## 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.

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• Last Updated Apr 22, 2021
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