Four research participants take a test of manual dexterity (high scores mean better dexterity) and an anxiety test (high scores mean more anxiety). The scores are as follows.
Person Dexterity Anxiety
1 1 10
2 1 8
3 2 4
4 4 –2
(a) Make a scatter diagram of the scores; (b) describe in words the general pattern of correlation, if any; (c) figure the correlation coefficient; (d) figure whether the correlation is statistically significant (use the .05 significance level, two-tailed); (e) explain the logic of what you have done, writing as if you are speaking to someone who has never heard of correlation (but who does understand the mean, deviation scores, and hypothesis testing); and (f) give three logically possible directions of causality, indicating for each direction whether it is a reasonable explanation for the correlation in light of the variables involved (and why).