Goodness-of-fit test idea
Big idea: Goodness-of-fit checks whether observed category counts match a claimed distribution.
Example: Is a die fair? Compare observed rolls to expected equal frequencies.
Same chi-squared framework: You still use chi-squared formula. The difference is one categorical variable with expected proportions.
Expected counts from proportions
Worked example
A spinner has 4 colors with expected proportions 0.1, 0.2, 0.3, 0.4. After 200 spins, find expected counts.
Step by step
- Multiply total by each proportion
- E1=200×0.1=20, E2=40, E3=60, E4=80
- Check total expected = 200
Final answer
Expected counts are 20, 40, 60, 80.
Never wonder what to study next
Get a personalized daily plan based on your exam date, progress, and weak areas. We'll tell you exactly what to review each day.
Try Free Study Plan7-day free trial • No card required
Chi-squared and degrees of freedom
Degrees of freedom: For goodness-of-fit with k categories and no estimated parameters, df = k - 1.
Worked example
There are 6 categories. What is df?
Solution
- Use df = k - 1
- df = 6 - 1 = 5
Final answer
Degrees of freedom = 5.
Interpretation and exam communication
Weak conclusion
- Only writes reject/fail reject
- No context
- No mention of model fit
Strong conclusion
- States decision and context
- Explains fit to claimed distribution
- Uses significance level language
Exam Tips:
- State H0 and H1 in words.
- Use p-value or critical-value rule consistently.
- Final sentence must reference context data.