This page lists all of the tutorials available on Statology.

**Introduction to Statistics**

**Descriptive vs. Inferential Statistics: What’s the Difference?**

**Descriptive Statistics**

**Measures of Central Tendency – Mean, Median, and Mode**

**Measures of Dispersion – Range, Interquartile Range, Variance, and Standard Deviation**

**Visualizing Data**

**Bar Charts & Histograms**

**Boxplots**

**Stem and leaf plots**

**Scatterplots**

Ogive (Cumulative Frequency Polygon)

How to Find Conditional Relative Frequency in a Two-Way Table

**Dixon’s Q Test for Detecting Outliers**

Ogive (Cumulative Frequency Polygon)

How to Find Conditional Relative Frequency in a Two-Way Table

**Study Design**

**Four Methods of Collecting Data**

**Sampling Methods**

What is a Representative Sample and Why is it Important?

Random Selection vs. Random Assignment

Confidentiality vs Anonymity: What’s the Difference?

Understanding Lurking Variables: An Explanation & Examples

Nonresponse Bias: Explanation, Examples, & How to Prevent It

Undercoverage Bias: Explanation, Examples, & How to Prevent It

Pseudoreplication in Statistics: An Explanation, Examples, & What to Do About It

A Simple Explanation of Internal Consistency

What is a Representative Sample and Why is it Important?

Random Selection vs. Random Assignment

Confidentiality vs Anonymity: What’s the Difference?

Understanding Lurking Variables: An Explanation & Examples

Nonresponse Bias: Explanation, Examples, & How to Prevent It

Undercoverage Bias: Explanation, Examples, & How to Prevent It

Pseudoreplication in Statistics: An Explanation, Examples, & What to Do About It

A Simple Explanation of Internal Consistency

**Probability**

**Intro to Probability**

Probability Using Sample Spaces

The Addition Rule for Probability

The Multiplication Rule for Probability

Conditional Probability and Independence

Probability Using Sample Spaces

The Addition Rule for Probability

The Multiplication Rule for Probability

Conditional Probability and Independence

**Counting, Combinations, and Permutations**

**Counting Outcomes Using Tree Diagrams**

Permutations

Combinations

Practice Problems with Permutations & Combinations

Probability with Permutations & Combinations

Permutations

Combinations

Practice Problems with Permutations & Combinations

Probability with Permutations & Combinations

**Random Variables**

**Discrete Random Variables**

Continuous Random Variables

CDF vs. PDF: What’s the Difference?

The Normal Distribution

Empirical Rule (Practice Problems)

Can a Z-Score Be Negative?

**Converting Between Z-Scores and Percentiles Using the Normal Distribution**

Transforming Random Variables

Combining Random Variables

Combining Normal Random Variables

Binomial Experiments: An Explanation + Examples

The Binomial Distribution

The Uniform Distribution

The Geometric Distribution

The Negative Binomial Distribution

The Poisson Distribution

The Hypergeometric Distribution

The Multinomial Distribution

Continuous Random Variables

CDF vs. PDF: What’s the Difference?

The Normal Distribution

Empirical Rule (Practice Problems)

Can a Z-Score Be Negative?

Transforming Random Variables

Combining Random Variables

Combining Normal Random Variables

Binomial Experiments: An Explanation + Examples

The Binomial Distribution

The Uniform Distribution

The Geometric Distribution

The Negative Binomial Distribution

The Poisson Distribution

The Hypergeometric Distribution

The Multinomial Distribution

**Sampling Distributions**

**What is a Sampling Distribution?**

Understanding the Central Limit Theorem

Finding the Difference Between Means

**Finding the Difference Between Proportions**

Understanding the Central Limit Theorem

Finding the Difference Between Means

**Confidence Intervals**

**Introduction to Confidence Intervals**

Confidence Interval for a Mean

Confidence Interval for a Difference in Means

Confidence Interval for a Proportion

Confidence Interval for a Difference in Proportions

A Simple Explanation of Bootstrapping in Statistics with an Example

How to Create a Confidence Interval Using the F Distribution

Confidence Interval for a Mean

Confidence Interval for a Difference in Means

Confidence Interval for a Proportion

Confidence Interval for a Difference in Proportions

A Simple Explanation of Bootstrapping in Statistics with an Example

How to Create a Confidence Interval Using the F Distribution

**Hypothesis Testing**

**Introduction to Hypothesis Testing**

Hypothesis Testing for a Mean

How to Calculate a P-Value from a T-Test By Hand

Hypothesis Testing for a Difference in Means

A Guide to Welch’s t-test (When to Use it + Examples)

