# Statistics Level 2 Training Course

## Overview

This training course covers advanced statistics. It explains most of the tools commonly used in research, analysis and forecasting. It provides short explanations of the theory behind the formulas.

This course does not relate to any specific field of knowledge, but can be tailored if all the delegates have the same background and goals.

Some basic computer tools are used during this course (notably Excel and OpenOffice)

## Requirements

The delegates should have completed Statistics Level 1 course or have equivalent work experience.

## Course Outline

### Describing Bivariate Data

• Introduction to Bivariate Data
• Values of the Pearson Correlation
• Guessing Correlations Simulation
• Properties of Pearson’s r
• Computing Pearson’s r
• Restriction of Range Demo
• Variance Sum Law II
• Exercises

### Probability

• Introduction
• Basic Concepts
• Conditional Probability Demo
• Gamblers Fallacy Simulation
• Birthday Demonstration
• Binomial Distribution
• Binomial Demonstration
• Base Rates
• Bayes’ Theorem Demonstration
• Monty Hall Problem Demonstration
• Exercises

### Normal Distributions

• Introduction
• History
• Areas of Normal Distributions
• Varieties of Normal Distribution Demo
• Standard Normal
• Normal Approximation to the Binomial
• Normal Approximation Demo
• Exercises

### Sampling Distributions

• Introduction
• Basic Demo
• Sample Size Demo
• Central Limit Theorem Demo
• Sampling Distribution of the Mean
• Sampling Distribution of Difference Between Means
• Sampling Distribution of Pearson’s r
• Sampling Distribution of a Proportion
• Exercises

### Estimation

• Introduction
• Degrees of Freedom
• Characteristics of Estimators
• Bias and Variability Simulation
• Confidence Intervals
• Exercises

### Logic of Hypothesis Testing

• Introduction
• Significance Testing
• Type I and Type II Errors
• One- and Two-Tailed Tests
• Interpreting Significant Results
• Interpreting Non-Significant Results
• Steps in Hypothesis Testing
• Significance Testing and Confidence Intervals
• Misconceptions
• Exercises

### Testing Means

• Single Mean
• t Distribution Demo
• Difference between Two Means (Independent Groups)
• Robustness Simulation
• All Pairwise Comparisons Among Means
• Specific Comparisons
• Difference between Two Means (Correlated Pairs)
• Correlated t Simulation
• Specific Comparisons (Correlated Observations)
• Pairwise Comparisons (Correlated Observations)
• Exercises

### Power

• Introduction
• Factors Affecting Power
• Why power matters
• Exercises

### Prediction

• Introduction to Simple Linear Regression
• Linear Fit Demo
• Partitioning Sums of Squares
• Standard Error of the Estimate
• Prediction Line Demo
• Inferential Statistics for b and r
• Exercises

### ANOVA

• Introduction
• ANOVA Designs
• One-Factor ANOVA (Between-Subjects)
• One-Way Demo
• Multi-Factor ANOVA (Between-Subjects)
• Unequal Sample Sizes
• Tests Supplementing ANOVA
• Within-Subjects ANOVA
• Power of Within-Subjects Designs Demo
• Exercises

### Chi Square

• Chi Square Distribution
• One-Way Tables
• Testing Distributions Demo
• Contingency Tables
• 2 x 2 Table Simulation
• Exercises