Statistical Analysis for Education and Psychology Researchers

Subjects Storytelling Row totals

+pictures

Storytelling

alone

Silent

reading R R^2

1 1 0 1 2 4

2 1 1 0 2 4

3 0 1 0 1 1

4 1 0 0 1 1

5 1 1 0 2 4

6 1 1 1 3 9

7 1 1 1 3 9

8 0 0 0 0 0

9 1 0 1 2 4

10 1 0 1 2 4

11 0 0 1 1 1

(C)olumn

Totals

8 5 6 ΣC=

ΣR=N=19

Σ(R^2 )=41

(C)olumn

Total^2

64 25 36 Σ(C^2 )=125

Figure 6.7: Contingency table for

vocabulary acquisition experiment

For completeness all subjects are shown in the computation of Q. If subjects 6 and 7, (all
1’s) and subject 8 (all 0’s) were excluded from the computation, we would obtain the
same value of Q that we obtain with all subjects included in the analysis.
The null hypothesis is that there is no difference in vocabulary acquisition under the
different teaching approaches. Alpha is set to 5 per cent and the number of cells is 33
(11×3). After adjusting for the 3 rows with all 0’s or all 1’s (subjects 6, 7, and 8) the
number of cells reduces to 24 (8×3) which is the minimum number for use of the χ^2
approximation.
The computational steps are as follows:
Step 1 Compute the column and row totals and the square of the column and row totals.
Step2 Sum the column totals which should equal the sum of the row totals, here, ΣC=ΣR=N=19. N
is the grand total.
Step3 Sum the squares of the column and row totals here, Σ(C^2 )=125 and Σ(R^2 )=41
Step4 The test statistic Q is evaluated as:

Cochran‘s

Q—6.7

where J is the number of treatments (columns), R^2 is the row total squared for each row,
C^2 is the column total squared for each column, and N^2 is the grand total squared. Here Q
is:

Statistical analysis for education and psychology researchers 198