PSYC FPX 3700 Assessment 4

Student Name

Capella University

PSYC-FPX3700 Statistics for Psychology

Prof. Name

Date

Assessment 4 Part 1: Correlation for Relations

Overview of the Study

The dataset used in this section, titled Assessment_4a_Data.csv, was obtained from the Assessment 4 module on Canvas. The data represents a hypothetical yet realistic sample of students enrolled in an introductory statistics course. Before taking their first examination, all students completed two separate measures of test anxiety—Old_Test_Anxiety and New_Test_Anxiety.

The Old_Test_Anxiety instrument is a long-established measure that has been previously validated and found to be highly reliable. However, researchers have expressed concern that some items on this older scale may no longer adequately represent current student experiences. Consequently, they developed a new version of the test anxiety survey, referred to as New_Test_Anxiety. The aim of this study is to examine the relationship between the two measures and to determine whether the new scale demonstrates validity in comparison to the established measure.

Dataset Variables

The dataset includes the following variables:

Variable Name	Measurement Level	Description
Student_ID	Nominal	Unique identification number for each participant
Primary_Degree	Categorical	Student’s primary degree (BA, BS, or BSN)
GPA	Continuous	Grade point average at the beginning of the term
Old_Test_Anxiety	Continuous	Score from the established test anxiety scale
New_Test_Anxiety	Continuous	Score from the newly developed test anxiety scale

Creating Visualizations in JASP

Using JASP, scatterplots and histograms were constructed for both Old_Test_Anxiety and New_Test_Anxiety scores. The scatterplot revealed a strong, positive, and linear relationship between the two variables. The histograms for each variable indicated that the data were approximately normally distributed, with no extreme outliers that might violate assumptions of normality or linearity.

Why Pearson’s r is Appropriate

Question: Explain why it is appropriate to use Pearson’s r as a measure of the correlation between the Old_Test_Anxiety and New_Test_Anxiety variables.

Answer: Pearson’s r is the most appropriate measure of correlation in this context because both Old_Test_Anxiety and New_Test_Anxiety are continuous variables that display an approximately linear relationship in the scatterplot. Furthermore, there are no extreme outliers, and the distributions appear roughly normal, fulfilling the assumptions necessary for the use of Pearson’s correlation coefficient.

Computing and Interpreting Pearson’s r

After running the correlation analysis in JASP, the results revealed a strong positive correlation between the two measures: r = .919, 95% CI [.863, .952], n = 54, p < .001.

Question: Is there evidence of a relationship between Old_Test_Anxiety and New_Test_Anxiety in the population? How was this determined?

Answer: Yes. The correlation coefficient of r = .919, with a p value less than .001, provides strong evidence that the relationship between Old_Test_Anxiety and New_Test_Anxiety is statistically significant. The high magnitude of r indicates that the two measures share a strong linear association, suggesting that the new instrument effectively measures the same construct as the established one.

Reliability and Validity Implications

Question: Explain how the correlation you computed could be used to support a specific type of reliability or validity.

Answer: The strong positive correlation between Old_Test_Anxiety and New_Test_Anxiety supports convergent validity, a form of construct validity. Convergent validity is demonstrated when two instruments that measure the same underlying construct (in this case, test anxiety) produce similar results. Because both scales assess the same psychological concept, their strong association suggests that the New_Test_Anxiety measure is a valid instrument for assessing test anxiety among students.

Part 2: Linear Regression

Study Overview

In this portion of the assessment, the dataset titled Assessment_4b_Data.csv was utilized. This dataset represents a hypothetical group of students from a large introductory statistics course. Before completing a quiz on data visualization, each student completed a survey assessing their self-efficacy in data visualization skills. The purpose of this study is to determine whether self-efficacy can predict performance on the quiz.

Dataset Variables

Variable Name	Measurement Level	Description
id	Nominal	Unique identifier for each student
quiz_score	Continuous	Quiz score assessing knowledge of data visualization
self_efficacy	Continuous	Composite score reflecting students’ self-efficacy in data visualization

Constructing Visualizations in JASP

Using JASP, three graphs were constructed:

Scatterplot – displaying self_efficacy on the x-axis and quiz_score on the y-axis.
Residuals vs. Predicted Values Plot – used to assess homoscedasticity and independence of errors.
Histogram/QQ Plot of Residuals – used to evaluate the normality of residuals.

Evaluating Assumptions of Simple Linear Regression

The following assumptions were examined using the graphs created in JASP:

Assumption	Graph Used	Observation	Conclusion
Linearity	Scatterplot	Data points followed an approximately straight, upward trend around the fitted regression line.	The linearity assumption is satisfied.
Independence of Errors	Residuals vs. Predicted Values Plot	Residuals were randomly dispersed around zero with no discernible pattern.	Independence of errors supported.
Normality of Residuals	QQ Plot of Standardized Residuals	Points closely aligned with the reference line, showing no strong deviation.	Residuals are approximately normal.
Equal Error Variances (Homoscedasticity)	Residuals vs. Predicted Values Plot	The vertical spread of residuals appeared constant across predicted values.	Homoscedasticity is met.

Constructing and Interpreting the Regression Model

A simple linear regression analysis was performed with self_efficacy as the independent variable and quiz_score as the dependent variable.

Question: Is self_efficacy a statistically significant predictor of quiz_score? How was this determined?

Answer: Yes, self-efficacy significantly predicted quiz performance. The unstandardized slope coefficient (b) was 0.387, indicating that for every one-unit increase in self-efficacy, quiz score increased by approximately 0.39 points. The model results were statistically significant: t(134) = 8.69, p < .001. The regression equation explained 36% of the variance in quiz scores, R² = .36, F(1, 134) = 75.42, p < .001.

APA-Style Summary Sentence

Self-efficacy was a statistically significant predictor of quiz performance, F(1, 134) = 75.42, p < .001, R² = .36.

This finding suggests that students who report higher confidence in their ability to interpret and create data visualizations tend to perform better on related assessments. The positive relationship between self-efficacy and quiz performance highlights the importance of developing students’ confidence and self-perceived competence as part of effective instruction in data analysis.

References

American Psychological Association. (2020). Publication manual of the American Psychological Association (7th ed.). APA Publishing.

Field, A. (2018). Discovering statistics using IBM SPSS statistics (5th ed.). SAGE Publications.

PSYC FPX 3700 Assessment 4

JASP Team. (2025). JASP (Version 0.18.2) [Computer software]. https://jasp-stats.org

Tabachnick, B. G., & Fidell, L. S. (2019). Using multivariate statistics (7th ed.). Pearson Education.