Q. How do I interpret the output from a hypothesis test?
There are two important outputs from a hypothesis test: the test statistic and the p-value. Both can be used to evaluate the results of the hypothesis test.
A test statistic is a value calculated from the sample. It is standardized so that it can be compared to a known point, or “critical value”, on a sampling distribution. For example, in large sample tests we often standardize the test statistic to follow a standard normal distribution.
The critical value depends on the sampling distribution and the significance level \(\alpha\). If the test statistic is more extreme than the critical value, you reject the null hypothesis. In the graph below depicting a right-tailed hypothesis test, the test statistic would be more extreme than the critical value if it fell in the red region.
The other approach is to use a p-value. A p-value is the probability of observing a more extreme test statistic under the null hypothesis. If the p-value is less than the significance level, you reject the null hypothesis. In other words, smaller p-values signify stronger evidence against the null hypothesis. In practice, p-values are easier because they don’t require finding a critical value.