ABSTRACT
The numerator is the difference between the two means. As you can see, the larger
the difference, the larger the value oft.
The subscripts (m and D) indicate that it is the standard deviation of the mean
difference. Following is the formula for Smn (an alternative equation is included in
Appendix J near the end of this book):
Where
To use this formula, first list the two sets of scores, making sure that two paired
scores are on each line. Table 1 on the next page illustrates this. In column 1 are
the names of the pairs. For instance, each pair could be identical twins, one of whom
was randomly assigned to the experimental group, while the other was assigned to
Pair A 8 5 3 9 PairB 12 10 2 4 PairC 10 11 -1 1 PairD 9 6 3 9 PairE 18 15 3 9 PairF 11 7 4 16 PairG 8 2 6 36
the control group. 1 The difference between each pair of scores was computed and
entered in the column under D. Then the differences were squared and entered in
the column under D 2• Substituting into the formula for the standard error of the
mean difference, we obtain
'LD2 - ('LD) 2 + n n(n -1)
84-(20)2 + 7
7(6)
Before solving for the value oft, we must first compute the two means: m1 =
76/7 = 10.857 and mz = 5617 = 8.000. We now have the three values required by the formula for t. These have been substituted into the following formula:
1 = m1 - m2 = 10.857-8.000 = 2.857 = 3.576 = 3.58 smD .799 .799
