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Parametric Methods will provide the participant with the knowledge and skills necessary to employ parametric tools and methods. Parametric methods represent a class of statistical tools that are mathematical procedures for testing statistical hypotheses, often related to the mean and variance. Of interest, this particular class of statistics assumes that the underlying distributions of the variables being assessed belong to known family of probability distributions. An example is a statistical procedure called Analysis-of-Variance, or simply ANOVA. Use of this statistical method assumes that the underlying distributions are normally distributed and that the variances of the distributions being compared are similar. Parametric techniques are very powerful tools because they are quite robust to violations of the underlying assumptions.
This is to say they often retain considerable power to detect differences or similarities (between means and variances) even when the underlying assumptions are violated. However, when the violations become quite marked, nonparametric methods are often invoked. Of course, this capability is vital to the effective use Design of Experiments (DOE) and can also be readily and broadly applied to the practice of Measurement Systems Analysis (MSA), Statistical Process Control (SPC) and Process Characterization Studies (PCS). Owing to the versatility of this course, it represents a vital link between the theory of Six Sigma and the real-world of process improvement.
Reinforcement of major concepts, techniques, and application is realized through exercises, scenarios, and case studies. The following prerequisite topics are listed in sequential learning order: Basic Statistics, Hypothesis Testing and Confidence Intervals. Total instructional time for this topic is 8 hours and 20 minutes.
- Mean Differences - Determine if two means are statistically different from each other
- Variance Differences - Determine if two variances are statistically different from each other
- Variation Total - Compute and interpret the total sums-of-squares
- Variation Within - Compute and interpret the within-group sums-of-squares
- Variation Between - Compute and interpret the between-group sums-of-squares
- Variation Analysis - Explain how the analysis of variances can reveal mean differences
- One-Way ANOVA - Construct and interpret a one-way analysis-of-variance table
- Two-Way ANOVA - Construct and interpret a two-way analysis-of-variance table
- N-Way ANOVA - Construct and interpret an N-way analysis-of-variance table
- ANOVA Graphs - Construct and interpret a main effects plot as well as an interaction plot
- Linear Regression - Conduct a linear regression and construct an appropriate model
- Multiple Regression - Conduct a multiple regression and construct an appropriate model
- Residual Analysis - Compute and analyze the residuals resulting from a simple regression
- Parametric Simulation - Apply general regression methods to the process simulator