We use this T test when the scores in the second group are not tied
to the scores in the first. A common research application occurs when we
wish to compare a control group to a treatment group. We are not
dependent on one class of students to give us pre- and post-test results.
Example: Two samples of students have practiced vocabulary in Spanish.
One allowed English whenever students found it convenient to do so; the
other practiced in a saturation-style environment where no speaking of
English was allowed.
The number of Spanish words that they were able to
use appropriately on a word-usage test of .84 reliability is shown below.
English-Spanish
Spanish saturation
10, 14, 13, 11, 9
11, 15, 12, 13, 12
20, 12, 17, 16, 18
14, 16, 19, 15
Sum of X =120
1
sum of X =147
2
2
Sum of X =1,470
1
2
sum of X =2,451
1
n =10
1
n =9
2
_
X =12.0
1
_
X =16.3
2
_
X
T=
_
- X
2
1
-----------S
diff
S
=
diff
2
2
(120)
+ 2, 451 - (147)
10
9
----------------------------------10 + 9 -2
1, 470 -
9 + 10
10 x 9
= .994
T=
16.3 - 12.0
.994
= 4.33.
With 10 + 9 -2 df, .01 level the null
hypothesis is rejected. Saturation results
in more vocabulary learning than being
allowed to revert to English on whim.