Question:
Which of the following is the differential test i.e. it does not require the need to make assumption of population following normal or differential distributed?
Which of the following is the differential test i.e. it does not require the need to make assumption of population following normal or differential distributed?
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In GPAT, remember: Parametric = Normality assumed, Non-parametric = No normality assumption. Kruskal-Wallis is a non-parametric alternative to one-way ANOVA.
Updated On: Jul 14, 2026
- ANOVA
- Student T test
- Fisher LSD test
- Kruskal-Wallis test
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The Correct Option is D
Approach Solution - 1
The Kruskal-Wallis test is a non-parametric statistical test used to compare three or more independent groups. Unlike parametric tests like ANOVA or t-tests, it does not assume normal distribution of the data. Instead, it ranks the data and compares the mean ranks between the groups.
Key Characteristics:
- It is an extension of the Mann–Whitney U test to more than two groups.
- Useful when data is ordinal or not normally distributed.
- It compares medians rather than means.
Analysis of Other Options:
- (a) ANOVA: Assumes data is normally distributed and groups have equal variances.
- (b) Student T test: A parametric test that compares means and assumes normality.
- (c) Fisher LSD test: A post-hoc test following ANOVA, also assumes normal distribution.
Key Characteristics:
- It is an extension of the Mann–Whitney U test to more than two groups.
- Useful when data is ordinal or not normally distributed.
- It compares medians rather than means.
Analysis of Other Options:
- (a) ANOVA: Assumes data is normally distributed and groups have equal variances.
- (b) Student T test: A parametric test that compares means and assumes normality.
- (c) Fisher LSD test: A post-hoc test following ANOVA, also assumes normal distribution.
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Approach Solution -2
The question is looking for a test that can compare groups without needing to assume the data follows a normal distribution. The way to answer this is to check the assumptions each listed test needs.
- ANOVA: Analysis of variance compares the means of three or more groups, but it only gives valid results when the data in each group is roughly normally distributed and the group variances are similar. It needs the normality assumption, so it does not fit.
- Student T test: This test compares the means of two groups and also assumes the underlying population is normally distributed. Since it relies on this assumption, it is ruled out.
- Fisher LSD test: This is a follow up test run after ANOVA to find which specific group pairs differ. Because it is built on top of ANOVA, it inherits the same normality assumption and cannot be the answer.
- Kruskal-Wallis test: This test compares three or more groups by ranking all the data together instead of working with the raw values and their means. Since it works on ranks, it does not need the data to follow any particular distribution, which is exactly what the question is asking for.
Only the Kruskal-Wallis test avoids the normality assumption that the other three tests all depend on.
So the correct answer is Kruskal-Wallis test.
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