Explain the relationship between sample size requirements and target statistical power for an independent-samples -test when assuming a large population effect. In your explanation, detail how the required sample size per group changes as the researcher seeks to increase power from to , and explain why sample sizes in psychological research must generally be larger than researchers might intuitively expect to achieve high power.
Question: Explain the relationship between sample size requirements and target statistical power for an independent-samples -test when assuming a large population effect. In your explanation, detail how the required sample size per group changes as the researcher seeks to increase power from to , and explain why sample sizes in psychological research must generally be larger than researchers might intuitively expect to achieve high power.
Sample answer: To achieve high statistical power, sample sizes must be larger than often realized. For an independent-samples -test with a large population effect, a researcher requires approximately participants per sample to reach a power of . To increase that power to a high level of , the required sample size increases to participants per sample. This demonstrates that obtaining very high statistical power requires a substantial increase in sample size (more than doubling the participants per group), which highlights that researchers cannot simply rely on small samples even when expecting a large effect in the population.
Key points:
- Reaching a statistical power of requires approximately participants per sample.
- Reaching a statistical power of requires approximately participants per sample.
- Increasing statistical power from to requires more than doubling the group sample size.
- High statistical power generally demands sample sizes that are larger than researchers often realize, even with a large population effect.
Rubric: To receive full credit, the answer must accurately state that participants per sample are needed for power and participants per sample are needed for power. It must also explain that increasing power requires a non-linear, more than double increase in sample size per group, and explain the general principle that high statistical power requires larger sample sizes than researchers typically realize.
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