Information Technology Reference
In-Depth Information
SAT Study
650
600
550
500
450
400
6
8
2
4
0
Months of Study
Figure 7.21
Plot of SAT study time means.
lines to make this clear), and this linear component of the functions should
also be statistically significant.
Figures 7.20G and H depict relatively pure cubic functions. It is not
likely that either the linear or quadratic components would be statistically
significant.
7.21.5 OUR EXAMPLE STUDY
Figures 7.21 presents a plot of the results of our hypothetical SAT study
time example. As you can see, there is a substantial linear component
to the function, which almost certainly would translate to a statistically
significant
F
ratio associated with this linear contrast. At the same time,
the function does appear to flatten out at the end, and this could produce
a statistically significant quadratic component as well.
We can go even further in our description of the outcome of a trend
analysis. Because we are dealing with sums of squares that are additive, we
can quantify the strength of each polynomial contrast that is significant
with respect to either the between-groups variance or with respect to
the total variance. We do this by calculating eta squared values for the
particular reference point as follows:
To calculate the percentage of between-groups variance, a particular
polynomial component (e.g., linear, quadratic) accounts for
sum of squares for the polynomial component
sum of squares for between groups
eta squared
=
.
(7.7)
