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Diagnose the researcher's misunderstanding regarding the relationship between statistical significance and effect size. Based on the provided context, justify why reporting Cohen's is necessary in this scenario and explain what the calculated value of reveals about the program's practical impact.
Case context: A research group evaluates a new anxiety-reduction program using two independent samples of participants (total ). They perform a null hypothesis significance test and find a statistically significant difference between the treatment and control group means (). However, the absolute difference between the group means is extremely small relative to the variability, resulting in a calculated Cohen's of . One researcher suggests they do not need to report Cohen's because the significant -value already proves the program has a strong effect.
Question: Diagnose the researcher's misunderstanding regarding the relationship between statistical significance and effect size. Based on the provided context, justify why reporting Cohen's is necessary in this scenario and explain what the calculated value of reveals about the program's practical impact.
Sample answer: The researcher is incorrect because statistical significance () only indicates that the observed difference is unlikely to be due to chance, but with a large sample size (), even a trivial difference can be statistically significant. Reporting Cohen's is necessary because it quantifies the actual magnitude of the effect. A Cohen's of reveals that the standardized difference between the means is extremely small, meaning the program has a very weak relationship strength and negligible practical impact, despite being statistically significant.
Key points:
- Identifies the error: statistical significance (-value) does not measure the actual magnitude of an effect.
- Explains that a large sample size () can yield a significant -value even when the actual difference is minimal.
- Explains that Cohen's is necessary to show the standardized difference or strength of the relationship.
- Interprets Cohen's as indicating an extremely small magnitude or weak relationship, demonstrating low practical impact.
Rubric: Students should identify that statistical significance does not measure effect magnitude, explain that large sample sizes can lead to significant results for tiny differences, and use the Cohen's value of to explain that the program's practical effect is very small.
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Research Methods in Psychology - 4th American Edition @ KPU
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