# What is the coefficient of determination? What is the coefficient of alienation? Why is it important to know the amount of shared variance when interpreting both the significance and the meaningfulness of a correlation coefficient?

Some questions in Part A require that you access data fromStatistics for People Who (ThinkThey) Hate Statistics.This data is available on the student website under the Student Text Resources link.

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1. Use the following data to answer Questions 1a and 1b.

 Total no. of problems correct (out of a possible 20) Attitude toward test taking (out of a possible 100) 17 94 13 73 12 59 15 80 16 93 14 85 16 66 16 79 18 77 19 91

a. Compute the Pearson product-moment correlation coefficient by hand and show all your work.

b. Construct a scatterplot for these 10 values by hand. Based on the scatterplot, would you predict the correlation to be direct or indirect? Why?

2. Rank the following correlation coefficients on strength of their relationship (list the weakest first):

 0.71 0.36 0.45 0.47 0.62

3. Use IBM SPSS software to determine the correlation between hours of studying and grade point average for these honor students. Why is the correlation so low?

 Hours of studying GPA 23 3.95 12 3.90 15 4.00 14 3.76 16 3.97 21 3.89 14 3.66 11 3.91 18 3.80 9 3.89

4. Look at the following table. What type of correlation coefficient would you use to examine the relationship between ethnicity (defined as different categories) and political affiliation? How about club membership (yes or no) and high school GPA? Explain why you selected the answers you did.

 Level of Measurement and Examples Variable X Variable Y Type of correlation Correlation being computed Nominal (voting preference, such as Republican or Democrat) Nominal (gender, such as male or female) Phi coefficient The correlation between voting preference and gender Nominal (social class, such as high, medium, or low) Ordinal (rank in high school graduating class) Rank biserial coefficient The correlation between social class and rank in high school Nominal (family configuration, such as intact or single parent) Interval (grade point average) Point biserial The correlation between family configuration and grade point average Ordinal (height converted to rank) Ordinal (weight converted to rank) Spearman rank correlation coefficient The correlation between height and weight Interval (number of problems solved) Interval (age in years) Pearson product-moment correlation coefficient The correlation between number of problems solved and the age in years

5. When two variables are correlated (such as strength and running speed), it also means that they are associated with one another. But if they are associated with one another, then why does one not cause the other?

6. Given the following information, use Table B.4 in Appendix B ofStatistics for People Who (Think They) Hate Statisticsto determine whether the correlations are significant and how you would interpret the results.

a. The correlation between speed and strength for 20 women is .567. Test these results at the .01 level using a one-tailed test.

b. The correlation between the number correct on a math test and the time it takes to complete the test is .45. Test whether this correlation is significant for 80 children at the .05 level of significance. Choose either a one- or a two-tailed test and justify your choice.

c. The correlation between number of friends and grade point average (GPA) for 50 adolescents is .37. Is this significant at the .05 level for a two-tailed test?

7. Use the data in Ch. 15 Data Set 3 to answer the questions below. Do this one manually or use IBM SPSS software.

a. Compute the correlation between income and level of education.

b. Test for the significance of the correlation.

c. What argument can you make to support the conclusion that lower levels of education cause low income?

8. Use the following data set to answer the questions. Do this one manually.

a. Compute the correlation between age in months and number of words known.

b. Test for the significance of the correlation at the .05 level of significance.

c. Recall what you learned in Ch. 5 ofSalkind (2011)about correlation coefficients and interpret this correlation.

 Age in months Number of words known 12 6 15 8 9 4 7 5 18 14 24 18 15 7 16 6 21 12 15 17

9. How does linear regression differ from analysis of variance?

10. Betsy is interested in predicting how many 75-year-olds will develop Alzheimer s disease and is using level of education and general physical health graded on a scale from 1 to 10 as predictors. But she is interested in using other predictor variables as well. Answer the following questions.

a. What criteria should she use in the selection of other predictors? Why?

b. Name two other predictors that you think might be related to the development of Alzheimer s disease.

c. With the four predictor variables (level of education, general physical health, and the two new ones that you name), draw out what the model of the regression equation would look like.

11. Joe Coach was curious to know if the average number of games won in a year predicts Super Bowl performance (win or lose). The x variable was the average number of games won during the past 10 seasons. The y variable was whether the team ever won the Super Bowl during the past 10 seasons. Refer to the following data set:

 Team Average no. of wins over 10 years Bowl? (1 = yes and 0 = no) Savannah Sharks 12 1 Pittsburgh Pelicans 11 0 Williamstown Warriors 15 0 Bennington Bruisers 12 1 Atlanta Angels 13 1 Trenton Terrors 16 0 Virginia Vipers 15 1 Charleston Crooners 9 0 Harrisburg Heathens 8 0 Eaton Energizers 12 1

a. How would you assess the usefulness of the average number of wins as a predictor of whether a team ever won a Super Bowl?

b. What s the advantage of being able to use a categorical variable (such as 1 or 0) as a dependent variable?

c. What other variables might you use to predict the dependent variable, and why would you choose them?

From Salkind (2011). Copyright 2012 SAGE. All Rights Reserved. Adapted with permission.

PartB

Some questions in Part B require that you access data fromUsing SPSS for Windows and Macintosh. This data is available on the student website under the Student Text Resources link. The data for this exercise is in thedata file named Lesson 33 Exercise File 1.

Peter was interested in determining if children who hit a bobo doll more frequently would display more or less aggressive behavior on the playground. He was given permission to observe 10 boys in a nursery school classroom. Each boy was encouraged to hit a bobo doll for 5 minutes. The number of times each boy struck the bobo doll was recorded (bobo). Next, Peter observed the boys on the playground for an hour and recorded the number of times each boy struck a classmate (peer).

1. Conduct a linear regression to predict the number of times a boy would strike a classmate from the number of times the boy hit a bobo doll. From the output, identify the following:

a. Slope associated with the predictor

b. Additive constant for the regression equation

c. Mean number of times they struck a classmate

d. Correlation between the number of times they hit the bobo doll and the number of times they struck a classmate

e. Standard error of estimate

From Green & Salkind (2011). Copyright 2012 Pearson Education. All Rights Reserved. Adapted with permission.

PartC

Complete the questions below. Be specific and provide examples when relevant.

Cite any sources consistent with APA guidelines.

 Question Answer Draw a scatterplot of each of the following:   A strong positive correlation A strong negative correlation A weak positive correlation A weak negative correlation   Give a realistic example of each. What is the coefficient of determination? What is the coefficient of alienation? Why is it important to know the amount of shared variance when interpreting both the significance and the meaningfulness of a correlation coefficient? If a researcher wanted to predict how well a student might do in college, what variables do you think he or she might examine? What statistical procedure would he or she use?

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