Statistics Question

1Complete an SPSS data analysis report focused on analyzing correlations
between a set of assigned variables.
Introduction
Note: The assessments in this course build upon each other, so you are strongly
encouraged to complete them in sequence.
Throughout the course, you have been exploring various concepts and building
your skills in statistical analysis. In this assessment, you will discuss the steps
taken to complete an SPSS data analysis report focused on analyzing
correlations between a set of assigned variables.
Overview
Note: The assessments in this course build upon each other, so you are strongly
encouraged to complete them in sequence.
Throughout the course, you have been exploring various concepts and building
your skills in statistical analysis, all in preparation for this culminating
assessment, your research report. In this final assessment, you will complete an
SPSS data analysis report focused on analyzing correlations between a set of
assigned variables.
Exploring the associations between some variables in the courseroom using
correlations might provide some important information about learner success.
You’ll need to pay attention to both magnitude, which is the strength of the
association, and directionality, which is the direction (positive or negative) of the
association. During this assessment, you’ll start learning about how to best
approach correlational analyses like these and start getting some answers. You’ll
explore the relationships that may or may not exist in your courseroom data.
Preparation
•
•
Download the SPSS data file grades.sav and save the file for future reference
on your computer’s hard drive in a place where you will remember where it
is.
Review the associated variable structure table for the data set titled “Data Set
Instructions [PDF],” which includes the names and scales of measurement for
each of the variables in the data set.
Resources
2
Be sure to visit the Resources for this assessment to help you with the steps of
your research report, such as information on correlations, what statistical test to
run, and writing your results in APA style.
Instructions
You will complete this assessment using the Data Analysis and Application
Template [DOC] (also known as the DAA Template).
• Refer to IBM SPSS Step-By-Step Guide: Correlations [PDF] for additional
information on using SPSS for this assessment.
• Review the Copy/Export Output Instructions [PDF] for help copying SPSS
output into your DAA Template.
• Use the Data Set Instructions [PDF] for information on the data set.
The grades.sav file is a sample SPSS data set. The data represent a teacher’s
recording of student demographics and performance on quizzes and a final exam
across three sections of the course. Each section consists of 35 students (N =
105). There are 21 variables in grades.sav.
This assessment is on correlations. You will analyze the following variables in
the grades.sav data set:
SPSS Variables and Definitions
SPSS Variable
Definition
Quiz 1
Quiz 1: Number of correct answers
GPA
Previous grade point average
Total
Total number of points earned in class
Final
Final exam: Number of correct answers
The Data Analysis and Application Template has five sections:
•
•
•
•
•
The Data Analysis Plan.
Testing Assumptions.
Results and Interpretation.
Statistical Conclusions.
Application.
Step 1: The Data Analysis Plan
3
In Step 1:
•
•
Name the four variables used in this analysis and whether they are
categorical or continuous.
State a research question, null hypothesis, and alternate hypothesis for one XY pair. For example, you could articulate a research question, null hypothesis,
and alternate hypothesis for quiz1 (X) and final (Y).
Step 2: Testing Assumptions
Test for one of the assumptions of correlation—normality.
•
•
•
Create a descriptive statistics table in SPSS to assess normality. This table
should include the four variables named above.
Paste the table in the DAA Template.
Interpret the skewness and kurtosis values and how you determined whether
the assumption of normality was met or violated.
Step 3: Results and Interpretation
In Step 3:
•
•
Paste the SPSS output of the intercorrelation matrix for all specified variables:
o First, report the lowest magnitude correlation in the intercorrelation
matrix, including degrees of freedom, correlation coefficient, p value,
and effect size. Interpret the effect size. Specify whether or not to reject
the null hypothesis for this correlation.
o Second, report the highest magnitude correlation in the
intercorrelation matrix, including degrees of freedom, correlation
coefficient, p value, and effect size. Interpret the effect size. Specify
whether or not to reject the null hypothesis for this correlation.
o Third, report the correlation between GPA and final, including degrees
of freedom, correlation coefficient, p value, and effect size. Interpret the
effect size. Analyze the correlation in terms of the null hypothesis.
