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The dependent-samples $$t$$-test can be conceptually understood as a specialized application of the one-sample $$t$$-test. The critical step linking the two statistical procedures is the conversion of each participant's paired measurements into a single difference score. Once this mathematical reduction is complete, the paired data forms a single distribution. The analysis then proceeds exactly like a one-sample $$t$$-test performed directly on these difference scores, where the sample mean difference is evaluated against a hypothetical population mean ($$\mu_0$$) of $$0$$, representing the baseline expectation of no overall change or effect between the two measured conditions.

Conceptualizing the Dependent-Samples t-Test as a One-Sample t-Test

When conceptualizing a dependent-samples t-test as a one-sample t-test on difference scores, the sample mean difference is evaluated against a hypothetical population mean of ____.

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