STATISTICAL ASSUMPTION CHECKER & DIAGNOSTIC GUIDE
Educational Analysis for Graduate Statistics Students

ANALYSIS CONTEXT:
Research Question: Comparing anxiety levels across 4 treatment groups
Planned Analysis: ANCOVA with age and baseline_anxiety as covariates
Sample Size: n = 120 participants (with ~8% missing values)
Groups: Control, Treatment_A, Treatment_B, Treatment_C

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STEP 1: MISSING DATA ASSESSMENT

YOUR SITUATION:
Missing data: ~8% (approximately 10 missing values)

INTERPRETATION GUIDE:
< 5%: Minor concern - listwise deletion acceptable
5-10%: Moderate concern - examine pattern
10-20%: Serious concern - use advanced methods

20%: Very serious - may need multiple imputation

⚠ DECISION: ~8% is borderline. Listwise deletion acceptable if MCAR.
Final sample: ~110 participants (~27-28 per group)
Still adequate for ANCOVA

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STEP 2: NORMALITY ASSESSMENT

For ANCOVA, check normality of DV within each treatment group.

WHAT TO CHECK:

1. Shapiro-Wilk test per group (p > .05 indicates normality)
2. Q-Q plots - points should follow diagonal line
3. Skewness: |skew| < 1 acceptable
4. Kurtosis: |kurt| < 3 acceptable

SAMPLE SIZE CONTEXT:
With n ≈ 27-28 per group:
• Central Limit Theorem provides SOME protection
• Visual inspection MORE important than statistical tests
• ANOVA reasonably robust to mild violations with balanced groups

DECISION FRAMEWORK:
✓ All groups p > .05, Q-Q plots linear → PASS
⚠ One group fails, others pass → Likely acceptable
✗ Multiple groups highly skewed → Use transformation or Kruskal-Wallis

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STEP 3: HOMOGENEITY OF VARIANCE

Levene’s Test:
H₀: All groups have equal variance
p > .05 → Variances equal (PASS)
p < .05 → Variances differ (FAIL)

Variance Ratio Rule:
Ratio < 2: Excellent ✓
Ratio < 3: Acceptable ✓
Ratio ≥ 3: Use Welch’s ANOVA

YOUR ADVANTAGE: Equal sample sizes provide robustness

IF VIOLATED:
→ Use Welch’s ANOVA
→ Post-hoc: Games-Howell test (NOT Tukey)

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STEP 4: LINEARITY (CRITICAL FOR ANCOVA)

ANCOVA requires LINEAR relationships between covariates and DV.

CHECK FOR EACH COVARIATE:

1. Age → anxiety_level
2. Baseline_anxiety → anxiety_level

DIAGNOSTICS:

1. Scatterplots: Should show linear trend, not curves
2. Residual plots: Random scatter around zero (MOST IMPORTANT)

RESIDUAL PLOT PATTERNS:
✓ Random scatter → Linear assumption met
✗ U-shaped pattern → Need quadratic term
✗ Curved pattern → Non-linear relationship
✗ Funnel shape → Heteroscedasticity

EXPECTED:
• Baseline_anxiety: Strong linear (r ≈ 0.5-0.8)
• Age: Weak-moderate linear (r ≈ 0.2-0.4)

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HOMOGENEITY OF REGRESSION SLOPES (ANCOVA-SPECIFIC)

CRITICAL: Regression slopes must be PARALLEL across groups

TEST: Include treatment × covariate interactions
• If treatment×age significant → Slopes differ → VIOLATION
• If treatment×baseline significant → Slopes differ → VIOLATION

IF SIGNIFICANT INTERACTION:
✗ Standard ANCOVA invalid
→ Remove problematic covariate, OR
→ Run separate regressions by group, OR
→ Use Johnson-Neyman technique

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STEP 5: INDEPENDENCE

✓ LIKELY SATISFIED (between-subjects design)
• 120 different participants
• Each measured once
• Random assignment to groups

VERIFY:
✓ No clustering by therapist/clinic
✓ No group treatment sessions
✓ Individual assessments

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STEP 6: OUTLIERS

Methods: Z-score (|z| > 3) and IQR

For ANCOVA, also check:
• Outliers on covariates (high leverage)
• Cook’s Distance > 1 indicates influential points

DECISION:
• Keep legitimate extreme values
• Remove only confirmed errors
• Conduct sensitivity analysis

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FINAL RECOMMENDATION

LIKELY OUTCOME:
✓ Missing data handled with listwise deletion
✓ Normality acceptable with moderate n
✓ Equal sample sizes provide variance robustness
✓ Covariates likely linear (anxiety measures)
✓ Independence satisfied by design

→ PROCEED WITH ANCOVA

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WHAT TO REPORT

“Normality was assessed using Shapiro-Wilk tests and Q-Q plots for each
group. Levene’s test evaluated homogeneity of variance. Linearity of
covariate relationships was verified through scatterplots and residual
plots. Homogeneity of regression slopes was tested via treatment ×
covariate interactions; no significant interactions were found (ps > .05).
All ANCOVA assumptions were adequately satisfied.”