ANOVA
Slide 1
Analysis of variance frequently is used to analyze experimental data. It’s reasonable to assume
that you’ve seen analysis of variance in your statistics courses. Therefore, my goal is merely to
remind you about the topic, to allow you to review the basic equations for analysis of variance,
and to provide you some examples that reinforce how analysis of variance works.
Slide 2
In this schematic here, we see four different groups with four different means on a single
variable. Analysis of variance can evaluate whether or not the mean scores for these four
groups differ statistically from one another; in particular, if the difference between group 1 and
group 3 is sufficient to justify a differential marketing strategy for each group.
Slide 3
The next dozen or so slides present the basic equations and statistical tests associated with
analysis of variance. Analysis of variance is analogous to market segmentation. What are
marketers doing when they segment markets? Ideally, they’re trying to identify homogenous
groups of people who on average differ as much between groups as possible. Marketers want
people within a market segment to be as similar as possible with one another and the averages
between segments to be as different as possible. If the difference between segments is trivial,
then a mass marketing rather than target marketing approach is most cost effective.
Analogously, for analysis of variance researchers who want to reject the null hypothesis would
want the differences in within-group scores to be relatively smaller than differences in betweengroup scores. In other words, within-group variability should be meaningfully less than between
group variability. If true, then groups differ meaningfully from one another because they vary
from each other far more than the natural variability within a group.
Slide 4 to Slide 11 (No Audio)
Slide 12
The F test truly drives home this analogy between analysis of variance and market
segmentation. The F test, which controls for degrees of freedom, takes the ratio of variancebetween-groups to variance-within-groups. If the between-group variability is meaningfully
greater than the within group-variability, then the F ratio is statistically significant.
Slide 13 to Slide 17 (No Audio)
Slide 18
Assume this example depicts three different ad copy tests. To make it simple, also assume five
study participants saw each ad. In situation A, the five people who saw ad #1 each rated it a 20,
the five different people who saw ad #2 rated it a 30, and the five still different people who saw
ad #3 and rated it 40. Mean scores for the 20 ratings (group 1) is 20, for the 30 ratings (group 2)
is 30, and for the 40 ratings (group 3) is 40. The overall mean is 30. A sum-of-squares analysis
would determine if the three means—of 20, 30, and 40—differ meaningfully from one another.
The within-group sum-of-squares is zero (0) because everyone in each group answered
identically. The between-group sum-of-squares, which relates to the group means, is 1000. The
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total sum-of-squares also is 1000. In situation B, the group that saw ad #1 rated it between 10
and 30, the group that saw ad #2 rated it between a 10 and 50, and the group that saw ad #3
rated it between a 10 and a 70. Notice that the means of those groups are identical to the
corresponding means in for situation A. In situations A and B, the mean for group 1 is 20, for
group 2 is 30, and for group 3 is 40. The group means are equally different in both cases and
the overall mean is the same in both cases, but the sum of squares are vastly different. The
total sum of squares in situation B is 4850 as opposed to 1000. The sum of squares between
groups is identical in both situations. In situation A, the sum of squares is 0 because everyone
within each group responded identically. In situation B, everyone within the group responded
differently. What does this mean for whether or not these groups differ meaningfully from one
another?
Slide 19
The F ratio tells us is that in situation A the group means differ meaningfully from one another.
In fact, the F ratio is infinite because the denominator is zero (0). However, there’s so much
within-group variability in situation B that the group means don’t differ meaningfully from one
another. Although the within-group means and overall mean are the same for situations A and
B, in situation A the means differ meaningfully and in situation B they don’t differ meaningfully.
Slide 20
The next two slides show two pricing experiments. In both cases, the data analysis lends itself
to an analysis of variance approach. The first slide shows three different price points: $0.39,
$0.44, and $0.49. The researcher wants to relate these price points to different quantities sold at
different stores. The slide shows that 50 units were sold at the $0.39 price point, 40 units were
sold at the $0.44 price point, and 35 units were sold at the $0.49 price point. Do the units sold at
each price point differ meaningfully from one another? I’ll leave you to perform the calculations
and make the assessment.
Slide 21
Here’s another pricing experiment that would lend itself to an analysis of variance. In this case,
the regular price, a reduced price, and a cents-off coupon are compared relative to their
influence on sales. Again, I’ll leave you to conduct the analysis and decide if the mean
difference in sales, across these three different conditions, is meaningful.
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