to reduce the chance of error when performing multiple tests. For example, the Ferroni method reduces the overall error rate by distributing the significance level among the tests. The Shidak method provides a more powerful but slightly improved means of control.
The impact of family-wise and experimental error rates
Controlling the family-wise error rate may be a priority in many situations, especially when the study results may have a significant impact on clinical or policy decisions. In contrast, experimental error rates are typically used in methods that require greater diversity and flexibility.
ConclusionIn summary, although both the family-wise error rate and the experimental error rate are intended to prevent Type I errors when conducting multiple hypothesis tests, their applicable scenarios and control strategies are different. Understanding these differences will help researchers make better choices when designing experiments.
So, how do you balance the trade-off between controlling the family-wise error rate and the experimental error rate when designing experiments and analyzing data?