Interpret statistical results against the null hypothesis, and state whether it is
accepted or rejected.
Step 4: Statistical Conclusions
In Step 4:
•
•
•
Provide a brief summary of your analysis and the conclusions drawn.
Analyze the limitations of the statistical test.
Provide any possible alternate explanations for the findings and potential
areas for future exploration.
Step 5: Application
4
In Step 5:
Analyze how you might use correlations in your field of study.
• Name an independent variable and dependent variable that would work for
such an analysis and why studying it may be important to the field or
practice.
Submit your completed Data Analysis and Application Template as an attached
Word document in the assessment area.
•
Competencies Measured
By successfully completing this assessment, you will demonstrate your
proficiency in the course competencies through the following assessment scoring
guide criteria:
•
•
•
Competency 3: Evaluate confidence and significance of statistical data.
o Name the variables and include the scale of measurement. State the
research question and null and alternate hypothesis, with no more than
one error.
o Communicate the assumptions associated with the primary inferential
statistic and how they were tested. Import assumption testing table
from SPSS.
Competency 4: Apply quantitative analysis to individual, organizational, and
social issues.
o Paste the SPSS output for main inferential statistic(s) as discussed in
the instructions and interpret the results of the main inferential test,
with no more than one error.
o Summarize briefly the analysis and the conclusions drawn. Analyze
limitations of the test and provide alternate explanations for findings
and potential areas for future exploration, with no more than one
error.
o Communicate how research could be applied to one’s own field of
study and the value and implications of this analysis to this field, with
no more than one error.
Competency 5: Communicate quantitative analysis effectively in a manner
consistent with expectations for psychology professionals.
o Support hypothesis and arguments with relevant scholarly literature.
o Convey purpose, in an appropriate tone and style, incorporating
supporting evidence and adhering to organizational, professional, and
scholarly writing standards.
o Apply APA formatting to in-text citations and references.
o Incorporate feedback from prior assessments.
1
Data Analysis and Application
Learner Name
Capella University
2
Data Analysis Plan
There are 21 variables in the SPSS data set named grades.sav but only four variables will be used in this
analysis. The variables are “Quiz 1”, which refers to the number of correct answers in quiz 1; “GPA”, which refers
to the previous grade point average; “Total”, which refers to the total number of points earned in class; and
“Final”, which refers to the number of correct answers in the final exam. All four variables are continuous.
This analysis answers the research question, “Is there a correlation between variables Quiz 1 and Final?”
The null and alternative hypotheses are stated below:
H0: There is no correlation between variables Quiz 1 and Final.
H1: There is a correlation between variables Quiz 1 and Final.
Testing Assumptions
The summary of the descriptive statistics for the four variables is shown below.
Descriptive Statistics
N
Minimum
Maximum
Mean
Std. Deviation
Statistic
Statistic
Statistic
Statistic
Statistic
Skewness
Kurtosis
Statistic
Std. Error
Statistic
Std. Error
quiz1
105
0
10
7.47
2.481
-.851
.236
.162
.467
gpa
105
1.08
4.00
2.8622
.71266
-.220
.236
-.688
.467
total
105
54
123
100.09
13.427
-.757
.236
1.146
.467
final
105
40
75
61.84
7.635
-.341
.236
-.277
.467
Valid N (listwise)
105
Based on the summary above, we will determine whether the assumption of normality was met or
violated. If the skewness is between -0.50 to 0.50, the data is fairly symmetrical; if it is between 0.50 to 1 or
between -1 to -0.50, the data is moderately skewed; and if is greater than 1 or lesser than -1, the data is highly
skewed. On the other hand, if the kurtosis is less than 0, it is called platykurtic distribution, which means that the
distribution is light-tailed; and if it is greater than 0, it is called leptokurtic distribution, which means that the
distribution is “heavy-tailed” (McNeese, 2016).
