Nonparametric Tests in Six Sigma Analysis

Hypothesis testing is a process of assuming an initial claim about the population characteristics and then statistically testing this claim using sample data. Testing hypotheses is a very important activity in Six Sigma projects in the areas of analysis, decision making, and change implementation. In conventional hypothesis tests called parametric tests a sample statistic is obtained to estimate a population parameter and hence requires a number of assumptions to be made about the underlying population; such as the normality of data.

However, another category of hypothesis tests called nonparametric tests is used when some of these assumptions (such as normality of data) cannot be safely made. Nonparametric tests require fewer assumptions and are often used when the data is from an unknown or non-normal population. Nonparametric tests are not completely free from assumptions, however. For instance, they still require the data to be from an independent random sample. The course aims to familiarize learners with approaches for analyzing nonparametric data, particularly the use of four nonparametric tests for validating hypotheses: Mood's Median tests, Levene's tests, Kruskal-Wallis tests, and Mann-Whitney tests.

This course is aligned with the ASQ Certified Six Sigma Black Belt certification exam and is designed to assist learners as part of their exam preparation. It builds on foundational knowledge that is taught in SkillSoft's ASQ-aligned Green Belt curriculum.

• Match approaches for working with nonparametric data to descriptions.
• Identify statements that define nonparametric tests.
• Recognize situational factors that call for a nonparametric method and choose the appropriate test, in a given scenario.
• Identify the limitations of nonparametric tests.
• Identify key characteristics and assumptions of Mood's Median test.
• Validate a hypothesis test for equality of medians using Mood's Median test.
• Select the situation that is best suited for a Kruskal-Wallis test.
• Validate a hypothesis by performing a Kruskal-Wallis test.
• Recognize examples of business problems that are suitable for a Mann-Whitney test and identify the assumptions that must hold true.
• Validate a hypothesis by calculating the Mann-Whitney test statistic and interpreting the result.
• Recognize how the test statistic is calculated for a Mann-Whitney test.
• Recognize examples of business problems that are suitable for L.