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.

Association Between Two 

Explore Categorical Data

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

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 ...

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. 

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

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.

ANOVA (One-Way)

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

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

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.

Mean vs. Median

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

Statistics

The Art & Science of Learning from data

Agresti    Franklin    Klingenberg

Association and Linear Regression

Interactive Web Apps

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.

Explore Quantitative Data

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

Explore Linear Regression 

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

Bootstrap Confidence Intervals & Permutation Tests

Inference for a Mean 

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

Chi-Squared Distribution 

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

Random Numbers 

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

Sample Mean

Sample Mean

Sample Proportion

One Sample Inference: Confidence Intervals & Significance Tests

Fisher's Exact Test

Visualize and run Fisher's exact test for

2 x 2 contingency tables.

Errors and Power

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

Sampling Distribution for the 

Sampling Distributions and the Central Limit Theorem

Binomial Distribution

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

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.

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?

Normal Distribution 

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

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

Permutation Test for 

Bootstrap

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

Coming soon ...

Comparing Two Proportions

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

Inference for a Proportion

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

Sampling Distribution for the