For variable Quiz 1, skewness = -0.851 and kurtosis = 0.162; therefore, the data is moderately skewed and
the distribution is lightly-tailed. For variable GPA, skewness = -0.220 and kurtosis = -0.688; therefore, the data is
fairly symmetrical and the distribution is lightly-tailed. For variable Total, skewness = -0.757 and kurtosis = 1.146;
therefore, the data is moderately skewed and the distribution is heavy-tailed. Lastly, for variable Final, skewness =
-0.341 and kurtosis = -0.277; therefore, the data is fairly symmetrical and the distribution is lightly-tailed. We can
conclude that the variables met the assumption of normality.
3
Results and Interpretation
The summary of the intercorrelation matrix for all four variables is shown below:
Correlations
quiz1
quiz1
Pearson Correlation
gpa
1
Sig. (2-tailed)
N
gpa
total
final
105
total
final
.152
.797**
.499**
.121
.000
.000
105
105
105
1
.318**
.379**
.001
.000
Pearson Correlation
.152
Sig. (2-tailed)
.121
N
105
105
105
105
Pearson Correlation
.797**
.318**
1
.875**
Sig. (2-tailed)
.000
.001
N
105
105
105
105
Pearson Correlation
.499**
.379**
.875**
1
Sig. (2-tailed)
.000
.000
.000
N
105
105
105
.000
105
**. Correlation is significant at the 0.01 level (2-tailed).
The correlation between Quiz 1 and GPA has the lowest magnitude correlation in the intercorrelation
matrix. It has a degree of freedom of 103, a correlation coefficient of 0.152, and a p-value of 0.121. The p-value is
greater than 0.05; therefore, the correlation is not significant. We do not reject the null hypothesis for this
correlation.
The correlation between Total and Final has the highest magnitude correlation in the intercorrelation
matrix. It has a degree of freedom of 103, a correlation coefficient of 0.875, and a p-value of 0.000. The p-value is
lesser than 0.05; therefore, the correlation is significant. We then reject the null hypothesis for this correlation.
The correlation between GPA and Final has a degree of freedom of 103, a correlation coefficient of 0.379,
and a p-value of 0.000. The p-value is lesser than 0.05; therefore, the correlation is significant. We then reject the
null hypothesis for this correlation.
The correlation between GPA and Total has a degree of freedom of 103, a correlation coefficient of 0.318,
and a p-value of 0.001. The p-value is lesser than 0.05; therefore, the correlation is significant. We then reject the
null hypothesis for this correlation.
The correlation between Quiz 1 and Total has a degree of freedom of 103, a correlation coefficient of
0.797, and a p-value of 0.000. The p-value is lesser than 0.05; therefore, the correlation is significant. We then
reject the null hypothesis for this correlation.
The correlation between Quiz 1 and Final has a degree of freedom of 103, a correlation coefficient of
0.499, and a p-value of 0.000. The p-value is lesser than 0.05; therefore, the correlation is significant. We then
reject the null hypothesis for this correlation. We have sufficient evidence that there is a correlation between Quiz
1 and Final.
4
Statistical Conclusions
There are four variables used in conducting the analysis namely Quiz 1, GPA, Total and Final. These
variables are used to test the normality and correlation. Based on the results, only the correlation between Quiz 1
and GPA is not significant and the rest correlations are significant. We can conclude that the lower the correlation
coefficient, the higher the p-value, and the higher the probability of not rejecting the null hypothesis.
The major limitation of the statistical test is the inability to establish causality or nonlinear relationships.
We cannot determine if the insignificant correlation between the two variables has no relationship or if there
might be a non-linear relationship between the two variables. Also, we cannot make conclusions about the causeand-effect relationship between the variables.
Aside from the four variables, there is another continuous variable in the data set, such as Review and
there are also categorical variables, such as grade. Using these two, we can also explore and determine the
correlation between a continuous variable and a categorical variable.
