Contents
How are P-values distributed?
The distribution of p values under H 0 The p value is 1−FT(T). If FT is continuous, the p value is uniformly distributed on [0,1]. For example, the distribution of the two-sample t-test is continuous, and the distribution of its p value has a uniform [0,1] distribution.
Is P value a random variable?
Students will learn the logic behind rejecting the null hypothesis (H0) when p is small, instead of simply memorizing recipes; they will not learn incorrect interpretations such as “the p-value is the probability that H0 is true.” In our approach, it is emphasized that p-values are transformations of a test statistic …
Why are p values uniformly distributed in the H0?
If p values are uniformly distributed under the H0 that means that it is as likely to see a p-value of .05 as a p-value of .80, but this is not true, as it is less likely to observe a p-value of .05 than a p-value of .80, because that is precisely the definition of the normal distribution from which the p-value are taken.
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.
Is the p-value distribution in a discrete case uniform?
It is a necessary condition for the p-value distribution to be uniform! But hey, not all is lost for the discrete case. As you increase the parameter of the discrete distribution of , the distribution of the p-value itself, becomes more and more uniform (just like the lower-right plot).
Why are p-values calculated from a normal distribution?
The reason is that the p-values are calculated based on the standard normal distribution yet the sample comes from a normal distribution with mean of 0 and a standard deviation of 3. This will result into many more points in the tails than it would be for a sample coming from the standard normal distribution.