Tutorials


Introduction to Statistics
A quick introduction to statistics
Variables

Descriptive Statistics
Measuring  “The Center” – Mean, Median, and Mode
Measuring “The Spread” – Range, Interquartile Range, Standard Deviation, and Variance
Measuring “Position” – Percentiles, Quartiles, and Z-Scores

Visualizing Data
Bar Charts & Histograms
Boxplots
Stem and leaf plots
Scatterplots
Frequency Tables
Ogive (Cumulative Frequency Polygon)
How to Find Conditional Relative Frequency in a Two-Way Table
Classifying the Shapes of Distributions
Comparing Distributions
Dixon’s Q Test for Detecting Outliers

Study Design
Four Methods of Collecting Data
Sampling Methods
The Characteristics of an Experiment
Experimental Design
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

Probability
Intro to Probability
Probability Using Sample Spaces
Set Operations – Unions, Intersections, Complements, and More
Theoretical vs. Experimental Probability
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

Random Variables
Discrete Random Variables
Continuous Random Variables
CDF vs. PDF: What’s the Difference?
The Normal Distribution
Empirical Rule (Practice Problems)
Converting Between Z-Scores and Percentiles Using the Normal Distribution
Transforming Random Variables
Combining Random Variables
Combining Normal Random Variables
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

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

Hypothesis Testing
Introduction to Hypothesis Testing
Hypothesis Testing for a Mean
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

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?

Regression
Pearson Correlation Coefficient
Introduction to Simple 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)

ANOVA
One-Way ANOVA
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

Statistical Theory
Expected Value of a Binomial Distribution