Mood's Median Test is a non-parametric statistical test used in the Analyze Phase of Lean Six Sigma to determine whether two or more groups have the same median. This test is particularly valuable when comparing central tendencies across multiple populations or treatment groups.
Unlike parametric …Mood's Median Test is a non-parametric statistical test used in the Analyze Phase of Lean Six Sigma to determine whether two or more groups have the same median. This test is particularly valuable when comparing central tendencies across multiple populations or treatment groups.
Unlike parametric tests that assume normal distribution, Mood's Median Test makes minimal assumptions about the underlying data distribution, making it robust for analyzing data that may be skewed or contain outliers. This characteristic makes it especially useful in real-world process improvement scenarios where data rarely follows perfect statistical distributions.
The test works by first calculating the overall median of all combined data points. Each observation is then classified as either above or below this grand median. A contingency table is created showing the count of observations above and below the median for each group. A chi-square test is then applied to this contingency table to determine if the distribution of values above and below the median differs significantly among groups.
The null hypothesis states that all groups have the same median, while the alternative hypothesis suggests at least one group has a different median. If the p-value is less than the chosen significance level (typically 0.05), you reject the null hypothesis and conclude that significant differences exist between group medians.
In Lean Six Sigma applications, Mood's Median Test helps practitioners identify whether process changes, different suppliers, machines, or operators produce significantly different results. For example, a Green Belt might use this test to compare median cycle times across three production shifts or median defect rates among different manufacturing locations.
The test is available in statistical software packages like Minitab, making it accessible for practitioners. While less powerful than the Kruskal-Wallis test for detecting differences, Mood's Median Test remains useful when dealing with data containing extreme outliers, as it focuses solely on whether observations fall above or below the median rather than their actual values.
Mood's Median Test: Complete Guide for Six Sigma Green Belt Analyze Phase
What is Mood's Median Test?
Mood's Median Test is a non-parametric statistical test used to determine whether two or more independent groups have the same median. It is particularly useful when comparing central tendencies across multiple populations when the data does not meet the assumptions required for parametric tests like ANOVA.
Why is Mood's Median Test Important in Six Sigma?
In the Analyze Phase of DMAIC, practitioners must identify root causes of variation and defects. Mood's Median Test is important because:
• It works with non-normal data, which is common in real-world processes • It is robust to outliers, making it reliable when extreme values are present • It helps compare process performance across different conditions, machines, operators, or time periods • It requires minimal assumptions about data distribution • It supports data-driven decision making when parametric alternatives are not appropriate
How Does Mood's Median Test Work?
Step 1: Calculate the Grand Median Combine all data from all groups and find the overall median value.
Step 2: Create a Contingency Table For each group, count how many observations fall above the grand median and how many fall at or below it. This creates a 2 x k table (where k is the number of groups).
Step 3: Perform Chi-Square Test Apply the chi-square test to the contingency table to determine if the distribution of values above and below the median differs significantly among groups.
Step 4: Interpret Results Compare the p-value to your significance level (typically α = 0.05): • If p-value ≤ α: Reject the null hypothesis; the medians are significantly different • If p-value > α: Fail to reject the null hypothesis; no significant difference in medians
Key Assumptions of Mood's Median Test
• The samples are independent and randomly selected • The measurement scale is at least ordinal • The populations have similar shapes (though not necessarily normal)
When to Use Mood's Median Test
• When data is not normally distributed • When outliers are present in the dataset • When comparing medians of two or more independent groups • When sample sizes are small • As an alternative to the Kruskal-Wallis test when robustness to outliers is needed
Mood's Median Test vs. Other Tests
Compared to Kruskal-Wallis: Mood's test is more robust to outliers but generally has less statistical power
Compared to ANOVA: Mood's test does not require normality assumptions but compares medians rather than means
Exam Tips: Answering Questions on Mood's Median Test
1. Recognize When to Apply the Test Look for keywords like: non-normal data, outliers present, comparing medians, multiple independent groups, ordinal data, or robust test needed.
2. Know the Hypotheses • H₀: All group medians are equal • H₁: At least one group median differs from the others
3. Remember the Process Grand median → Contingency table → Chi-square calculation → P-value interpretation
4. Understand P-value Interpretation A small p-value (typically < 0.05) indicates significant differences among group medians.
5. Know Its Limitations Lower statistical power compared to parametric tests and the Kruskal-Wallis test; best used when outlier resistance is the priority.
6. Compare and Contrast Be prepared to explain why you would choose Mood's Median Test over ANOVA or Kruskal-Wallis in specific scenarios.
7. Watch for Trick Questions Remember that Mood's test compares medians, not means. If a question asks about comparing means with non-normal data, a different approach may be needed.
8. Practice Interpreting Results Given a p-value and significance level, be ready to state the conclusion in context of the business problem.