Database Reference
In-Depth Information
calls Gen Z? Is their perception of sophistication really different from those of their
grandmothers?
Analysis of variance (ANOVA) to the rescue!
6.3 INDEPENDENT SAMPLES: ONE-FACTOR ANOVA
To put your question into statistical terms, you want to test the hypothesis that dif-
ferences in perception of sophistication are different for different age-groups. In this
kind of scenario, we'll use an independent sample ANOVA to test this hypothesis;
the test statistic for ANOVA is the F-statistic.
The samples being independent simply means that each task or design is experi-
enced by different people.
ANOVA can be used in many different situations, but there are often two UX
situations when this kind of test is especially appropriate. One case is when we have
one task or design and we wish to compare groups of people who differ in some
attribute(s). This is the case here: We have ive age-groups (brackets), and various
people in each age-group providing an evaluation of the same page. The second sce-
nario may be to have a number of groups evaluating a number of different designs or
completing different tasks (one group per design or task).
When using ANOVA, it is not important that we have the same number of
people evaluating each of the designs, or evaluating the ease-of-use of the differ-
ent tasks being studied. And the sample sizes do not affect the analysis method-
ology and workings of the software at all; it would not matter if each age-group
consisted of around 3 people or around 3000 people. Of course, the results are
more accurate if we have larger sample sizes. (However, if one were allocating
people to each design or task, it would be most eficient to split the folks as near
as possible to having an equal amount for each design or task.) As can be seen in
Table 6.1 , we have sample sizes of 28, 26, 26, 23, and 23, respectively.
SIDEBAR: HOW ANOVA IS WORKING UNDER THE HOOD
With more than two means to compare, the calculations are more detailed and complicated, but
ultimately, we will get a p -value from the software, which will still “say it all.” We have made the
conscious decision to not include all these details, but you may be interested in a look under the
hood. Read on….
As its name implies, ANOVA computes the variance due to differences between groups, and
the variability between individuals within groups. Then, after taking into account the number of
columns we have and the sample size of each column, the two variance types are put into ratio to
one another. The value of the ratio (called the “F-statistic”) determines if we should reject the null
hypothesis that all the true column means are equal; the alternate hypothesis is that the true column
means are not all equal.
In our example, we examine the differences among the ive column (i.e., age-group) means and
look at how much they vary from one another. That is done by irst computing the mean of all the
data, called by the grandiose name of the “grand mean.” The grand mean for our data in Table 6.1 is
3.39. Then, each column mean difference from this grand mean is calculated:
Continued
 
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