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In null hypothesis testing, alpha ($$\alpha$$) is the predetermined criterion used to decide how low a $$p$$ value must be before a sample result is considered unlikely enough to reject the null hypothesis. It is almost always set to $$.05$$. This means that if there is a $$5\%$$ chance or less of observing a result at least as extreme as the sample result when the null hypothesis is true, researchers will reject the null hypothesis.

Alpha (Level of Significance)

When a $$p$$ value is greater than the alpha criterion ($$>.05$$), researchers retain the null hypothesis, concluding there is not enough evidence to reject it. Importantly, retaining the null hypothesis is not the same as proving it is true; it simply means the data does not provide sufficient evidence to support the alternative hypothesis. Consequently, researchers use terminology like 'fail to reject the null hypothesis' or 'retain the null hypothesis,' but they never state that they 'accept' the null hypothesis.

Retaining the Null Hypothesis

There is an inherent inverse relationship between the probability of committing a Type I error and a Type II error. If researchers attempt to reduce Type I errors by setting a stricter alpha level (e.g., $$.01$$), they make it harder to reject true null hypotheses, but they inadvertently make it harder to reject false ones, thereby increasing the risk of Type II errors. Conversely, raising the alpha level (e.g., $$.10$$) reduces Type II errors but increases Type I errors. The standard alpha level of $$.05$$ serves as a conventional balance to keep both error rates acceptable.

Trade-off Between Type I and Type II Errors

A Type I error is a false positive in null hypothesis testing. It occurs when a researcher mistakenly concludes that their results are statistically significant—thereby rejecting the null hypothesis—when, in reality, the null hypothesis is true and there is no actual relationship in the population. These errors happen because random sampling error can occasionally produce extreme results even when no true effect exists. The predetermined alpha level dictates the probability of committing this error when the null hypothesis is true.

Type I Error

In null hypothesis testing, the predetermined criterion used to decide how low a $$p$$ value must be before a sample result is considered unlikely enough to reject the null hypothesis is called ____.

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