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Posted: December 20th, 2021
Test for the significance of the correlation, discussion help
Question description
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.
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
Compute the Pearson
product-moment correlation coefficient by hand and show all your work.Construct a scatterplot for
these 10 values by hand. Based on the scatterplot, would you predict the
correlation to be direct or indirect? Why?Rank the following correlation coefficients
on strength of their relationship (list the weakest first):
+.71
+.36
–.45
.47
–.62
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
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
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?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.The correlation between
speed and strength for 20 women is .567. Test these results at the .01 level
using a one-tailed test.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.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?Use the data in Ch. 15 Data Set 3 to answer
the questions below. Do this one manually or use IBM® SPSS® software.Compute the correlation
between income and level of education.Test for the significance
of the correlation.What argument can you make
to support the conclusion that lower levels of education cause low income?Use the following data set to answer the
questions. Do this one manually.Compute the correlation
between age in months and number of words known.Test for the significance
of the correlation at the .05 level of significance.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
How does linear regression differ from
analysis of variance?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.What criteria should she
use in the selection of other predictors? Why?Name two other predictors
that you think might be related to the development of Alzheimer’s disease.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.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
How would you assess the
usefulness of the average number of wins as a predictor of whether a team ever
won a Super Bowl?What’s the advantage of
being able to use a categorical variable (such as 1 or 0) as a dependent
variable?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).
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:Slope associated with the
predictorAdditive constant for the
regression equationMean number of times they
struck a classmateCorrelation between the
number of times they hit the bobo doll and the number of times they struck a
classmateStandard error of estimate
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