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When conducting a one-sample $$t$$-test, the degrees of freedom ($$df$$) are calculated by subtracting one from the total sample size ($$N - 1$$). This specific calculation dictates the exact shape of the $$t$$ distribution, enabling researchers to accurately identify the $$p$$ value associated with their test statistic.

Degrees of Freedom (One-Sample t-Test)

A critical value is a predetermined threshold on a statistical distribution used to make a decision about the null hypothesis. Derived from the specified alpha level (such as $$\alpha = 0.05$$) and the degrees of freedom, it marks the boundary of the most extreme expected scores. If a calculated test statistic falls beyond this critical value, the result is deemed statistically significant, leading to the rejection of the null hypothesis.

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