The Art & Science of Learning from data

**Agresti Franklin Klingenberg**

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

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

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

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

Visualize and run Fisher's exact test for

2 x 2 contingency tables.

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

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

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

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

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

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

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

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

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

Find the probability for the number of successes in n Bernoulli trials. Explore how the distribution 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.

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

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

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

Explore the shape for various parameter values and find and visualize probabilities and percentiles.

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.

Coming soon...

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

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

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

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

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

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

Coming soon ...

Coming soon ...

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