Comparing more than two means: two factor ANOVA with independent samples; the important role of interaction - Improving the User Experience through Practical Data Analytics - page 192

SIDEBAR: INCREASE SHELF SPACE, PROMOTION, OR BOTH?
To illustrate an interaction effect, let's pick a simple supermarket example. Suppose that we double
the shelf space we allocate to apples and increase sales by 30%. It is no surprise that increasing shelf
space increases sales! Now suppose that we increase our promotion of the apples from none to a “stan-
dard promotion—if we promote” (e.g., signs all over the supermarket indicating that brand of apples is
now available), and sales increase 40%. It is not surprising that increasing promotion increases sales!
Both of these types of increases were predictable and, while not satisfying what might be called hard
science, have been veriied time and time again in the world of marketing.
Now, what if we both double the shelf space and increase the promotion from none to stan-
dard promotion. Will we get an increase of 70%, which is the sum of the individual increases
(30% + 40%)? Or will we get a sales increase, for example, of only 60% (less than the sum of the
separate increases—some cannibalization occurred)? Or, will we get an increase of, say, 80% (more
than the sum of the separate effects—some reinforcement occurred)?
The answer is that we don't know —until we try it (at least) a few times!!! Most often, there are
really no hard and fast rules for predicting interaction effects. This illustrates the fact that often,
we know virtually for sure what the direction of the result will be when changing the level of an
individual factor, such as shelf space or promotion, but do not know what the value of an interaction
effect will be—will the result from the two boosts provide an increase of 60% or 70% or 80%, or
what? Unless, amazingly, this particular combination was studied a lot in the past, and it was pub-
lished (not proprietary), how would anyone know? This is all the more reason that an experiment
cannot afford to ignore potential interaction effects.

8.3.2 INTERACTION—DEFINITION 2
Take a look at Table 8.4 . Again, the two rows stand for the length of a Web page (shorter,
longer), and the two columns stand for the shading (black and white, multicolored),
and the values in the cells are the mean satisfaction rating (using the 1-5 Likert scale)
of the design by a large number of respondents, with independent samples.
Now, the number in the bottom right cell in Table 8.4 is 4.9. And now, there is
interaction, since the value is not equal to (but, in this case, exceeds) 4.7.
What is the effect of changing from a length of shorter to longer? Well, if we use
a shading of black and white, the effect is +0.4 (i.e., going from 3.5 to 3.9); however,
if we use a shading of multicolored, the effect is +0.6 (going from 4.3 to 4.9). So,
what is the effect? The answer is that it depends on the shading! At shading = black
and white, it's +0.4, while at shading = multicolored, it's +0.6. This leads us to the
second deinition of interaction:

Interaction = If the effect of changing the level of one factor depends on the
level of another factor, we have interaction between the factors.

Table 8.4 Alternate 2 × 2 Table of Ratings of Length and Shading of Pages

Black and White Multicolored

Shorter 3.5 4.3

Longer 3.9 4.9