Permutation Test

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

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

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.

Explore Quantitative Data

Find summary statistics and construct inter-active histograms, boxplots, dotplots or stem & leaf plots. For one or several samples. 

One Sample Inference: Confidence Intervals & Significance Tests

Coming soon ...

t Distribution 

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

Distributions: Explore the Shape, Find Probabilities and Percentiles

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

Permutation Test for 

Sample Mean (continuous population)

Sample Proportion

Coming soon ...

Comparing Two Proportions

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

F Distribution 

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

Sampling Distribution for the

Guess the Correlation

Randomly generate scatterplots to guess the correlation coefficient r. Optionally, display the regression line. How do your guesses correlate with the actual values?

Sampling Distribution for the

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

Sampling Distributions and the Central Limit Theorem

Random Numbers 

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

Association and Linear Regression

Interactive Web Apps

Explore Categorical Data

Construct frequency and contingency tables and bar graphs to explore distributions of categorical variables. For one or two variables. 

Bootstrap Confidence Intervals & Permutation Tests

Time Series

Plot a simple time series and add a smooth or linear trend.

Fit Linear Regression Model 

Supply your own data to construct an interactive scatterplot and superimpose a regression line. Obtain the intercept, slope, r and r-squared. Dispaly and analyze residuals. Make predictions or obtain confidence or prediction intervals.

Explore Linear Regression 

Create scatterplots from scratch by clicking in an empty plot and creating points. Investigate the effect of outliers on the regression line. Simulate linear or non-linear relationships.

Inference for a Proportion

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

Categorical Variables

Construct 2x2 contingency tables, obtain conditional proportions and get a bar graph. Find the difference or ratio of proportions. Built the sampling distribution via resampling.

Independence (Categ. Data)

Poisson Distribution 

Explore how the shape of the Poisson Distribution depends on λ and find probabilities of various kinds

Association Between Two 

ANOVA (One-Way)

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

Sampling Distribution for the 

Chi-squared Test

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

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

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

Sample Mean (discrete population)

Fisher's Exact Test

Visualize and run Fisher's exact test for

2 x 2 contingency tables.

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

Chi-Squared Distribution 

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

Mean vs. Median

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

Multivariate Relationships

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


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

Comparing Two Means

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

Errors and Power

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

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.

Inference for a Mean 

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

Explore Coverage 

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





Construct interactive scatterplots, hover over points, move them around or overlay a smooth trend line. Find the correlation coefficient r. Built the sampling distribution of r via bootstrapping or permutation, one resample at a time.