Timeline for Does statistically insignificant difference of means imply equality of means?

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May 25 '14 at 19:54 history edited
May 18 '14 at 20:02 comment This question asks the same in terms of confidence intervals. Those are generally more instructive than $p$-values, because they live on the scale you measured, so you should prefer the confidence intervals anyway.
May 18 '14 at 19:03 comment I take "how equal" to be a bit of an odd way to put it. We can estimate the difference between the means, $\mu_A - \mu_B$, and estimate the uncertainty around that difference, but how does one thing be more equal than another. Typically we test the hypothesis $\mu_A - \mu_B = 0$, but in non-inferiority or equivalence testing we flip the hypothesis to be something like $|\mu_A - \mu_B| < 2$, e.g. the absolute value of the difference of the means is less than 2 (for one possible example). The number you choose should be based on other criteria - not based on the observed data.