Making Statistics Make Sense

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

13. Jimmy and Mr. Snoothouse

• 13.1 Jimmy and Mr. S. discuss the t versus z issue in confidence intervals
• 13.2 Jimmy and Mr. Snoothouse discuss a hypothesis testing example
• 13.3 Jimmy and Mr. Snoothouse discuss the interpretation of a confidence interval