Elegant Statistics
by Benjamin Faber

Introduction

Welcome to Elegant Statistics. This site contains a set of Rich Internet Application Simulators for the teaching of statistical concepts. All of the simulators are written in HTML5 and JavaScript/jQuery.

JavaScript/jQuery is currently blocked in your browser. Please adjust your settings to allow it to run before proceeding.

This site is currently in Beta testing, so errors should be expected. The simulators are designed to run primarily in the Chrome browser, but should work across all modern browsers, although JavaScript performance will likely differ.

If you find any errors or problems, have ideas for improvements or changes, or want to give any sort of feedback, please send it to bfaber@csbsju.edu. Please include as much detail as possible about the problems you encountered.

Additional simulators are currently in development and will be added to the site when they reach completion.

Index of Simulators

The following simulators are available.
Hover over an item to see the concepts covered.
Click on any description to try it out.

Histograms and Binning

  • Making a Histogram from data
  • Distribution Shape
  • Bin Width
  • Interaction between Sample Size and Bin Width

Graphs of Relationships

  • Categorical and Continuous variables
  • Bar Graphs, Box Plots, and Scatter Plots
  • Appropriateness of graph types
  • Relationship between histograms and graphs

Central Tendency and Variability

  • Parametric and Non-parametric statistics
  • Skew and Variability
  • Influence of Outliers
  • Calculation of Descriptive Statistics

Sampling Distributions

  • Sample Size and Sampling Distribution
  • Central Limit Theorem and Law of Large Numbers
  • Estimating parameters from samples
  • Biased and Unbiased estimates

Null Hypothesis Significance Testing

  • Influences on NHST
  • Random sampling
  • Sampling Distributions
  • Z-test for individuals and larger samples

Decision Errors and Power

  • Confidence Intervals
  • Effect Size
  • Decision Errors
  • Power

Correlation and r-value

  • Linear Correlation
  • Non-Linear Correlation
  • Calculation of r-value
  • Guessing r from a Scatterplot

Regression

  • Linear Regression
  • Structural Model (ANOVA table)
  • Calculation of F, r2, and p-value
  • Minimizing SSresidual, Least Squares Error

T-Tests

  • One Sample T-test
  • Two Sample Unpaired and Paired T-tests
  • Influence of Correlation on Paired T-test
  • Effect Size (Cohen's d)

ANOVA

  • 1-Way ANOVA
  • 2-Way ANOVA
  • Interactions and Main Effects
  • Repeated Measures and Mixed Design

Chi-Square

  • χ² Goodness of Fit test
  • χ² test of Independence
  • Observed values and Expected models
  • Contingencies, Interactions, and Independence

General Linear Model

  • Relationships amongst tests
  • Picking the appropriate statistic
  • Regression, T-tests, ANOVA, χ², Mixed Models
  • Interactions

Explanation of Design

At the top of the page for each simulator, you will see a menu containing a set of symbols. Each symbol represents a mode of interacting with the simulators as follows: