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Independent T-Test Assumption Checking
Complete assumption validation for comparing two groups with a t-test. Demonstrates the five key assumptions (missing data, normality, homogeneity of variance, independence, outliers) with educational explanations, Q-Q plot interpretation guidance, and methods section template.
Input
What you provide to the skill
I’m comparing exam scores between 45 students using traditional vs experimental study methods. I have complete data and plan to run an independent t-test.
Output
What the skill generates for you
STATISTICAL ASSUMPTION CHECKER & DIAGNOSTIC GUIDE
Educational Tool for Graduate Statistics Students
YOUR ANALYSIS CONTEXT:
Research Question: Comparing exam scores between study methods
Variables: study_method (Traditional vs Experimental), exam_score
Planned Test: Independent samples t-test
Sample Size: n = 45 students per group (90 total)
Data Status: Complete data, no missing values
======================================================================
CHECK 1: MISSING DATA
WHY THIS MATTERS:
Missing values block all subsequent diagnostics. You must handle them
before checking other assumptions.
YOUR DATA ASSESSMENT:
Total observations: 90
Total missing values: 0
✓ PASS: No missing data detected
======================================================================
CHECK 2: NORMALITY
WHY THIS MATTERS:
Independent samples t-test assumes the outcome variable is normally
distributed within each group. When data are normal, the sampling
distribution of means is also normal, making p-values accurate.
WHAT YOU NEED TO KNOW:
• Check normality SEPARATELY for each group
• Visual inspection (Q-Q plot) is most important
• With n=45 per group, you have moderate sample size
• Central Limit Theorem provides some protection
TRADITIONAL GROUP (n=45):
Shapiro-Wilk Test:
W-statistic: 0.9816
p-value: 0.6592
Interpretation: PASS - Cannot reject normality (p > 0.05) ✓
EXPERIMENTAL GROUP (n=45):
Shapiro-Wilk Test:
W-statistic: 0.9837
p-value: 0.7591
Interpretation: PASS - Cannot reject normality (p > 0.05) ✓
HOW TO INTERPRET THE Q-Q PLOTS:
The Q-Q plot compares your data’s quantiles to a normal distribution.
✓ Points follow the diagonal line closely → Data is normal
✗ S-shaped curve → Skewed distribution
✗ Points curve away at both ends → Heavy or light tails
SAMPLE SIZE CONTEXT:
Moderate sample (n=45)
• Central Limit Theorem provides good robustness ✓
• Parametric tests reasonably robust to mild violations
• Statistical tests have adequate power to detect problems
✓ NORMALITY DECISION: PASS
======================================================================
CHECK 3: HOMOGENEITY OF VARIANCE
WHY THIS MATTERS:
Standard t-test assumes both groups have equal variance. If violated,
pooled variance estimate is wrong → p-values unreliable.
Variance Ratio (max/min): 1.547
Rule of thumb: Ratio < 3 suggests homogeneity
Your ratio: ✓ EXCELLENT (< 2)
Levene’s Test:
F-statistic: 3.1829
p-value: 0.0782
Interpretation: PASS - Cannot reject equal variances (p > 0.05) ✓
✓ HOMOGENEITY DECISION: PASS - Proceed with standard t-test
======================================================================
CHECK 4: INDEPENDENCE
WHY THIS MATTERS:
t-test assumes each observation is independent. Violations inflate
false positive rates.
YOUR DESIGN ASSESSMENT:
• Different students in each condition ✓
• Each student measured once ✓
• No clustering structure ✓
• Random assignment to groups ✓
✓ INDEPENDENCE: PASS - Met by study design
======================================================================
CHECK 5: OUTLIERS
Z-score method (|z| > 3): 0 outliers
IQR method: 0 outliers
✓ NO OUTLIERS DETECTED
======================================================================
COMPREHENSIVE SUMMARY
ASSUMPTION RESULTS:
- No Missing Data: ✓ PASS
- Normality: ✓ PASS
- Homogeneity of Variance: ✓ PASS
- Independence: ✓ PASS (by design)
- Outliers: NONE DETECTED
✓ ALL ASSUMPTIONS MET - PROCEED WITH STANDARD T-TEST
======================================================================
WHAT TO REPORT IN YOUR PAPER
“Assumptions for independent samples t-test were evaluated. Both groups
showed normal distributions (Shapiro-Wilk p > .05) supported by Q-Q plot
inspection. Levene’s test indicated homogeneity of variance (F = 3.18,
p = .078). No outliers were detected. Independence was satisfied by
design. Therefore, standard independent samples t-test was appropriate.”
About This Skill
Educational guide for graduate statistics students learning to test and interpret parametric test assumptions including normality, homogeneity of variance, linearity, independence, and outliers with clear explanations.
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