?? STATISTICAL INFERENCE: A COMPREHENSIVE GUIDE TO HYPOTHESIS TESTING AND DECISION MAKING

Detailed Test Guidelines

1. T-Tests

• Independent T-test For: Two separate groups Examples: Control vs. Treatment groups Men vs. Women scores Old vs. New method
• Paired T-test For: Before/After comparisons Examples: Pre/Post training scores Before/After treatment Weight loss measurements

2. ANOVA Tests

• One-way ANOVA For: Three+ groups, one factor Examples: Three teaching methods Four drug doses Multiple brands comparison
• Two-way ANOVA For: Two factors together Examples: Gender × Age effects Temperature × Humidity Method × Class size

3. Chi-Square Tests

• Goodness of Fit For: Comparing to expected pattern Examples: Dice fairness Population distribution Production quality
• Independence Test For: Category relationships Examples: Gender vs. Voting Education vs. Job Age vs. Preferences

4. Poisson Distribution

• For: Rare event counting
• Examples: Customer arrivals System failures Accident occurrences

Quick Check Lists

Use T-Test When:

? Comparing two groups ? Data is numerical ? Normal distribution ? Sample size < 30

Use ANOVA When:

? Three or more groups ? Numerical data ? Normal distribution ? Similar group variances

Use Chi-Square When:

? Working with categories ? Enough data per category (>5) ? Independent observations ? Comparing patterns

Use Poisson When:

? Counting rare events ? Events are independent ? Fixed time/space intervals ? Constant average rate

Common Mistakes to Avoid

DON'T Use T-Test When:

? More than two groups

? Categorical data

? Highly skewed data

DON'T Use ANOVA When:

? Only two groups

? Dependent samples

? Very unequal variances

DON'T Use Chi-Square When:

? Small samples (<5 per category)

? Numerical data

? Dependent events

DON'T Use Poisson When:

? Common events

? Changing rates

? Dependent events