Marshall University School of Medicine
Department of Biochemistry and Microbiology
BMS 617
Lecture 14: Two-Way ANOVA
Marshall University Genomics Core Facility
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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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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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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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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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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All possible comparisons
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