Assignment
2: Power
Due Feb. 14(A2&B2)
& Feb. 16(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 18, Population Mean A = 175 and
Population Mean B = 151. The standard
deviation is 48.
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 18, Population Mean A = 175 and
Population Mean B = 163. The standard
deviation is 48.
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 18, Population Mean A = 6 and
Population Mean B = 5. The standard
deviation is 4.
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 0.6. 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 0.2. 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 does this 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 20 participants or 75
participants (assuming all other things are equal)? Explain your reasoning. (2 marks)
11) Assume
that you have an effect size of 0.75.
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 = 0.8? (1 mark)
12) What is the
relationship between rho and power? (2 marks)
13) In
general, would you expect a within-subjects design or a between-subjects design
to be more powerful? Explain your
reasoning. (2 marks)
14) Enter the
following information into the appropriate spaces on the simulation page: N = 40,
Pop Mean A = 915, Pop Mean B = 879, rho = 0, sd = 54. 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)
15) 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 = 915, Pop Mean B = 879, rho = 0, sd
= 54. 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)
16) Your
father has high blood pressure and the doctor said that he needs to lose weight
because he is a great risk for a heart attack.
You decide to look into diet programs that will help him lose the weight. You request information from two different weight
loss programs. One program, Julie Craig,
sends you information regarding the effectiveness of their program. You also receive information regarding the
effectiveness of a new diet program on the market, the
n = 25 n = 4523
sd = 40 sd = 40
effect size = 0.75 effect size =
0.10
p = .04 p
= .001
If your father’s weight was 260 pounds before
the program started, what would your father’s final weight be after the
implementation of each program, assuming his improvements were typical or
average (show your calculations)? (4
marks)
Which program would you select for your father
(assume the programs cost the same amount)?
Explain your reasoning. (2 marks)