Statistics

The Art & Science of Learning from data

Agresti    Franklin    Klingenberg

Permutation Test for 

Sample Mean

Sample Proportion

Fisher's Exact Test

Visualize and run Fisher's exact test for

2 x 2 contingency tables.

Coming soon ...

Comparing Two Proportions

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

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

Sampling Distribution for the

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.

Mean vs. Median

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

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

F Distribution 

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

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.

Bootstrap

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

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.

Permutation Test

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

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.

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

t Distribution 

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

Normal Distribution 

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

Sample Mean

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.

Fit Linear Regression Model 

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

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. 

Guess the Correlation

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

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.

Sampling Distribution for the 

Distributions: Explore the Shape, Find Probabilities and Percentiles

Association and Linear Regression

Interactive Web Apps

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.

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.

ANOVA (One-Way)

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

Explore Linear Regression 

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

One Sample Inference: Confidence Intervals & Significance Tests

Comparing Two Means

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

Coming soon ...

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 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.