A. Measuring and modeling relationships between variables

1. Correlation coefficient
   Calculate and interpret the correlation coefficient and its confidence interval, and describe the difference between correlation and causation. (Analyze)
   NOTE: Serial correlation will not be tested.
2. Regression
   Calculate and interpret regression analysis, and apply and interpret hypothesis tests for regression statistics,. Use the regression model for estimation and prediction, analyze the uncertainty of the estimate, and perform a residuals analysis to validate the model. (Evaluate)
   NOTE: Models that have non-linear parameters will not be tested.
3. Multivariate tools
   Use and interpret multivariate tools such as principal components, factor analysis, discriminant analysis, multiple analysis of variance (MANOVA), etc., to investigate sources of variation. (Analyze)
4. Multi-vari studies
   Use and interpret charts of these studies and determine the difference between positional, cyclical and temporal variation. (Analyze)
5. Attributes data analysis
   Analyze attributes data using logit, probit, logistic regression, etc., to investigate sources of variation. (Analyze)

B. Hypothesis Testing

1. Terminology
   Define and interpret the significance level, power, type I and type II errors of statistical tests. (Evaluate)
2. Statistical vs practical significance
   Define, compare and interpret statistical and practical significance. (Evaluate)
3. Sample size
   Calculate sample size for common hypothesis tests (e.g., equality of means, equality of proportions, etc.) (Apply)
4. Point and interval estimates
   Define and distinguish between confidence and prediction intervals. Define and interpret the efficiency and bias of estimators. Calculate tolerance and confidence intervals. (Evaluate)
5. Tests for means, variances and proportions
   Use and interpret the results of hypothesis tests for means, variances and proportions. (Evaluate)
6. Analysis of Variance (ANOVA)
   select, calculate and interpret the results of ANOVAs. (Evaluate)
7. Goodness-of-fit (chi square) tests
   Define, select and interpret the results of these tests. (Evaluate)
8. Contingency tables
   Select, develop and use contingency tables to determine statistical significance (Evaluate)
9. Non-parametric tests
   Select, develop and use various nonparametric tests including Mood's Median, Levene's test, Kruskal-Wallis, Mann Whitney, etc. (Evaluate)

C. Failure Mode and Effects Analysis (FMEA)

Describe the purpose and elements of FMEA, including risk priority number (RPN), and evaluate FMEA results for processes, products and services. Distinguish between design FMEA (DFMEA) and process FMEA (PFMEA), and interpret results from each. (Evaluate)

D. Additional analysis methods

1. Gap analysis
   Use various tools and techniques (gap analysis, scenario planning, etc.) to compare the current and future state in terms of pre-defined metrics. (Analyze)
2. Root cause analysis
   Define and describe the purpose of root cause analysis, recognize the issues involved in identifying a root cause, and use various tools (e.g., the 5 whys, Pareto charts, fault tree analysis, cause and effect diagrams etc. for resolving chronic problems. (Evaluate)
3. Waste analysis
   Identify and interpret the 7 classic wastes (overproduction, inventory, defects, over-processing, waiting, motion and transportation) and other forms of waste such as resources under-utilization, etc. (Analyze)