Tutorials

This page lists all of the tutorials available on Statology.

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

Descriptive Statistics
Measures of Central Tendency
Measures of Dispersion
How Do Outliers Affect the Mean?
Is the Interquartile Range Affected By Outliers?
Range Rule of Thumb
Can Kurtosis Be Negative?
SOCS: A Helpful Acronym for Describing Distributions
Standard Deviation vs. Standard Error
How to Calculate a Pooled Standard Deviation
Kendall’s Tau
Bivariate Analysis

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
Introduction to Density Curves

Probability
Theoretical Probability
Posterior Probability
How to Interpret Odds Ratios
Law of Large Numbers
Set Operations
The General Multiplication Rule

Study Design
Explanatory & Response Variables
Sampling Methods
Snowball Sampling
Maximum Variation Sampling
What is a Representative Sample?
What is a Sampling Frame?
Random Selection vs. Random Assignment
Confidentiality vs Anonymity
Lurking Variables
Concomitant Variables
Extraneous Variables
Intervening Variables
Matched Pairs Design
Pretest-Posttest Design
Split-Plot Design
Permuted Block Randomization
Nonresponse Bias
Undercoverage Bias
Neyman Bias
Referral Bias
Pseudoreplication in Statistics
A Simple Explanation of Internal Consistency
Treatment Diffusion
Split-Half Reliability
A Guide to the Benjamini-Hochberg Procedure
What is Latin Hypercube Sampling?
Reverse Causation

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
The Multinomial Coefficient
Empirical Rule (Practice Problems)
Comparing Z-Scores from Different Distributions
Can a Z-Score Be Negative?
What is a Bimodal Distribution?
Binomial Experiments
Understanding the Shape of a Binomial Distribution
A Simple Explanation of Continuity Correction

Sampling Distributions
What is a Sampling Distribution?
Central Limit Theorem
The Large Sample Condition

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
What is the Finite Population Correction Factor?

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
How to Find Z Alpha/2 (za/2)
What is the Family-wise Error Rate?
What is a Standardized Test Statistic?
The 10% Condition
The Success/Failure Condition
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
Phi Coefficient
How to Calculate Expected Frequency
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
Standardized vs. Unstandardized 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?
What is Zero-Order Correlation?
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?
What are Instrumental Variables?
What is Omitted Variable Bias?
What is a Brier Score?
What is a Parsimonious Model?
What is the PRESS Statistic?

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