This is Jeremy Balka’s statistics website containing introductory statistics videos.

I have a PhD in statistics, and have taught introductory statistics courses on many occasions.

I try to be concise, and use real data in the vast majority of cases. Some of these videos move at a quick pace, especially my earlier ones, and they are not designed to be lecture replacements.

### 1. Discrete Probability Distributions

- 1.1 An Introduction to Discrete Random Variables and Discrete Probability Distributions
- 1.2 The Expected Value and Variance of Discrete Random Variables
- 1.3 Introduction to the Bernoulli Distribution
- 1.4 The Bernoulli Distribution: Deriving the Mean and Variance
- 1.5 An Introduction to the Binomial Distribution
- 1.6 Binomial/Not Binomial: Some Examples
- 1.7 The Binomial Distribution: Mathematically Deriving the Mean and Variance
- 1.8 An Introduction to the Hypergeometric Distribution
- 1.9 An Introduction to the Poisson Distribution
- 1.10 The Poisson Distribution: Mathematically Deriving the Mean and Variance
- 1.11 Discrete Probability Distributions: Example Problems (Binomial, Poisson, Hypergeometric, Geometric)
- 1.12 The Relationship Between the Binomial and Poisson Distributions
- 1.13 Proof that the Binomial Distribution tends to the Poisson Distribution
- 1.13 An Introduction to the Multinomial Distribution
- 1.14 An Introduction to the Geometric Distribution
- 1.15 An Introduction to the Negative Binomial Distribution
- 1.16 Introduction to the Multinomial Distribution
- 1.17 Poisson or Not? (When does a random variable have a Poisson distribution?)
- 1.18 Overview of Some Discrete Probability Distributions (Binomial,Geometric,Hypergeometric,Poisson,NegB)

### 2. Continuous Random Variables & Continuous Probability Distributions

- 2.1 An Introduction to Continuous Probability Distributions
- 2.2 Finding Probabilities and Percentiles for a Continuous Probability Distribution
- 2.3 Deriving the Mean and Variance of a Continuous Probability Distribution
- 2.4 Introduction to the Continuous Uniform Distribution
- 2.5 An Introduction to the Normal Distribution
- 2.6 Standardizing Normally Distributed Random Variables
- 2.7 The Normal Approximation to the Binomial Distribution
- 2.8 Normal Quantile-Quantile Plots
- 2.9 An Introduction to the Chi-Square Distribution
- 2.10 An Introduction to the t Distribution (Includes some mathematical details)
- 2.11 An Introduction to the F Distribution

### 3. Using Tables to Find Areas and Percentiles

- 3.1 Finding Areas Using the Standard Normal Table (for tables that give the area to left of z)
- 3.2 Finding Percentiles Using the Standard Normal Table (for tables that give the area to left of z)
- 3.3 Finding Areas Using the Standard Normal Table (for tables that give the area between 0 and z)
- 3.4 Finding Percentiles Using the Standard Normal Table (for tables that give the area between 0 and z)
- 3.5 Using the t Table to Find Areas and Percentiles
- 3.6 R Basics: Finding Percentiles and Areas for the t Distribution
- 3.7 Using the F Table to Find Areas and Percentiles
- 3.8 Finding Percentiles and Areas for the F Distribution Using R
- 3.9 Using the Chi-square Table to Find Areas and Percentiles
- 3.10 Using R to Find Chi-square Areas and Percentiles

### 4. Sampling Distributions

- 4.1 Sampling Distributions: Introduction to the Concept
- 4.2 The Sampling Distribution of the Sample Mean
- 4.3 Introduction to the Central Limit Theorem
- 4.4 Deriving the Mean and Variance of the Sample Mean
- 4.5 Proof that the Sample Variance is an Unbiased Estimator of the Population Variance
- 4.7 Confidence Intervals for One Mean: Assumptions

### 5. Confidence Intervals

- 5.1 Introduction to Confidence Intervals
- 5.2 Deriving a Confidence Interval for the Mean
- 5.3 Intro to Confidence Intervals for One Mean (Sigma Known)
- 5.4 Finding the Appropriate z Value for the Confidence Interval Formula
- 5.5 Confidence Intervals for One Mean: Interpreting the Interval
- 5.6 What Factors Affect the Margin of Error?
- 5.7 Confidence Intervals for One Mean: Sigma Not Known (t Method)
- 5.8 Intro to the t Distribution (non-technical)
- 5.9 Confidence Intervals for One Mean: Determining the Required Sample Size
- 5.10 Confidence Intervals for One Mean: Investigating the Normality Assumption

