I'm performing an analysis by fitting data points to an exponential distribution and testing the adequacy of this fit using the Kolmogorov-Smirnov test. The standard ks test null hypothesis: the data is indeed derived from an exponential distribution. The ks test statistic is compared with a critical value and the null hypothesis is rejected if it exceeds this critical value. I used this paper to find the critical values. I find the test statistic falls below this threshold, even for a significance level as high as 0.20.

Now here is my question. I've read that a smaller p-value provides stronger evidence supporting an alternative hypothesis, and that one usually looks to 0.05 as a threshold to reject the null hypothesis. However, no significance level is considered to support the null hypothesis. Is there any way to interpret the conventional p-value as supporting the null hypothesis? Is there anything wrong with this interpretation?


1 Answer 1


In this case, you would never be able to interpret the p-value in terms of the "flipped" null hypothesis because it's possible for a non-exponential distribution to be arbitrarily close to the actual exponential distribution. That means such a test has 0 power always. In fact, considering all possible alternatives, non-exponential distributions (specifically the empirical distribution function) will always fit the data as good if not better than the exponential maximum likelihood estimate.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.