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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