Correlations

In statistics, dependence or association is any statistical relationship, whether causal or not, between two random variables or bivariate data. In the broadest sense correlation is any statistical association, though it commonly refers to the degree to which a pair of variables are linearly related. Familiar examples of dependent phenomena include the correlation between the physical statures of parents and their offspring, and the correlation between the demand for a limited supply product and its price.^{[citation needed]}

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Correlations are useful because they can indicate a predictive relationship that can be exploited in practice. For example, an electrical utility may produce less power on a mild day based on the correlation between electricity demand and weather. In this example, there is a causal relationship, because extreme weather causes people to use more electricity for heating or cooling. However, in general, the presence of a correlation is not sufficient to infer the presence of a causal relationship (i.e., correlation does not imply causation).

Formally, random variables are dependent if they do not satisfy a mathematical property of probabilistic independence. In informal parlance, correlation is synonymous with dependence. However, when used in a technical sense, correlation refers to any of several specific types of relationship between mean values.^{[clarification needed]} There are several correlation coefficients, often denoted $rho$ or $r$ , measuring the degree of correlation. The most common of these is the Pearson correlation coefficient, which is sensitive only to a linear relationship between two variables (which may be present even when one variable is a nonlinear function of the other). Other correlation coefficients have been developed to be more robust than the Pearson correlation – that is, more sensitive to nonlinear relationships.^[1]^[2]^[3] Mutual information can also be applied to measure dependence between two variables.

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Correlations

See the Resources area for links to resources that you will use for this assignment:

You will complete this assignment using the Data Analysis and Application (DAA) Template.
Read the SPSS Data Analysis Report Guidelines for a more complete understanding of the DAA Template and how to format and organize your assignment.
Refer to IBM SPSS Step-By-Step Guide: Correlations for additional information on using SPSS for this assignment.
If necessary, review the Copy/Export Output Instructions to refresh your memory on how to perform these tasks. As with your previous two assignments, your submission should be in narrative format with supporting statistical output (table and graphs) integrated into the narrative in the appropriate places (not all at the end of the document).

You will analyze the following variables in the grades.sav data set:

gender
gpa
total
final

Step 1: Write Section 1 of the DAA.

Provide the context of the grades.sav data set.
Include a definition of the specified variables and corresponding scales of measurement.
Indicate the type of correlation for each X, Y pair (Pearson’s r, Spearman’s r, point-biserial r, et cetera).
Specify the sample size of the data set.

Step 2: Write Section 2 of the DAA.

Test the assumptions of correlation for gpa and final.
Paste the SPSS histogram output for each variable and discuss your visual interpretations.
Paste SPSS descriptives output showing skewness and kurtosis values and interpret them.
Paste SPSS scatter plot output with “gpa” set to the horizontal axis and “final” set to the vertical axis. Conduct a visual inspection of the scatter plot to analyze other assumptions of correlation.
Summarize whether or not the assumptions of correlation are met.

Step 3: Write Section 3 of the DAA.

Specify a research question related to gpa and final.
Articulate the null hypothesis and alternative hypothesis.
Specify your alpha level.

Step 4: Write Section 4 of the DAA.

Paste the SPSS output of the intercorrelation matrix for all specified variables.
- 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.
- 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.
- Third, report the correlation between gpa and final, including degrees of freedom, correlation coefficient, pvalue, and effect size. Interpret the effect size. Analyze the correlation in terms of the null hypothesis.

Step 5: Write Section 5 of the DAA.

Discuss the implications of this correlation as it relates to the research question.
Conclude with an analysis of the strengths and limitations of correlational analysis.

Submit your DAA Template as an attached Word document in the assignment area.

Resources

APA Style and Format.

ADDITIONAL INSTRUCTIONS FOR THE CLASS

Discussion Questions (DQ)

Initial responses to the DQ should address all components of the questions asked, include a minimum of one scholarly source, and be at least 250 words.
Successful responses are substantive (i.e., add something new to the discussion, engage others in the discussion, well-developed idea) and include at least one scholarly source.
One or two sentence responses, simple statements of agreement or “good post,” and responses that are off-topic will not count as substantive. Substantive responses should be at least 150 words.
I encourage you to incorporate the readings from the week (as applicable) into your responses.

Weekly Participation

Your initial responses to the mandatory DQ do not count toward participation and are graded separately.
In addition to the DQ responses, you must post at least one reply to peers (or me) on three separate days, for a total of three replies.
Participation posts do not require a scholarly source/citation (unless you cite someone else’s work).
Part of your weekly participation includes viewing the weekly announcement and attesting to watching it in the comments. These announcements are made to ensure you understand everything that is due during the week.

APA Format and Writing Quality

Familiarize yourself with APA format and practice using it correctly. It is used for most writing assignments for your degree. Visit the Writing Center in the Student Success Center, under the Resources tab in LoudCloud for APA paper templates, citation examples, tips, etc. Points will be deducted for poor use of APA format or absence of APA format (if required).
Cite all sources of information! When in doubt, cite the source. Paraphrasing also requires a citation.
I highly recommend using the APA Publication Manual, 6th edition.

Use of Direct Quotes

I discourage overutilization of direct quotes in DQs and assignments at the Masters’ level and deduct points accordingly.
As Masters’ level students, it is important that you be able to critically analyze and interpret information from journal articles and other resources. Simply restating someone else’s words does not demonstrate an understanding of the content or critical analysis of the content.
It is best to paraphrase content and cite your source.

LopesWrite Policy

For assignments that need to be submitted to LopesWrite, please be sure you have received your report and Similarity Index (SI) percentage BEFORE you do a “final submit” to me.
Once you have received your report, please review it. This report will show you grammatical, punctuation, and spelling errors that can easily be fixed. Take the extra few minutes to review instead of getting counted off for these mistakes.
Review your similarities. Did you forget to cite something? Did you not paraphrase well enough? Is your paper made up of someone else’s thoughts more than your own?
Visit the Writing Center in the Student Success Center, under the Resources tab in LoudCloud for tips on improving your paper and SI score.

Late Policy

The university’s policy on late assignments is 10% penalty PER DAY LATE. This also applies to late DQ replies.
Please communicate with me if you anticipate having to submit an assignment late. I am happy to be flexible, with advance notice. We may be able to work out an extension based on extenuating circumstances.
If you do not communicate with me before submitting an assignment late, the GCU late policy will be in effect.
I do not accept assignments that are two or more weeks late unless we have worked out an extension.
As per policy, no assignments are accepted after the last day of class. Any assignment submitted after midnight on the last day of class will not be accepted for grading.

Communication

Communication is so very important. There are multiple ways to communicate with me:
- Questions to Instructor Forum: This is a great place to ask course content or assignment questions. If you have a question, there is a good chance one of your peers does as well. This is a public forum for the class.
- Individual Forum: This is a private forum to ask me questions or send me messages. This will be checked at least once every 24 hours.

Correlations

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Correlations

Correlations