Bivariate Analysis Quick Reference

Decision guide for choosing and interpreting two-variable analyses in South Asian development research

METHOD SELECTION FLOWCHART

Variable 1	Variable 2	Method	South Asian Example
Continuous (Age, Income, Distance)	Continuous (Test scores, Yield, Rate)	Correlation + Regression	Years of education × Monthly income
Categorical (Gender, Caste, Region)	Continuous (Income, Health score)	t-test / ANOVA	Urban/Rural × Household income
Categorical (Treatment/Control)	Categorical (Success/Failure)	Chi-square test	Training program × Job placement
Continuous (Distance, Age, Score)	Binary (Yes/No, Pass/Fail)	Logistic Regression	Distance to clinic × Vaccination (Y/N)

CORRELATION ANALYSIS

When to use: Both variables continuous, want to measure relationship strength

Coefficient ranges:

r = -1: Perfect negative
r = 0: No relationship
r = +1: Perfect positive

Strength guide:
|r| < 0.3 = Weak
0.3 ≤ |r| < 0.7 = Moderate
|r| ≥ 0.7 = Strong

Key assumptions:
• Linear relationship
• Normal distribution
• No extreme outliers

SA Context: Check for seasonal patterns, cultural factors affecting linearity

SIMPLE REGRESSION

When to use: Want to predict one continuous variable from another

Key outputs:

Slope (β₁): Change in Y per unit X
Intercept (β₀): Y when X = 0
R²: % variance explained
p-value: Statistical significance

Model: Y = β₀ + β₁X
Slope interpretation: "For every 1-unit increase in X, Y changes by β₁ units"

Check for:
• Linear relationship
• Independence of residuals
• Equal variance (homoscedasticity)
• Normal residuals

SA Context: Consider clustering (villages, households), seasonal effects

CHI-SQUARE TEST

When to use: Both variables categorical, testing independence

Hypotheses:

H₀: Variables are independent
H₁: Variables are associated

If p < 0.05: Reject H₀
Variables are significantly associated

Requirements:
• Expected cell counts ≥ 5
• Independent observations
• Random sampling

SA Context: Be careful with caste/religion categories - ensure adequate sample sizes

T-TEST COMPARISON

When to use: Compare continuous outcome across 2 groups

Types:

Independent samples: Different people
Paired samples: Same people, 2 times

Effect size (Cohen's d):
0.2 = Small
0.5 = Medium
0.8 = Large effect

Check for:
• Normal distribution in each group
• Equal variances (Levene's test)
• Independent observations

SA Context: Consider cultural factors in group differences (urban/rural, gender roles)

Method	Minimum Sample	Recommended	Notes
Correlation	n ≥ 30	n ≥ 100	Larger samples for stability
Regression	n ≥ 50	n ≥ 100	More observations = better predictions
t-test	n ≥ 15 per group	n ≥ 30 per group	Equal group sizes preferred
Chi-square	Expected ≥ 5 per cell	Expected ≥ 10 per cell	Fisher's exact for small samples

TROUBLESHOOTING COMMON ISSUES

Problem: Non-linear relationship
Try log transformation or Spearman correlation

Problem: Outliers affecting results
Check if outliers are data errors or genuine cases
Report results with and without outliers

Problem: Assumption violations
Use robust methods (non-parametric tests)
Bootstrap confidence intervals

Problem: Small sample size
Use exact tests (Fisher's exact for chi-square)
Focus on effect sizes rather than p-values

Problem: Missing data
Check if missing is random
Consider implications for generalizability

INTERPRETATION CHECKLIST

□ Statistical significance: Is p-value < 0.05?
□ Practical significance: Is the effect size meaningful?
□ Confidence intervals: What's the range of plausible values?
□ Assumptions met: Are statistical assumptions satisfied?
□ Context considered: Does result make sense in SA development context?
□ Causation vs correlation: Are you claiming causation appropriately?
□ Generalizability: Can findings apply to broader population?
□ Policy implications: What actions does this suggest?

SOUTH ASIAN DEVELOPMENT CONTEXT REMINDERS

• Cultural factors: Consider how social norms affect variable relationships
• Seasonal patterns: Agricultural and monsoon cycles affect many outcomes
• Geographic clustering: Villages/districts may be more similar than random
• Gender dynamics: Male-female differences may reflect structural inequalities
• Caste/class effects: Social hierarchies influence access and outcomes
• Informal economy: Many relationships may not follow formal sector patterns
• Policy context: Government programs and policies affect variable relationships