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About
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Chapters
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https://www.jbstatistics.com/chapters-lessons/
1. Discrete Probability Distributions
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https://www.jbstatistics.com/category/discrete-probability-distributions/
2. Continuous Random Variables & Continuous Probability Distributions
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https://www.jbstatistics.com/category/continuous-random-variables-continuous-probability-distributions/
3. Using Tables to Find Areas and Percentiles
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https://www.jbstatistics.com/category/using-tables-to-find-areas-percentiles/
4. Sampling Distributions
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https://www.jbstatistics.com/category/sampling-distributions/
5. Confidence Intervals
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https://www.jbstatistics.com/category/confidence-intervals/
6. Hypothesis Testing
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https://www.jbstatistics.com/category/hypothesis-testing/
7. Inference for Two Means
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https://www.jbstatistics.com/category/inference-for-two-means/
8. Inference for Proportions
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https://www.jbstatistics.com/category/inference-for-proportions/
9. Chi-square Tests
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https://www.jbstatistics.com/category/chi-square-tests/
10. Variances
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https://www.jbstatistics.com/category/variances/
11. ANOVA
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https://www.jbstatistics.com/category/anova/
12. Regression
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https://www.jbstatistics.com/category/regression/
13. Jimmy and Mr. Snoothouse
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https://www.jbstatistics.com/category/jimmy-and-mr-snoothouse/
Text Resources
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https://www.jbstatistics.com/text-resources/
Contact
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https://www.jbstatistics.com/contact/
1. Discrete Probability Distributions
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/category/discrete-probability-distributions/
1.1 An Introduction to Discrete Random Variables and Discrete Probability Distributions
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https://www.jbstatistics.com/introduction-to-discrete-random-variables-and-discrete-probability-distributions/
1.2 The Expected Value and Variance of Discrete Random Variables
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https://www.jbstatistics.com/expected-value-and-variance-of-discrete-random-variables/
1.3 Introduction to the Bernoulli Distribution
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https://www.jbstatistics.com/introduction-to-the-bernoulli-distribution/
1.4 The Bernoulli Distribution: Deriving the Mean and Variance
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https://www.jbstatistics.com/the-bernoulli-distribution-deriving-the-mean-and-variance/
1.5 An Introduction to the Binomial Distribution
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https://www.jbstatistics.com/introduction-to-the-binomial-distribution/
1.6 Binomial/Not Binomial: Some Examples
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https://www.jbstatistics.com/binomial-not-binomial-some-examples/
1.7 The Binomial Distribution: Mathematically Deriving the Mean and Variance
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https://www.jbstatistics.com/the-binomial-distribution-mathematically-deriving-the-mean-and-variance/
1.8 An Introduction to the Hypergeometric Distribution
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https://www.jbstatistics.com/the-hypergeometric-distribution-introduction/
1.9 An Introduction to the Poisson Distribution
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https://www.jbstatistics.com/introduction-to-the-poisson-distribution/
1.10 The Poisson Distribution: Mathematically Deriving the Mean and Variance
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https://www.jbstatistics.com/the-poisson-distribution-mathematically-deriving-the-mean-and-variance/
1.11 Discrete Probability Distributions: Example Problems (Binomial, Poisson, Hypergeometric, Geometric)
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https://www.jbstatistics.com/discrete-probability-distributions-some-examples-binomial-poisson-hypergeometric-geometric/
1.12 The Relationship Between the Binomial and Poisson Distributions
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https://www.jbstatistics.com/the-relationship-between-the-binomial-and-poisson-distributions/
1.13 Proof that the Binomial Distribution tends to the Poisson Distribution
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https://www.jbstatistics.com/proof-that-the-binomial-distribution-tends-to-the-poisson-distribution/
1.13 An Introduction to the Multinomial Distribution
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https://www.jbstatistics.com/introduction-to-the-multinomial-distribution/
1.14 An Introduction to the Geometric Distribution
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https://www.jbstatistics.com/introduction-to-the-geometric-distribution/
1.15 An Introduction to the Negative Binomial Distribution
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https://www.jbstatistics.com/introduction-to-the-negative-binomial-distribution/
1.16 Introduction to the Multinomial Distribution
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https://www.jbstatistics.com/introduction-to-the-multinomial-distribution-2/
