Web Apps

New mobile app: Resampling (Bootstrap Confidence Intervals)

The Art & Science of Learning from Data

Exploratory Data Analysis

Explore Categorical Data

Explore Quantitative Data

Construct frequency and contingency tables and bar graphs to explore distributions of categorical variables.

For one or two variables.

Explore Quantitative Data

Find summary statistics and construct interactive histograms, boxplots, dotplots or stem & leaf plots.

For one, two, or more groups.

Time Series Plots

Explore Quantitative Data

Time Series Plots

Plot a simple time series and add a smooth or linear trend. Use preloaded data or provide your own.

Mean vs. Median

Time Series Plots

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

Random Numbers

Mean vs. Median

Random Numbers

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

Association, Correlation & Regression

Association Between Two Categorical Variables (2x2 tables)

Screenshot of Association between two categorical variables web app

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

Scatterplots & Correlation

Association Between Two Categorical Variables (2x2 tables)

Screenshot of Scatterplots and Correlation wb app

Construct interactive scatterplots, hover over points, move them around (or remove them) and overlay a smooth trend line. Find the correlation coefficient r and see if it is robust to outliers. Built the sampling distribution of r via resampling.

Guess the Correlation

Association Between Two Categorical Variables (2x2 tables)

Explore Linear Regression

Screenshots of Guess the Correlation web app

Randomly generate scatterplots to guess the correlation coefficient r. 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 to add or remove points. Investigate the effect of outliers on the correlation coefficient or regression line. Simulate linear or non-linear relationships.

Linear Regression

Explore Linear Regression

Multivariate Relationships

Fit a simple linear regression model and obtain the regression equation and related statistics such as r-squared. Make predictions and construct confidence intervals. Display and analyze residuals.

Multivariate Relationships

Explore Linear Regression

Multivariate Relationships

Link to Multivariate Relationship web app.

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

Multiple Linear Regression

Mobile Only: The Art of Stat: Regression app (for iOS or Android) fits multiple linear regression models, with both quantitative and categorical predictors, and two-way interactions. Obtain parameter estimates and standard errors, find predicted values and analyze residual plots.

Exponential Regression

Multiple Linear Regression

Mobile only: The Art of Stat: Regression app (for iOS or Android) fits exponential regression models. You can get parameter estimates and confidence intervals, visualize the predicted curve, and find predicted values or inspect a residual plot.

Logistic Regression

Multiple Linear Regression

Logistic Regression

Mobile only: The Art of Stat: Regression app (for iOS or Android) fits logistic regression models. You can get parameter estimates and confidence intervals, visualize the predicted logistic model, get a confidence band, or predict probabilities for user-supplied x-values.

Distributions: Explore Shapes & Find Probabilities

Binomial Distribution

Explore how the shape of the Binomial distribution depends on the parameter n (the sample size) and p (the probability of success in a Bernoulli trial). Find and visualize probabilities of various kinds.

Normal Distribution

Binomial Distribution

See how the shape of the normal distribution depends on the mean and standard deviation. Find and visualize one- and two-tailed probabilities and percentiles (critical values).

t Distribution

Binomial Distribution

Chi-Squared Distribution

See how the shape of the t distribution depends on the degrees of freedom. Find and visualize one-and two-tailed probabilities and percentiles (critical values).

Chi-Squared Distribution

See how the shape of the Chi-Squared distribution depends on the degrees of freedom. Find and visualize probabilities and percentiles (critical values).

F Distribution

Chi-Squared Distribution

Poisson Distribution

See how the shape of the F distribution depends on the degrees of freedom. Find and visualize probabilities and percentiles (critical values).

Poisson Distribution

Chi-Squared Distribution

Poisson Distribution

Explore how the shape of the Poisson distribution depends on the parameter λ (the mean). Find and visualize probabilities of various kinds.

Art of Stat: Distributions

The Art of Stat: Distribution app (for iOS or Android) lets you explore and work with a variety of continuous and discrete probability distribution, including all the ones above, right on your phone. Download the app from the app store.

Sampling Distributions and the Central Limit Theorem

Sampling Distribution of the Sample Proportion

Sampling Distribution of the Sample Mean (Continuous Population)

Screenshot of Sampling Distribution for the Sample Poportion web app.

Experience how the sampling distribution of the sample proportion builds up one sample at a time. Use sliders to explore the shape of the sampling distribution as the sample size n increases, or as the population proportion p changes. Overlay a normal distribution to explore the Central Limit Theorem.

Sampling Distribution of the Sample Mean (Continuous Population)

Screenshot of the Sampling Distribution for the Sample Mean web app. (For a continuous population.)

Experience how the sampling distribution of the sample mean builds up one sample at a time. Use a variety of real or theoretical continuous population distributions (or create your own) to draw samples from. Move sliders to explore when the Central Limit Theorem kicks in.

