Question

A corporate trainer administered a test to eight employees prior to their participation in a training program. The trainer administered the test again after participation. Raw test scores from each administration are as follows:

Test-Taker First Administration Second Administration

John 6 6

Doug 5 4

Christina 8 7

Sammy 4 2

Todd 4 8

Terri 2 1

Abel 6 7

Theresa 3 3

Answer the following questions

1. What is the test-retest reliability coefficient for the test?

2. What is the standard error of measurement for the first and second administration?

3. What is the confidence interval at which we may be 95% certain of Abel's true score on the first administration? Given the confidence interval, could we feel confident that Abel's true score on the first administration is higher than Todd's true score on the first administration?

Answer 1

1)

The test-retest relaibility coefficient for the two sets of data is determine by the Pearson's correlation coefficient. The test-retest relaibility coefficient vary between 0 to 1 where stands for no reliability and 1 stands for perfect reliability. The coefficient is obtained using the formula as shown below,

x	y	x^2	y^2	xy
6	6	36	36	36
5	4	25	16	20
8	7	64	49	56
4	2	16	4	8
4	8	16	64	32
2	1	4	1	2
6	7	36	49	42
3	3	9	9	9
Sum=38	Sum=38	Sum=206	Sum=228	Sum=205

(In excel use formula =CORREL() to calculate Pearson coefficient)

2)

The standard error is obtained using the formula,

For first test,

6	4.75	1.5625
5	4.75	0.0625
8	4.75	10.5625
4	4.75	0.5625
4	4.75	0.5625
2	4.75	7.5625
6	4.75	1.5625
3	4.75	3.0625
Sum=38		Sum=25.5

For second test,

y
6	4.75	1.5625
4	4.75	0.5625
7	4.75	5.0625
2	4.75	7.5625
8	4.75	10.5625
1	4.75	14.0625
7	4.75	5.0625
3	4.75	3.0625
38		47.5

3)

The confidence intervals for both the test are computed using the formula,

For first test,

We are 95% confidence that the true score of Abel's will lie in the interval, [3.6400, 5.8599]

The true score of Abel is outside the 95% confidence interval which lies in the right tail of the distribution and the Todd's true score lies within the confidence interval hence we can be 95 % confiedence that Abel's true score on the first administration is higher than Todd's true score on the first administration