### Measuring and Modeling Relationships between Variables in Six Sigma

**Overview/Description**

As a Six Sigma team moves into the Analyze stage of the DMAIC process, it looks more closely at the variables and variable interrelationships identified during the Measure stage. As part of the analysis, a scatter diagram of dependent and independent variables is drawn to visualize the form, strength, and direction of their relationships. By determining their correlation coefficient, a linear relationship can be quantified and identified as positive, negative, or neutral. Then, using regression analysis, a model is developed to describe the relationship as a linear equation and then used for predictions and estimations. However, it is essential to analyze the uncertainty in the estimate, to test that the relationship between variables is statistically significant, and that the model is valid. This course discusses two important tools – correlation and regression analysis for measuring and modeling relationships between variables. In terms of correlation, it takes learners through examples of scatter diagrams for two variables, the calculation and interpretation of the correlation coefficient, and the interpretation of its confidence interval. The course also draws learners’ attention to some key considerations in correlation analysis, such as correlation and causation. In terms of regression analysis, the course discusses the simple linear regression model, how to create it using sample data, interpret and use it, and conduct a hypothesis test to check that the relationship between the variables is statistically significant. Finally, the course looks into how residual analysis is used to test the validity of the regression model. 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.

**Target Audience**

Candidates seeking Six Sigma Black Belt certification, quality professionals, engineers, production managers, frontline supervisors, and all individuals charged with responsibility for improving quality and processes at the organizational or departmental level, including process owners and champions

**Prerequisites**

Proficiency at the Green Belt level with simple linear correlation and regression concepts as scoped in the ASQ – Six Sigma Green Belt Body of Knowledge (BOK)

**Measuring and Modeling Relationships between Variables in Six Sigma**

- calculate and interpret the correlation coefficient r
- recognize the characteristics exhibited by a given scatter diagram
- recognize key considerations related to correlation analysis
- calculate and interpret the equation for the line of least squares in a given scenario
- use the p-value method to validate a hypothesis test for a given regression equation
- interpret graphs used to perform a residual analysis

### Basics of Hypothesis Testing and Tests for Means in Six Sigma

**Overview/Description**

In the Analyze phase of the DMAIC methodology, Six Sigma teams analyze the underlying causes of issues that need to be addressed for the successful completion of their improvement projects. To that end, teams conduct a number of statistical analyses to determine the nature of variables and their interrelationships in the process under study. It is rarely possible to study and analyze the full scope of population data pertaining to all processes, products, or services, so Six Sigma teams typically collect samples of the population data to be analyzed, and based on that sample data, they make hypotheses about the entire population. Because there is a lot at stake in forming the correct conclusions about the larger population, Six Sigma teams validate their inferences using hypothesis tests. This course builds on basic hypothesis testing concepts, terminologies, and some of the most commonly used hypothesis tests – one- and two-sample tests for means. The course also discusses the importance of sample size and power in hypothesis testing, as well as exploring issues relating to point estimators and confidence intervals in hypothesis testing. 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.

**Target Audience**

Candidates seeking Six Sigma Black Belt certification, quality professionals, engineers, production managers, frontline supervisors, and all individuals charged with responsibility for improving quality and processes at the organizational or departmental level, including process owners and champions

**Prerequisites**

Proficiency at the Green Belt level with basic hypothesis testing and test for means concepts as scoped in the ASQ – Six Sigma Green Belt Body of Knowledge (BOK)

**Basics of Hypothesis Testing and Tests for Means in Six Sigma**

- use key hypothesis testing concepts to interpret a testing scenario
- recognize the implications of a hypothesis test result for statistical and practical significance
- use the margin of error formula to determine sample size for a given alpha risk level
- match definitions to key attributes of point estimates
- distinguish between statements expressing confidence, tolerance, and prediction intervals
- recognize how confidence intervals are used in statistical analysis
- calculate the confidence interval for the mean and interpret the results in a given scenario
- calculate the tolerance interval in a given scenario
- perform key steps in a one-sample hypothesis test for means, and interpret the result
- test a hypothesis using a two-sample test for means

### Tests for Variances and Proportions, ANOVA, and Goodness-of-fit in Six Sigma

**Overview/Description**

As a Six Sigma team moves into the Analyze phase of a project, team members begin analyzing the information and data collected in the earlier phases. During the Analyze phase, Six Sigma teams identify possible sources of variation, underlying root causes, and areas for improvement. It is here where assumptions or hypotheses about a process, product, or service are made and validated using tests based on sample data. This course aims to familiarize you with some of the advanced hypothesis tests used in Six Sigma. You are taken through the key steps in testing hypotheses for proportions, variances, and analysis of variance (ANOVA), and their underlying assumptions, with the help of examples and case studies. You will also learn how to use goodness-of-fit test statistics and contingency tables for validating hypotheses about various aspects of the variables being analyzed. 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.

