Q 585. Under what situations should someone use the Mood's Median test? Elaborate with examples. Also highlight what are the limitations in its usage.

 

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Mood’s Median Test

 

It is a non-parametric statistical test which is generally used to determine the significant differences between the two medians or the two independent groups.

As suggested, this should be used when we have ordinal data. Also, other assumptions like- ANOVA and T-test are not met.

In below situations we can use Mood’s Median Test

·       When we have ordinal data

·       When we are comparing two sets, both should be independent. No influence should be imposed on each other.

·       Homogeneity of medians – This test is more useful when medians are different among the group.

·       Small sample size – This test can work accurately when sample size is small. Where we think that assumptions might be disregarded due to lack of normality.

·       Non normal data distribution – When data is not normally distributed and equal variance are not met. We can use Mood’s Median Test. It can give better result.

 

Real scenario:

·       Exam Scores which are on scale of 1 to 10.

·       Customer Satisfaction level on a scale from 1 to 5.

 

Limitations:

Limited power – This test has limited power as compared to another test like – ANOVA and T-test.

Fit for medians only – This test is generally used to compare medians among groups.

Difficulty in handling tied values – When we have multiple observation which are having same values, this test can become less effective.

Not applicable to small sample sizes – when we have extremely small sample sizes. This test can’t give better result.

Assume ordinality- In this test we generally assume that data is measured on ordinal scale.

 

In the end – this test is generally a valuable tool when we are dealing with ordinal data and non-parametric assumptions.

Mood’s Median test - It is a non-parametric hypothesis test (other way to one-way Anova) that compares the medians for 2 independent(X) samples.

This test should be used having dependent variable (X) as continuous or discrete variable and independent variable as discrete variable with 2 or more attributes.

This test works well for smaller sample size and few samples contains outliers since it emphases on median of samples

Example:

For a organization, CSAT (customer satisfaction) survey is conducted each year for several clients to know the satisfaction level of the customer. Mood’s Median test can be used to know the overall satisfaction of the client for the organization.

Dependent variable is considered as

·       Net Promoter Score with 11-point rating from 0 to 10 with 0 having lowest customer satisfaction and 10 having highest customer satisfaction

Independent variable is considered as

·       Transformation with 7-point rating from 0 to 7 with 0 having no automation (fully manual) and 7 having full automation in all process

·       Standardization of process with 7-point rating from 0 to 7 with no standardization of process and 7 having full standardization in all process

Hypothesis test:

Null Hypothesis: The median of all NPS of CSAT survey are equal

Alternate Hypothesis: The median of all NPS of CSAT survey are not equal (at least 1 NPS is different from other)

Limitation:

·       Outliers (if many) are not considered in this test

·       It is more useful for smaller sample size

Mood’s Median test is a non-parametric test that is used to compare medians for two samples to find out if they are different. It will give information as to whether it is likely that the two independent groups have been drawn from populations with same median. It is particularly useful when the data is not normally distributed or when the sample sizes are small. Mood's Median test (non-parametric) is an alternative to one-way ANNOVA (parametric). This test works when dependent variable is continuous or discrete-count and the independent variables are discrete with two or more attributes.

 

How to perform Mood’s Median test –

1. Define the null hypothesis that there is no difference in the medians of the populations from which samples came from.
2. Determine the overall median.
3. For each sample, count how many observations are greater than the overall median, and how many are equal to or less than it.
4. Run a chi square test to determine whether to reject the null hypothesis. Calculate the chi square statistics, based on the difference between observed and expected frequencies above and below the overall median.
5. If the calculated test statistics is greater than the critical value, reject the null hypothesis meaning there is a significant difference in medians between the samples.

 

Limitation of Mood Median’s test –

1. It is designed specifically for comparing the medians for two independent samples. In case of more than 2 samples, this test is not directly applicable.
2. Mood median’s test (non-parametric) typically have lower efficiency compared to parametric counterparts (ex. t-test or ANOVA)
3. Mood Median’s test may lose power when dealing with small sample sizes, the test may not have enough statistical power to detect significant differences in median if they exist.
4. Mood’s median test has poor power for normally distributed data, even worse power for short-tailed distributions.
5. It only considers median value and doesn’t consider other aspect of data distribution. Ex. It does not provide information about shape of distribution or potential identifier.
6. It assumes that the data is continuous and cannot be used if discrete.
7. Test assumes there are no tied observations in the data (i.e. data with the same value).
8. Mood Median test assesses whether there is significant differences between the median of two samples. It does not provide information about the direction of difference or the magnitude of the effect.
9. Decision on rejecting or failing to reject null hypothesis does not directly consider context of specific research question and the consequences of type I and II errors.
10. Observations need to be independent both within and between samples

 

Examples where Mood’s Median test can be used –

1. Used to compare the median of customer satisfaction levels (dependent variable) of different account holders (independent variables: current account and saving account customers)
2. To compare medians of different machining times of different production lines (line 1, 2 and 3). Similarly comparing medians of manufacturing cycle time of different production lines (A, B and C).
3. Comparing the medians of monthly satisfaction ratings of six customers over last two years
4. Comparing the medians of number of calls per week at a service hotline separated by four different call types (complaint, technical questions, positive feedback or product info) over last six month
5. In medical study, researchers investigate the effectiveness of two treatments (treatment 1 and treatment 2) on reducing pain levels in the patients with certain conditions.
6. Marketing company can assess the preference for two product designs (Design A and Design B) among potential customers. They can conduct a survey where participants can rank their preferred designs from 1 to 5.
7. Researchers can study the impact of two different waste disposal methods (method X and method Y) on pollutant levels in nearby water bodies.
8. HR dept can compare job performance ratings of employees who underwent two different training.

 

Appropriateness of using Mood Median test depends on the nature of the data and specific research question. Mood median test offers a robust alternative when dealing with non-normal or ordinal data.  

 

This was a relatively easy question to answer. Many answers have not been approved as they had high AI-generated content.

 

Among the answers that have been approved, Ankur Sarkar has given the best answer. He has rightly highlighted the limitations of Mood's Median test.