1. Lecture 14: Two-Way ANOVA
BMS 617
Lecture 14: Two-Way ANOVA
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Two-Way ANOVA
In one-way ANOVA, we measured a continuous variable in three or more different categorical groups
We think of this as one dependent variable (the continuous “outcome” variable) and one independent variable (the group)
Often, an experiment will examine the effect of two (or more) variables on the same dependent variable
If the independent variables are categorical, we use a two-way ANOVA for this
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Example
The TALLYHO (TH) strain of mouse is appears more susceptible to obesity and diabetes than the standard lab mouse
To test this, we fed TH mice three different diets (standard chow, low-fat high carb, and high-fat). We compared the effect of the diet in TH mice to standard mice by feeding standard (B6) mice the same three diets.
Measured body weight (and other variables) after 16 weeks.
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4. Experimental Design for TH/B6 diet
There are two independent variables, both of which are categorical
Strain (TH/B6)
Diet (Chow/LF/HF)
The dependent variable is body weight, which is continuous
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5. Hypotheses for TH/B6 diet study
There are three hypotheses we can test in this study:
Diet affects body weight, in either mouse strain
The different strains have different body weights, given any (fixed) diet
The effect of diet is different between the different strains
The first two we call “main effects”
The last is the “interaction” between the two main effects
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6. Two-Way ANOVA gets complex!
Two-Way ANOVA can get complex
With t-tests (and one-way ANOVA) we distinguish between “paired” or “repeated measures” data and “unpaired” or (unmatched) data
In Two-Way ANOVA, one, both, or none of the variables may represent repeated measures
This affects the way the analysis should be performed
We will focus only on experimental designs with no repeated measures
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Balanced designs
Two-Way ANOVA works best with balanced designs
Same number of data points in each condition
Not always possible
But try to organize your experiments this way if possible
Gives most statistical power per data point
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Demo
Demo of body weight analysis
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Sample output
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Interpretation
The main effect for Strain is statistically significant
So we reject the null hypothesis that both strains have the same body weight when diet is kept fixed
The main effect for diet is statistically significant
So we reject the null hypothesis that all three diets result in the same body weight when strain is kept fixed
The interaction is also statistically significant
We reject the null hypothesis that the effect of diet is the same for both strains
Or equivalently, that the difference between the strains is the same for all three diets
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11. Where are the differences?
To determine where the differences lie, we need to perform multiple comparisons
Might be interested in comparing only one of the variables
The other is used solely as it is a confounding variable
Might need to compare each value of a variable to a control, or might need to compare across all groups
Essential to use a comparison that accounts for the multiple tests being peformed
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12. All possible comparisons
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