STATISTICS 402 - Assignment 5
Due March 9, 2015
1. An experiment will be performed on individuals with elevated serum cholesterol. We
want to see if the type of drug (Lipitor® or Zocor®) has an effect on the change in
serum cholesterol (serum cholesterol level before treatment – serum cholesterol level
after three months of treatment). A second factor, the amount of drug (0 mg/day, 10
mg/day and 20 mg/day), will also be investigated in a two factor completely
randomized experiment.
a) What is the response?
b) What are the experimental units?
c) The experimenter will use factorial crossing to create the treatment combinations.
How many treatment combinations will there be in the experiment? List all the
treatment combinations.
d) The experimenter would like to be able to detect a difference in treatment
population means of 1.4 standard deviations with Alpha = 0.05 and Beta = 0.10.
How many experimental units will the experimenter need?
e) With this number of units, what size difference in factor level population means
can be detected when Alpha=0.05 and Beta=0.10?
f) Because of budget constraints, only 6 units are available for each treatment
combination. How does this choice affect the size of the detectable difference in
treatment population means? in factor level population means? Use Alpha=0.10
and Beta=0.10.
g) Explain how you would randomly assign treatments to the experimental units.
Include a table that indicates the random assignment of treatments for this
experiment to experimental units. Remember the budget constraints in f).
2. An experiment is performed by researchers in kinesiology on the effects of step
height and stepping frequency on the change in heart rate. Forty eight individuals are
recruited from students majoring in kinesiology. They all give their consent to
participate in the experiment. Each individual is asked to step up onto a platform and
step down repeatedly. The height of the platform will be either 15 cm or 30 cm. The
rate at which a participant steps will be 14, 21, 28 or 35 steps per minute. A
combination of platform height and stepping frequency will be assigned to each
participant completely at random so that 6 participants are assigned each
combination. Participants step up and down off the platform for 5 minutes. The
change in heart rate (heart rate after stepping – heart rate before stepping) is
calculated for each participant.
a) What is the response?
b) What are the conditions?
c) How many treatments are there?
d) What are the experimental units?
e) What is an outside variable that is controlled in this experiment?
f) What is an outside variable that is not controlled in this experiment?
g) Describe, in some detail, what contributes to chance, random, error variation in
this experiment.
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h) Give the full model describing the relationship between the response, conditions
and random error. Be sure to define all the terms in the model within the context
of the problem.
A JMP data table is posted on the course website. Use JMP to analyze the data.
i) Estimate the treatment effects.
j) Test the hypothesis that all the treatment effects are zero against the alternative
that at least one is not zero. Be sure to give an appropriate null and alternative
hypothesis. Report the value of the appropriate test statistic, P-value, decision,
reason for the decision and a conclusion within the context of the problem.
k) Estimate the step height effects.
l) Test the hypothesis that the effects of step height are zero against the alternative
that at least one is not zero. Be sure to give an appropriate null and alternative
hypothesis using the notation from your answer to h). Report the value of the
appropriate test statistic, P-value, decision, reason for the decision and a
conclusion within the context of the problem.
m) Where are the statistically significant differences in step height sample means?
Support you answer statistically.
n) Estimate the stepping frequency effects.
o) Test the hypothesis that all the stepping frequency effects are zero against the
alternative that at least one is not zero. Be sure to give an appropriate null and
alternative hypothesis using the notation from your answer to h). Report the value
of the appropriate test statistic, P-value, decision, reason for the decision and a
conclusion within the context of the problem.
p) Where are the statistically significant differences in stepping frequency sample
means? Support you answer statistically.
q) Are there any interaction effects that are different from zero? Be sure to give an
appropriate null and alternative hypothesis using the notation from your answer to
h). Report the value of the appropriate test statistic, P-value, decision, reason for
the decision and a conclusion within the context of the problem.
r) Construct an interaction plot. Comment on the plot and what it tells you about the
interaction between the two factors. Be specific and be sure your answer deals
with the context of this experiment.
s) Based on the analysis of these data, what combination of step height and stepping
frequency would you recommend if someone wanted to increase their heart rate
the most?
t) Construct plots of residuals versus the levels of the two factors. Describe the plots
and indicate what this tells you about the Fisher conditions necessary for the
analysis of variance.
u) Construct plots of the distribution of residuals. Describe each of the plots in the
distribution of residuals. Indicate what this tells you about the Fisher conditions
necessary for the analysis of variance.
Turn in the JMP output that you have used to answer the questions.
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