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The formal process of null hypothesis testing relies on a specific sequence of logical steps to decide between interpretations of a statistical relationship. First, researchers temporarily assume that the null hypothesis is true (i.e., there is no relationship in the population). Second, they determine the probability of obtaining their sample relationship under this assumption. Finally, if the sample result is extremely unlikely given a true null hypothesis, they reject the null hypothesis in favor of the alternative hypothesis; if the result is not extremely unlikely, they retain the null hypothesis.

General Logic of Null Hypothesis Testing

The logic of null hypothesis testing can be applied to real research scenarios. For example, if researchers find a very small difference in talkativeness between men and women ($$d = 0.06$$), they would determine this result is fairly likely even if there were no true difference in the population, leading them to retain the null hypothesis. Conversely, if researchers find a strong correlation ($$r = +.60$$) between daily hassles and stress symptoms, they would determine this sample result is highly unlikely if there were no true relationship, leading them to reject the null hypothesis in favor of the alternative.

Examples of Null Hypothesis Testing Decisions

In the logic of null hypothesis testing, researchers reject the null hypothesis in favor of the alternative hypothesis if they determine that the observed sample relationship would be extremely unlikely to occur if the null hypothesis were actually true. This formal decision indicates that the sample data provides sufficient statistical evidence to conclude that a genuine relationship exists within the broader population.

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