1.17 Poisson or Not? (When does a random variable have a Poisson distribution?)
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https://www.jbstatistics.com/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)
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https://www.jbstatistics.com/overview-of-some-discrete-probability-distributions-binomialgeometrichypergeometricpoissonnegb/
2. Continuous Random Variables & Continuous Probability Distributions
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/category/continuous-random-variables-continuous-probability-distributions/
2.1 An Introduction to Continuous Probability Distributions
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https://www.jbstatistics.com/introduction-to-continuous-probability-distributions/
2.2 Finding Probabilities and Percentiles for a Continuous Probability Distribution
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https://www.jbstatistics.com/finding-probabilities-and-percentiles-for-a-continuous-probability-distribution/
2.3 Deriving the Mean and Variance of a Continuous Probability Distribution
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https://www.jbstatistics.com/deriving-the-mean-and-variance-of-a-continuous-probability-distribution/
2.4 Introduction to the Continuous Uniform Distribution
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https://www.jbstatistics.com/introduction-to-the-continuous-uniform-distribution/
2.5 An Introduction to the Normal Distribution
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https://www.jbstatistics.com/introduction-to-the-normal-distribution/
2.6 Standardizing Normally Distributed Random Variables
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https://www.jbstatistics.com/standardizing-normally-distributed-random-variables/
2.7 The Normal Approximation to the Binomial Distribution
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https://www.jbstatistics.com/2-7-the-normal-approximation-to-the-binomial-distribution/
2.8 Normal Quantile-Quantile Plots
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https://www.jbstatistics.com/normal-quantile-quantile-plots/
2.9 An Introduction to the Chi-Square Distribution
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https://www.jbstatistics.com/introduction-to-the-chi-square-distribution/
2.10 An Introduction to the t Distribution (Includes some mathematical details)
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https://www.jbstatistics.com/introduction-to-the-t-distribution/
2.11 An Introduction to the F Distribution
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https://www.jbstatistics.com/introduction-to-the-f-distribution/
3. Using Tables to Find Areas and Percentiles
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/category/using-tables-to-find-areas-percentiles/
3.1 Finding Areas Using the Standard Normal Table (for tables that give the area to left of z)
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https://www.jbstatistics.com/finding-areas-using-the-standard-normal-table-for-tables-area-to-left-of-z/
3.2 Finding Percentiles Using the Standard Normal Table (for tables that give the area to left of z)
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https://www.jbstatistics.com/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)
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https://www.jbstatistics.com/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)
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https://www.jbstatistics.com/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
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https://www.jbstatistics.com/using-the-t-table-to-find-areas-and-percentiles/
3.6 R Basics: Finding Percentiles and Areas for the t Distribution
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https://www.jbstatistics.com/r-basics-finding-percentiles-and-areas-for-the-t-distribution/
3.7 Using the F Table to Find Areas and Percentiles
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https://www.jbstatistics.com/using-the-f-table-to-find-areas-and-percentiles/
3.8 Finding Percentiles and Areas for the F Distribution Using R
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https://www.jbstatistics.com/finding-percentiles-and-areas-for-the-f-distribution-using-r/
3.9 Using the Chi-square Table to Find Areas and Percentiles
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https://www.jbstatistics.com/using-the-chi-square-table-to-find-areas-and-percentiles/
3.10 Using R to Find Chi-square Areas and Percentiles
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https://www.jbstatistics.com/using-r-to-find-chi-square-areas-and-percentiles/
4. Sampling Distributions
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/category/sampling-distributions/
4.1 Sampling Distributions: Introduction to the Concept
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https://www.jbstatistics.com/sampling-distributions-introduction-to-the-concept/
4.2 The Sampling Distribution of the Sample Mean
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https://www.jbstatistics.com/the-sampling-distribution-of-the-sample-mean/
4.3 Introduction to the Central Limit Theorem
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https://www.jbstatistics.com/introduction-to-the-central-limit-theorem/
4.4 Deriving the Mean and Variance of the Sample Mean
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https://www.jbstatistics.com/deriving-the-mean-and-variance-of-the-sample-mean/
4.5 Proof that the Sample Variance is an Unbiased Estimator of the Population Variance
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https://www.jbstatistics.com/proof-that-the-sample-variance-is-an-unbiased-estimator-of-the-population-variance/
4.7 Confidence Intervals for One Mean: Assumptions
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https://www.jbstatistics.com/4-7-confidence-intervals-for-one-mean-assumptions/
5. Confidence Intervals
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/category/confidence-intervals/
5.1 Introduction to Confidence Intervals
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https://www.jbstatistics.com/introduction-to-confidence-intervals/
5.2 Deriving a Confidence Interval for the Mean
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https://www.jbstatistics.com/deriving-a-confidence-interval-for-the-mean/
5.3 Intro to Confidence Intervals for One Mean (Sigma Known)
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https://www.jbstatistics.com/intro-to-confidence-intervals-for-one-mean-sigma-known/
5.4 Finding the Appropriate z Value for the Confidence Interval Formula
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https://www.jbstatistics.com/finding-the-appropriate-z-value-for-the-confidence-interval-formula/
5.5 Confidence Intervals for One Mean: Interpreting the Interval
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https://www.jbstatistics.com/confidence-intervals-for-one-mean-interpreting-the-interval/
