Tests of Differences between Means, Dependent Means (1 of 4)

When the same subjects are tested in two experimental conditions, scores in the two conditions are not independent because subjects who score well in one condition tend to score well in the other condition. This non-independence must be taken into account by the statistical analysis. The t test used when the scores are not independent is sometimes called a correlated t test and sometimes called a related-pairs t test. (Click here to see the advantage of testing the same subjects in both conditions.)

Consider an experimenter interested in whether the time it takes to respond to a visual signal is different from the time it takes to respond to an auditory signal. Ten subjects are tested with both the visual signal and with the auditory signal. (To avoid confounding with practice effects, half are in the auditory condition first and the other half are in the visual task first). The reaction times (in milliseconds) of the ten subjects in the two conditions are shown below.

Subject    Visual     Auditory
   1         420         380
   2         235         230
   3         280         300
   4         360         260
   5         305         295
   6         215         190
   7         200         200
   8         460         410
   9         345         330
  10         375         380