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To illustrate a one-tailed test, consider a scenario with $$24$$ degrees of freedom where the researcher sets the alpha level at $$.05$$. Depending on their pre-registered directional hypothesis, the researcher uses only a single critical value: either $$-1.711$$ if predicting a lower sample mean, or $$1.711$$ if predicting a higher sample mean (represented by green vertical lines in the accompanying distribution). By redefining 'extreme' to refer to only one tail of the distribution, the critical value becomes less severe, making it easier to reject the null hypothesis if the result falls in the expected direction. However, if the sample mean differs in the unexpected direction, the null hypothesis cannot be rejected at all, regardless of the effect size.

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