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Conceptualizing the Dependent-Samples t-Test as a One-Sample t-Test
The dependent-samples -test can be conceptually understood as a specialized application of the one-sample -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 -test performed directly on these difference scores, where the sample mean difference is evaluated against a hypothetical population mean () of , representing the baseline expectation of no overall change or effect between the two measured conditions.
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Research Methods in Psychology - 4th American Edition @ KPU
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Null and Alternative Hypotheses for the Dependent-Samples t-Test
Conceptualizing the Dependent-Samples t-Test as a One-Sample t-Test
How is a difference score calculated in the initial step of a dependent-samples t-test?
A researcher conducts a study measuring participants' stress levels before and after a mindfulness workshop. When computing a difference score for each participant, the researcher subtracts the pretest score from the posttest score for the first 15 participants but then switches to subtracting the posttest score from the pretest score for the remaining 15 participants. This approach is acceptable because both subtraction directions are valid ways to compute difference scores.