Statistical Analysis for Education and Psychology Researchers

The 95 per cent CI for the population value of the mean difference, ‘occasion 2−
occasion 1’Z speaker scores is −5.009, to 12.409.

Interpretation

We can be 95 per cent certain that the difference between occasion 1 and occasion 2
speaker scores falls within the interval −5.009, to 12.409. This confidence interval
includes the value zero, which provides a simultaneous test of the null hypothesis. As the
value of zero difference falls within the confidence interval, there is no evidence to reject
the null hypothesis, and we conclude that there is no significant difference between the
mean occasion 1 and occasion 2 speaker scores.

Computer Analysis

SAS code for the t-test is,

Data a;

input caseno occ1 occ2 @@;

diff= occ2 − occ1;

cards;

1 14 17 2 26 13 3 37 17 4 0 6 5 13 13 6 0 20 7 0 6

8 5 19 9 0 12 10 0 9

;

proc means n mean stderr t prt;

var diff;

run;

The variable ‘diff’ can be entered in a data step as in this example. The MEANS
statement computes the average difference on the specified variable diff. The same
analysis can be performed using PROC UNIVARIATE with the variable diff. Output
from PROC MEANS is shown in Figure 8.12.
Analysis variable: DIFF
N Mean Std Error T Prob>|T|
10 3.7000000 3.8501082 0.9610119 0.3617

Figure 8.12: Paired t-test comparing

difference scores, post-pre, for speaker

test items

Interpretation

The mean difference is 3.7, the same as in the worked example. The margin of error is
rather large, 3.850 (Standard error of difference), t is 0.961 which has an associated
(exact) probability of 0.3617. The mean difference in speaker scores is not statistically
significant.

Inferences involving continuous data 307