![]() If we like to bound these over-fitting probabilities by α, then we can assign different values for each α(k a,k b). Consider a one-variant experiment concerning a random. ![]() The new procedure has the following properties: In this section we review the sequential probability ratio test (SPRT) for testing simple hypotheses. Consider an example where K min= 0 and K max= 4. Notice that the individual significance level depends on the number of joinpoints k a under the null. The new procedure set α(k a,k b)=α/(K max-k a). Let α(k a,k b) be the significance level of each individual test H 0: k=k a vs. The new adjustment procedure controls the overall over-fitting probabilities. The Bonferroni adjustment is conservative because the actual overall significance level is usually less than the nominal level α. The problem of sequentially testing the unknown drift of a Brownian motion is the continuous analogue of Wald and Wolfowitzs. Each of these permutation test are carried out a significance level of α 1=α/(K max-K min), i.e., if the p-value < α 1, then it rejects the null. Let be the final selected number of Joinpoints.īecause multiple tests are performed, Bonferroni adjustment is used to ensure that the approximate overall type I error is less than the specified significance level (significance level is also called the α-level, default α=.05). ![]() If the null is rejected, then increase k a by 1 otherwise, decrease k b by 1. The procedure begins with k a= K min and k b= K max. Each one tests the null hypothesis H 0: k = k a against the alternative hypothesis H 1: k = k b. The Joinpoint program uses a sequence of "permutation" tests to select the final model. ![]()
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