Assignment
2: Power
Due Feb.
15(A2&B2) & Feb.17(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.
1) You are
conducting a between-subjects test with an n of 15, Population Mean A = 50 and
Population Mean B = 36. The standard
deviation is 21.
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 15, Population Mean A = 50 and
Population Mean B = 43. The standard
deviation is 21.
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 15, Population Mean A = 5 and
Population Mean B = 2. The standard
deviation is 9.
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 does this tell you about the
relationship between the number of participants required in an experiment and
effect size? (3 marks)
9) What is
the relationship between power and sample size? (2 marks)
10) Would you
expect the Type II error to be greater in a study with 20 participants or 100
participants (assuming all other things are equal)? Explain your reasoning. (2 marks)
11) Assume
that you have an effect size of 0.6. How
many participants would you need to have power of .95 in a within-subjects
experiment with:
a. rho = 0? (1 mark)
b. rho = 0.5? (1 mark)
c. rho = 0.9? (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 =
32, Pop Mean A = 67, Pop Mean B = 54, rho = 0, sd = 26. 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) Your
little brother just brought home his report card and he received a grade of 45%
in reading. It is clear that he is
having trouble and you decide to look into programs that will help him improve
his reading. You request information
from two different reading programs. One
program, Reading is Fun, sends you information regarding the effectiveness of
their program. You also receive
information regarding the effectiveness of a new program on the market, Phonix. Both
programs conducted stats on the pre-program and post-program performance, in
the form of a t-test examining % grade improvement in reading, and have
provided the p values from their respective tests. The information you obtained
is listed below.
n = 3560 n
= 15
sd = 20 sd = 20
effect size =
0.12 effect
size = 0.85
p = .001 p = .035
What would your little brother’s final reading grade
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 little
brother (assume the programs cost the same amount)? Explain your reasoning. (2 marks)