Tests of Differences between Means, Dependent Means (2 of 4)
The first step in testing the difference between means is to
compute a difference score for each subject. The difference score is
simply the difference between the two conditions. The difference
scores are shown below:
Sub Visual Auditory Vis-Aud
1 420 380 40
2 235 230 5
3 280 300 -20
4 360 260 100
5 305 295 10
6 215 190 25
7 200 200 00
8 460 410 50
9 345 330 15
10 375 380 -5
Mean 319.5 297.5 22
Notice that the difference between the visual mean (319.5) and the auditory
mean (297.5) is the same as the mean of the difference scores (22). This
will always be the case: The difference between the means will always
equal the mean of the difference scores. The
significance
test of the difference between means consists of determining whether
the mean of difference scores is significantly different from zero. If
it is, then the difference between means is significant. The procedure
for testing whether a mean is significantly different from zero is given
in the section "
Tests of µ, standard deviation
estimated."