Understanding the p-value Distribution when the Null Hypothesis is True: Exploring Uniformity and Implications

P- value Distribution when Ho is true

When the null hypothesis (Ho) is true, the p-value distribution follows a uniform distribution

When the null hypothesis (Ho) is true, the p-value distribution follows a uniform distribution. This means that all values between 0 and 1 are equally likely to be observed as the p-value.

In hypothesis testing, the p-value is the probability of obtaining a test statistic as extreme as, or more extreme than, the one observed, assuming the null hypothesis is true. Since the null hypothesis assumes no effect or difference between groups, when it is true, any observed differences are due to random chance.

Let’s consider an example to understand the p-value distribution when Ho is true. Suppose we are conducting a two-sample t-test to compare the mean scores of two groups, A and B. The null hypothesis states that the means of both groups are equal.

If the null hypothesis is true, any observed difference in the means is simply due to random sampling variability. The p-value in this case is a measure of how likely it is to observe a difference as extreme as, or more extreme than, the one we obtained, assuming the null hypothesis is true.

If we were to repeat the study multiple times under the assumption that the null hypothesis is true, and calculate the p-value every time, we would find that the p-values follow a uniform distribution.

This means that any value between 0 and 1 is equally likely to be observed as the p-value, as long as the null hypothesis is true. In other words, the p-value can take on any value between 0 and 1 with equal probability.

It is important to note that this uniform distribution of p-values under the null hypothesis assumes that the assumptions of the statistical test are met, including the assumptions of normality and independence. If these assumptions are violated, the p-value distribution may be affected.

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