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Is it true that the p-value is the probability that the null hypothesis is true?
The p-value is the probability that the null hypothesis is true. A low p-value shows that the effect is large or that the result is of major theoretical, clinical or practical importance. A non-significant result, leading us not to reject the null hypothesis, is evidence that the null hypothesis is true.
Is 0.03 significant p-value?
The p-value 0.03 means that there’s 3% (probability in percentage) that the result is due to chance — which is not true. A p-value doesn’t *prove* anything. It’s simply a way to use surprise as a basis for making a reasonable decision.
Why are p-values uniformly distributed under the null hypothesis?
Under the null hypothesis, your test statistic T has the distribution F (t) (e.g., standard normal). We show that the p-value P = F (T) has a probability distribution Pr (P < p) = Pr (F − 1 (P) < F − 1 (p)) = Pr (T < t) ≡ p; in other words, P is distributed uniformly.
How to find the probability distribution of P?
We show that the p-value P = F (T) has a probability distribution Pr (P < p) = Pr (F − 1 (P) < F − 1 (p)) = Pr (T < t) ≡ p; in other words, P is distributed uniformly. This holds so long as F ( ⋅) is invertible, a necessary condition of which is that T is not a discrete random variable.
Why do we use a uniform p-value?
The whole point of using the correct distribution (normal, t, f, chisq, etc.) is to transform from the test statistic to a uniform p-value. If the null hypothesis is false then the distribution of the p-value will (hopefully) be more weighted towards 0.
When is the probability of rejecting a null hypothesis alpha?
We want the probability of rejecting a true null hypothesis to be alpha, we reject when the observed p-value < α, the only way this happens for any value of alpha is when the p-value comes from a uniform distribution.