Thanks for you help.

Peter

- Thread starter Peter A Noble
- Start date

Thanks for you help.

Peter

Thanks for you help.

Peter

Otherwise, your general thought process for selecting the paired t-test is correct because the observations are not likely to be independent of one another as you noted.

I perform a two way paired T-test to prove the null.

You might want to consider an analytic method that is specifically tailored to cases where the intent is to provide evidence

I think your choice of a paired t-test makes sense, but do keep in mind here that a non-significant result will not "prove" the null to be true. In general, we cannot use statistical analyses to "prove" things; "proof" implies absolute certainty, and statistical analyses always come with some uncertainty attached. More specifically, a non-significant result simply indicates that you don't have evidence to reject the null; it doesn't mean the null is necessarily true (given that there are always other plausible explanations for a non-significant result, such as imperfect power).

You might want to consider an analytic method that is specifically tailored to cases where the intent is to provide evidence*for* a null hypothesis. E.g., Bayesian estimation with a ROPE, Bayes factors (exclude the self-plug), or equivalence testing. None of these methods will allow you to prove the null with *certainty*, but all of them will allow for a slightly more useful conclusion than "I couldn't find evidence to reject the null".

You might want to consider an analytic method that is specifically tailored to cases where the intent is to provide evidence