Statistical Analysis for Education and Psychology Researchers

Row Pct^

Col Pct 1 2 3 Total

1 19 32 10 61

31.15 52.46 16.39

46.34 49.23 33.33

2 9 10 5 24

37.50 41.67 20.83

21.95 15.38 16.67

3 13 23 15 51

25.49 45.10 29.41

31.71 35.38 50.00

Total 41 65 30 136

Statistic for table of row by col

Statistic DF Value Prob

Chi-square 4 3.515 0.476

Sample Size=136

Figure 6.6: SAS output for r×k Chi-

square analysis

Interpretation of Computer Output

The results of the analysis in Figure 6.6 show no difference in educational achievement
between the three populations: mothers working full-time; part-time; or at home,

is not significant. The interpretation is the same as that given in the
example from the literature section. An overall significant χ^2 value for a r×k table would
show that there are significant none chance deviations somewhere in the table. An
investigator is usually interested in which cells the important discrepancies appear. The
expected option in the tables statement of PROC FREQ produces expected cell
frequencies under the null hypothesis of homogeneity of proportions (or independence).
The cells with the largest discrepancy between observed and expected values can easily
be identified.

6.7 Cochran’s Q Test

When to Use

This procedure is appropriate when a research design involves subjects each performing
under different treatment conditions (repeated measures) for which the response
(outcome) variable is binary (scored 1, 0). The response variable is designated arbitrarily
1 for success and 0 for failure. The repeated measures may be two or more observations
on the same subjects over a series of independent trials (treatment conditions) or it may
involve matched subjects. Cochran’s Q test is appropriate for detecting whether the
proportions of successes are constant over trials (treatment groups).

Inferences involving binomial and nominal count data 195