Association Between Two 

Explore statistical concepts in an interactive way

The following apps have graphs that update with clicks on buttons or sliders. Each explores a different statistical topic and allows results to be saved. ​Click on a picture to start the corresponding app.

Multivariate Relationships

Construct interactive scatterplots to explore the relationship between two quantitative variables while accounting for a third (categorical or quantitative) grouping variable.

Permutation Test for 

Sample Mean

Chi-squared Test

Test for independence, homogeneity or goodness of fit in contingency tables. Analyze observed & expected counts and residuals.

Guess the Correlation

For a given scatterplot, guess the correlation. Optionally display the regression line. How do your guesses correlate with the actual values?

Explore Linear Regression 

Create scatterplots from scratch by clicking in an empty plot. Investigate the effect of outliers. Simulate linear or non-linear relationships.

Coming soon ...

Comparing Two Proportions

Confidence interval and significance test for the difference of two proportions. Independent & dependent samples.

Bootstrap Confidence Intervals & Permutation Tests

Inference for a Proportion

Find confidence intervals and test hypo-theses about a population proportion. Visualize the interval or P-value.

Two Sample Inference: Confidence Intervals & Significance Tests for Comparing Groups

For discrete variables. Define your own discrete distribution (such as uniform or skewed) and explore the sampling distribution. 

Sampling Distribution for the

For continuous variables. Choose from many different population distributions (or built your own) and explore the sampling distribution.

See how the sampling distribution builds up with repeated sampling and explore how its shape depends on n and p.

Sampling Distribution for the 

Chi-Squared Distribution 

Explore how the shape depends on the degrees of freedom. Find and visualize percentiles and probabilities.

Normal Distribution 

Explore how mean and standard deviation change the shape and find percentiles (critical values) or probabilities.

Binomial Distribution

Find the probability for the number of successes in n Bernoulli trials. Explore how the distribution depends on n and p.

Distributions: Explore the Shape, Find Probabilities and Percentiles

Mean vs. Median

Explore the relationship between the mean and median for data coming from a variety of distributions, or enter your own data. 

Random Numbers 

Generate random numbers or flips of a (biased) coin. Keep track of generated numbers with bar chart.

​​Exploratory Analysis (One and Two Samples), Random Numbers

Fit Linear Regression Model 

Supply your own data to fit a linear regression model. Get the estimate of the slope and explore residuals.

F Distribution 

Explore how the shape depends on the two sets of degrees of freedom. Find and visualize percentiles and probabilities.

Visualize and run a permutation test for testing independence in a contingency table using Pearson's Chi-squared statistic.

Inference for a Mean 

Find confidence intervals and test hypo-theses about a population mean. Visualize the interval or P-value.

Errors and Power

Explore probabilities of Type I and Type II errors and connections to sample size, significance level and true parameter value.

Sampling Distributions and the Central Limit Theorem

t Distribution 

Explore how the degrees of freedom effect the shape and find percentiles, probabilities and P-values

Association Between Two 

Quantitative Variables

Find Pearson's or Spearman's correlation coefficient and build their sampling distribution to assess the strength of the relationship.

Sample Mean

Coming soon...

Sampling Distribution for the

Explore Coverage 

What does 95% confidence mean? What affects the width of an interval? Visualize with intervals for proportions or means.

ANOVA (One-Way)

Analysis of Variance for one factor, including multiple comparisons of means (Tukey, Dunnett, Bonferroni). (soon)

Bootstrap

Create the bootstrap distribution of the mean, median or standard deviation and find the bootstrap confidence interval.

One Sample Inference: Confidence Intervals & Significance Tests

Permutation Test

Visualize and run a permutation test comparing two samples with a quantitative response.

Comparing Two Means

Confidence interval and significance test for the difference of two means. Independent & dependent samples.

Coming soon ...

Statistics

The Art & Science of Learning from data

Agresti    Franklin    Klingenberg

Association and Linear Regression

Interactive Web Apps

Categorical Variables

Find the difference or ratio of proportions and build their sampling distribution to assess the strength of the relationship.

Independence (Categ. Data)

Poisson Distribution 

Explore the shape for various parameter values and find and visualize probabilities and percentiles.

Sample Proportion

Explore Quantitative Data

Find summary statistics and construct histograms, boxplots, dotplots or stem & leaf plots. For one or two samples. 

Explore Categorical Data

Construct frequency tables and bargraphs to explore distributions of categorical variables. For one or two samples. 

Fisher's Exact Test

Visualize and run Fisher's exact test for

2 x 2 contingency tables.