In the field of education, correlation research is beneficial. It can be used to predict, validate, and verify.
Correlation tells us the direction of the relationship between the two variables, whether it is positive or negative. It
also tells us.
Application
In the field of education, correlation research is beneficial. It can be used to predict, validate, and verify.
Correlation tells us the direction of the relationship between the two variables, whether it is positive or negative. It
also tells us the strength of the relationship (Overview of correlation). For instance, we want to determine whether
the student’s Mathematics score has an association with his or her GPA.
5
References
McNeese, B. (2016, February). Are the skewness and Kurtosis Useful Statistics? BPI Consulting. Retrieved January 8,
2023, from https://www.spcforexcel.com/knowledge/basic-statistics/are-skewness-and-kurtosis-usefulstatistics#skewness
Overview of correlation. Psychological Statistics. (n.d.). Retrieved January 8, 2023, from
https://www.uv.es/visualstats/vista-frames/help/lecturenotes/lecture11/overview-ovrh.html
1
Data Analysis and Application
Learner Name
Capella University
2
Data Analysis Plan
There are 21 variables in the SPSS data set named grades.sav but only four variables will be used in this
analysis. The variables are “Quiz 1”, which refers to the number of correct answers in quiz 1; “GPA”, which refers
to the previous grade point average; “Total”, which refers to the total number of points earned in class; and
“Final”, which refers to the number of correct answers in the final exam. All four variables are continuous.
This analysis answers the research question, “Is there a correlation between variables Quiz 1 and Final?”
The null and alternative hypotheses are stated below:
H0: There is no correlation between variables Quiz 1 and Final.
H1: There is a correlation between variables Quiz 1 and Final.
Testing Assumptions
The summary of the descriptive statistics for the four variables is shown below.
Descriptive Statistics
N
Minimum
Maximum
Mean
Std. Deviation
Statistic
Statistic
Statistic
Statistic
Statistic
Skewness
Kurtosis
Statistic
Std. Error
Statistic
Std. Error
quiz1
105
0
10
7.47
2.481
-.851
.236
.162
.467
gpa
105
1.08
4.00
2.8622
.71266
-.220
.236
-.688
.467
total
105
54
123
100.09
13.427
-.757
.236
1.146
.467
final
105
40
75
61.84
7.635
-.341
.236
-.277
.467
Valid N (listwise)
105
Based on the summary above, we will determine whether the assumption of normality was met or
violated. If the skewness is between -0.50 to 0.50, the data is fairly symmetrical; if it is between 0.50 to 1 or
between -1 to -0.50, the data is moderately skewed; and if is greater than 1 or lesser than -1, the data is highly
skewed. On the other hand, if the kurtosis is less than 0, it is called platykurtic distribution, which means that the
distribution is light-tailed; and if it is greater than 0, it is called leptokurtic distribution, which means that the
distribution is “heavy-tailed” (McNeese, 2016).
For variable Quiz 1, skewness = -0.851 and kurtosis = 0.162; therefore, the data is moderately skewed and
the distribution is lightly-tailed. For variable GPA, skewness = -0.220 and kurtosis = -0.688; therefore, the data is
fairly symmetrical and the distribution is lightly-tailed. For variable Total, skewness = -0.757 and kurtosis = 1.146;
therefore, the data is moderately skewed and the distribution is heavy-tailed. Lastly, for variable Final, skewness =
-0.341 and kurtosis = -0.277; therefore, the data is fairly symmetrical and the distribution is lightly-tailed. We can
conclude that the variables met the assumption of normality.
