### Statistics 2

1. How large a sample was needed for the Voss et al. (2004) study according to the power analysis? Was this the minimum sample size needed for the study or did the researchers allow for sample mortality? Answer: After conducting a power analysis, the researchers planned a sample size of 96 patients for their study. The 96 subjects allowed for 30 subjects per group for the three study groups plus 6 subjects for sample mortality or attrition. 2. What was the sample size for the Voss et al. (2004) study? Was this sample size adequate for this study? Provide a rationale for your answer.

Answer: The sample size for this study was N = 62. The power analysis indicated that a sample of 96 was needed and the 62 subjects in the sample were less than was projected by the power analysis. However, preliminary analyses after the 62 patients were enrolled revealed significant groups differences. Since significant group differences were found, then the sample size was adequate and no Type II error occurred of saying the groups were not significantly different when they were. 3. What effect size was used in conducting the power analysis for this study?

What effect size was found during data analysis and how did this effect the sample size needed for this study? Answer: A moderate effect size of 0. 33 was used to conduct the power analysis. During data analysis, the researchers indicated that significant group differences and large effect sizes were found for anxiety, pain sensation, and pain distress. Since a large effect size was found during data analysis, the sample size of 62 was adequate to detect significant group differences versus the 96 projected in the power analysis.

The larger the effect size, the smaller the sample needed to detect group differences. 4. What power was used to conduct the power analysis in the Voss et al. (2004) study? What amount of error exists with this power level? Provide a rationale for your answer. Answer: The researchers set the power at the standard 0. 8 or 80%. This is considered the minimum acceptable power to use in conducting a study. When power is set at 80%, then the possible error is 0. 0 or 20% or 100% – 80% = 20%. 5. If researchers set the power at 90% to conduct their power analysis, would there be less or more chance of a Type II error, than setting the power at 80%? Provide a rationale for your answer. Answer: If the researchers set the power at 90%, there is less of a chance for a Type II error than if they set the power at 80%. At a power of 90%, the chance of error is 10% or 100% – 90% = 10%. A power of 80% has a 20% chance or error or 100% – 80% = 20%.