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Course Outline
Scientific Method, Probability & Statistics
- A brief historical overview of statistics
- The basis for confidence in research conclusions
- Integrating probability with decision-making processes
Preparing for Research (Defining "What" and "How")
- The macro view: Understanding research as a process with inputs and outputs
- Strategies for data collection
- Questionnaires and measurement techniques
- Determining what variables to measure
- Conducting observational studies
- Principles of experimental design
- Data analysis and graphical visualization methods
- Essential research skills and techniques
- Managing the research lifecycle
Analyzing Bivariate Data
- Introduction to bivariate data concepts
- Understanding Pearson Correlation values
- Simulation exercise: Guessing correlations
- Key properties of Pearson's r
- Calculating Pearson's r
- Demonstration: The restriction of range effect
- The Variance Sum Law II
- Practice exercises
Probability Theory
- Introduction to probability concepts
- Fundamental principles
- Demonstration of conditional probability
- Simulation: The Gambler's Fallacy
- Demonstration: The Birthday Paradox
- The Binomial Distribution
- Demonstration of binomial scenarios
- Understanding base rates
- Demonstration: Bayes' Theorem
- Demonstration: The Monty Hall Problem
- Practice exercises
Normal Distributions
- Introduction to normal distribution
- Historical context
- Calculating areas under normal distribution curves
- Demonstration: Variations of normal distributions
- The Standard Normal Distribution
- Approximating the Binomial Distribution using the Normal model
- Demonstration of normal approximation techniques
- Practice exercises
Sampling Distributions
- Introduction to sampling distributions
- Basic simulation demonstrations
- Demonstration: The impact of sample size
- Demonstration: The Central Limit Theorem
- The sampling distribution of the mean
- The sampling distribution of the difference between means
- The sampling distribution of Pearson's r
- The sampling distribution of a proportion
- Practice exercises
Estimation Techniques
- Introduction to statistical estimation
- Understanding degrees of freedom
- Characteristics of effective estimators
- Simulation: Bias and variability
- Constructing Confidence Intervals
- Practice exercises
The Logic of Hypothesis Testing
- Introduction to hypothesis testing frameworks
- Principles of significance testing
- Understanding Type I and Type II errors
- One-tailed versus two-tailed tests
- Interpreting significant results
- Interpreting non-significant results
- Step-by-step hypothesis testing procedure
- The relationship between significance testing and confidence intervals
- Addressing common misconceptions
- Practice exercises
Testing Means
- Testing a single mean
- Demonstration of the t-distribution
- Comparing two means from independent groups
- Simulation: Robustness of statistical tests
- Conducting all pairwise comparisons among means
- Performing specific comparisons
- Comparing two means from correlated pairs
- Simulation: Correlated t-tests
- Specific comparisons for correlated observations
- Pairwise comparisons for correlated observations
- Practice exercises
Statistical Power
- Introduction to statistical power
- Example calculations
- Factors that influence statistical power
- Practice exercises
Prediction via Regression
- Introduction to simple linear regression
- Demonstration: Linear fitting
- Partitioning sums of squares
- Understanding the standard error of the estimate
- Demonstration: The prediction line
- Inferential statistics for slope (b) and correlation (r)
- Practice exercises
Analysis of Variance (ANOVA)
- Introduction to ANOVA
- Overview of ANOVA designs
- One-Factor ANOVA (Between-Subjects)
- Demonstration: One-way ANOVA
- Multi-Factor ANOVA (Between-Subjects)
- Handling unequal sample sizes
- Supplementary tests for ANOVA results
- Within-Subjects ANOVA
- Demonstration: Power of within-subjects designs
- Practice exercises
Chi-Square Tests
- The Chi-Square Distribution
- Analyzing one-way frequency tables
- Demonstration: Testing distributions
- Contingency tables analysis
- Simulation: 2 x 2 contingency tables
- Practice exercises
Case Studies
Detailed analysis of selected real-world case studies
Requirements
Participants must possess a strong understanding of descriptive statistics (including mean, median/mode, standard deviation, and variance) as well as a foundational knowledge of probability.
We recommend attending the preparatory course: Statistics Level 1 if you need to strengthen your foundational skills.
35 Hours
Testimonials (3)
knowledge of the trainer, tailor based, all topics covered
eleni - EUAA
Course - Forecasting with R
The variation with exercise and showing.
Ida Sjoberg - Swedish National Debt Office
Course - Econometrics: Eviews and Risk Simulator
The real life applications using Statcan and CER as examples.
