# Analyze the computation, application, strengths, and limitations of various statistical tests.

For this two-part assessment, you will respond to a question about interpreting correlations and use SPSS software to complete a data analysis and application report.

You will examine three fundamental inferential statistics, including correlation, *t *tests, and analysis of variance (ANOVA). The first inferential statistic we will focus on is correlation, denoted *r*, which estimates the strength of a linear association between two variables. By contrast, *t *tests and ANOVAs will examine group differences on some quantitative dependent variable.

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By successfully completing this assessment, you will demonstrate your proficiency in the following course competencies and assessment criteria:

- Competency 1: Analyze the computation, application, strengths, and limitations of various statistical tests.
- Develop a conclusion including strengths and limitations of correlation.

- Competency 2: Analyze the decision-making process of data analysis.
- Analyze the assumptions of correlation.

- Competency 3: Apply knowledge of hypothesis testing.
- Develop a research question, null hypothesis, alternative hypothesis, and alpha level.

- Competency 4: Interpret the results of statistical analyses.
- Interpret the correlation output.

- Competency 5: Apply a statistical program’s procedure to data.
- Apply the appropriate SPSS procedures to check assumptions and calculate the correlations.

- Competency 6: Apply the results of statistical analyses (your own or others) to your field of interest or career.
- Develop a context for the data set, including a definition of required variables and scales of measurement.

- Competency 7: Communicate in a manner that is scholarly, professional, and consistent with the expectations for members in the identified field of study.
- Communicate in a manner that is scholarly, professional, and consistent with the expectations for members in the identified field of study.

Read Assessment 2 Context [DOC] for important information on the following topics:

- Interpreting correlation: Magnitude and sign.
- Assumptions of correlation.
- Hypothesis testing of correlation.
- Effect size in correlation.
- Alternative correlation coefficients.
- Correlation—application.
- Proper reporting of correlations.
*r*, degrees of freedom, and correlation coefficient.- Probability values.
- Effect size.

#### Preparation

Read Assessment 2 Context (linked in the Resources) to learn about the concepts used in this assessment. This assessment contains two parts. Follow the instructions provided for each part. Submit both parts of your assessment as Word documents.

#### Part 1: Interpreting Correlations

A meta-analysis (Anderson & Bushman, 2001) reported that the average correlation between time spent playing video games (X) and engaging in aggressive behavior (Y) in a set of 21 well-controlled experimental studies was *r*+ = .19. This correlation was judged to be statistically significant. In your own words, what can you say about the nature of the relationship? Write a one-page response to this question.

#### Part 2: Correlations

You will use the following resources for this assessment. They are linked in the Resources.

- Complete this part of the assessment using the
**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 assessment. - Refer to
**IBM SPSS Step-By-Step Instructions: Correlations**for additional information on using SPSS for this assessment. - If necessary, review the
**Copy/Export Output Instructions**to refresh your memory on how to perform these tasks. As with your previous two assessments, your submission should be narrative with supporting statistical output (table and graphs) integrated into the narrative in the appropriate place (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 a 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 (for example, 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,*p*value, 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.