Statistics for Researchers Training Course

Scientific Method, Probability & Statistics

• Very short history of statistics
• Why can be "confident" about the conclusions
• Probability and decision making

Preparation for research (deciding "what" and "how")

• The big picture: research is a part of a process with inputs and outputs
• Gathering data
• Questioners and measurement
• What to measure
• Observational Studies
• Design of Experiments
• Analysis of Data and Graphical Methods
• Research Skills and Techniques
• Research Management

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
• Example Calculations
• Factors Affecting Power
• 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

Case Studies

Analysis of selected case studies