Page 185 - Intermediate Statistics for Dummies

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Part III: Comparing Many Means with ANOVA
are different, where the population means µ represent those from the age
groups, respectively. Over the years of this contest, you have collected data
on 200 children from each age group, so you have some prior ideas about
what the distances typically look like. This year, you have 20 entrants, 5 in
each age group. You can see the data from this year, in inches, in Table 9-1.
Watermelon Seed Spitting Distances for Four Child
Table 9-1
12–14 Years
15–17 Years
6–8 Years
38
38
44
44
47
43
39
39
40
45
40
42
45
40
44
44
45
43
41 9–11 Years Age Groups (Measured in Inches)
46
Do you think you see a difference in distances for these age groups based
on this data? If you just combined all the data, you would see quite a bit of
difference (the range of the combined data goes from 38 inches to 47 inches).
Perhaps accounting for which age groups each contestant is in does explain
at least some of what’s going on. But don’t stop there. In the next section, you
see the official steps you need to do to answer your question.
Walking through the steps of ANOVA
You have decided on the quantitative response variable (y) you want to com-
pare for your k various population (or treatment) means, and you collected a
random sample of data from each population. Now you’re ready to conduct
ANOVA on your data to see whether the population means are different for
your response variable, y.
The characteristic that defines these populations is called the treatment vari-
able, x. Statisticians use the word treatment in this context because one of the
biggest uses of ANOVA is for designed experiments where subjects are
randomly assigned to treatments, and the responses are compared for the
various treatment groups. So statisticians oftentimes use the word treatment
even when the study isn’t an experiment, and they’re comparing regular
populations. Hey, don’t blame me! I’m just following the proper statistical
terminology.