# Identifying the Influential Factors in Math Grades: An SPSS Analysis

Our focus extends to the time spent on math homework, the educational background of parents, students' math self-efficacy, and the shadow of math anxiety. Leveraging the capabilities of SPSS, we identify and interpret significant predictors, quantify the variance explained by our model, and scrutinize assumptions. This exploration encapsulates not just statistical outcomes but a comprehensive understanding of the dynamics that shape academic success in the realm of mathematics.

## Problem Description:

The SPSS assignment addresses various statistical scenarios, each requiring the selection of an appropriate test. The objective is to analyze datasets related to college students' behaviours, perceptions, and academic performance using statistical tests such as One-way ANOVA, Multiple Regression, Chi-Square Test of Independence, Dependent samples t-tests, Independent samples t-tests, and Correlation.

### Statistical Test Selections and Explanations

a. Work Experience and GPA Analysis

• Test: One-way ANOVA
• Explanation: To determine if work experience during college influences 4-year cumulative GPAs across four groups.

b. Learning and Study Strategies Impact on GPA

• Test: Multiple Regression
• Explanation: Analyzing how various learning and study strategies predict adult learners' GPA while controlling for demographic variables.

c. Political Affiliation and Associate's Degree

• Test: Factorial ANOVA
• Explanation: Examining whether political affiliation affects the likelihood of having an associate's degree among four-year transfer students.

d. Program Effect on Gender Differences

• Test: Chi-Square Test of Independence
• Explanation: Investigating if the effect of a program differs by gender, determining the joint effect of both factors.

e. Instructors' Efficacy Comparison

• Test: Dependent samples t-tests
• Explanation: Comparing instructors' efficacy for creating a positive learning climate with instructional strategies within the same group of faculty.

f. Comparison of First-Generation and Continuing-Generation Students

• Test: Independent samples t-tests
• Explanation: Assessing the difference in tutoring hours between first-generation and continuing-generation students.

g. College GPA and AP Classes Relationship

• Test: Correlation
• Explanation: Investigating the relationship between college GPA and the number of AP classes completed.

________________________________________

### Dataset Analysis Using SPSS

A. Relationship Between Living on Campus and Gender

• Test: Pearson Chi-Square Test
• Result: Chi-Square = 1.33, p = 0.249
• Interpretation: Proportion of students living on/off campus is not affected by gender. Table 1: The relationship between living in campus and gender

B. Relationship Between Time Studying and Time Partying

• Test: Correlation
• Result: Correlation = -0.167, p = 0.000
• Interpretation: Significant negative relationship; more time studying correlates with less time partying. Table 2: Relationship between time partying and time studying

C. Relationship Between Time Socializing and Time Partying

• Test: Correlation
• Result: Correlation = 0.529, p = 0.000
• Interpretation: Significant positive relationship; more time socializing correlates with more time partying. Table 3: Relationship between time partying and time socializing

### Dataset Analysis: Sex, Campus Living, and Time Partying

A. Test Selection for Interaction

• Test: Interaction Term in Regression Model
• Explanation: To check if differences in time spent partying depend on both sex and campus living situation.

B. Assumption Check

• Randomness of Residuals: Violated

C. Main Effects of Independent Variables

• Sex: p = 0.906 (Not significant)
• First Year Housing: p = 0.064 (Not significant) Table 4: Effects of independent and dependent variables

D. Interaction Effect

• Result: Interaction term p = 0.016 (Significant)
• Interpretation: Time spent partying tends to decrease when gender changes from male to female and housing status changes from on-campus to off-campus.

E. Effect Sizes

• Effect Size: 0.238 (Small)

### Analysis of Multiple Regression Model

A. Significant Predictor Variables

• Pared (Parents' Education): p-value=0.007 (<0.05), indicating significance.
• Hwork (Time Spent on Math Homework): p-value=0.048 (<0.05), suggesting significance.
• math_selfefficacy (Math Self-efficacy): p-value=0.000 (<0.05), demonstrating significance.
• math_anxiety (Math Anxiety): p-value=0.296 (>0.05), indicating non-significance. Table 5: predictor variables that influence math grades

Interpretation: The education level of parents, time spent on math homework, and students' math self-efficacy significantly influence math grades. However, math anxiety does not have a significant impact.

B. Variance Explanation and Significance

• Variance Explained (r²): 32.7%
• Model Significance: p-value=0.000 (<0.05)

Interpretation: The model explains 32.7% of the variance in math grades, and the overall model is statistically significant.

C. Assumption Violations

• Normality of Residuals: Residuals are normally distributed.
• Random Distribution Violation: Residuals increase with the increase in the dependent variable, violating the assumption of random distribution.

### True/False Statements

Multicollinearity arises when predictors are highly correlated with other predictors in a multiple regression model.

• True

Assumptions for a chi-square test of independence require cells of expected frequencies to have a sample size of at least five.

• True

In a regression model with a single independent and dependent variable, the standardized beta coefficient is the equivalent to the coefficient of a bivariate correlation between the independent and the dependent variables.

• True

When you have two non-continuous variables, a correlation is the most appropriate statistical test.

• True

### Relations in Journal of College Student Development Study Table 6: correlation matrix of demographic variables

a. GPA and CAM (Career Athletic Motivation Score)

• Correlation: -0.215
• Significance: p < 0.01
• Effect Size: Small
• Interpretation: A small negative correlation exists; as career athletic motivation increases, GPA tends to decrease.

b. GPA and AM (Academic Motivation)

• Correlation: 0.353
• Significance: p < 0.01
• Effect Size: Small
• Interpretation: A small positive correlation is observed; higher academic motivation is associated with higher GPA.

c. GPA and SAM (Student Athlete Motivation)

• Correlation: -0.118
• Significance: p < 0.01
• Effect Size: Small
• Interpretation: A small negative correlation; as student-athlete motivation increases, GPA tends to decrease.

Extra Credit - Interaction Effect

The figure indicates a significant interaction effect. When low belonging changes to high belonging, the change in the dependent variable is much higher than in the case of the same change in growth mindset for low belonging. This suggests that the impact of belonging on the dependent variable is more pronounced when accompanied by a shift from low to high belonging.