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.

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

Time Series Plot

Plot a simple time series (Under Construction)

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

Sample Proportion

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

Random Numbers 

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

Explore Categorical Data

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

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.

Permutation Test

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

Distributions: Explore the Shape, Find Probabilities and Percentiles

Interactive Web Apps

Coming soon ...

Comparing Two Proportions

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

Sampling Distribution for the 

Multivariate Relationships

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

Comparing Two Means

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

Coming soon ...

Categorical Variables

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

Chi-squared Test

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

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

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 

Fisher's Exact Test

Visualize and run Fisher's exact test for

2 x 2 contingency tables.

Association and Linear Regression

Permutation Test for 

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

Sampling Distribution for the

F Distribution 

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

ANOVA (One-Way)

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

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

Association Between Two 

Bootstrap Confidence Intervals & Permutation Tests

Binomial Distribution

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

Independence (Categ. Data)

One Sample Inference: Confidence Intervals & Significance Tests

Normal Distribution 

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

Poisson Distribution 

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

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 inter-active histograms, boxplots, dotplots or stem & leaf plots. For one or several samples. 

Inference for a Proportion

Find confidence intervals and test hypo-theses about a population proportion. 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.

Sample Mean (discrete population)

STATISTICS

THE ART & SCIENCE OF LEARNING FROM DATA

AGRESTI  ·  FRANKLIN  ·  KLINGENBERG

Sample Mean (continuous population)

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

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.

Mean vs. Median

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

Bootstrap

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

Sampling Distribution for the