**Target Audience**

Candidates seeking Six Sigma Black Belt certification, quality professionals, engineers, production managers, frontline supervisors, and all individuals charged with responsibility for improving quality and processes at the organizational or departmental level, including process owners and champions

**Prerequisites**

Proficiency at the Green Belt level with hypothesis tests for variances, proportions, ANOVA, and chi-square in Six Sigma as scoped in the ASQ – Six Sigma Green Belt Body of Knowledge (BOK)

**Tests for Variances and Proportions, ANOVA, and Goodness-of-fit in Six Sigma**

- perform key steps in a hypothesis test for proportions, and interpret the results
- perform key steps in a one-sample hypothesis test for variance, and interpret the results
- distinguish between characteristics of one-sample tests for variance and two-sample tests for variance
- perform key steps in a one-way ANOVA and interpret the results
- interpret results in a two-way ANOVA
- recognize examples of business problems that warrant a two-way ANOVA
- determine whether a goodness-of-fit test was calculated and interpreted correctly
- identify business problems or organizational questions that are suitable for a goodness-of-fit test
- use a contingency table to test the relationship between two variables
- identify statements that describe the purpose of contingency tables

### Multivariate Tools and Nonparametric Tests in Six Sigma

**Overview/Description**

In the Analyze phase of the DMAIC methodology, a Six Sigma team begins to analyze the root causes of the problems that it identified in the earlier stages. This analysis may require churning out huge volumes of data of different types. Sometimes this data is of a multivariate nature, meaning that many dependent and independent variables need to be considered simultaneously. As such, Six Sigma teams often use advanced multivariate tools to manage this type of data. Another set of advanced statistical analysis tools used in this phase is nonparametric tests. 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, a nonparametric test is used when some of these assumptions, such as normality of data, cannot be safely made. This course deals with multivariate and categorical data analysis tools such as factor analysis, discriminant analysis, and multiple analysis of variance (MANOVA). The course also aims to familiarize learners with approaches for analyzing nonparametric data, particularly the use of Kruskal-Wallis and Mann-Whitney tests for validating hypotheses. 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.

**Target Audience**

Candidates seeking Six Sigma Black Belt certification, quality professionals, engineers, production managers, frontline supervisors, and all individuals charged with responsibility for improving quality and processes at the organizational or departmental level, including process owners and champions

**Prerequisites**

Proficiency at the Green Belt level with population parameters, sample statistics, and basic hypothesis testing methodology as scoped in the ASQ – Six Sigma Green Belt Body of Knowledge (BOK)

**Multivariate Tools and Nonparametric Tests in Six Sigma**

- interpret factor scores as part of factor analysis (FA)
- interpret the results of a discriminant analysis
- interpret the results of a multiple analysis of variance (MANOVA)
- 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
- 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

### FMEA and Other Nonstatistical Analysis Methods in Six Sigma

**Overview/Description**

Getting to the source of why something has gone wrong in a system or process is critical to identifying the changes necessary for resolving the problem. During the Analyze phase of a Six Sigma project, a Black Belt practitioner utilizes a variety of statistical and nonstatistical tools and methods for analyzing systems and processes to identify variation and defects, reduce costs, eliminate waste, and reduce cycle time. While many of the tools used in the Analyze phase are statistical and quantitative in nature, there are many useful nonstatistical methods. Nonstatistical methods help in the analysis by including qualitative considerations in identifying potential problems, their root causes, and their impacts. They help prioritize these causes and generate initial ideas for resolving problems when a project enters the Improve phase. This course covers the use of various nonstatistical analysis methods including failure modes and effects analysis (FMEA), gap analysis, scenario planning, root cause analysis, the 5 Whys, fault tree analysis (FTA), and waste analysis. 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.

**Target Audience**

Candidates seeking Six Sigma Black Belt certification, quality professionals, engineers, production managers, frontline supervisors, and all individuals charged with responsibility for improving quality and processes at the organizational or departmental level, including process owners and champions

**Prerequisites**

Proficiency at the Green Belt level with failure modes and effects analysis (FMEA), root cause analysis tools, and waste analysis in Six Sigma as scoped in the ASQ – Six Sigma Green Belt Body of Knowledge (BOK)

**FMEA and Other Nonstatistical Analysis Methods in Six Sigma**

- interpret a failure modes and effects analysis (FMEA) worksheet to prioritize failures for improvement
- recognize the distinctions and relationships between Process FMEAs and Design FMEAs
- calculate the risk priority number (RPN) for a given cause of failure
- identify the purpose of gap analysis in Six Sigma
- sequence examples of the performance of each step in a gap analysis
- recognize activities performed in the scenario planning process
- identify the characteristics of scenario planning
- match suggested steps in a root cause analysis to associated activities
- identify errors made by a team conducting a 5 Whys analysis, in a given scenario
- interpret a fault tree analysis (FTA)
- classify situations as more suitable for fault tree analysis (FTA) or for failure modes and effects analysis (FMEA)
- recognize the type of waste expressed in a conventional statement and associate it with Lean Six Sigma thinking for eliminating that waste