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?

• A. ANOVA
• B. Student T test
• C. Fisher LSD test
• D. Kruskal-Wallis test

Hint:

In GPAT, remember: Parametric = Normality assumed, Non-parametric = No normality assumption. Kruskal-Wallis is a non-parametric alternative to one-way ANOVA.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
A test is called parametric when it needs the data to follow a known distribution, usually a normal one, before its results can be trusted. A test is called non-parametric, or distribution free, when it works without that assumption. The question wants the non-parametric option among the four.

Step 2: Key Formula or Approach:
Non-parametric tests usually work by converting raw scores into ranks and comparing those ranks across groups, instead of comparing means directly. So the approach here is to ask which of the four listed tests uses ranks rather than raw means, and does not need normal or symmetric data.

Step 3: Detailed Explanation:
ANOVA compares group means directly and needs the groups to be normally distributed with similar spread, so it is a parametric test.
The Student T test compares two group means and also needs the population to be normal, so it is parametric too.
The Fisher LSD test is applied after ANOVA to compare specific pairs of groups, and since it depends on the ANOVA result, it carries the same normality requirement.
The Kruskal-Wallis test replaces the raw data with ranks before comparing the groups, which means its result does not depend on the data being normal or following any set distribution.

Step 4: Final Answer:
The Kruskal-Wallis test is the one that does not require the assumption of a normal or symmetric population distribution.