PSYC FPX 3700 Assessment 4

PSYC FPX 3700 Assessment 4

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Name

Capella University

PSYC-FPX3700 Statistics for Psychology

Prof. Name

Date

Assessment 4

Part 1: Correlation for Relations

For this assessment, the dataset titled Assessment_4a_Data.csv was utilized. The data represents a simulated sample of students from a large introductory statistics class. Each student completed two scales measuring test anxiety prior to their first exam: Old_Test_Anxiety and New_Test_Anxiety.

The Old_Test_Anxiety measure is an established and validated tool known for its reliability. However, researchers expressed concern that some of its items may no longer fully capture modern student experiences with test anxiety. As a result, a New_Test_Anxiety scale was created to address potential limitations of the original measure. To evaluate the comparability of the two scales, students completed both assessments before their first exam.

Variables in the Dataset

Visual Analysis: Scatterplot and Histograms

Using JASP, both a scatterplot and histograms were constructed for the Old_Test_Anxiety and New_Test_Anxiety variables. The scatterplot revealed a positive and approximately linear relationship between the two measures, suggesting that students who scored higher on the old measure also tended to score higher on the new one. The histograms showed both variables to be approximately normally distributed without extreme skewness or outliers, confirming that the assumptions required for Pearson’s correlation were satisfied.

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. Refer to the plots you made in the previous question.

Answer:
The use of Pearson’s r is appropriate because both the Old_Test_Anxiety and New_Test_Anxiety variables are continuous and demonstrate an approximately linear relationship. The scatterplot indicates that data points cluster around a straight line, while the histograms suggest that the variables exhibit no severe deviations from normality. Additionally, there are no notable outliers that could distort the correlation. Together, these factors justify using Pearson’s correlation coefficient as the measure of association.

Statistical Correlation Analysis

Using JASP, Pearson’s correlation coefficient was calculated. The results indicated a strong, positive correlation between Old_Test_Anxiety and New_Test_Anxiety, r = .919, 95% CI [.863, .952], n = 54, p < .001. This outcome provides compelling evidence of a significant relationship between the two variables in the population, meaning that the new test-anxiety scale performs similarly to the established one.

Reliability and Validity Interpretation

Question: Explain how the correlation you computed could be used to support a specific type of reliability or validity. Be sure to clearly state which type of reliability or validity is supported.

Answer:
The strong positive correlation observed between the new and old measures supports convergent validity. Convergent validity assesses whether two measures that theoretically evaluate the same construct—here, test anxiety—are highly related. Since both instruments produce similar results, the new test demonstrates validity by aligning closely with an established, reliable measure. Therefore, the correlation provides evidence that the New_Test_Anxiety scale effectively measures the same underlying psychological construct as the original assessment.

Part 2: Linear Regression

The second part of this assessment used the dataset Assessment_4b_Data.csv, which includes responses from students who completed a self-efficacy survey related to data visualization before taking a quiz on that topic. The purpose of this analysis was to determine whether self-efficacy could statistically predict quiz performance.

Dataset Variables

Graphical Analysis and Assumption Testing

Using JASP, the following plots were created:

1. Scatterplot (Self-Efficacy vs. Quiz Score):
   The scatterplot displayed an upward linear pattern, suggesting a positive relationship between self-efficacy and quiz performance. Students with higher self-efficacy scores tended to achieve higher quiz scores.
2. Residuals vs. Predicted Values Plot:
   The residuals were randomly dispersed around the zero line, showing no systematic pattern, which indicates that the assumptions of linearity and independence of errors were satisfied.
3. Histogram and Q–Q Plot of Residuals:
   The histogram showed a roughly bell-shaped curve, and the Q–Q plot displayed points closely aligned with the diagonal reference line. These results confirm the normality of residuals and homogeneity of variance (homoskedasticity).

Checking Assumptions of Simple Linear Regression

Regression Model and Statistical Significance

A simple linear regression was performed with self_efficacy as the predictor variable and quiz_score as the outcome variable. The results showed that self-efficacy significantly predicted quiz performance, b = 0.387, t(134) = 8.69, p < .001. The overall model was also significant, F(1, 134) = 75.42, p < .001, accounting for 36% of the variance in quiz scores (R² = .36).

This suggests that students with greater confidence in their data visualization skills tend to perform better on related quizzes, highlighting the importance of psychological self-belief in academic success.

APA-Style Summary of Regression Model

In APA format, the regression results can be summarized as follows:

Self-efficacy significantly predicted quiz scores, F(1, 134) = 75.42, p < .001, R² = .36.

This indicates that approximately 36% of the variability in quiz scores can be explained by students’ levels of self-efficacy regarding data visualization.

References

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

PSYC FPX 3700 Assessment 4

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

JASP Team. (2023). JASP (Version 0.18) [Computer software]. https://jasp-stats.org

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