t-test for Dependent Samples - Arrangement of Data

Technically, we can apply the t-test for dependent samples to any two variables in our data set and the selection of variables is identical to that used for Correlations. However, applying this test will make very little sense if the values of the two variables in the data set are not logically and methodologically comparable. For example, if you compare the average WCC in a sample of patients before and after a treatment but use a different counting method or different units in the second measurement, then a highly significant t-test value could be obtained due to an artifact; that is, to the change of units of measurement. Following, is an example of a data set (spreadsheet) that can be analyzed using the t-test for dependent samples.

 

WCC

before

WCC

after

case 1

111.9

113

case 2

109

110

case 3

143

144

case 4

101

102

case 5

80

80.9

...

...

...

 

average change between WCC

"before" and "after" = 1

The average difference between the two conditions is relatively small (d=1) as compared to the differentiation (range) of the raw scores (from 80 to 143, in the first sample). However, the t-test for dependent samples analysis is performed only on the paired differences, "ignoring" the raw scores and their potential differentiation. Thus, the size of this particular difference of 1 will be compared not to the differentiation of raw scores but to the differentiation of the individual difference scores, which is relatively small: 0.2 (from 0.9 to 1.1). Compared to that variability, the difference of 1 is extremely large and can yield a highly significant t value.