Homework # 2
Due February 12, 1998
 
1. The multivariate delta method can be used to find the standard error of any function of random variables. Write one function of correlations that you think might be useful to test. You don't need to do any derivations. Pick one that we have not discussed in class. 

2. In one sample of 100 subjects the correlation between intentions to use condoms and actual use of condoms was .25. In another sample, (N=80), the correlation was equal to .1. Is there a statistically significant difference between these two correlations with alpha=.05 and a two-tailed test? 

3. Test the statistical significance of a correlation in your own data. 

4. A researcher is interested in children's mental health after divorce. Parental warmth is one variable that is thought to protect children from symptoms after divorce. The researcher is primarily interested in whether mother's warmth is a greater predictor than father's warmth. The correlation between mother's warmth and child's mental health was .3. The correlation between father's warmth and child's mental health was .2. The correlation between mother's and father's warmth was .4. Why can't the .3 and .2 correlations be compared using the formula used in question 2? Are the correlations significantly different? N=80. 

5. The data from a two-by-two table of frequencies were used to compute the phi correlation and the product moment correlation. Does the value of the two correlations differ. 

6. Describe one situation where R2 is small but the effect is important. 

7. In class, we calculated regression coefficients without adjusting for measurement error and then adjusting for measurement error. 

  1. What happened as the reliability (r11) of the covariate increased? 
  2. What is the maximum correlation that X1 (assuming a reliability of .6) can have with any other variable? 
  3. What do these results suggest about multiple regression when the predictors have considerable measurement error? 
Optional

8. Cohen (1988) and others argue for different effect sizes based on the value of the correlation coefficient. Given how the size of the correlation can depend on characteristics of the data, do you think it is a good idea to use the correlation as an effect size measure? 

9. Using the covariance matrix among correlations, find the variance of the difference between two independent correlations using the multivariate delta method. 

  

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