The Friedman Test is a non-parametric statistical method used in the Analyze Phase of Lean Six Sigma to compare three or more related groups or treatments when the data does not meet the assumptions required for parametric tests like repeated measures ANOVA. This test is particularly valuable when …The Friedman Test is a non-parametric statistical method used in the Analyze Phase of Lean Six Sigma to compare three or more related groups or treatments when the data does not meet the assumptions required for parametric tests like repeated measures ANOVA. This test is particularly valuable when dealing with ordinal data or when the assumption of normality cannot be satisfied.
The test was developed by economist Milton Friedman and serves as an alternative to the one-way repeated measures analysis of variance. It ranks data within each block or subject, then analyzes whether the distributions across multiple conditions are significantly different from each other.
In Lean Six Sigma projects, the Friedman Test is commonly applied when teams need to evaluate the same subjects under multiple conditions or time periods. For example, if a quality improvement team wants to assess operator performance across different shifts, or evaluate customer satisfaction ratings for the same products measured at various intervals, this test provides reliable results.
The test procedure involves the following steps: First, data is arranged in a matrix where rows represent blocks (subjects or matched groups) and columns represent treatments or conditions. Next, values within each row are ranked from lowest to highest. The sum of ranks for each column is then calculated. Finally, the Friedman test statistic is computed and compared against a chi-square distribution to determine statistical significance.
Key assumptions include: the data should come from related samples, the dependent variable should be at least ordinal in nature, and the samples should be randomly selected from the population.
When the p-value falls below the chosen significance level (typically 0.05), the null hypothesis is rejected, indicating that at least one treatment differs significantly from the others. Post-hoc tests can then identify which specific pairs of treatments show significant differences, helping Green Belt practitioners pinpoint areas requiring improvement in their process optimization efforts.
Friedman Test: Complete Guide for Six Sigma Green Belt
What is the Friedman Test?
The Friedman Test is a non-parametric statistical test used to detect differences across multiple test attempts or treatments when the same subjects are measured under different conditions. It is essentially the non-parametric alternative to the one-way repeated measures ANOVA.
Why is the Friedman Test Important?
In Six Sigma projects, the Friedman Test is crucial because:
• It allows analysis when data does not meet normality assumptions • It handles ordinal data effectively (rankings, ratings, survey responses) • It is robust against outliers • It enables comparison of multiple related samples • It is useful when sample sizes are small
When to Use the Friedman Test:
• You have three or more related groups or conditions • The dependent variable is ordinal or continuous but not normally distributed • The same subjects are measured multiple times • You want to compare treatments, time periods, or conditions
How the Friedman Test Works:
1. Rank the data: For each subject (block), rank the observations across all conditions from 1 to k (number of conditions)
2. Sum the ranks: Calculate the sum of ranks for each condition across all subjects
3. Calculate the test statistic: The Friedman statistic (χ²) is computed based on the rank sums
4. Compare to critical value: If the calculated statistic exceeds the critical chi-square value, reject the null hypothesis
Hypotheses:
• Null Hypothesis (H₀): There is no difference between the conditions/treatments • Alternative Hypothesis (H₁): At least one condition differs from the others
Key Assumptions:
• One group measured on three or more occasions • Data can be ranked within each block • Samples are randomly selected • Observations are independent between blocks
Exam Tips: Answering Questions on the Friedman Test
1. Recognition Questions: Look for keywords like 'non-parametric,' 'repeated measures,' 'ordinal data,' 'three or more related samples,' or 'rankings.' These signal Friedman Test scenarios.
2. Distinguish from Similar Tests: • Kruskal-Wallis: Used for independent groups (not repeated measures) • Wilcoxon Signed-Rank: Only compares two related samples • Repeated Measures ANOVA: Parametric version requiring normal distribution
3. Common Exam Scenarios: • Comparing employee performance ratings over multiple quarters • Evaluating customer satisfaction across different service methods • Analyzing defect rates across shifts with the same operators
4. Remember the Requirements: • At least 3 conditions or time points • Same subjects in each condition • Data that is ordinal or non-normal continuous
5. Post-hoc Testing: If exam questions mention significant Friedman results, know that post-hoc tests (like Wilcoxon tests with Bonferroni correction) are needed to identify which specific groups differ.
6. Interpretation: A significant result (p < 0.05) means at least one treatment or condition is different from the others, but does not tell you which one specifically.
Quick Reference Formula Context: The test statistic follows a chi-square distribution with (k-1) degrees of freedom, where k is the number of conditions being compared.
Final Exam Tip: When facing scenario-based questions, first check: (1) Are the samples related/paired? (2) Are there 3+ conditions? (3) Is the data non-normal or ordinal? If all three answers are yes, the Friedman Test is likely the correct choice.