8-1 Basics of Hypothesis Testing 385 MEMORY HINT FOR TYPE I AND TYPE II ERRORS Remember “routine for fun,” and use the consonants from those words (RouTiNe FoR FuN) to remember that a type I error is RTN: Reject True Null (hypothesis), and a type II error is FRFN: Fail to Reject a False Null (hypothesis). HINT FOR DESCRIBING TYPE I AND TYPE II ERRORS Descriptions of a type I error and a type II error refer to the null hypothesis being true or false, but when wording a statement representing a type I error or a type II error, be sure that the conclusion addresses the original claim (which may or may not be the null hypothesis). See Example 2. Describing Type I and Type II Errors EXAMPLE 2 Consider the claim that a medical procedure designed to increase the likelihood of a baby girl is effective, so that the probability of a baby girl is p 7 0.5. Given the following null and alternative hypotheses, write statements describing (a) a type I error, and (b) a type II error. H0: p = 0.5 H1: p 7 0.5 1original claim that will be addressed in the final conclusion2 YOUR TURN. Do Exercise 25 “Type I and Type II Errors.” SOLUTION a. Type I Error: A type I error is the mistake of rejecting a true null hypothesis, so the following is a type I error: In reality p = 0.5, but sample evidence leads us to conclude that p 7 0.5. (In this case, a type I error is to conclude that the medical procedure is effective when in reality it has no effect.) b. Type II Error: A type II error is the mistake of failing to reject the null hypothesis when it is false, so the following is a type II error: In reality p 7 0.5, but we fail to support that conclusion. (In this case, a type II error is to conclude that the medical procedure has no effect, when it really is effective in increasing the likelihood of a baby girl.) Controlling Type I and Type II Errors Step 4 in our standard procedure for testing hypotheses is to select a significance level a (such as 0.05), which is the probability of a type I error. The values of a, b, and the sample size n are all related, so if you choose any two of them, the third is automatically determined (although b can’t be determined until an alternative value of the population parameter has been specified along with a and n). Good Practices ■ Consider the seriousness of a type I error (with probability a) and also consider the seriousness of a type II error (with probability b). ■ One common practice is to select the significance level a, then select a sample size that is practical, so the value of b is determined. ■ If it’s important to reduce the probability a (the probability of a Type I error) and the probability b (the probability of a Type II error), select a and b accordingly and then the required sample size n is automatically determined. P-Hacking Researchers often feel strong pressure to obtain meaningful results, such as a result that a potential drug is effective. When conducting an experiment, “P-hacking” is cheating to obtain such meaningful results. Some of the methods used to P-hack: Repeat the experiment many times, but include only those cases with a P-value less than 0.05; throw out any sample data that cause the P-value to exceed 0.05; discontinue sampling once a P-value less than 0.05 has been obtained. One effective way to prevent P-hacking is to use “preregistration,” whereby a detailed research plan is prepared in advance and preregistered at an online registry, such as Open Science Framework. d i
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