# Z-test for acceptance of null hypothesis

Everywhere you look it's all about finding whether you can reject that two samples are different or not.

But how do you interpret it, when you go the "opposite" way around? E.g. I have two values, from experiment and theory that are similar. A Z-test reveals they're only 0.1 sigmas apart.

There's no way that they would be different, but could the wording be turned around so that we could say "we're extremely sure that they're the similar, which validates experiment and theory"?

Is it valid to say, similar to rejection at $p=\alpha$, to accept values as being "similar enough" at $p=1-\alpha$?

• One kind of answer is to consider an equivalence test. equivalence is a tag here for your searches. Jan 18, 2018 at 13:10
• -test reveals they're only 0.1 sigmas apart. What is sigma here ? true S.D. or standard error ? What is your formula computing Z statistic? what is your data and more .
– user10619
Jan 18, 2018 at 13:17
• For this problem I'm only given two means and their associated errors (on the means). I used z = mu2 - mu1 / sqrt(sig2 + sig1) Jan 18, 2018 at 13:19