One of the common uses for correlation is to evaluate the reliability or validity of a psychological or educational test. For example, a valid test should be strongly related to some criterion measure that is logically related to the construct behind the test. For example, the SAT is used as one measure in college admissions because it is moderately correlated with grade point averages. (Only moderately, though, so the SAT should not be used as the sole entrance requirement).
- Similarly, let's say that you come up with a test that is supposed to measure sales ability. To validate the test, you take a sample of new hires at a company and give them your test, and then later assess the number of products they sold for the company over a 6-month period. Use SPSS to answer a. through c.
| Score (X) |
Number of Products Sold (Y) |
| 49 |
81 |
| 50 |
88 |
| 53 |
87 |
| 55 |
99 |
| 60 |
91 |
| 55 |
89 |
| 60 |
95 |
| 50 |
90 |
- Construct a scatterplot of the data in SPSS and paste it into this assignment (make sure the axes are labeled appropriately). Predict the strength and direction of the correlation you expect to find (do this by visual examination only, as discussed in your text). Explain what your scatterplot looks like to support your prediction.
- Use SPSS to calculate the correlation coefficient between the two sets of scores (include your SPSS output for descriptive statistics and the correlation). What is the direction and strength of the correlation? State your conclusion in APA style.
- What if you find out that you scored the test incorrectly and that everyone's score on the aptitude test was supposed to be 5 points higher than the original scoring. Will this affect the correlation obtained in part b.? Explain why or why not? Verify your belief by running the correlation in SPSS again with 5 points added to all the aptitude scores (include your SPSS output for descriptive statistics and the correlation). Was your belief verified by this recalculation?
- Another test of sales ability is created and you get the following data to evaluate its validity:
| Score (X) |
Number of Products Sold (Y) |
XY |
X2 |
Y2 |
| 49 |
81 |
|
|
|
| 50 |
88 |
|
|
|
| 53 |
87 |
|
|
|
| 55 |
99 |
|
|
|
| 60 |
91 |
|
|
|
| 55 |
89 |
|
|
|
| 60 |
95 |
|
|
|
| 50 |
90 |
|
|
|
| ΣX = |
ΣY = |
ΣXY = |
ΣX2 = |
ΣY2 = |
- Calculate the correlation coefficient by hand (must show work in the table above and in the space below).
- Identify the critical value for the correlation and determine if the correlation is significant.
- What is the effect size (coefficient of determination) for the correlation? Explain what the effect size tells you about the proportion of variability in number of products sold that is predicted by the test.