# is this interpretation of the p-value legit?

The interpretation of the p-value is a very difficult thing because what is legit and what is not is very close together. The p-value is the probability of the resulting test statistic if the null hypothesis $H_0$ is true; that means $\Pr(\mathrm{data}|H_0)$. A lot of people make the mistake of confusing this with $\Pr(H_0|\mathrm{data})$, which is wrong. Now to my question: I stumbled upon an online independent t-test and the result was a p-value of 0.20. The given interpretation was the following: "There is a 79.76% chance the proportions are different."

My question: is this interpretation legit? Or is it the same confusion as mentioned above (e.g. it describes the probability of $H_0$). Thanks in advance!

• "the p-value is the probability of the resulting test statistic if h0 is true". That's not correct. "[...] the p-value is the probability of obtaining a test statistic at least as extreme as the one that was actually observed, assuming that the null hypothesis is true". (from Wikipedia) – boscovich May 31 '13 at 13:45
• This interpretation is wrong. As you said: the $p$-value is the probability of observing a $t$-value at least as extreme as the one you found if the null hypothesis were true. – COOLSerdash May 31 '13 at 13:46
• Because the test was already performed, the conclusion of whether the means are different or not different should not have a probability attached to it. You either reject, or not reject, cannot 20.24% reject. – Penguin_Knight May 31 '13 at 13:47