Statistical Analysis and APA Reporting Templates
Multiple Linear Regression Analysis
Purpose: Predict a continuous dependent variable using two or more predictors.
Assumptions: Linearity, independence, homoscedasticity, normality of residuals, and no multicollinearity.
How to Read:
- Model Summary: R²
- ANOVA: F and p
- Coefficients: B, β, t, and p
Interpretation Formula: F(df1, df2) = value, p = value, R² = value.
Effect Size: R² = .02 (small), .13 (medium), .26 (large).
APA Template for Reporting Model and Predictors:
ANOVA Table: Regression: F(2, 47) = 18.34, p = .001
APA Template:
A multiple linear regression was conducted to determine if hours studied and class attendance significantly predicted students’ final exam scores. The predictors significantly explained the variance in exam scores, F(2, 47) = 18.34, p = .001, R² = .439, indicating that the model accounted for 43.9% of the total variance.
- Hours Studied: B = 4.50, SE = 1.10, β = .52, t(47) = 4.09, p = .001.
- Attendance: B = 0.25, SE = 0.08, β = .31, t(47) = 3.12, p = .003.
Independent Samples t-Test
Purpose: Compare the means of two independent groups.
Assumptions: Independence, normality, and homogeneity of variance.
How to Read: Group Statistics, Levene’s Test, t, df, and p.
Effect Size: Cohen’s d (.20 small, .50 medium, .80 large).
APA Template:
An independent-samples t-test was conducted to determine if there was a significant difference in annual salary between male and female employees. Levene’s test indicated equal variances assumed, F = 0.35, p = .556. Male employees (M = 55,000.00, SD = 4,500.00) reported significantly higher annual salaries than female employees (M = 51,000.00, SD = 4,200.00), t(58) = 3.56, p = .001, d = 0.92.
Paired Samples t-Test
Purpose: Compare the same participants at two different time points.
How to Read: Paired Samples Statistics and Paired Samples Test.
Effect Size: dz (.20 small, .50 medium, .80 large).
APA Template:
A paired-samples t-test was computed to evaluate the impact of a clinical mindfulness intervention on patients’ clinical anxiety levels. There was a statistically significant decrease in anxiety scores from pre-intervention (M = 7.80, SD = 1.40) to post-intervention (M = 4.20, SD = 1.10), t(24) = 14.40, p < .001, dz = 2.88.
One-Way ANOVA
Purpose: Compare three or more independent groups.
How to Read: Descriptives, ANOVA table, and Post Hoc tests.
Effect Size: η² or ηp² (.01 small, .06 medium, .14 large).
APA Template:
A one-way between-subjects ANOVA was conducted to compare the effect of three treatment protocols on patient well-being scores. There was a statistically significant effect of treatment type on well-being, F(2, 37) = 5.65, p = .007, ηp² = .234. Post hoc Tukey HSD comparisons indicated that CBT Therapy scores were significantly higher than those of the Meditation and Control groups.
Pearson Correlation
Purpose: Examine the strength and direction of a relationship.
Interpretation: .10 weak, .30 moderate, .50 strong.
APA Format: r(df) = value, p = value.
APA Template:
A Pearson correlation coefficient was calculated to assess the linear relationship between employee job satisfaction and workplace stress. There was a significant negative correlation, r(28) = -.58, p = .002.
Chi-Square Test of Independence
Purpose: Examine the relationship between categorical variables.
How to Read: Crosstabs and the Chi-Square table.
Effect Size: Cramer’s V (.10 small, .30 medium, .50 large).
APA Template:
A chi-square test of independence was performed to examine the relation between completing a corporate training program and employment outcomes. The relationship was statistically significant, χ²(1, N = 80) = 13.33, p < .001, V = .41.
SPSS Output Interpretation Checklist
- State the specific statistical test used.
- Report assumptions where relevant.
- Report descriptive statistics (e.g., Mean and Standard Deviation).
- Report the test statistic, degrees of freedom, and p-value.
- Report the effect size.
- Interpret the findings within the specific context of the study.