Methods & Tools: Analyze
VI. Six Sigma Improvement Methodology and Tools – Analyze
A. Exploratory data analysis
1. Multi-vari studies: Use multi-vari studies to interpret the difference between positional, cyclical, and temporal variation; design sampling plans to investigate the largest sources of variation; create and interpret multi-vari charts.


2. Measuring and modeling relationships between variables
a. Simple and multiple least-squares linear regression: Calculate the regression equation; apply and interpret hypothesis tests for regression statistics; use the regression model for estimation and prediction, and analyze the uncertainty in the estimate.


b. Simple linear correlation: Calculate and interpret the correlation coefficient and its confidence interval; apply and interpret a hypothesis test for the correlation coefficient; understand the difference between correlation and causation.


c. Diagnostics: Analyze residuals of the model.

B. Hypothesis testing
1. Fundamental concepts of hypothesis testing
a. Statistical vs. practical significance: Define, compare, and contrast statistical and practical significance.


b. Significance level, power, type I and type II errors: Apply and interpret the significance level, power, type I, and type II errors of statistical tests.


c. Sample Size: Understand how to calculate sample size for any given hypothesis test.


2. Point and interval estimation: Define and interpret the efficiency and bias of estimators; compute, interpret and draw conclusions from statistics such as standard error, tolerance intervals, and confidence intervals; understand the distinction between confidence intervals and prediction intervals.


3. Tests for means, variances, and proportions: Apply hypothesis tests for means, variances, and proportions, and interpret the results.


4. Paired-comparison tests: Define, determine applicability, apply, and interpret paired-comparison parametric hypothesis tests.


5. Goodness-of-fit tests: Define, determine applicability, apply, and interpret chi-square tests.


6. Analysis of variance (ANOVA): Define, determine applicability, apply, and interpret ANOVAs.


7. Contingency tables: Define, determine applicability, and construct a contingency table and use it to determine statistical significance.


8. Non-parametric tests: Define, determine applicability, and construct various non-parametric tests including Mood’s Median, Levene’s test, Kruskal-Wallis, Mann-Whitney, etc.

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