These graphs show the results of three trials (t_{1}, t_{2}, and t_{3}) comparing the 1-month HHS after miniincision or standard incision hip arthroplasty under the theory of (**A**) Fisher and (**B**) Neyman and Pearson. For these trials, α = 5% and β = 10%. Trial 1 yields a standardized difference between the groups of 0.5 in favor of the standard incision; Trials 2 and 3 yield standardized differences of 1.8 and 2.05, respectively. The corresponding p values are 0.62, 0.074, and 0.042 for Trials 1, 2, and 3, respectively. (**A**) Fisher’s p value for Trial 2 is represented by the gray area under the null hypothesis; it corresponds to the probability of observing a standardized difference of 1.8 (Point 2) or more extreme differences (gray area on both sides) considering the null hypothesis is true. According to Fisher, Trials 2 and 3 provide fair evidence against the null hypothesis of no difference between treatments; the decision to reject the null hypothesis of no difference in these cases will depend on other important information (previous data, etc). Trial 1 provides poor evidence against the null as the difference observed, or one more extreme, had 62% probability of resulting from chance alone if the treatments were equal. (**B**) Under the Neyman and Pearson theory, the Types I (α = 0.05, gray area under the null hypothesis) and II (β = 0.1, shaded area under the alternative hypothesis) error rates and the difference to be detected (δ = 10) define a critical region for the test statistic (|t test| > 1.97). If the test statistic (standardized difference here) falls into that critical region, the null hypothesis is rejected; this is the case for Trial 3. Trials 1 and 2 do not fall into the critical region and the null is not rejected. According to Neyman and Pearson’s theory, the null hypothesis of no difference between treatments is rejected after Trial 3 only. The distributions depicted are the probability distribution functions of the t test with 168 degrees of freedom.

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