What is a test statistic?

A test statistic is a standardized value that is calculated from sample data during a hypothesis test. You can use test statistics to determine whether to reject the null hypothesis. The test statistic compares your data with what is expected under the null hypothesis. The test statistic is used to calculate the p-value. When the data show strong evidence against the assumptions in the null hypothesis, the magnitude of the test statistic becomes large and the test's p-value can become small enough to reject the null hypothesis.

For example, the test statistic for a Z-test is the Z-value. Suppose you perform a two-tailed Z-test with an α of 0.05, and obtain a Z-value of 2.5. This Z-value corresponds to a p-value of 0.0124. Because this p-value is less than α, you declare statistical significance and reject the null hypothesis.

Different hypothesis tests use different test statistics based on the probability model assumed in the null hypothesis. Common tests and their test statistics include:

Hypothesis test Test statistic
Z-test Z-value
t-tests t-value
ANOVA F-value
Chi-square tests Chi-square

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