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What is the difference between a test statistic and a critical value?

Updated: 10/31/2022

Wiki User

10y ago

A test statistic is a value calculated from a set of observations.

A critical value depends on a null hypothesis about the distribution of the variable and the degree of certainty required from the test. Given a null hypothesis it may be possible to calculate the distribution of the test statistic. Then, given an alternative hypothesis, it is may be possible to calculate the probability of the test statistic taking the observed (or more extreme) value under the null hypothesis and the alternative. Finally, you need the degree of certainty required from the test and this will determine the value such that if the test statistic is more extreme than the critical value, it is unlikely that the observations are consistent with the hypothesis so it must be rejected in favour of the alternative hypothesis.

It may not always be possible to calculate the distribution function for the variable.

Wiki User

10y ago