t-test (Change with Interval Data)
This type of t-test is used to determine if a group changed on some type of interval scale over time. For example, suppose that we had pre-tested a group of students on the number of errors they could identify in a list of math problems. After the pretest, suppose that we had given the students a class in math appreciation. After the class is finished, we retested them on their ability to find errors again, with the same set of math problems. We had hoped to demonstrate that a course in math appreciation would have some beneficial impact on the students' ability to identify math errors. Our data were as follows for our 8 persons class (Note that D indicates difference between pre- and post test scores.)
2
Pretest Post test D D
8 10 2 4
5 5 0 0
7 8 1 1
6 4 -2 4
3 6 3 9
8 9 1 1
1 2 1 1
4 6 2 4
Total 8 24
The formula for this t-test is given below.
Mean = 8/8 = 1.0

T =
X
D
S
D
N
Remember that the "Ds" in the formula indicate the differences between the pretest and posttests. Our first step is to calculate S.
S
D
=
24 -
8
2
8
7
=
24 8
=
7
2.29
= 1.51
Now, we are ready for the calculation of the t-test, as follows: t =
1.00
1.51
=
1.00
0.53
= 1.87
8
The degrees of freedom for this t-test are
DF = (N - 1),
where N is the number of subjects in the experiment.
DF = (8 - 1) = 7

For our problem, the critical value of t with 7 degrees of freedom (see the t-test table) is between
2.57 and 2.23. As you can see, our calculated value of t (1.87) did not exceed this range of critical values. Therefore, no significant change was observed in the number of errors identified from pretest to post test.
How to Perform the Calculations Using the Stats.Exe
I will demonstrate the program by using the example in this chapter. Select the t-test
(correlated) option from the main Stats.Exe
screen and click on the start calculations button.
During the beginning phase you will be given a variety of options for inputting and outputting the data. Simply select the options you wish. If you enter the data through the keyboard then the input would appear as follows:
8 10 (Enter) C [first score]
5 5 (Enter)
:
4 ,6 (Enter) C [last score]
The output would appear as follows:

Chapter Assignment

1. Suppose that a company wanted to know if a certain training program was effective in increasing the accuracy of drill holes in metal "skins" for an airplane they manufactured.
If the holes were drilled too large or too small they failed a tolerance test. Below is the number of failures for ten workers before and after the training program.
Before
3
4
2
After
2
0
1
2
5
3
3
1
3
3
0
4
1
1
2
0 1
2. Now the company wants to see if the training program maintained its effectiveness over an extended time period. Below is similar tolerance data collected on the ten workers after 6 months. What do you conclude?
6-Months
4
3
7
4
5
6
4
8
5
3