Which statement about null hypotheses and p-values is correct?

Which statement about null hypotheses and p-values is correct?

• A. The null hypothesis states no effect or difference; the p-value measures the probability of observed results under the null.
• B. The null hypothesis states there is an effect or difference; the p-value measures the likelihood of the data under the observed alternative.
• C. The null hypothesis states there is an effect; the p-value is the effect size.
• D. The null hypothesis is never tested; p-values are used only for confidence intervals.

Answer: (B)

The main idea here is how a null hypothesis and a p-value work together in hypothesis testing. The null hypothesis usually asserts that there is no effect or no difference between groups. The p-value then tells us how likely it would be to see data as extreme as what we observed if that null were true. In other words, it’s a probability calculated under the assumption that the null is correct, not under the alternative. A small p-value suggests the observed result would be unlikely under the null, which is why researchers often reject the null at a chosen significance level. A large p-value means the data are quite compatible with the null, so there isn’t strong evidence against it. It’s important to note that the p-value does not measure the probability that the null hypothesis is true, nor does it quantify the size of the effect. It reflects compatibility with the null given the observed data. So the statement that the null hypothesis states there is an effect and that the p-value measures likelihood under the observed alternative misconstrues the roles. The correct idea is that the null posits no effect, and the p-value assesses how surprising the data would be if that no-effect scenario were true.

The main idea here is how a null hypothesis and a p-value work together in hypothesis testing. The null hypothesis usually asserts that there is no effect or no difference between groups. The p-value then tells us how likely it would be to see data as extreme as what we observed if that null were true. In other words, it’s a probability calculated under the assumption that the null is correct, not under the alternative.

A small p-value suggests the observed result would be unlikely under the null, which is why researchers often reject the null at a chosen significance level. A large p-value means the data are quite compatible with the null, so there isn’t strong evidence against it. It’s important to note that the p-value does not measure the probability that the null hypothesis is true, nor does it quantify the size of the effect. It reflects compatibility with the null given the observed data.

So the statement that the null hypothesis states there is an effect and that the p-value measures likelihood under the observed alternative misconstrues the roles. The correct idea is that the null posits no effect, and the p-value assesses how surprising the data would be if that no-effect scenario were true.