Assignment 2: Power

Due Feb. 13(A2&B2) & Feb. 15(C2)

TO BE COMPLETED INDIVIDUALLY

For this assignment, you will use the simulation site (http://www.ruf.rice.edu/~lane/stat_sim/index.html) you used for Assignment 1. For each of the following questions, use the Simulate 5000 button.

1) You are conducting a between-subjects test with an n of 24, Population Mean A = 553 and Population Mean B = 538. The standard deviation is 45.

a. Calculate the effect size of these data (show your work). (2 marks)

b. What is your Type II error rate (show your work)? (2 marks)

2) You are conducting a between-subjects test with an n of 24, Population Mean A = 553 and Population Mean B = 523. The standard deviation is 45.

a. Calculate the effect size of these data (show your work). (2 marks)

b. What is your Type II error rate (show your work)? (2 marks)

3) Compare the results that you obtained for questions 1 and 2. What is the relationship between effect size and power? (2 marks)

4) You are conducting a between-subjects test with an n of 24, Population Mean A = 8 and Population Mean B = 6. The standard deviation is 3.

a. Calculate the effect size of these data (show your work). (2 marks)

b. What is your Type II error rate (show your work)? (2 marks)

5) Now assume that you have an effect size of 1. How many participants (approx.) would you need to have power of .95 in a between-subjects experiment? (1 mark)

6) Assume that you have an effect size of 0.7. How many participants (approx.) would you need to have power of .95 in a between-subjects experiment? (1 mark)

7) Assume that you have an effect size of 0.3. How many participants (approx.) would you need to have power of .95 in a between-subjects experiment? (1 mark)

8) Compare the number of participants you needed in questions 5, 6 and 7. What do these results tell you about the relationship between effect size and the number of participants required in an experiment to have the desired power? (2 marks)

9) What is the relationship between sample size and power? (2 marks)

10) Would you expect the Type II error to be greater in a study with 30 participants or 150 participants (assuming all other things are equal)? Explain your reasoning. (2 marks)

11) Assume that you have an effect size of 0.60. How many participants would you need to have power of .95 in a within-subjects experiment with:

a. rho = 0? (1 mark)

b. rho = 0.4? (1 mark)

c. rho = 0.9? (1 mark)

12) Compare the number of participants you needed in 11 a), b) and c). What do these results tell you about the relationship between rho and the number of participants required in an experiment to have the desired power? (2 marks)

13) What is the relationship between rho and power? (2 marks)

14) In general, would you expect a within-subjects design or a between-subjects design to be more powerful? Explain your reasoning. (2 marks)

15) Enter the following information into the appropriate spaces on the simulation page: n = 50, Pop Mean A = 148, Pop Mean B = 122, rho = 0, sd = 52. What is the effect size (show your calculation)? Now conduct both a between-subject simulation and a within-subject simulation. Which test is more powerful? Why? (3 marks)

16) Now imagine that you only have access to a total of 12 participants. You can do one of two things, use a between-subjects design and randomly assign them to one of two conditions (n= 6) or you can use a within-subjects design. Enter the following information into the appropriate spaces on the simulation page: Pop Mean A = 148, Pop Mean B = 122, rho = 0, sd = 52. Conduct both a between-subject simulation and a within-subject simulation. Which design would be more powerful under these circumstances of limited participation and why? (3 marks)

17) A special education teacher was attempting to determine an appropriate program for children with attention deficit disorder. She found some journal articles on the topic. One article reported results from a study implementing a drug intervention program involving 3950 students with attention deficit disorder. A second article reported the results of a study that used a behaviour modification program with 30 attention deficit disorder students. In both studies, attentiveness was measured in each child before and after the program was implemented; the same standardized measure was used in both studies. Higher attentiveness scores were associated with better behaviour in class. Both studies used a t-test to analyze their data. The t-tests examining the improvement in attentiveness scores between pre-program and post-program (including p values) and other important information for each study are listed below.

Drug Intervention Behavioural Modification

n = 3950 n = 30

sd = 32 sd = 32

effect size = 0.20 effect size = 0.80

p = .001 p = .03

If the special education teacher had an attention deficit child who scored 22 on the attentiveness measure before the program was implemented, what would the child’s final attentiveness score be after the implementation of each program, assuming his improvements were typical or average (show your calculations)? (4 marks)

If you were the special education teacher, which program would you select for your attention deficit students? Explain your reasoning. (2 marks)