Q.21 Which statistical method is best suitable for testing the goodness of fit between an
observed and expected distribution?
1.Analysis of variance (ANOVA)
2.Chi-square test
3.F-Test
4.Kruskal-Wallis test
Chi-Square Test Goodness of Fit Observed Expected Distribution
The Chi-square test is the best statistical method for testing goodness of fit between observed and expected distributions.
Option Analysis
Analysis of Variance (ANOVA)
Compares means across multiple groups to detect differences, not distributions. Used for continuous data like treatment effects.
Chi-square test
Correct answer. Specifically designed for goodness-of-fit, it compares observed categorical frequencies (O) against expected (E) using χ² = Σ(Oᵢ - Eᵢ)²/Eᵢ, testing if sample matches hypothesized distribution (e.g., uniform, Poisson).
F-Test
Compares variances between two populations or within ANOVA models; assumes normality, unsuitable for categorical distribution fit.
Kruskal-Wallis test
Non-parametric ANOVA alternative for comparing medians across ≥3 independent groups; ranks data, not for single-sample fit.
Complete Guide: Chi-Square Test for Goodness of Fit
Chi-Square Goodness-of-Fit Mechanism
The test uses the formula χ² = Σ(Oᵢ - Eᵢ)²/Eᵢ where Oᵢ is observed frequency and Eᵢ is expected. Degrees of freedom = categories – 1. Reject null if p-value < 0.05, indicating poor fit.
Example: Testing if dice rolls are uniform (expected 1/6 each).
Method Comparison
| Method | Purpose | Data Type | Goodness-of-Fit? |
|---|---|---|---|
| ANOVA | Mean differences | Continuous | No |
| Chi-square | Distribution fit | Categorical counts | Yes |
| F-Test | Variance equality | Continuous | No |
| Kruskal-Wallis | Median comparison | Ordinal/ranked | No |
Applications in Biology
- Used in genetics (Mendelian ratios)
- Ecology (species distribution)
- Quality control
Assumptions: independent observations, expected ≥5 per cell.
