Non-parametric tests are statistical tests that do not make assumptions about data distribution. It analyses are employed when data does not fit certain assumptions required for parametric tests, such as the normal distribution assumption.

Non-parametric tests are used to verify hypotheses about data and compare groups or variables without making assumptions about its distribution. Common non-parametric tests include:

Wilcoxon rank-sum test: This statistical method can be used to compare two independent groups and determine if their medians differ significantly.

Kruskal-Wallis test: This statistical method can be used to compare the medians of three or more independent groups.

Wilcoxon Signed-Rank Test: This test can be used to compare two related groups and determine if their medians differ significantly.

Mann-Whitney U test: This statistical test can be used to compare two independent groups and determine if their medians are significantly different.

Kendall’s rank correlation: This test can be used to establish whether there is a statistically significant relationship between two ordinal variables.

Spearman’s rank correlation: This test can be used to establish whether there is a significant relationship between two continuous variables.

Non-parametric tests are helpful when the data are not normally distributed, are ordinal, or have a small sample size. They may also be employed to test hypotheses about the data when parametric assumptions cannot be fulfilled. Non-parametric tests offer a practical and secure way of analyzing data and making decisions based on its outcomes.

### How are Non-Parametric Tests used in Six Sigma?

Six Sigma utilizes non-parametric tests to analyze data and make decisions in a process improvement project. Non-parametric tests may be employed to:

Test Hypotheses About Data: Six Sigma practitioners use these tests to examine data hypotheses and determine if differences between groups or variables are significant.

Comparing Groups or Variables: Nonparametric tests can be used to compare medians, distributions or relationships between groups or variables in order to detect significant differences.

Identification of Patterns and Relationships: Nonparametric tests can be used to detect patterns and connections between variables that help explain cause-and-effect relationships in a process.

Making Data-Driven Decisions: Six Sigma professionals use non-parametric tests to make data-driven decisions about how to optimize a process.

Six Sigma practitioners rely on non-parametric tests because they are robust and can be applied to data that does not meet parametric assumptions. Non-parametric analyses offer a reliable way of analyzing information and making decisions based on those results, enabling Six Sigma professionals to enhance processes and reach their objectives more easily.