Information Technology Reference
In-Depth Information
Table 16.1.
A small hypothetical data set
Group
Score on
Adjusted score
membership
Case
dependent
Score on
on dependent
code
number
variable
covariate
variable
1
1
1
1
0.54610
1
2
2
5
2.29078
1
3
3
7
3.16312
2
4
5
6
5.31560
2
5
6
8
6.18794
2
6
8
11
7.49645
Mean
4.167
6.33
4.167
The scatterplot for these data is shown in Figure 16.1. As can be seen
in the plot, it appears that the line of best fit for these data points is a
straight line. This is confirmed by noting that the Pearson correlation of
the dependent variable and the covariate (the Pearson
r
assesses the degree
to which variables are linearly related) is 0.904. Thus, we would conclude
that these data meet the linearity of regression assumption.
To give you a sense of what adjusted scores look like, we present the
adjusted dependent variable values in the last column of Table 16.1. These
were generated by the SPSS GLM procedure (by saving the predicted
values in the ANCOVA analysis) and are shown to five decimal points to
reinforce the idea that these values are statistically produced.
Based on the straight line fit through the data points of Figure 16.1
(the linear model), given a value on the covariate of, say, 8, we would
Figure 16.1
Scatterplot to evaluate the linearity assumption.