Sampling Distribution of the Sample Mean (Discrete Population)

Sampling Distribution of the Sample Mean (Continuous Population)

Sampling Distribution of the Sample Mean (Discrete Population)

Screenshot of Sampling Distribution for the Sample Mean web app. (For a discrete population.)

Experience how the sampling distribution of the sample mean builds up one sample at a time. Use a variety of real or theoretical discrete population distributions (or create your own) to draw samples from. Move sliders to explore when the Central Limit Theorem kicks in.

Art of Stat: Concepts

Sampling Distribution of the Sample Mean (Discrete Population)

The Art of Stat: Concepts app (for iOS or Android) lets you explore the Central Limit Theorem and concepts such as Coverage Probability, Power and Correlation & Linear Regression right on your phone. Download the app from the app store.

Art of Stat: Concepts

Confidence Intervals & Significance Tests (One Sample)

Inference for a Proportion

Screenshot of the Inference for a Population Proportion web app.

Find confidence intervals or test hypotheses about a population proportion. Obtain the margin of error or the z-test statistic and visualize the interval or the P-value on a graph.

Inference for a Mean

Inference for a Proportion

Screenshot of the Inference for a Population Mean web app.

Find confidence intervals or test hypotheses about a population mean. Enter your own data or summary statistics. Use plots to check assumptions and visualize the interval or the P-value on a graph.

Bootstrap for One Sample

Inference for a Proportion

Bootstrap for One Sample

Screenshot of the Bootsrap for One Sample web app.

Create and visualize, step-by-step, the bootstrap distribution of the mean, median or standard deviation. Obtain summary statistics and find a percentile confidence interval.

Explore Coverage

Art of Stat: Inference

Bootstrap for One Sample

What does "95% confidence" mean? What affects the width of an interval? Explore these concepts for confidence intervals of proportions or means, using sliders to change parameters or the sample size.

Errors and Power

Art of Stat: Inference

Visualize and explore relationships between Type I and Type II errors and the power of a test for proportions or means. See how they depend on sample size and the true values of population parameters.

Art of Stat: Inference

The Art of Stat: Inference app (for iOS and Android) carries out one- and two-sample tests, right on your phone. Download it now.

Confidence Intervals & Tests Comparing Two Groups

Compare Two Proportions

Bootstrap for Two Samples

Compare Two Proportions

Confidence intervals or hypotheses tests about the difference of two population proportions. Obtain the margin of error or the z-test statistic and visualize the interval or the P-value on a graph.

For two independent or dependent samples.

Compare Two Means

Bootstrap for Two Samples

Compare Two Proportions

Screenshot o the Compare Two Means web app.

Confidence intervals or hypotheses tests about the difference of two population means. Enter your own data or summary statistics. Visualize the interval or the P-value on a graph.

For two independent or dependent samples.

Bootstrap for Two Samples

Create and visualize, step-by-step, the bootstrap distribution for the difference of means or medians. Obtain summary statistics (such as percentiles) of the bootstrap distribution and find a percentile confidence interval.

Permutation Test

Difference & Ratio of Proportions

Bootstrap for Two Samples

Create and visualize, step-by-step, the permutation distribution for statistics such as the difference of means or medians or the t-statistic. Obtain summary statistics (such as percentiles) and find the permutation P-value.

Difference & Ratio of Proportions

Screenshot of th Association Between Two Catgorical Variables web app.

Find the bootstrap or permutation distribution for the difference or ratio of two proportions, or for the odds-ratio. Use these to obtain percentile confidence intervals or permutation P-values for testing whether there is no association.

Fisher's Exact Test

Difference & Ratio of Proportions

Visualize and run Fisher's exact test for

2 x 2 contingency tables. Obtain the exact P-value for one- or two-sided tests.

Inference for Comparing Several Groups

Chi-Squared Test

Kruskal-Wallis Test

Chi-Squared Test

Screenshot of the Chi-Squard Test web app.

Test for independence, homogeneity or goodness of fit in contingency tables. Enter your own data as raw observations or as a contingency table. Obtain observed and expected counts and find residuals.

ANOVA (One-Way)

Kruskal-Wallis Test

Chi-Squared Test

Screenshot of the ANOVA (One-Way) web app.

Obtain the ANOVA table, F-statistic and side-by-side boxplots to check assumptions. Carry out pairwise comparisons, including simultaneous confidence intervals for pairwise differences of means.

Kruskal-Wallis Test

Permutation Test for Independence

Under Construction

Permutation Test for Independence

Visualize and run a permutation test for testing independence in a contingency table. Obtain the permutation P-value of the Pearson Chi-squared statistic without relying on asymptotical results.

Art of Stat: Inference

Permutation Test for Independence

Art of Stat: Inference

The Art of Stat: Inference app (for iOS and Android) carries out the Chi-Squared Test or ANOVA, including all pairwise comparisons, right on your phone. Download it now.