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2.4.3 Comparing More Than Two Samples
We don't always compare only two samples. Sometimes we want to compare
three, four, or even six different samples. Fortunately, there is a way to do this
without a lot of pain. An ANOVA lets you determine whether there is a signifi-
cant difference across more than two groups.
Excel lets you perform three types of ANOVAs. We will give an example for just
one type of ANOVA, called a single-factor ANOVA. A single-factor ANOVA is used
when you just have one variable you want to examine. For example, you might be
interested in comparing task completion times across three different prototypes.
Let's consider the data shown in Figure 2.6 , which shows task completion
times for three different designs. There were a total of 30 participants in this
study, with each using only one of the three designs.
EXCEL TIP
To run an ANOVA in Excel requires the Analysis ToolPak. From the “Data” tab, choose
the “Data Analysis” button, which is probably on the far right of the button bar. Then
choose “ANOVA: Single Factor.” This just means that you are looking at one variable
(factor). Next, define the range of data. In our example ( Figure 2.6 ), the data are in col-
umnsB,C,andD.Wehavesetanalphalevelto0.05andhaveincludedourlabelsin
the first row.
Results are shown in two parts (the right-hand portion of Figure 2.6 ). The top
part is a summary of the data. As you can see, the average time for Design 2 is quite
a bit slower, and Designs 1 and 3 completion times are faster. Also, the variance
is greater for Design 2 and less for Designs 1 and 3. The second part of the output
lets us know whether this difference is significant. The p value of 0.000003 reflects
the statistical significance of this result. Understanding exactly what this means
is important: It means that there is a significant effect of the “designs” variable.
Figure 2.6 Task completion times for three different designs (used by different participants) and results of a single-factor ANOVA.
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