STAT 602 - Repeated Measures and MANOVA Examples
(Spring 2015)
Example 1: Histamine Level in Dogs
As an example, consider a study by Cole and Grizzle (1966). The results are in the
Dogs.JMP table shown below. Sixteen dogs are assigned to four groups defined by variables drug (morphine/trimeth) and histamine dep1etion (Y/N) , each having two levels.
The dependent variable is the blood concentration of histamine at 0, 1, 3, and 5 minutes after injection of the drug. The log of the concentration is used to minimize the correlation between the mean and variance of the data.
For now pretend that there is no depletion effect and we have a drug effect only. We can use a Repeated Measures analysis to analyze the log(Histamine) levels.
Then select Repeated Measures from the Choose Response pull-down menu.
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STAT 602 - Repeated Measures and MANOVA Examples
(Spring 2015)
Is there a Drug effect?
Is there a Time effect?
Is there a Drug*Time interaction effect?
The Drug effect by itself is a Between Subjects effect because we are not looking for trends over time Within Subjects. Within Subject Effect tests are on the following page.
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STAT 602 - Repeated Measures and MANOVA Examples
(Spring 2015)
Within Subject Effect Tests
The plot of the Drug and Time effects is again shown below.
We could do the same type of analysis for the Depletion effect ignoring the Drug effect, but this is really a two factor experiment and should be analyzed as such, i.e. two-way repeated measures MANOVA.
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STAT 602 - Repeated Measures and MANOVA Examples
(Spring 2015)
The plots for both the Drug and Depletion effects are shown below.
The combined effects are shown in the table of means below the plots.
To determine which effects are significant we first consider the Between Subject effects and then consider the Within Subject effects.
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STAT 602 - Repeated Measures and MANOVA Examples
(Spring 2015)
Between Subject Effect Tests
Within Subject Effect Tests
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STAT 602 - Repeated Measures and MANOVA Examples
(Spring 2015)
The three-way interaction between Time*Drug*Depletion is significant however we have no visualization of this interaction effect. To see this effect more clearly we can use the column I have labeled as Group in the spreadsheet above which specifies the four treatment combinations defined by Drug and Depletion.
Visualization of the combined effects of Drug and Depletion
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STAT 602 - Repeated Measures and MANOVA Examples
(Spring 2015)
Non-Repeated Measures MANOVA
measurements are on different scales and measuring different attributes
Suppose we are interested in analyzing multiple responses simultaneously. For example suppose we measure multiple attributes on each experimental unit in one factor setting as in the nutritional analysis of frozen pizzas sampled from 12 different brands. A portion of these data is shown below:
As there is no time element to these data and the measured nutritional variables are on vastly different scales, it doesn’t make sense to look at within “subject” effects. You might wonder why we don’t just conduct a separate one-way ANOVA with k = 12 levels for each of the seven measured responses. The diagram below will help illustrate the advantage of analyzing these data in a multivariate manner.
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STAT 602 - Repeated Measures and MANOVA Examples
(Spring 2015)
Diagram illustrating the advantage of a multivariate analysis
To conduct a MANOVA analysis to examine potential differences between these 12 frozen pizza brands.
The results are shown below:
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STAT 602 - Repeated Measures and MANOVA Examples
(Spring 2015)
What makes the 12 pizza brands different?
More plots to examine frozen pizza brand differences.
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STAT 602 - Repeated Measures and MANOVA Examples
(Spring 2015)
Parallel Coordinate Plot
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