SPSS Textbook Examples Design & Analysis by Keppel Chapter 7

Chapter 7

Chapter 7: Analysis of Trend

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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