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

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

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

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

Coming soon ...

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

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

Find Pearson's or Spearman's correlation coefficient and build their sampling distribution to assess the strength of the relationship.

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.

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

The Art & Science of Learning from data

**Agresti Franklin Klingenberg**

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

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

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

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

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

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

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

Visualize and run Fisher's exact test for

2 x 2 contingency tables.

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

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

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

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

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

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

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

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

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

Coming soon ...

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

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