STATISTICS 402 - Assignment 4
Due March 5, 2007
1. In an attempt to find an effective treatment for the ingestion of a fast acting
deadly poison, chemists have come up with a potential antidote. An experiment is
to be performed with three different exposures to the poison (1-Low, 2-Medium,
and 3-High). Additionally, four different amounts, relative to body weight, of the
antidote will be administered 0.5 mg/g, 1 mg/g, 1.5 mg/g, and 2 mg/g. The
experiment will be performed on mice. The mice will all be of the same age and
approximately the same size. The mice will be exposed to the poison and given
the antidote and there survival time (hours) will be recorded.
a) Identify the response, conditions and experimental units.
b) Give an example of an outside variable that is controlled in the study. How is
it controlled?
c) How many treatment combinations are there? List all the treatment
combinations.
d) If the experimenter wishes to detect a difference in means for the three poison
exposure levels as small as 0.9 standard deviations with Alpha=0.05 and
Beta=0.05, how many mice are needed?
e) With the number of mice you found in c), how small a difference in means for
the four amounts of the antidote can be found with Alpha=0.05 and
Beta=0.10?
f) The experimenter is only able to use 4 mice for each treatment combination.
For Alpha=0.05 and Beta=0.10 what is the size of the difference in means
( ∆ σ ) for the poison exposure levels? for the antidote amount levels?
g) The experimenter comes to you for advice on randomization. She explains
she can only use 4 mice per treatment combination. Explain to the
experimenter how to randomly assign the mice. Do the randomization you
describe. Turn in your randomized assignment of the mice with this
assignment.
2. The experiment described in problem 1 is run. The data are available on the
course web site in the file Poison.JMP. Download this file and use JMP to help
with the analysis of the data.
a) Analyze and comment on the distribution of survival time.
b) Fit a model that includes Poison, Antidote and Poison*Antidote interaction
effects. Give the value of R2 and the value of the estimate of the error
standard deviation, σ.
c) Test the hypothesis that there are no differences among the population
treatment means. Be sure to include the F statistic, P-value, decision, reason
for the decision and a conclusion.
d) Test the hypothesis that the poison exposure effects are all zero. Be sure to
include the F statistic, P-value, decision, reason for the decision and a
conclusion.
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e) Where are the statistically significant differences among the poison exposure
means? Use the LSD (Student’s t) multiple comparisons procedure.
f) Test the hypothesis that the antidote amount effects are all zero. Be sure to
include the F statistic, P-value, decision, reason for the decision and a
conclusion.
g) Where are the statistically significant differences among the antidote amount
means? Use the HSD (Tukey-Kramer) multiple comparisons procedure.
h) Is a linear contrast on antidote amount statistically significant? If it is, what
does this indicate?
i) Test the hypothesis that the interaction effects are all zero. Be sure to include
the F statistic, P-value, decision, reason for the decision and a conclusion.
j) Construct and comment on the interaction plot.
k) Construct plots of residuals versus each of the factors in the experiment.
Comment on the plots.
l) Analyze the distribution of residuals. Comment on what the analysis of
residuals says about the conditions necessary for statistical analysis.
3. An alternative analysis uses 1/(Survival Time) as the response. This response can
be thought of loosely as a “rate of death” or deaths per hour. If a mouse survives
1 hour, then there is 1 death in that hour. If a mouse survives 0.5 hours followed
by a second mouse surviving 0.5 hours, then there are 2 deaths (1/0.5) in that
hour. If a mouse survives 2 hours, then there is an average of 1 death per 2 hours,
½=0.5 deaths per hour.
a) Construct a new column in your JMP table and use the column formula to
calculate 1/(Survival Time). Fit a model with 1/(Survival Time) as the
response and Poison, Antidote and Poison*Antidote as effects.
b) Test the hypothesis that the poison exposure effects are all zero. Be sure to
include the F statistic, P-value, decision, reason for the decision and a
conclusion.
c) Where are the statistically significant differences among the poison exposure
means? Use the LSD (Student’s t) multiple comparisons procedure.
d) Test the hypothesis that the antidote amount effects are all zero. Be sure to
include the F statistic, P-value, decision, reason for the decision and a
conclusion.
e) Where are the statistically significant differences among the antidote amount
means? Use the HSD (Tukey-Kramer) multiple comparisons procedure.
f) Test the hypothesis that the interaction effects are all zero. Be sure to include
the F statistic, P-value, decision, reason for the decision and a conclusion.
m) Construct plots of residuals versus each of the factors in the experiment.
Comment on the plots.
n) Analyze the distribution of residuals. Comment on what the analysis of
residuals says about the conditions necessary for statistical analysis.
g) Comment on any differences in conclusions between this alternative analysis
and the analysis in problem 3.
Remember to turn in copies of your JMP output with your assignment.
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