### 6. Hypothesis Testing

- 6.1 An Introduction to Hypothesis Testing
- 6.2 Z Tests for One Mean: Introduction
- 6.3 Z Tests for One Mean: The Rejection Region Approach
- 6.4 Z Tests for One Mean: The p-value
- 6.5 Z Tests for One Mean: An Example
- 6.6 What is a p-value?
- 6.7 Type I Errors, Type II Errors, and the Power of the Test
- 6.8 One-Sided Test or Two-Sided Test?
- 6.9 Statistical Significance versus Practical Significance
- 6.10 The Relationship Between Confidence Intervals and Hypothesis Tests
- 6.11 Calculating Power and the Probability of a Type II Error (A One-Tailed Example)
- 6.12 Calculating Power and the Probability of a Type II Error (A Two-Tailed Example)
- 6.13 What Factors Affect the Power of a Z Test?
- 6.14 Hypothesis Testing in 17 Seconds
- 6.15 t Tests for One Mean: Introduction
- 6.16 t Tests for One Mean: An Example
- 6.17 t Tests for One Mean: Investigating the Normality Assumption
- 6.18 Hypothesis tests on one mean: t or z?
- 6.19 Using the t Table to Find the P-value in One-Sample t Tests
- 6.20 Finding Areas Under the t Distribution

### 7. Inference for Two Means

- 7.1 Inference for Two Means: Introduction
- 7.2 The Sampling Distribution of the Difference in Sample Means
- 7.3 Pooled-Variance t Tests and Confidence Intervals: Introduction
- 7.4 Pooled-Variance t Tests and Confidence Intervals: An Example
- 7.5 Welch (Unpooled Variance) t Tests and Confidence Intervals: Introduction
- 7.6 Welch (Unpooled Variance) t Tests and Confidence Intervals: An Example
- 7.7 Pooled or Unpooled Variance t Tests and Confidence Intervals? (To Pool or not to Pool?)
- 7.8 An Introduction to Paired-Difference Procedures
- 7.9 An Example of a Paired-Difference t Test and Confidence Interval
- 7.10 Pooled-Variance t Procedures: Investigating the Normality Assumption

### 8. Inference for Proportions

- 8.1 An Introduction to Inference for a Proportion
- 8.2 The Sampling Distribution of the Sample Proportion
- 8.3 Inference for a Proportion: An Example of a Confidence Interval and a Hypothesis Test
- 8.4 Confidence Intervals for a Proportion: Determining the Minimum Sample Size
- 8.5 An Introduction to Inference for Two Proportions
- 8.6 Inference for Two Proportions: An Example of a Confidence Interval and a Hypothesis Test

### 9. Chi-square Tests

- 9.1 Chi-square Tests for One-way tables
- 9.2 Chi-square tests: Goodness of fit for the binomial distribution
- 9.3 Chi-square Tests for Two-way Tables (Chi-square Tests of Independence)
- 9.4 Chi-square tests for count data: Finding the p-value

### 10. Variances

- 10.1 An Introduction to Inference for One Variance (Assuming a Normally Distributed Population)
- 10.2 Inference for One Variance: An Example of a Confidence Interval and a Hypothesis Test
- 10.3 Deriving a Confidence Interval for a Variance (Assuming a Normally Distributed Population)
- 10.4 Hypothesis Tests for Equality of Two Variances
- 10.5 Inference for a Variance: How Robust are These Procedures?
- 10.6 An Introduction to Inference for the Ratio of Two Variances
- 10.7 Inference for Two Variances: An Example of a Confidence Interval and a Hypothesis Test
- 10.8 Deriving a Confidence Interval for the Ratio of Two Variances
- 10.9 The Sampling Distribution of the Ratio of Sample Variances
- 10.10 Inference for the Ratio of Variances: How Robust are These Procedures?

### 11. ANOVA

- 11.1 One-Way ANOVA: Introduction
- 11.2 One-Way ANOVA: The Formulas
- 11.3 One-Way ANOVA: An Example
- 11.4 One-Way ANOVA: LSD confidence intervals
- 11.5 One-Way ANOVA: Finding the p-value

### 12. Regression

- 12.1 Introduction to Simple Linear Regression
- 12.2 Simple Linear Regression: The Least Squares Regression Line
- 12.3 Simple Linear Regression: Interpreting Model Parameters
- 12.4 Simple Linear Regression: Assumptions
- 12.5 Checking assumptions with residual plots
- 12.6 Inference on the slope (the formulas)
- 12.7 Inference on the Slope (An Example)
- 12.8 The Correlation Coefficient and Coefficient of Determination
- 12.9 Simple Linear Regression: An Example
- 12.10 Simple Linear Regression: Always Plot Your Data!
- 12.11 Simple Linear Regression: Transformations
- 12.12 Estimation and Prediction of the Response Variable in Simple Linear Regression
- 12.13 Leverage and Influential Points in Simple Linear Regression
- 12.14 The Pooled-Variance t Test as a Regression