STATISTICS 402 - Assignment 4
Due March 6, 2013
1. In a study on memory similar to the one described in homework 2, problem 2 c) a second
factor – Age or the participant is included. In this study the five memorizing methods:
Counting, Rhyming, Adjective, Imagery and Intentional are assigned at random to 50 older
literate adults and 50 younger literate adults. Participants read through the same list of words
three times, they are then asked to write down all the words they can remember. Each
participant is given 3 minutes to write down the words. The number of words correctly
recalled is noted for each subject.
a) Is age an observational or an experimental variable? Explain briefly.
b) Is memorizing method an observational or an experimental variable? Explain briefly.
c) How many treatment groups are there in the full experiment?
d) What is the size of the difference in age means (younger literate adults compared to older
literate adults) that can be detected with Alpha = 0.01 and Beta = 0.20?
e) What is the size of the difference in memorization method means that can be detected
with Alpha = 0.05 and Beta = 0.05?
f) Will the experiment be able to detect a 2.0 standard deviation difference in treatment
means with Alpha = 0.05 and Beta = 0.10? Explain briefly.
2. A JMP data table for the experiment described in 1 is on the course web site:
www.public.iastate.edu/~wrstephe/stat402.html. Use JMP to analyze the data from this
experiment. Turn in the JMP output and use it to answer the following questions.
a) Analyze the distribution of the number of words recalled for the 100 participants.
Comment on the shape, center and variability.
b) Fit a model that includes Age Group, Learning Group and Age Group*Learning Group
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 within the context of the problem.
d) Test the hypothesis that the age effects are zero. Be sure to include the F statistic, Pvalue, decision, reason for the decision and a conclusion.
e) Is there a “best” age group in terms of number of words recalled? Explain briefly.
f) Test the hypothesis that the memorization method effects are zero. Be sure to include the
F statistic, P-value, decision, reason for the decision and a conclusion within the context
of the problem.
g) Where are the statistically significant differences among the learning group means? Use
the HSD (Tukey-Kramer) multiple comparisons procedure.
h) Is there a “best” memorizing method? Explain briefly.
i) Test the hypothesis that the interaction effects are zero. Be sure to include the F statistic,
P-value, decision, reason for the decision and a conclusion within the context of the
problem.
j) Construct an interaction plot. Describe the plot and indicate how it is consistent with the
test in i).
k) Construct plots of residuals versus each of the factors in the experiment. Comment on
the plots, specifically, what do the plots tell you about the Fisher conditions?
l) Analyze the distribution of residuals. Comment on what the analysis of residuals says
about the Fisher conditions.
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