7. Trend Analysis in a One Way ANOVA, Pages 143-150 of
Keppel
Example 7a. SPSS MANOVA
Example 7b. SPSS GLM
Example 7c. SAS PROC GLM
7. Trend Analysis in a One Way ANOVA, Pages 143-150 of Keppel
Pages 143-150 of Keppel illustrate how to perform trend analysis in a one way Analysis of Variance. This example compares the comprehension score (score) for three different instruction techniques. The data for this experiment is shown below.
| a=1 | a=2 | a=3 | a=4 |
| 7 9 9 9 9 11 12 12 14 14 13 18 18 20 20 20 21 22 22 24 |
13 18 12 17 16 20 21 22 22 22 25 25 21 23 25 24 22 26 27 26 |
19 20 19 19 19 20 21 22 23 23 25 22 24 24 25 25 26 26 26 28 |
13 12 14 11 16 17 17 18 22 21 19 23 23 23 24 24 25 25 29 25 |
This can be analyzed using SPSS manova, SPSS glm, or SAS proc glm. All of these examples use the CHAP7 (SPSS, SAS) data file. The following examples illustrate two comparisons: first, a comparison of group 1 with groups 2 and 3, and second a comparison of groups 2 and 3.
Example 7a. SPSS MANOVA
MANOVA numcorr BY a(1,4) /ERROR = W /CONTRAST(a) = POLYNOMIAL /DESIGN = a(1) a(2) a(3) .
The /contrast subcommand is used to specify comparisons among treatment means and we use the special keyword polynomial to indicate that we want orthogonal trend coefficients. Since there are 4 levels of factor a there can be thee tests of trend, linear, quadratic and cubic. On the /design subcommand, a(1) refers to the test of linear trend, a(2) refers to a test of quadratic trend, and a(3) refers to a test of cubic trend.
Finally, the /error=w is shown even though it was not necessary in this situation. If we had only included one or two of the tests of trend on the /design subcommand, then we would have wanted to include the /error=w to tell SPSS to use the within cells variance for computing the error term. Otherwise, some versions of SPSS use WITHIN+RESIDUAL as the error term and this would be a less powerful test due to the addition of residual variance in the error term.
Example 7b. SPSS GLM
GLM numcorr BY a /LMATRIX a -3 -1 1 3 /LMATRIX a 1 -1 -1 1 /LMATRIX a -1 3 -3 1.
or
GLM numcorr BY a /CONTRAST(a) = POLYNOMIAL.
Example 7c. SAS PROC GLM
PROC GLM DATA=chap7; CLASS a; MODEL numcorr = a; CONTRAST "a linear" a -3 -1 1 3 ; CONTRAST "a quad" a 1 -1 -1 1 ; CONTRAST "a cubic" a -1 3 -3 1 ; RUN;
Summary
Under construction.
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