Course: Applied Statistics and Data Analysis | MTC — Assignment 01
Supervised by: Dr. Noha Nabawy
Date: March 10, 2026
A complete statistical analysis report of a student performance dataset (n=20) using IBM SPSS Statistics v29. The analysis covers the full data science pipeline: data preparation, outlier detection, descriptive statistics, inferential testing, and correlation analysis — with the aim of understanding the relationships between gender, study hours, GPA, and attendance.
- Prepare the dataset: recode string variables, handle missing data, detect and treat outliers
- Compute descriptive statistics for StudyHours, GPA, and Attendance — disaggregated by gender
- Test whether GPA differs significantly between male and female students (independent-samples t-test)
- Quantify the linear association between weekly study hours and GPA (Pearson correlation)
- Present findings through professional tables and embedded SPSS output charts
| Variable | Type | Description | Scale |
|---|---|---|---|
| ID | Numeric | Unique student identifier | Nominal |
| Gender | String → Recoded | Student gender (Male/Female) | Nominal |
| StudyHours | Numeric | Weekly hours devoted to studying | Ratio |
| GPA | Numeric | Grade Point Average (0.0–4.0) | Ratio |
| Attendance | Numeric | Class attendance percentage (0–100) | Ratio |
| Finding | Result | Statistical Status |
|---|---|---|
| Missing GPA values | 1 of 20 (5%) | Excluded via listwise deletion |
| Outlier — Study Hours | Case 19: 200 hrs/week | Filtered — sensitivity analysis run |
| Female mean GPA | 3.41 | Slightly higher than males |
| Male mean GPA | 3.12 | Not significantly different |
| GPA gender difference | t(16) = -1.44, p = .170 | Not statistically significant |
| Study Hours vs. GPA | r = .876, p < .001 | Strong positive correlation |
📌 Key Takeaway: Study effort is a strong predictor of GPA, while gender differences are not statistically significant in this sample.
- Recoded string
Gendervariable to numeric using SPSS syntax (RECODE) - Identified 1 system-missing GPA value (5%) — applied listwise deletion
- Retained all other variables for the missing case
- Detected extreme outlier: Case 19 (Male) — 200 hrs/week via Boxplot & Stem-and-Leaf plots
- Outlier inflated male mean from 13.0 → 31.7 hrs and SD from 7.4 → 59.5 (706% inflation)
- Applied sensitivity filter:
StudyHours < 50→ N reduced to 19
| Variable | N | Min | Max | Mean | Std. Dev |
|---|---|---|---|---|---|
| StudyHours | 19 | 7 | 30 | 13.21 | 5.308 |
| GPA | 18 | 2.5 | 4.0 | 3.267 | 0.4393 |
| Attendance | 18 | 65 | 98 | 83.94 | 9.334 |
Hypotheses:
- H₀: No significant difference in mean GPA between males and females
- H₁: Significant difference exists (α = .05, two-tailed)
Results:
| Group | N | Mean GPA | Std. Dev |
|---|---|---|---|
| Male | 9 | 3.122 | 0.4969 |
| Female | 9 | 3.411 | 0.3408 |
- Levene's Test: F = 0.970, p = .339 → Equal variances assumed
- t-Test: t(16) = -1.44, p = .170 → Fail to reject H₀
- Cohen's d = -0.678 → Medium effect size (small sample limits power)
- r = .876, n = 18, p < .001 (filtered dataset)
- r² ≈ .77 → ~77% of GPA variance explained by study hours
- Full-dataset scatterplot shows R² = 0.019 — demonstrates severe outlier suppression effect
# Gender Recoding
RECODE Gender ('Male'=1)('Female'=2) INTO Gendernum.
VARIABLE LABELS Gendernum '1=Male, 2=Female'.
EXECUTE.
# Outlier Filter
COMPUTE filter=StudyHours < 50.
VARIABLE LABELS filter 'StudyHours < 50 FILTER'.
FILTER BY filter.
EXECUTE.
| Tool | Purpose |
|---|---|
| IBM SPSS Statistics v29 | Full statistical analysis platform |
| Descriptive Statistics (EXAMINE) | Mean, SD, Skewness, Boxplots |
| Independent-Samples t-Test | GPA comparison by gender |
| Pearson Correlation (CORRELATIONS) | Study Hours vs. GPA relationship |
| Boxplots & Stem-and-Leaf Plots | Outlier detection & visualization |
| Bar Charts & Scatterplots | Result visualization |
- Small sample size (N=20) limits statistical power and generalizability
- One extreme outlier required exclusion, reducing male group to n=9
- Cross-sectional design prevents causal inference
- r=.876 may partly reflect confounds (prior ability, course difficulty)
- IBM Corp. (2023). IBM SPSS Statistics for Windows, Version 29.0. Armonk, NY: IBM Corp.
- Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum.
- Field, A. (2018). Discovering Statistics Using IBM SPSS Statistics (5th ed.). SAGE Publications.
- Tabachnick, B. G., & Fidell, L. S. (2019). Using Multivariate Statistics (7th ed.). Pearson.
Mohamed Abd Elsalam Mohamed Gharieb
Data Scientist & ML Engineer | IBM & Google Certified
Prepared under supervision of Dr. Noha Nabawy | Applied Statistics and Data Analysis — MTC | March 2026