Non-Significant Change in Slopes

Sometimes, the change in the slopes between two segments is not statistically significant (p-value>0.05) from the t-test, but there is a joinpoint between the two segments or vice versa. Why?


The Joinpoint program shows the estimates of the regression coefficients, i.e., intercepts and slopes, and the changes of the slopes. The p-values of the slope changes are calculated from the t-test based on asymptotic normality. Based on a p-value greater than 0.05, one might say the two slopes are not statistically different and hence conclude that the two segments are the same. But using the p-value from a t-test is not as accurate as that from the permutation test, since the t-test is an asymptotic test and the variances are calculated using the information matrix conditional on the estimated joinpoints without imposing the continuity constraint and omitting the offending observations. The software (with the permutation test procedure) does not require the asymptotic normality and maintains the correct Type I error probability level and hence the number of joinpoints determined by the software is more reliable.




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