University of Phoenix
Material
Time to Practice Week Five
Complete Parts A, B, and C below.
Part A
Some questions in Part A require that you access data from
Statistics for People Who (Think They) Hate
Statistics. This data is available on the student website
under the Student Text Resources link.
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):
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 of
Statistics for People Who (Think They) Hate
Statistics to 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 of Salkind
(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 Alzheimers 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 Alzheimers 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. Whats 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.
Part B
Some questions in Part B require that you access data from
Using 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.
Part C
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?
|
|
|
What is the meaning of the
p value of a correlation coefficient?
|
|
University of Phoenix Material
Time to Practice Week Five
Complete Parts A, B, and C below.
Part A
Some questions in Part A require that you access data from
Statistics for People Who (Think They) Hate
Statistics. This data is available on the student website
under the Student Text Resources link.
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):
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 of
Statistics for People Who (Think They) Hate
Statistics to 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 of Salkind
(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 Alzheimers 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 Alzheimers 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. Whats 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.
Part B
Some questions in Part B require that you access data from
Using 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.
Part C
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?
|
|
|
What is the meaning of the
p value of a correlation coefficient?
|
|
