Which one of the following is a non-parametric test?

Correct option is A

The χ2\chi^2χ²-test (Chi-Square test) is a non-parametric test used to determine if there is a significant association between categorical variables or to test the goodness of fit. Non-parametric tests do not assume any specific distribution of the data (e.g., normal distribution), making them suitable for analyzing nominal or ordinal data.

• t-test, z-test, and F-test are parametric tests, meaning they rely on specific assumptions about the population distribution, such as normality or homogeneity of variances.

Key Reasons:

1. The χ2\chi^2χ^$2$-test is applied to frequency data or observed vs. expected data.
2. It does not require assumptions about the population distribution (non-parametric).
3. Common applications include testing independence in contingency tables or goodness-of-fit for categorical data.

Information Booster

Parametric vs. Non-Parametric Tests

1. Parametric Tests:

   • Assume a specific distribution (usually normal).
   • Examples: t-test, z-test, F-test.
   • Applied when data are measured on an interval or ratio scale.

2. Non-Parametric Tests:

   • No distributional assumptions.
   • Suitable for nominal or ordinal data.
   • Examples: χ2\chi^2χ^$2$-test, Mann-Whitney U test, Kruskal-Wallis test.

Additional Knowledge

1. t-test: Compares means of two groups under the assumption of normality.
2. z-test: Used for comparing proportions or means with a large sample size.
3. F-test: Compares variances of two or more groups, often used in ANOVA.
4. Why Non-Parametric Tests?
   • Useful when assumptions of parametric tests (normality, equal variances) are violated.
   • Robust for small sample sizes or skewed data.

Thus, the χ2\chi^2χ^$2$-test is the correct answer as it is a prominent non-parametric test.