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### 5.3 Hypothesis Testing

One of the most fundamental purposes of statistical analysis is hypothesis testing. Researchers commonly need to test hypotheses about a set of data. For example, she might want to test whether one set of data comes from the same distribution as another, or whether the mean of a dataset significantly differs from a particular value. This section presents just some of the possible tests that PSPP offers.

The researcher starts by making a null hypothesis. Often this is a hypothesis which he suspects to be false. For example, if he suspects that A is greater than B he will state the null hypothesis as A = B.2

The p-value is a recurring concept in hypothesis testing. It is the highest acceptable probability that the evidence implying a null hypothesis is false, could have been obtained when the null hypothesis is in fact true. Note that this is not the same as “the probability of making an error” nor is it the same as “the probability of rejecting a hypothesis when it is true”.

### (2)

This example assumes that it is already proven that B is not greater than A.