5.6 What Factors Affect the Margin of Error?
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https://www.jbstatistics.com/what-factors-affect-the-margin-of-error/
5.7 Confidence Intervals for One Mean: Sigma Not Known (t Method)
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https://www.jbstatistics.com/confidence-intervals-for-one-mean-sigma-not-known-t-method/
5.8 Intro to the t Distribution (non-technical)
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https://www.jbstatistics.com/intro-to-the-t-distribution-non-technical/
5.9 Confidence Intervals for One Mean: Determining the Required Sample Size
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https://www.jbstatistics.com/confidence-intervals-for-one-mean-determining-the-required-sample-size/
5.10 Confidence Intervals for One Mean: Investigating the Normality Assumption
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https://www.jbstatistics.com/confidence-intervals-for-one-mean-investigating-the-normality-assumption/
6. Hypothesis Testing
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/category/hypothesis-testing/
6.1 An Introduction to Hypothesis Testing
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https://www.jbstatistics.com/an-introduction-to-hypothesis-testing/
6.2 Z Tests for One Mean: Introduction
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https://www.jbstatistics.com/z-tests-for-one-mean-introduction/
6.3 Z Tests for One Mean: The Rejection Region Approach
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https://www.jbstatistics.com/z-tests-for-one-mean/
6.4 Z Tests for One Mean: The p-value
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https://www.jbstatistics.com/z-tests-for-one-mean-the-p-value/
6.5 Z Tests for One Mean: An Example
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https://www.jbstatistics.com/z-tests-for-one-mean-an-example/
6.6 What is a p-value?
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https://www.jbstatistics.com/what-is-a-p-value/
6.7 Type I Errors, Type II Errors, and the Power of the Test
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https://www.jbstatistics.com/type-i-errors-type-ii-errors-and-the-power-of-the-test/
6.8 One-Sided Test or Two-Sided Test?
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https://www.jbstatistics.com/one-sided-test-or-two-sided-test/
6.9 Statistical Significance versus Practical Significance
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https://www.jbstatistics.com/statistical-significance-versus-practical-significance/
6.10 The Relationship Between Confidence Intervals and Hypothesis Tests
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https://www.jbstatistics.com/the-relationship-between-confidence-intervals-and-hypothesis-tests/
6.11 Calculating Power and the Probability of a Type II Error (A One-Tailed Example)
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https://www.jbstatistics.com/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)
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https://www.jbstatistics.com/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?
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https://www.jbstatistics.com/what-factors-affect-the-power-of-a-z-test/
6.14 Hypothesis Testing in 17 Seconds
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https://www.jbstatistics.com/hypothesis-testing-in-17-seconds/
6.15 t Tests for One Mean: Introduction
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https://www.jbstatistics.com/t-tests-for-one-mean-introduction/
6.16 t Tests for One Mean: An Example
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https://www.jbstatistics.com/t-tests-for-one-mean-an-example/
6.17 t Tests for One Mean: Investigating the Normality Assumption
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https://www.jbstatistics.com/t-tests-for-one-mean-investigating-the-normality-assumption/
6.18 Hypothesis tests on one mean: t or z?
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https://www.jbstatistics.com/hypothesis-tests-on-one-mean-t-or-z/
6.19 Using the t Table to Find the P-value in One-Sample t Tests
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https://www.jbstatistics.com/using-t-table-to-find-p-value-in-one-sample-test/
6.20 Finding Areas Under the t Distribution
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https://www.jbstatistics.com/finding-areas-under-the-t-distribution/
7. Inference for Two Means
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/category/inference-for-two-means/
7.1 Inference for Two Means: Introduction
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https://www.jbstatistics.com/inference-for-two-means-introduction/
7.2 The Sampling Distribution of the Difference in Sample Means
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https://www.jbstatistics.com/the-sampling-distribution-of-the-difference-in-sample-means/
7.3 Pooled-Variance t Tests and Confidence Intervals: Introduction
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https://www.jbstatistics.com/pooled-variance-t-tests-and-confidence-intervals-introduction/
7.4 Pooled-Variance t Tests and Confidence Intervals: An Example
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https://www.jbstatistics.com/pooled-variance-t-tests-and-confidence-intervals-an-example/
7.5 Welch (Unpooled Variance) t Tests and Confidence Intervals: Introduction
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https://www.jbstatistics.com/welch-unpooled-variance-t-tests-and-confidence-intervals-introduction/
7.6 Welch (Unpooled Variance) t Tests and Confidence Intervals: An Example
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https://www.jbstatistics.com/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?)
