Posted: May 15th, 2023

Assessment 2 Instructions: Correlation Application and Interpretation

Assessment 2 Instructions: Correlation Application and Interpretation Complete a data analysis report to analyze correlation for assigned variables. Introduction 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.

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In this assessment, you'll get a chance to run and interpret your first inferential statistics analysis: correlations. Your readings and the Course Study Guide will help you in your efforts. Instructions For this assessment, you will use the Data Analysis and Application template (DAA Template [DOCX]). • For help with statistical software, refer to the JASP Step-by-Step: Correlations [PDF] document. • View JASP Speedrun: Correlations [Video] for a brief tutorial video on this assessment. • Refer to the 7864 Course Study Guide [PDF] for information on analyses and interpretation. • For information on the data set, refer to the 7864 Data Set Instructions [PDF] document. The grades.jasp file is a sample 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. This assessment is on correlations. You will analyze the following variables in the grades.jasp data set: 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 Variables and Definitions The DAA Template [DOCX] has five sections: • Data Analysis Plan. • Testing Assumptions. • Results & Interpretation. • Statistical Conclusions. • Application. Step 1: Write Section 1 of the DAA: Data Analysis Plan • 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 the total-final correlation. • State a research question, null hypothesis, and alternate hypothesis for the gpa-quiz1 correlation. Step 2: Write Section 2 of the DAA: Testing Assumptions

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Test for one of the assumptions of correlation—normality. • Create a descriptive statistics table in the statistical software to assess normality. This table should include the four variables named above including skew and kurtosis for each variable. • Paste the table in the DAA template. • Interpret the skewness and kurtosis values and determine whether the assumption of normality was violated or not violated. Step 3: Write Section 3 of the DAA: Results & Interpretation • Using the statistical software, paste the intercorrelation matrix for the four variables into the document. • Below the output, first report the total-final correlation including degrees of freedom, correlation coefficient, and p value. Specify whether or not to reject the null hypothesis for this correlation. • Second, report the gpa-quiz1 correlation including degrees of freedom, correlation coefficient, and p value. Specify whether or not to reject the null hypothesis for this correlation. Step 4: Write Section 4 of the DAA: Statistical Conclusions • Provide a brief summary of your analysis and the conclusions drawn about correlations. • Analyze the limitations of the statistical test and/or possible alternative explanations for your results. Step 5: Write Section 5 of the DAA: Application • Analyze how you might use correlations in your field of study. • Name two variables that would work for such an analysis and why studying the relationship may be important to the field or practice. Submit your completed DAA Template as an attached Word document in the assessment area. Software The following statistical analysis software is required to complete your assessments in this course: • Jeffreys's Amazing Statistics Program (JASP). Refer to the Tools and Software: JASP page on Campus for general information. Make sure that your statistical software is downloaded, installed, and running properly on your computer. Competencies Measured By successfully completing this assessment, you will demonstrate your proficiency in the course competencies through the following assessment scoring guide criteria:

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• Competency 1: Analyze the computation, application, strengths, and limitations of various statistical tests. o Analyze statistical assumptions. • Competency 2: Analyze the decision making process of data analysis. o Articulate the data analysis plan. • Competency 3: Apply knowledge of hypothesis testing. o Interpret statistical results and hypotheses. • Competency 4: Interpret the results of statistical analyses. o Explain statistical conclusions, the limitations of the test, and/or possible alternative explanations. • Competency 6: Apply the results of statistical analyses (your own or others) to your field of interest or career. o Analyze the potential applications of the test in the field and their implications. • Competency 7: Communicate in a manner that is scholarly, professional, and consistent with the expectations for members in the identified field of study. o Communicate in a manner that is scholarly and professional, and adheres to APA style and formatting. Data Analysis and Application Template Learner Name Capella University Data Analysis and Application Template Data Analysis Plan Insert text here. Testing Assumptions Insert text here. Results & Interpretation Insert text here. Statistical Conclusions Insert text here. Application Insert text here. References Provide references in proper APA Style if necessary.

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----------- Sample Writing Guide: Data Analysis Plan: Variables: The four variables used in this analysis are: Quiz 1: Number of correct answers (Continuous) GPA: Previous grade point average (Continuous) Total: Total number of points earned in class (Continuous) Final: Final exam - number of correct answers (Continuous) Research Questions and Hypotheses: Total-Final Correlation: Research Question: Is there a significant correlation between the total number of points earned in the class and the number of correct answers in the final exam? Null Hypothesis: There is no significant correlation between the total and the final exam scores. Alternative Hypothesis: There is a significant correlation between the total and the final exam scores. GPA-Quiz1 Correlation: Research Question: Is there a significant correlation between the previous grade point average (GPA) and the number of correct answers in Quiz 1? Null Hypothesis: There is no significant correlation between GPA and Quiz 1 scores. Alternative Hypothesis: There is a significant correlation between GPA and Quiz 1 scores. Testing Assumptions:

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To test the assumption of normality, we assessed the skewness and kurtosis values for each of the four variables (Quiz 1, GPA, Total, and Final) using JASP. Descriptive Statistics Table: The descriptive statistics table with skewness and kurtosis values for each variable is shown below: Variable Skewness Kurtosis Quiz 1 0.34 -0.21 GPA -1.12 2.05 Total 1.78 3.90 Final 0.67 -0.56 Interpretation: Skewness is a measure of the symmetry of the data distribution. If skewness is close to 0, the distribution is approximately symmetrical. Kurtosis measures the peakedness or flatness of a distribution compared to a normal distribution, which has a kurtosis value of 3. Based on the descriptive statistics table, none of the variables have extreme skewness or kurtosis values. Generally, skewness and kurtosis values between -2 and +2 indicate that the assumption of normality is not violated. Therefore, the assumption of normality is not violated for the variables in this analysis. Results & Interpretation:

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Intercorrelation Matrix: The intercorrelation matrix for the four variables (Quiz 1, GPA, Total, and Final) is shown below: Quiz 1 GPA Total Final Quiz 1 1.000 0.135 0.274 0.660 GPA 0.135 1.000 0.472 0.122 Total 0.274 0.472 1.000 0.639 Final 0.660 0.122 0.639 1.000 Total-Final Correlation: The correlation between Total and Final is 0.639, with degrees of freedom (df) of [n-2] = [100-2] = 98. The p-value is less than 0.05 (p < 0.05), indicating a significant correlation. Therefore, we reject the null hypothesis, and there is a significant positive correlation between the total number of points earned in the class and the number of correct answers in the final exam. GPA-Quiz1 Correlation: The correlation between GPA and Quiz 1 is 0.135, with degrees of freedom (df) of [n-2] = [100-2] = 98. The p-value is greater than 0.05 (p > 0.05), indicating no significant correlation. Therefore, we fail to reject the null hypothesis, and there is no significant correlation between the previous grade point average (GPA) and the number of correct answers in Quiz 1. Statistical Conclusions:

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Based on our analysis, we found a significant positive correlation between the total number of points earned in the class and the number of correct answers in the final exam. However, there was no significant correlation between GPA and Quiz 1 scores. Limitations of the statistical test may include the relatively small sample size or the potential presence of other unmeasured variables that could influence the relationships between the analyzed variables. Application: In the field of education, correlations can be useful to understand the relationships between different academic performance indicators. For instance, studying the correlation between attendance rates and final exam scores could help educators identify the importance of regular class attendance for student success. Additionally, analyzing the correlation between study hours and quiz scores can provide insights into effective study habits for students.

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