Chapter 15: Correlation Problems

1. Describe what is meant by a negative relationship and a positive relationship between two variables.

2. Compute the Pearson correlation for the following data.

X Y

2 3

3 1

6 5

4 4

5 2

3. Compute the Pearson correlation for the following data.

X Y

8 0

6 1

4 4

3 6

4 6

5 1

4. A sample of n = 25 pairs of scores (X and Y values) produces a correlation of r = -0.40. Are these sample data sufficient to conclude that there is a significant non-zero correlation between X and Y in the population? Use a two-tailed test at the .05 level of significance.

5. The following data show the results from an independent-measures study comparing two treatments.

a. Compute the independent-measures t statistic for these data.

b. Compute the percentage of variance explained by the treatment effect (r2).

c. Convert the data into a form suitable for calculating the point-biserial correlation and compute the correlation. (You should find that squaring the point-biserial correlation will produce the same r2 value that you obtained in part b.

Treatment

I II

1 6

6 13

6 12

3 9

M = 4 M = 10

SS = 18 SS = 30

6. A psychologist would like to evaluate the relationship between verbal skills as measured by the Scholastic Achievement Test (SAT) and performance on an anagram task. (Anagrams are words with the letters scrambled. The task is to unscramble the letters and identify the word.) Each subject is given a set of 10 anagrams, and the psychologist records how much time is needed to solve all 10. The anagram times and each subject's SAT score are as follows. (Note that two subjects failed to complete all 10 anagrams.) Use a Spearman correlation to measure and describe the relationship between SAT and anagram performance.

Anagram SAT

Subject Time Score

1 104 480

2 195 410

3 50 590

4 93 510

5 failed 420

6 170 460

7 failed 380

8 67 570

9 45 640

10 58 600