Q7. Suppose a researcher wants to assess whether age of a person determines thei
ID: 3298009 • Letter: Q
Question
Q7. Suppose a researcher wants to assess whether age of a person determines their marital status. The researcher randomly sampled 200 respondents who belonged to one of the following five mutual exclusive categories by marital status-not married, married, separated, divorced or widowed. The researcher desires to have an effect size of 0.75. The researcher wants to determine the statistical power of the study. Answer the following questions based on the above problem:
Calculate the statistical power of the research study (You need to use G-power for your calculation). Show all the calculations- 2 points
Interpret your results- 1 point
What would be the power of the research study if sample size is reduced to 100?-
2 points
Compare & interpret the statistical power when sample size is 200 versus when it is 100- 2 points
Explanation / Answer
Answer:
Q7. Suppose a researcher wants to assess whether age of a person determines their marital status. The researcher randomly sampled 200 respondents who belonged to one of the following five mutual exclusive categories by marital status-not married, married, separated, divorced or widowed. The researcher desires to have an effect size of 0.75. The researcher wants to determine the statistical power of the study. Answer the following questions based on the above problem:
Calculate the statistical power of the research study (You need to use G-power for your calculation). Show all the calculations- 2 points
F tests - ANOVA: Fixed effects, omnibus, one-way
Analysis: Post hoc: Compute achieved power
Input: Effect size f = 0.75
err prob = 0.05
Total sample size = 200
Number of groups = 5
Output: Noncentrality parameter = 112.5
Critical F = 2.4179625
Numerator df = 4
Denominator df = 195
Power (1- err prob) = 1.0000000
Interpret your results- 1 point
The test has maximum power to detect the mean difference between the groups when sample size is 200.
What would be the power of the research study if sample size is reduced to 100?-
F tests - ANOVA: Fixed effects, omnibus, one-way
Analysis: Post hoc: Compute achieved power
Input: Effect size f = 0.75
err prob = 0.05
Total sample size = 100
Number of groups = 5
Output: Noncentrality parameter = 56.2500000
Critical F = 2.4674936
Numerator df = 4
Denominator df = 95
Power (1- err prob) = 0.9999972
Compare & interpret the statistical power when sample size is 200 versus when it is 100- 2 points
The test has high power to detect the mean difference between the groups when sample size is 100. Even the sample is reduced to 100, the test has high power( power= 0.9999972) compared to sample size of 200 (power = 1.0).
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