Insignificant p-value

Question

I've a question regarding insignificant p-value.

If I got p-value greater than 0.05, does that mean my result is biological insignificant?

Can anyone help me to clear this up?

Answer 1

Suppose you are testing $H_0: \mu = 100$ against $H_a: \mu \ne 100,$ where the value of $\mu$ may be of importance in biology.

If the p-value of a test exceeds 5%, then there is not sufficient evidence to reject $H_0.$ Then you would say there is not evidence of a statistically significant change in $\mu$ (from 100) according to the data used for the test.

Even if the p-value is smaller than 5% and you can claim a statistically significant change, that does not mean that the effect is of practical importance in biology, That is for an biologist to say. (I think this is an example of what @EricWong says in his Comment.)

Maybe you have a huge amount of data and you can claim $\mu \approx 100.5$ instead of $\mu = 100.$ The change by 0.5 might be 'real', but a biologist might say that's not an important difference. (She might say, "I'd be really interested if you told me the change is 5, but people would laugh if I wrote a paper claiming a difference of 0.5.")

If a study is wisely planned with about the right number $n$ of observations, then statistical significance and practical importance will amount to about the same thing. That takes more careful advance planning than one often sees in practice.