# 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

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