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A team plans to run 10 independent tests and wants the chance of any false alarm, over all ten, to…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
A team plans to run independent tests and wants the chance of any false alarm, over all ten, to stay at about . It uses the Bonferroni correction, which divides by the number of tests. Find the level for each test. Find the chance of at least one false alarm when every null idea is true, to four decimal places. Compare it with the chance when each test uses .
Need a reminder? The key ideaShow
Reject the null idea when the p-value is at most . A Type I error is a false alarm and a Type II error a missed effect. Among independent tests of true null ideas, the chance of at least one false alarm is .
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. .
Step 2. .
Step 3. Without the correction: .
Answer: , about , against about .
The price. Each test is now much stricter, so a real but small effect is easier to miss. Fewer false alarms come with more Type II errors.
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