Q.6 Which of the following is a non-parametric test?
(1) Chi-square test
(2) T-test
(3) F-test
(4) Z-test
Non-Parametric Tests Explained: MCQ Answer Revealed
Non-parametric tests analyze data without assuming a specific distribution (such as normality).
They are ideal for ordinal, nominal, or non-normal continuous data.
In the MCQ: “Which of the following is a non-parametric test?”
The correct answer is:
✔ Option (1) – Chi-square Test
Correct Answer: Chi-square Test
The Chi-square (χ²) test is a classic non-parametric test that compares
observed and expected frequencies in categorical data.
Key Uses:
- Test of Independence (e.g., gender vs voting preference)
- Goodness-of-Fit (e.g., testing dice fairness)
Assumptions:
- No assumption of normal distribution
- Expected frequency ≥ 5 in at least 80% of cells
Formula:
χ² = Σ ((Oi − Ei)² / Ei)
Where:
- Oi = Observed frequency
- Ei = Expected frequency
Why Not the Other Options?
Option (2) – T-test (Parametric)
Used to compare means of small samples. Assumes normal distribution and equal variances.
Formula:
t = (x̄₁ − x̄₂) / √(s²(1/n₁ + 1/n₂))
Option (3) – F-test (Parametric)
Tests equality of variances, commonly used in ANOVA. Assumes normality.
Formula:
F = s₁² / s₂²
Option (4) – Z-test (Parametric)
Used for large samples (n > 30). Requires known population variance and normality.
Formula:
z = (x̄ − μ) / (σ / √n)
Quick Comparison: Parametric vs Non-Parametric Tests
| Test | Type | Key Assumption | Data Type | Best For |
|---|---|---|---|---|
| Chi-square | Non-parametric | Frequency counts | Categorical | Independence / Goodness-of-fit |
| T-test | Parametric | Normality | Continuous (means) | Small sample means |
| F-test | Parametric | Normality | Continuous (variance) | Variance comparison |
| Z-test | Parametric | Normality (large sample) | Continuous (means) | Large sample means |
Real-World Applications
Parametric tests like T-test and Z-test are ideal for normally distributed data
such as enzyme activity levels.
However, the Chi-square test is widely used in genetics
(Mendelian ratios), microbiome studies (species counts),
and survey analysis (categorical responses).
