 ## Permutation Test

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

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

## Normal Distribution

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

## Binomial Distribution

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

## Explore Quantitative Data

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

# One Sample Inference: Confidence Intervals & Significance Tests

Coming soon ...

## t Distribution

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

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

Coming soon ...

## Comparing Two Proportions

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

## F Distribution

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

## Guess the Correlation

Randomly generate scatterplots to guess the correlation coefficient r. Optionally, display the regression line. How do your guesses correlate with the actual values?

## Sampling Distribution for the

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

# Sampling Distributions and the Central Limit Theorem

## Random Numbers

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

# Interactive Web Apps

## Explore Categorical Data

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

# Bootstrap Confidence Intervals & Permutation Tests

## Time Series

Plot a simple time series and add a smooth or linear trend.

## Fit Linear Regression Model

Supply your own data to construct an interactive scatterplot and superimpose a regression line. Obtain the intercept, slope, r and r-squared. Dispaly and analyze residuals. Make predictions or obtain confidence or prediction intervals.

## Explore Linear Regression

Create scatterplots from scratch by clicking in an empty plot and creating points. Investigate the effect of outliers on the regression line. Simulate linear or non-linear relationships.

## Inference for a Proportion

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

## Categorical Variables

Construct 2x2 contingency tables, obtain conditional proportions and get a bar graph. Find the difference or ratio of proportions. Built the sampling distribution via resampling.

## Poisson Distribution

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

## ANOVA (One-Way)

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

## 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.

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

## Fisher's Exact Test

Visualize and run Fisher's exact test for

2 x 2 contingency tables.

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

## Chi-Squared Distribution

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

## Mean vs. Median

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

## Multivariate Relationships

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

## Bootstrap

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

## Comparing Two Means

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

## Errors and Power

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

## 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.

STATISTICS

THE ART & SCIENCE OF LEARNING FROM DATA

AGRESTI  ·  FRANKLIN  ·  KLINGENBERG

## Correlation

Construct interactive scatterplots, hover over points, move them around or overlay a smooth trend line. Find the correlation coefficient r. Built the sampling distribution of r via bootstrapping or permutation, one resample at a time.