PSYC FPX 3700 Assessment 4

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 Dataset

The dataset Assessment_4a_Data.csv represents a hypothetical collection of data from students enrolled in a large introductory statistics course. Prior to taking their first exam, these students participated in two different assessments designed to measure test anxiety—an existing scale labeled Old_Test_Anxiety and a newly developed instrument referred to as New_Test_Anxiety. The original test is recognized for its strong psychometric properties, while the newer version was designed to modernize certain outdated items.

Researchers aimed to determine the extent to which scores from the new test align with those from the established measure, providing evidence for the reliability and validity of the new instrument.

Description of Variables

Variable Name	Measurement Level	Description
Student_ID	Nominal	Unique identifier for each student
Primary_Degree	Categorical	Indicates student’s degree type: BA, BSN, or BS
GPA	Continuous	Student’s grade point average at the beginning of the term
Old_Test_Anxiety	Continuous	Score on the original test anxiety measure
New_Test_Anxiety	Continuous	Score on the newly developed test anxiety scale

Constructing Scatterplots and Histograms in JASP

Using JASP, scatterplots and histograms were constructed for Old_Test_Anxiety and New_Test_Anxiety. The scatterplot depicted a strong, positive, and linear relationship between the two anxiety scores. Both histograms appeared approximately normal, with no extreme skewness or outliers, meeting the assumptions required for Pearson’s correlation.

Why Pearson’s r is Appropriate

Pearson’s r is an appropriate measure of association for these two variables because both Old_Test_Anxiety and New_Test_Anxiety are continuous and appear linearly related. The scatterplot indicates a direct, positive trend, while the histograms suggest normal distributions without severe deviations. Additionally, there are no major outliers that could distort the correlation coefficient, confirming the suitability of Pearson’s r for this analysis.

Correlation Analysis

After computing Pearson’s correlation coefficient (r) in JASP, the results demonstrated a strong positive relationship between the two measures of test anxiety, r = .919, p < .001, 95% CI [.863, .952], n = 54. This high correlation indicates that students who scored high on the old measure also tended to score high on the new one.

This finding provides robust evidence that the two tests measure similar underlying constructs, supporting the consistency of the new test with the established measure.

Evidence of Relationship and Statistical Significance

The p-value associated with the correlation is less than .001, which indicates that the relationship between Old_Test_Anxiety and New_Test_Anxiety is statistically significant. The probability of obtaining such a strong correlation by chance is extremely low, suggesting that the observed relationship reflects a true pattern within the population of students.

Reliability and Validity Implications

The high correlation between the two anxiety measures supports convergent validity—a subtype of construct validity. Convergent validity occurs when two instruments that purport to measure the same construct yield similar results. In this case, the new test demonstrates strong convergent validity with the old, well-established measure, implying that the new test effectively assesses test anxiety in a consistent manner. This evidence strengthens confidence in the new survey’s psychometric soundness and practical utility for future educational assessments.

Part 2: Linear Regression

Overview of the Dataset

The dataset Assessment_4b_Data.csv contains information from another group of students enrolled in the same introductory statistics course. Before completing a quiz on data visualization, these students rated their self-efficacy—their perceived confidence in performing data visualization tasks. The goal of this study was to determine whether self-efficacy scores could predict actual quiz performance.

Description of Variables

Variable Name	Measurement Level	Description
id	Nominal	Unique identifier for each participant
quiz_score	Continuous	Score obtained on a data visualization quiz
self_efficacy	Continuous	Composite measure of confidence in data visualization abilities

Constructing Graphs in JASP

Three primary visualizations were generated in JASP:

1. Scatterplot – Self-efficacy (x-axis) versus quiz score (y-axis)

2. Residuals vs. Predicted Values Plot – Used to check homoscedasticity and independence of residuals

3. Histogram and Q–Q Plot of Residuals – Used to assess normality of residuals

Evaluation of Regression Assumptions

Assumption	Graph Used	Observation	Interpretation
Linearity	Scatterplot	Data points show a straight, upward trend around the regression line.	The relationship between variables is approximately linear.
Independence of Errors	Residuals vs. Predicted Plot	Residuals appear randomly distributed with no systematic pattern.	The assumption of independent errors is supported.
Normality of Residuals	Q–Q Plot	Residual points closely follow the diagonal reference line.	Residuals are approximately normally distributed.
Equal Error Variances (Homoscedasticity)	Residuals vs. Predicted Plot	Vertical spread remains consistent across fitted values.	The assumption of equal variance is met.

Regression Model Results

A simple linear regression analysis was conducted with self_efficacy as the predictor and quiz_score as the outcome variable. Results revealed that self-efficacy is a significant predictor of quiz performance, b = 0.387, t(134) = 8.69, p < .001. The model was statistically significant, F(1, 134) = 75.42, p < .001, explaining 36% of the variance in quiz scores (R² = .36).

Statistical Significance of Predictor

The slope coefficient (b) of 0.387 indicates that for each one-unit increase in self-efficacy, quiz score increases by approximately 0.39 points, on average. The extremely low p-value (< .001) suggests that this effect is not due to random variation, confirming that self-efficacy is a meaningful predictor of performance in data visualization quizzes.

APA-Style Summary Statement

Self-efficacy significantly predicted quiz performance, F(1, 134) = 75.42, p < .001, R² = .36. This indicates that students with higher levels of self-efficacy tend to achieve higher quiz scores, underscoring the importance of self-perceived confidence in academic performance.

Discussion and Interpretation

The findings emphasize the critical role of self-efficacy in shaping students’ academic outcomes. Consistent with Bandura’s (1997) social cognitive theory, individuals who believe in their capabilities are more likely to perform effectively on academic tasks. The moderate-to-strong predictive power observed in this study highlights the potential benefits of fostering students’ self-confidence to enhance learning outcomes, particularly in data-driven disciplines like statistics.

References

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

Bandura, A. (1997). Self-efficacy: The exercise of control. W. H. Freeman.

PSYC FPX 3700 Assessment 4

Cohen, J., Cohen, P., West, S. G., & Aiken, L. S. (2013). Applied multiple regression/correlation analysis for the behavioral sciences (3rd ed.). Routledge.

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

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