Statistics for the Behavioral Sciences by Frederick J. Gravetter, Larry B. Wallnau ISBN 10: 1305504917 ISBN 13: 9781305504912

282 CHAPTER 9 | Introduction to the t Statistic
(a)
Original scores, including the treatment effect
8 9 10 11 12 13 14 15 16 17 18
No effect
m 5 10
FIGURE 9.6
Deviations from μ = 10
(no treatment effect) for the
scores in Example 9.2. The
colored lines in part (a) show
the deviations for the original
scores, including the treatment
effect. In part (b) the
colored lines show the deviations
for the adjusted scores
after the treatment effect has
been removed.
(b)
Adjusted scores with the treatment effect removed
5 6 7 8 9 10 11 12 13 14 15
No effect
m 5 10
at the attractive photograph, which means that their scores are generally greater than 10.
Thus, the treatment has pushed the scores away from μ = 10 and has increased the size of
the deviations.
Next, we will see what happens if the treatment effect is removed. In this example, the
treatment has a 3-point effect (the average increases from μ = 10 to M = 13). To remove
the treatment effect, we simply subtract 3 points from each score. The adjusted scores are
shown in Figure 9.6(b) and, once again, the deviations from μ = 10 are shown as colored
lines. First, notice that the adjusted scores are centered at μ = 10, indicating that there is
no treatment effect. Also notice that the deviations, the colored lines, are noticeably smaller
when the treatment effect is removed.
To measure how much the variability is reduced when the treatment effect is removed,
we compute the sum of squared deviations, SS, for each set of scores. The left-hand columns
of Table 9.2 show the calculations for the original scores (Figure 9.6(a)), and the
right-hand columns show the calculations for the adjusted scores (Figure 9.6(b)). Note
that the total variability, including the treatment effect, is SS = 153. However, when the
treatment effect is removed, the variability is reduced to SS = 72. The difference between
these two values, 153 – 72 = 81 points, is the amount of variability that is accounted for
by the treatment effect. This value is usually reported as a proportion or percentage of the
total variability:
variability accounted for
total variability
5 81 5 0.5294 s52.94%d
153