Stat 101B – Professor Esfandiari
Homework Two – Summer 21

Question one. Suppose that you are hired to offer a sampling plan for the study described below.
Answer questions 1 to 4.

A doctor wants to examine the effectiveness of a new medication on lowering blood pressure.
120 males in the fifty to seventy five age range volunteer to participate in the study. Assume that
half of the participants are older than 60.He is planning to create two experimental and one
control group. The two experimental groups will be taking 5mg and 10mg of the new medication
and the control group will be taking a sugar pill.

The researcher is also interested in finding out if the effect of the medication varies with age.

1) What steps will you take to divide the volunteers into the relevant groups.
2) Draw a schematic of the design, show the main effects as well as any interaction effect.
3) Write the equation for the linear model.
4) Show all the relevant means and how each component of the proposed linear model can
be estimated using sample means.
5) What is the formula for calculating sum of square of total for this study.

Example: The following is the schematic of a two-sample test of the mean

Experimental group Control group
1 1
2 2
. .
n n
Mean of experimental = "." Mean of control = ".#

Linear model (i stands for subject and j stands for the group)
$% = % + $%
".. = grand mean
% = ".& ? ".. $% = $%'".%








Question two.

Using diversity data, Conduct a two way anova and examine the effect of UCLA
climate(uclaclimate) and perception of discrimination (ucladiscp) on the students’ perception of
exclusion (uclaexclusionaryp).

For uclaclimate
a) Delete very uncomfortable and uncomfortable as sample sizes are too small compared to
other categories. Recode “very comfortable” to “excellent”, “comfortable” to “good” and
“somewhat comfortable” to “ok”. Make “OK” the base.

For perception of discrimination (ucladiscp)

b) Cut ucladiscp into two categories including (low = below median) and high (above
median)

c) Create a contingency table for discrimination by uclaclimate to make sure the frequency
within each cell is acceptable.

d) Run the model. Include the output.

e) Write the null and alternative hypotheses in symbols.

f) Write the research question and the conclusion you draw within context.

g) Create the interaction plot. Place campus climate on the on the X-axis, mean of
uclaexclusionaryp on the Y-axis and create two lines for discrimination.

In addition to the R commands given to you on cfu two way anova for drawing the
interaction plot, you can use the following command.

Interaction.plot(uclaclimate,discrimination,uclaexclusionaryp)

h) Make the table of means for ucla climate by discrimination.
i) Conduct post-hocs as needed and interpret the results within context.
j) Conduct test of simple main effects and report the results.
k) Interpret the interaction plot using the results you obtained from the test of simple main
effects.








Question three.
a) Calculate ^( for campus climate, discrimination, and their combined effect.
b) Add all three effect sizes and let the sum be the effect size.
c) Use the effect size you found in part b to complete the following table


Effect size Alpha Power What is sample size
This is what you found 0.05 Power = 0.90
This is what you found 0.01 Power = 0.90
This is what you found 0.05 Power = 0.95
This is what you found 0.01 Power = 0.95
Divide the effect size in half 0.05 Power = 0.90
Divide the effect size in half 0.01 Power = 0.90
Divide the effect size in half 0.05 Power = 0.95
Divide the effect size in half 0.01 Power = 0.95

What do you conclude about the relationship of alpha and power with sample size for a fixe
value of effect size

Effect size Alpha Sample size What is power
This is what you found 0.05 100
This is what you found 0.05 300
This is what you found 0.05 500
Divide the effect size in half 0.05 100
Divide the effect size in half 0.05 300
Divide the effect size in half 0.05 500

From the above, what do you learn about the relationship between…

a) Sample size and power
b) Effect size and power
c) Alpha and power