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Kudzu is a plant that was imported to the United States from Japan and now covers over seven million acres in the South. The plant contains chemicals called isoflavones that have been shown to have beneficial effects on bones. One study used three groups of rats to compare a control group with rats that were fed either a low dose or a high dose of isoflavones from kudzu. One of the outcomes examined was the bone mineral density in the femur (in grams per square centimeter). Here are the data.

TreatmentBone mineral density (g/cm2
Control 0.228 0.207 0.234 0.220 0.217 0.228 0.209 0.221 
 0.204 0.220 0.203 0.219 0.218 0.245 0.210 
Low dose 0.211 0.220 0.211 0.233 0.219 0.233 0.226 0.228 
 0.216 0.225 0.200 0.208 0.198 0.208 0.203 
High dose 0.250 0.237 0.217 0.206 0.247 0.228 0.245 0.232 
 0.267 0.261 0.221 0.219 0.232 0.209 0.255 

In this study there were three groups. Controls received a placebo, and the other two groups received either a low or a high dose of isoflavones from kudzu. You are planning a similar study of a new kind of isoflavone. Use the results of the study above to plan your study. Write a proposal explaining why your study should be funded.


The National Crime Victimization Survey estimates that there were over 400,000 violent crimes committed against women by their intimate partner that resulted in physical injury. An intervention study designed to increase safety behaviors of abused women compared the effectiveness of six telephone intervention sessions with a control group of abused women who received standard care. Fifteen different safety behaviors were examined. One of the variables analyzed was the total number of behaviors (out of 15) that each woman performed. Here is a summary of the means of this variable at baseline (just before the first telephone call) and at follow-up 3 and 6 months later.

Group Baseline 3 months 6 months 
Intervention10.4 12.5 11.9 
Control 9.6 9.9 10.4 

(a) Find the marginal means. Are they useful for understanding the results of this study?

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(b) Plot the means. Do you think there is an interaction? Describe the meaning of an interaction for this study.


The amount of chromium in the diet has an effect on the way the body processes insulin. In an experiment designed to study this phenomenon, four diets were fed to male rats. There were two factors. Chromium had two levels: low (L) and normal (N). The rats were allowed to eat as much as they wanted (M) or the total amount that they could eat was restricted (R). We call the second factor Eat. One of the variables measured was the amount of an enzyme called GITH. The means for this response variable appear in the following table.


(a) Make a plot of the mean GITH for these diets, with the factor Chromium on the x axis and GITH on the y axis. For each Eat group connect the points for the two Chromium means. 

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(b) Describe the patterns you see. Does the amount of chromium in the diet appear to affect the GITH mean? Does restricting the diet rather than letting the rats eat as much as they want appear to have an effect? Is there an interaction?

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(c) Compute the marginal means. Compute the differences between the M and R diets for each level of Chromium. Use this information to summarize numerically the patterns in the plot.

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