Q 586. Kruskal Wallis Test is an alternative to Mood's Median Test. Compare the two tests and highlight the differences in their assumptions, benefits, limitations, usage, etc. Provide examples to support your answer.

 

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Kruskal-Wallis Test

 

Kruskal-Wallis Test is known to be used as non-parametric test which his generally used when we want to compare the medians of 2 groups or more independent groups.

With the help of this test user able to know that the samples coming from the same group or any different group. Also, it can evaluate that is there any significant difference between them.

 

Although, both tests are quite similar in every manner however still there are few differences in their limitations:

 

Kruskal-Wallis Test	Mood's median test
This can be appropriate when sample size is large	This is useful for small sample size groups
More useful while comparing multiple factors	Can compare groups based on a single factor
It is more powerful when we are working for 3 or more than 3 groups.   Power increases when no of group increases	Less powerful while working on 2 or more than 2 groups.   Power decreases when group size increases.
This test is appropriate while comparing the central tendencies for 3 or mare than 3 independent groups.	This test is more useful when we want to compare 2 or more groups with non-normal data

 

Example:

Let suppose we want to compare performance of students in three different schools X, Y, Z.

When we collect the data, it will show the exam score for all students in every school. So, the scores would be ordinal data. Then

Our Ho is – no significant difference in performance.

and Ha is – significant difference in performance.

So, we should perform Kruskal Wallis test to check if there are significantly difference or not in the results.

In the end, both tests are quite similar with non-parametric alternatives to compare groups with ordinal data.  The main factor is depending on the numbers of groups which we are going to compare and specific research questions.

	Kruskal-Wallis test	Mood’s-Median test
Number of groups	Non-parametric test used to compare medians of two or more groups. Ex. Comparing exam scores of 3 groups. Kruskal Walley test will rank all exam scores from the combined three groups and calculate test statistics. Mood's Median test is not applicable in this scenario as it is specifically designed for comparing exactly two groups.	Non-parametric test used to compare medians between exactly two independent groups. Ex. Comparing satisfaction ratings of two group (before and after service improvement). In comparing exactly 2 group, we can use Mood’s Median test and also Kruskal Walley test.
Applicable scenario	Appropriate when there are three or more independent groups Ex. Comparing median weight of three different new born babies. Comparing the median employees in three different departments basis their performance rating. Comparing the median number of errors made by students in three different math classes.	Suitable when you have exactly two independent groups Ex. You are comparing the median scores of students on a math test before and after receiving tutoring. You are comparing the median heights of men and women. You are comparing the median number of days spent in hospital for patients with different types of cancer
Ranking process	It assigns a rank to each observation with the smallest observation getting the rank of 1 while the largest observation getting the rank of the total number of observations. These allotted ranks are used to compute the test statistics as a difference in the median between different samples.	Observations greater than median gets assigned a rank of 1. Observations equal to median gets assigned the rank of 0 while the ones smaller than median gets assigned the rank of (-1). It assigns rank basis if the observation is larger or smaller than overall median and these allotted ranks are used to calculate test statistics.
Assumptions	Groups being compared have similar shapes and variances. It does not assume specific data distribution. It assumes that the data from each sample is drawn from a continuous distribution (continuous like weight in kilograms or ordinal like Likert scale) It does not make any assumption about the shape of the distribution. Ex. Determine whether or not 3 drugs have different effect on knee pain in scale of 1 to 100.	It is a distribution independent test and does not assume any specific distribution for the data. It assumes that the data for each sample is drawn from a symmetric distribution. It assumes data for each sample comes from populations with a continuous rather than discrete distribution. The distributions of populations the samples were drawn from all have same shape. Ex. Determine if there exists statistical difference in sales volume between 2 cities.
Handle ties	Robust in handling ties naturally owing to its ranking procedure	Can be less robust to ties specifically in small samples
Outliers	Kruskal Walley test is more sensitive to outliers than Mood’s Median test as Kruskal Walley test takes into account the ranks of all observations. Few outliers in data can impact the ranks of other observations leading to incorrectly rejecting the null hypothesis.	Mood's median test is more robust to outliers than the Kruskal-Wallis test, but is less powerful in the absence of outliers. Mood’s median test takes into account whether an observation is smaller or larger than the median.
Power	Usually more powerful than Mood's Median test.	Less robust than Kruskal Walley test.
Sample size	With larger sample size tends to have higher statistical power It can still be applied to smaller samples but with reduced power	Generally more suitable for smaller sample size; less powerful with larger sample sizes
Post hoc testing (determine where difference lies)	If Kruskal Walley test indicates a significant difference among the group, post hoc tests can be conducted to determine which specific groups differ significantly from each other	Mood's Median test is not typically followed by post hoc tests since it only compares two groups directly

 

Test Name	Kruskal Wallis Test	Mood's Median Test
Method	The Kruskal-Wallis is a nonparametric test for comparing two or more sample medians, Statistic is based on comparing mean ranks for each group versus the mean rank for all observations.	It is one of the nonparametric test which is used to compare medians of two independent samples. It can also be used to estimate whether the median of any two independent samples is equal.
Differences	Samples are random samples The two samples are mutually independent The variable is continuous	The observations are independent both within and between samples. The observations come from a population with a continuous distribution The samples have drawn from the same population with equal medians
Benefits	It is used for comparing two or more independent samples of equal or different sample sizes.	Mood’s Median Test is suitable when the dependent variable is continuous or discrete count, and the independent variables are discrete with two or more attributes.
Limitations	The Kruskal- Wallis test is not as powerful as other parametric tests like ANOVA,  henec may need a larger sample size to get an adequate power level when using this test.	This test just takes into account whether a data element is larger or smaller than the median. It is more useful for smaller sample sizes when the data contains few outliers as this test only focuses on median value instead of ranking
Usage	This is used as a test of equality of medians or even means	It is used for determining whether the medians of two or more sample data sets come from the same population or not

Ankur Sarkar has provided the best answer to this question.

 

P.S. Many answers have not been approved due to a high % of AI-generated content and/or plagiarism.