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https://www.jbstatistics.com/pooled-or-unpooled-variance-t-tests-and-confidence-intervals-to-pool-or-not-to-pool/
7.8 An Introduction to Paired-Difference Procedures
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https://www.jbstatistics.com/an-introduction-to-paired-difference-procedures/
7.9 An Example of a Paired-Difference t Test and Confidence Interval
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https://www.jbstatistics.com/an-example-of-a-paired-difference-t-test-and-confidence-interval/
7.10 Pooled-Variance t Procedures: Investigating the Normality Assumption
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https://www.jbstatistics.com/pooled-variance-t-procedures-investigating-the-normality-assumption/
8. Inference for Proportions
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/category/inference-for-proportions/
8.1 An Introduction to Inference for a Proportion
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https://www.jbstatistics.com/inference-for-one-proportion-introduction/
8.2 The Sampling Distribution of the Sample Proportion
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https://www.jbstatistics.com/the-sampling-distribution-of-the-sample-proportion/
8.3 Inference for a Proportion: An Example of a Confidence Interval and a Hypothesis Test
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https://www.jbstatistics.com/inference-for-one-proportion-an-example/
8.4 Confidence Intervals for a Proportion: Determining the Minimum Sample Size
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https://www.jbstatistics.com/inference-for-one-proportion-determining-the-required-sample-size/
8.5 An Introduction to Inference for Two Proportions
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https://www.jbstatistics.com/inference-for-two-proportions-introduction/
8.6 Inference for Two Proportions: An Example of a Confidence Interval and a Hypothesis Test
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https://www.jbstatistics.com/inference-for-two-proportions-an-example/
9. Chi-square Tests
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/category/chi-square-tests/
9.1 Chi-square Tests for One-way tables
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https://www.jbstatistics.com/chi-square-tests-for-one-way-tables/
9.2 Chi-square tests: Goodness of fit for the binomial distribution
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https://www.jbstatistics.com/chi-square-tests-goodness-of-fit-for-the-binomial-distribution/
9.3 Chi-square Tests for Two-way Tables (Chi-square Tests of Independence)
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https://www.jbstatistics.com/chi-square-tests-for-two-way-tables-chi-square-tests-of-independence/
9.4 Chi-square tests for count data: Finding the p-value
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https://www.jbstatistics.com/chi-square-tests-for-count-data-finding-the-p-value/
10. Variances
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/category/variances/
10.1 An Introduction to Inference for One Variance (Assuming a Normally Distributed Population)
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https://www.jbstatistics.com/introduction-to-inference-for-one-variance/
10.2 Inference for One Variance: An Example of a Confidence Interval and a Hypothesis Test
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https://www.jbstatistics.com/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)
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https://www.jbstatistics.com/deriving-a-confidence-interval-for-a-variance-assuming-a-normally-distributed-population/
10.4 Hypothesis Tests for Equality of Two Variances
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https://www.jbstatistics.com/the-sampling-distribution-of-the-sample-variance/
10.5 Inference for a Variance: How Robust are These Procedures?
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https://www.jbstatistics.com/inference-for-a-variance-how-robust-are-these-procedures/
10.6 An Introduction to Inference for the Ratio of Two Variances
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https://www.jbstatistics.com/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
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https://www.jbstatistics.com/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
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https://www.jbstatistics.com/deriving-a-confidence-interval-for-the-ratio-of-two-variances/
10.9 The Sampling Distribution of the Ratio of Sample Variances
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https://www.jbstatistics.com/the-sampling-distribution-of-the-ratio-of-sample-variances/
