Based on the researcher's approach, explain how the dependent-samples design is being conceptualized as a one-sample -test. Specifically, explain what happens to the paired data structure and what the null hypothesis expectation of a population mean () of represents in the context of this meditation study.
Case context: A health psychologist is conducting a study to examine the effect of a new meditation app on participants' daily stress levels. She measures the daily stress levels (on a scale from 0 to 50) of 20 participants at baseline (before using the app) and again after two weeks of daily app usage. To analyze whether there is a change, she subtracts the post-test score from the pre-test score for each participant to obtain a set of difference scores, intending to run a one-sample -test on these difference scores.
Question: Based on the researcher's approach, explain how the dependent-samples design is being conceptualized as a one-sample -test. Specifically, explain what happens to the paired data structure and what the null hypothesis expectation of a population mean () of represents in the context of this meditation study.
Sample answer: By converting each participant's pre-test and post-test stress scores into a single difference score, the researcher mathematically reduces the paired data structure into a single distribution of difference scores. The analysis then proceeds exactly like a one-sample -test on these scores. Testing the sample mean difference against a hypothetical population mean () of represents the baseline expectation that using the meditation app has no overall effect or causes no change in stress levels between baseline and the two-week follow-up.
Key points:
- Paired measurements are reduced to a single distribution of difference scores.
- The analysis is conducted as a one-sample -test on the difference scores.
- The population mean () is set to .
- The value of represents the baseline expectation of no change or effect in stress levels.
Rubric: The response should be evaluated on the following criteria: 1. Explains that converting to difference scores collapses/reduces paired measurements into a single distribution. 2. States that the analysis is a one-sample t-test performed on these difference scores. 3. Explains that the population mean of 0 represents the null or baseline expectation that the app has no effect or causes no change in stress levels.
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Research Methods in Psychology - 4th American Edition @ KPU
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