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# Basic Statistics training, Hypothesis Testing, & Regression

The objective of the curriculum is to provide participants with the analytical tools and methods necessary to:

• Describe and summarize data effectively with descriptive statistics and graphical methods
• Correctly compare groups with respect to means, variability, and proportions by testing hypotheses
• Estimate key statistics and quantify uncertainty (confidence intervals)
• Characterize expected variation from sample data (tolerance intervals)
• Determine appropriate sample sizes to achieve adequate power for hypothesis tests
• Develop, validate, and utilize predictive models

Participants gain a solid understanding of important concepts and methods to analyze data and support effective decision making.  Many practical examples are presented to illustrate the application of technical concepts.

## Seminar Content (3 or 4 Days)

1. Basic Statistics & Distributions
• Data Types
• Populations & Samples
• Central Tendency and Variation
• Probability Distributions
• The Normal Distribution
• The Central Limit Theorem
2. Graphical Analysis
• Pareto Charts
• Run Charts
• Boxplots and Individual Value Plots
• Histograms
• Scatter Plots
3. Hypothesis Testing Concepts
• Test Statistics, Crit. Values, p-values
• One and Two Sided Tests
• Type I and Type II Errors
• Confidence Intervals for the Estimates
4. Hypothesis Tests for One and Two Groups
• Testing Means (1 sample t ,2 sample t and paired t tests)
• Testing Variances (Chi-Square, F test)
• Testing Proportions (overview)
• Tolerance Intervals (Range over which x% are expected to fall with specified confidence)
5. Hypothesis Tests for Multiple (>2) Groups
• Testing Means (ANOVA)
• Multiple Comparisons
• Testing Variances (Bartlett’s and Levene’s Test)
• Testing for Normality
• Data Transformations
6. Power & Sample Size
• Type II Errors and Power
• Factors affecting Power
• Computing Sample Sizes
• Power Curves
• Sample Sizes for Estimation
7. Relating Two Variables
• Scatter Plots
• Correlation Coefficient
8. Linear Models with a Single Factor
• Model Building Concepts
• Simple Linear Regression
• R Squared
• Residual Analysis
• Hypothesis Testing for the Model
• Making Predictions
• Confidence and Prediction Intervals
9. Linear Models with Multiple Factors
• Multiple Regression
• Testing for Significant Explanatory Variables
• Model Performance
• Model Building Strategies and Tools
• Confidence and Prediction Intervals
• Multi-collinearity
• Influential Data Points