10.10 Inference for the Ratio of Variances: How Robust are These Procedures?
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https://www.jbstatistics.com/inference-for-the-ratio-of-variances-how-robust-are-these-procedures/
11. ANOVA
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/category/anova/
11.1 One-Way ANOVA: Introduction
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https://www.jbstatistics.com/one-way-anova-introduction/
11.2 One-Way ANOVA: The Formulas
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https://www.jbstatistics.com/one-way-anova-the-formulas/
11.3 One-Way ANOVA: An Example
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https://www.jbstatistics.com/one-way-anova-an-example/
11.4 One-Way ANOVA: LSD confidence intervals
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https://www.jbstatistics.com/one-way-anova-lsd-confidence-intervals/
11.5 One-Way ANOVA: Finding the p-value
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https://www.jbstatistics.com/one-way-anova-finding-the-p-value/
12. Regression
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/category/regression/
12.1 Introduction to Simple Linear Regression
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https://www.jbstatistics.com/introduction-to-simple-linear-regression/
12.2 Simple Linear Regression: The Least Squares Regression Line
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https://www.jbstatistics.com/simple-linear-regression-the-least-squares-regression-line/
12.3 Simple Linear Regression: Interpreting Model Parameters
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https://www.jbstatistics.com/simple-linear-regression-interpreting-model-parameters/
12.4 Simple Linear Regression: Assumptions
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https://www.jbstatistics.com/simple-linear-regression-assumptions/
12.5 Checking assumptions with residual plots
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https://www.jbstatistics.com/checking-assumptions-with-residual-plots/
12.6 Inference on the slope (the formulas)
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https://www.jbstatistics.com/inference-on-the-slope-the-formulas/
12.7 Inference on the Slope (An Example)
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https://www.jbstatistics.com/inference-on-the-slope-an-example/
12.8 The Correlation Coefficient and Coefficient of Determination
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https://www.jbstatistics.com/the-correlation-coefficient-and-coefficient-of-determination/
12.9 Simple Linear Regression: An Example
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https://www.jbstatistics.com/simple-linear-regression-an-example/
12.10 Simple Linear Regression: Always Plot Your Data!
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https://www.jbstatistics.com/simple-linear-regression-always-plot-your-data/
12.11 Simple Linear Regression: Transformations
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https://www.jbstatistics.com/simple-linear-regression-transformations/
12.12 Estimation and Prediction of the Response Variable in Simple Linear Regression
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https://www.jbstatistics.com/estimation-and-prediction-of-the-response-variable-in-simple-linear-regression/
12.13 Leverage and Influential Points in Simple Linear Regression
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https://www.jbstatistics.com/leverage-and-influential-points-in-simple-linear-regression/
12.14 The Pooled-Variance t Test as a Regression
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https://www.jbstatistics.com/the-pooled-variance-t-test-as-a-regression/
13. Jimmy and Mr. Snoothouse
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/category/jimmy-and-mr-snoothouse/
13.1 Jimmy and Mr. S. discuss the t versus z issue in confidence intervals
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https://www.jbstatistics.com/jimmy-and-mr-s-discuss-the-t-versus-z-issue-in-confidence-intervals/
13.2 Jimmy and Mr. Snoothouse discuss a hypothesis testing example
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https://www.jbstatistics.com/jimmy-and-mr-snoothouse-discuss-a-hypothesis-testing-example/
13.3 Jimmy and Mr. Snoothouse discuss the interpretation of a confidence interval
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https://www.jbstatistics.com/jimmy-mr-snoothouse-confidence-interval/
1. Discrete Probability Distributions
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https://www.jbstatistics.com/category/discrete-probability-distributions/
2. Continuous Random Variables & Continuous Probability Distributions
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https://www.jbstatistics.com/category/continuous-random-variables-continuous-probability-distributions/
3. Using Tables to Find Areas and Percentiles
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https://www.jbstatistics.com/category/using-tables-to-find-areas-percentiles/
4. Sampling Distributions
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https://www.jbstatistics.com/category/sampling-distributions/
5. Confidence Intervals
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https://www.jbstatistics.com/category/confidence-intervals/
6. Hypothesis Testing
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https://www.jbstatistics.com/category/hypothesis-testing/
7. Inference for Two Means
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https://www.jbstatistics.com/category/inference-for-two-means/
8. Inference for Proportions
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https://www.jbstatistics.com/category/inference-for-proportions/
9. Chi-square Tests
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https://www.jbstatistics.com/category/chi-square-tests/
10. Variances
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https://www.jbstatistics.com/category/variances/
11. ANOVA
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https://www.jbstatistics.com/category/anova/
12. Regression
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https://www.jbstatistics.com/category/regression/
13. Jimmy and Mr. Snoothouse
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https://www.jbstatistics.com/category/jimmy-and-mr-snoothouse/
Visit the Youtube Channel
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https://www.youtube.com/channel/UCiHi6xXLzi9FMr9B0zgoHqA
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https://peterelmhirst.com
GeneratePress
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https://generatepress.com