Hypothesis Testing for a Difference in Paired Means

Hypothesis Testing for a Proportion

Hypothesis Testing for a Difference in Proportions

Three Ways to Find a P-Value from a t Statistic

Mann-Whitney U Test

**How to Interpret a P-Value of 0.000 **

An Explanation of P-Values and Statistical Significance

A Simple Explanation of Statistical vs. Practical Significance

Effect Size: What It Is and Why It Matters

Hypothesis Testing for a Mean

How to Calculate a P-Value from a T-Test By Hand

Hypothesis Testing for a Difference in Means

A Guide to Welch’s t-test (When to Use it + Examples)

Hypothesis Testing for a Difference in Paired Means

Hypothesis Testing for a Proportion

Hypothesis Testing for a Difference in Proportions

Three Ways to Find a P-Value from a t Statistic

Mann-Whitney U Test

An Explanation of P-Values and Statistical Significance

A Simple Explanation of Statistical vs. Practical Significance

Effect Size: What It Is and Why It Matters

**Chi-Square Tests**

**Chi-Square Test for Goodness of Fit**

Chi-Square Test for Homogeneity

Chi-Square Test for Independence

Chi-Square Test vs. t-Test: What’s the Difference?

Chi-Square Test for Homogeneity

Chi-Square Test for Independence

Chi-Square Test vs. t-Test: What’s the Difference?

**Regression**

**Pearson Correlation Coefficient**

What is Considered to Be a “Strong” Correlation?

**Introduction to Simple Linear Regression**

The Four Assumptions of Linear Regression

**Testing the Significance of a Regression Slope**

How to Read and Interpret a Regression Table

How to Interpret Regression Coefficients

A Simple Guide to Understanding the F-Test of Overall Significance in Regression

Understanding the Standard Error of the Regression

How to Calculate Residuals in Regression Analysis

**What is a Good R-squared Value?**

Understanding Heteroscedasticity in Regression

A Guide to Multicollinearity in Regression

How to Interpret the C-Statistic of a Logistic Regression Model

What is a Criterion Variable? (Explanation + Examples)

What is Considered to Be a “Strong” Correlation?

The Four Assumptions of Linear Regression

How to Read and Interpret a Regression Table

How to Interpret Regression Coefficients

A Simple Guide to Understanding the F-Test of Overall Significance in Regression

Understanding the Standard Error of the Regression

How to Calculate Residuals in Regression Analysis

Understanding Heteroscedasticity in Regression

A Guide to Multicollinearity in Regression

How to Interpret the C-Statistic of a Logistic Regression Model

What is a Criterion Variable? (Explanation + Examples)

**ANOVA**

**One-Way ANOVA**

How to Check ANOVA Assumptions

Kruskal-Wallis Test

One-Way Repeated Measures ANOVA

Two-Way ANOVA

A Guide to Using Post Hoc Tests with ANOVA

Understanding the Differences Between ANOVA, ANCOVA, MANOVA, and MANCOVA

What is the Difference Between a T-test and an ANOVA?

How to Check ANOVA Assumptions

Kruskal-Wallis Test

One-Way Repeated Measures ANOVA

Two-Way ANOVA

A Guide to Using Post Hoc Tests with ANOVA

Understanding the Differences Between ANOVA, ANCOVA, MANOVA, and MANCOVA

What is the Difference Between a T-test and an ANOVA?

**Matrix Algebra**

**Matrix Multiplication: (2×2) by (2×2)**

**Matrix Multiplication: (2×2) by (2×3)**

**Matrix Multiplication: (3×3) by (3×2)**

**Maximum Likelihood Estimation**

**Maximum Likelihood Estimation (MLE) for a Uniform Distribution**