# Training

# Basic Statistics, Hypothesis Testing, & Regression training

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)

- Basic Statistics & Distributions
- Data Types
- Populations & Samples
- Central Tendency and Variation
- Probability Distributions
- The Normal Distribution
- The Central Limit Theorem

- Graphical Analysis
- Pareto Charts
- Run Charts
- Boxplots and Individual Value Plots
- Histograms
- Scatter Plots

- 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

- 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)

- Hypothesis Tests for Multiple (>2) Groups
- Testing Means (ANOVA)
- Multiple Comparisons
- Testing Variances (Bartlett’s and Levene’s Test)
- Testing for Normality
- Data Transformations

- Power & Sample Size
- Type II Errors and Power
- Factors affecting Power
- Computing Sample Sizes
- Power Curves
- Sample Sizes for Estimation

- Relating Two Variables
- Scatter Plots
- Correlation Coefficient

- 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

- 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

# Why is this Course Important?

Many engineers, scientists, and business statistics training analysts struggle with the application of statistical methods when analyzing data to making decisions. Frequently, engineers and scientists react to data without considering the natural variation that exists. Non statisticians frequently seek help in tasks such as determining appropriate sample sizes, interpreting tests results, distinguishing statistical differences from practical differences, and developing predictive models. This course provides an in-depth treatment of statistical analysis methods to support decision making. The focus is on data organization, graphical methods, hypothesis testing, and predictive modeling.

# Typical Attendees:

- Product development personnel
- Research and development personnel
- Quality Statistics Training for personnel
- Product/Process Engineers
- Personnel utilizing data to make decisions and improve processes