Q36: Which one of the following non-parametric tests is analogous to... - Statistical Methods II - Agricultural Statistics- ICAR JRF/SRF 2024 | Agrigyan

• Kolmogorov-Smirnov Test vs. Chi-Square Goodness-of-Fit:
• The Kolmogorov-Smirnov (K-S) test is a non-parametric test used to test whether a sample comes from a specific continuous distribution, functioning as the non-parametric analogue to the Chi-square goodness-of-fit test.
• Key Advantages of K-S Test:
• Does not require binning data into arbitrary intervals or categories (unlike Chi-square).
• Works effectively with small sample sizes.
• Compares the empirical cumulative distribution function $F_n(x)$ with the theoretical CDF $F_0(x)$ using the supremum distance statistic: $D = \sup_x |F_n(x) - F_0(x)|$.
• Other Options:
• Median test / Mann-Whitney U test / Wilcoxon test: Used for testing differences in location/medians between two independent or paired groups, not goodness of fit.
• Conclusion: The analogue is the Kolmogorov-Smirnov test (Option 2).

Correct option: (2) Kolmogorov-Smirnov test