Statistical Analysis for Education and Psychology Researchers

equates with a greater number of correct responses). This finding is consistent with
Robinson and Robinson’s (1983) study.

Computer Analysis

Friedman’s ANOVA by ranks can be performed in SAS using PROC FREQ. The
following SAS code, using data from Table 7.7, illustrates how to perform this analysis.

data a;

input subject cond $ rank @@;

cards;

1 1 3.5 1 2 2 1 3 1 1 4 3.5

2 1 4 2 2 3 2 3 2 2 4 1

3 1 3 3 2 2 3 3 4 3 4 1

4 1 4 4 2 1 4 3 2 4 4 3

5 1 4 5 2 1 5 3 3 5 4 2

6 1 4 6 2 2 6 3 1 6 4 3

;

proc freq;

tables subject*cond*rank/noprint cmh;

run;

title 'Friedmans ANOVA by ranks test - worked example';

run;

SAS can handle repeated measurement designs using ordinal data with PROC CATMOD,
or with PROC FREQ, the later approach is by far the simplest. The tables statement in
PROC FREQ identifies the variables to be used in the contingency table analysis. When a
statement is of the form ABC (A, B and C representing different variables) the last
variable, here C, forms the columns of a contingency table; values of the next to last
variable form the rows, and the first variable is used as a stratifying factor, a separate
contingency table being produced for each level of stratification.
In a repeated measures design, if a subject is placed as the first variable in the tables
statement, it is used as a stratifying factor and a separate contingency table is produced
for each subject. In this example, if the option NOPRINT is not used (it suppresses
printing of the contingency tables) six separate contingency tables would be produced,
one for each subject in the design, each table would have as the columns, rank scores and
for the rows, the four conditions, mat, draw, verb and make. In the situation where there
is one subject per contingency table the Cochran-Mantel-Haenszel Chi-square statistic

(CMH statistic) is identical to the Friedman’s Chi-square, The CHM statistic can
only be interpreted in this way if the column variable is ordinal. The null-hypothesis
tested in this case is that the mean score (median) of the row variables (repeated
measures) are equal.

Interpretation of Computer Output

Output from PROC FREQ for the repeated measures analysis of spatial perspectives and
different modes of representation is shown in Figure 7.10.

Statistical analysis for education and psychology researchers 244