3
Results and Interpretation
The summary of the intercorrelation matrix for all four variables is shown below:
Correlations
quiz1
quiz1
Pearson Correlation
gpa
1
Sig. (2-tailed)
N
gpa
total
final
105
total
final
.152
.797**
.499**
.121
.000
.000
105
105
105
1
.318**
.379**
.001
.000
Pearson Correlation
.152
Sig. (2-tailed)
.121
N
105
105
105
105
Pearson Correlation
.797**
.318**
1
.875**
Sig. (2-tailed)
.000
.001
N
105
105
105
105
Pearson Correlation
.499**
.379**
.875**
1
Sig. (2-tailed)
.000
.000
.000
N
105
105
105
.000
105
**. Correlation is significant at the 0.01 level (2-tailed).
The correlation between Quiz 1 and GPA has the lowest magnitude correlation in the intercorrelation
matrix. It has a degree of freedom of 103, a correlation coefficient of 0.152, and a p-value of 0.121. The p-value is
greater than 0.05; therefore, the correlation is not significant. We do not reject the null hypothesis for this
correlation.
The correlation between Total and Final has the highest magnitude correlation in the intercorrelation
matrix. It has a degree of freedom of 103, a correlation coefficient of 0.875, and a p-value of 0.000. The p-value is
lesser than 0.05; therefore, the correlation is significant. We then reject the null hypothesis for this correlation.
The correlation between GPA and Final has a degree of freedom of 103, a correlation coefficient of 0.379,
and a p-value of 0.000. The p-value is lesser than 0.05; therefore, the correlation is significant. We then reject the
null hypothesis for this correlation.
The correlation between GPA and Total has a degree of freedom of 103, a correlation coefficient of 0.318,
and a p-value of 0.001. The p-value is lesser than 0.05; therefore, the correlation is significant. We then reject the
null hypothesis for this correlation.
The correlation between Quiz 1 and Total has a degree of freedom of 103, a correlation coefficient of
0.797, and a p-value of 0.000. The p-value is lesser than 0.05; therefore, the correlation is significant. We then
reject the null hypothesis for this correlation.
The correlation between Quiz 1 and Final has a degree of freedom of 103, a correlation coefficient of
0.499, and a p-value of 0.000. The p-value is lesser than 0.05; therefore, the correlation is significant. We then
reject the null hypothesis for this correlation. We have sufficient evidence that there is a correlation between Quiz
1 and Final.
4
Statistical Conclusions
There are four variables used in conducting the analysis namely Quiz 1, GPA, Total and Final. These
variables are used to test the normality and correlation. Based on the results, only the correlation between Quiz 1
and GPA is not significant and the rest correlations are significant. We can conclude that the lower the correlation
coefficient, the higher the p-value, and the higher the probability of not rejecting the null hypothesis.
The major limitation of the statistical test is the inability to establish causality or nonlinear relationships.
We cannot determine if the insignificant correlation between the two variables has no relationship or if there
might be a non-linear relationship between the two variables. Also, we cannot make conclusions about the causeand-effect relationship between the variables.
Aside from the four variables, there is another continuous variable in the data set, such as Review and
there are also categorical variables, such as grade. Using these two, we can also explore and determine the
correlation between a continuous variable and a categorical variable.
In the field of education, correlation research is beneficial. It can be used to predict, validate, and verify.
Correlation tells us the direction of the relationship between the two variables, whether it is positive or negative. It
also tells us.
Application
In the field of education, correlation research is beneficial. It can be used to predict, validate, and verify.
Correlation tells us the direction of the relationship between the two variables, whether it is positive or negative. It
also tells us the strength of the relationship (Overview of correlation). For instance, we want to determine whether
the student’s Mathematics score has an association with his or her GPA.
5
References
McNeese, B. (2016, February). Are the skewness and Kurtosis Useful Statistics? BPI Consulting. Retrieved January 8,
2023, from https://www.spcforexcel.com/knowledge/basic-statistics/are-skewness-and-kurtosis-usefulstatistics#skewness
Overview of correlation. Psychological Statistics. (n.d.). Retrieved January 8, 2023, from
https://www.uv.es/visualstats/vista-frames/help/lecturenotes/lecture11/overview-ovrh.html