Statistical Analysis for Education and Psychology Researchers

Interpretation

With alpha set to 5 per cent the obtained Q of 1.75 is first evaluated against the

conservative critical value of that is or 2×3.84=7.68. This
conservative estimate adjusts for heterogeneity in the covariances and the resultant
inflated Type I error rate. The observed value of Q, 1.75, fails to exceed this conservative
critical value (not significant at 5 per cent level) and Q is therefore tested against the
more liberal critical value. This liberal critical value is equivalent to χ^2 with (c−1) df.

Here we see the obtained value of Q, 1.75<5.99 the Q statistic fails to reach the
liberal critical value and is not significant at the 5 per cent level.
We do not reject the null hypothesis, the probabilities of 1’s (successes) are not
different under the three teaching approaches, and we conclude that vocabulary
acquisition is similar under the three approaches, storytelling enhanced by pictures,
storytelling alone and silent reading. The reader should carefully consider the design of
this experiment particularly threats to internal validity (are the three stories comparable,
are the target words comparable-what would be the advantages/ disadvantages of a
between subjects design?)

Computer Analysis

A SAS programme for calculating Cochran’s Q and evaluating the significance of the Q
statistic at the conservative and liberal critical values is presented in Figure 8, Appendix
A3. To use this programme two sections need to be edited: the number of variables, that
is treatment occasions (repeated measurements), t1 t2 t3...tn and the actual lines of data,
one subject per line. Three subjects are not included in the data input because they have
either all 0’s or all 1’s. The total number of lines of data input (subjects) is therefore
eight. With a larger data set a separate data file could be read using the INFILE statement
rather than entering data in the SAS programme with the CARDS statement. Illustrated in
Figure 6.8 is the data entry section of this SAS programme using the vocabulary
acquisition data.

** Filename:

COCHRAN.JOB

**;

**

**;

** Purpose: Cochran's Q

test **;

**

**;

** Tests whether there is a

difference between two or **;

** more treatments in a repeated

measures design when **;

** the response variable is

binary, 1 (success) 0 **;

Inferences involving binomial and nominal count data 199