Tutorials

This page lists all of the tutorials available on Statology.

Introduction to Statistics
Descriptive vs. Inferential Statistics
Statistic vs. Parameter
Levels of Measurement: Nominal, Ordinal, Interval and Ratio

Descriptive Statistics
Measures of Central Tendency – Mean, Median, and Mode
Measures of Dispersion – Range, Interquartile Range, Variance, and Standard Deviation
How Do Outliers Affect the Mean?
Is the Interquartile Range Affected By Outliers?
Can Kurtosis Be Negative?
SOCS: A Helpful Acronym for Describing Distributions
Standard Deviation vs. Standard Error: What’s the Difference?
Kendall’s Tau

Visualizing Data
Boxplots
Stem and Leaf Plots
Scatterplots
Conditional Relative Frequency in a Two-Way Table
Dixon’s Q Test for Detecting Outliers
Relative Frequency Histogram
How to Find Class Midpoints in a Frequency Distribution

Probability
Theoretical Probability
Posterior Probability
How to Interpret Odds Ratios
Law of Large Numbers
Set Operations

Study Design
Sampling Methods
Snowball Sampling
What is a Representative Sample and Why is it Important?
Random Selection vs. Random Assignment
Confidentiality vs Anonymity
Understanding Lurking Variables
Matched Pairs Design
Nonresponse Bias
Undercoverage Bias
Pseudoreplication in Statistics
A Simple Explanation of Internal Consistency
Treatment Diffusion
Split-Half Reliability
A Guide to the Benjamini-Hochberg Procedure

Random Variables
What Are Random Variables?
CDF vs. PDF: What’s the Difference?
The Normal Distribution
The Binomial Distribution
The Poisson Distribution
The Geometric Distribution
The Hypergeometric Distribution
The Negative Binomial Distribution
The Multinomial Distribution
Empirical Rule (Practice Problems)
Comparing Z-Scores from Different Distributions
Can a Z-Score Be Negative?
What is a Bimodal Distribution?
Binomial Experiments
A Simple Explanation of Continuity Correction

Sampling Distributions
What is a Sampling Distribution?
Central Limit Theorem

Confidence Intervals
What are Confidence Intervals?
Confidence Interval for a Mean
Confidence Interval for the Difference Between Means
Confidence Interval for a Proportion
Confidence Interval for the Difference in Proportions
Confidence Interval for a Standard Deviation
Confidence Interval for a Correlation Coefficient
How to Create a Confidence Interval Using the F Distribution
Margin of Error vs. Standard Error

Hypothesis Testing
Introduction to Hypothesis Testing
One Sample t-test
Two Sample t-test
Welch’s t-test
Mann-Whitney U Test
Paired Samples t-test
Wilcoxon Signed Rank Test
One Proportion Z-Test
Two Proportion Z-Test

P-values and Effect Size
How to Interpret a P-Value of 0.000 
How to Calculate a P-Value from a t Test By Hand
Three Ways to Find a P-Value from a t Statistic
An Explanation of P-Values and Statistical Significance
A Simple Explanation of Statistical vs. Practical Significance
Effect Size
Bayes Factor

Chi-Square Tests
Chi-Square Goodness of Fit Test
Chi-Square Test of Independence
Fisher’s Exact Test
Chi-Square Test vs. t-Test
Three Ways to Calculate Effect Size for a Chi-Square Test

Regression
Pearson Correlation Coefficient
What is Considered to Be a “Strong” Correlation?
How to Read a Correlation Matrix
Introduction to Simple Linear Regression
How to Perform Linear Regression by Hand
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
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
Examples of Using Linear Regression in Real Life
Examples of Using Logistic Regression in Real Life
How to Interpret the C-Statistic of a Logistic Regression Model
What is a Criterion Variable?
Instrumental Variables
What is a Brier Score?

ANOVA
One-Way ANOVA
Two-Way ANOVA
One-Way Repeated Measures ANOVA
How to Check ANOVA Assumptions
A Guide to Using Post Hoc Tests with ANOVA
How to Perform a One-Way ANOVA by Hand
How to Perform a Repeated Measures ANOVA By Hand
4 Examples of Using ANOVA in Real Life
ANCOVA
Understanding the Differences Between ANOVA, ANCOVA, MANOVA, and MANCOVA
What is the Difference Between a T-test and an ANOVA?
Kruskal-Wallis Test
Friedman Test

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

Time Series
Ljung-Box Test

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