Statistics Topics

Introduction to Statistics

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

Describing Data
Measures of Central Tendency
Measures of Dispersion
SOCS: A Helpful Acronym for Describing Distributions

Visualizing Data
Boxplots
Stem and Leaf Plots
Scatterplots
Relative Frequency Histogram
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
What is a Representative Sample?
What is a Sampling Frame?
Matched Pairs Design
Pretest-Posttest Design
Split-Plot Design
Permuted Block Randomization
Latin Hypercube Sampling

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 Uniform Distribution
The Exponential Distribution
The Hypergeometric Distribution
The Negative Binomial Distribution
The Multinomial Distribution

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

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)
Effect Size
Bayes Factor

Chi-Square Tests
Chi-Square Goodness of Fit Test
Chi-Square Test of Independence
Fisher’s Exact Test
Effect Size for a Chi-Square Test

Regression
Introduction to Simple Linear Regression
How to Perform Simple Linear Regression by Hand
Introduction to Multiple Linear Regression
How to Perform Multiple Linear Regression by Hand
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
Heteroscedasticity in Regression
Multicollinearity in Regression
The Breusch-Pagan Test

ANOVA
One-Way ANOVA
One-Way ANOVA by Hand
Two-Way ANOVA
Repeated Measures ANOVA
Repeated Measures ANOVA By Hand
ANOVA Post Hoc Tests
Dunnett’s Test for Multiple Comparisons
Dunn’s Test for Multiple Comparisons
ANCOVA
Kruskal-Wallis Test
Friedman Test

Resources:

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