STATISTICS

THE ART & SCIENCE OF LEARNING FROM DATA

AGRESTI · FRANKLIN · KLINGENBERG

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

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.

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

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

In the meantime, use the Multivariate Relationships app, which has some capablities to fit a multiple linear regression model with two explanatory variables.

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

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

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.

Fit and visualize a simple exponential regression model to data such as the number of COVID-19 infections in New York City in March 2020 (Example 16, Chapter 13).

Fit a logistic regression model with a single quantitative predictor. Obtain parameter estimates, a graph of the fitted probabilities and construct confidence intervals.

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

Visualize and run Fisher's exact test for

2 x 2 contingency tables.

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

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

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

Construct interactive scatterplots and super-impose a regression line. Obtain the regression equation, *r*, *r*-squared and obtain predictions. Display & analyze residuals.

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

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

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.

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

Coming soon ...

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

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

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

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 two sets of degrees of freedom. Find and visualize percentiles and probabilities.

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

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

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 and creating points. Investigate the effect of outliers on the regression line. Simulate linear or non-linear relationships.

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

Create the bootstrap distribution for the difference of means or medians, and find percentile confidence intervals.

Coming soon ...

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

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

In the meantime, the Boostrap for One Samples can do the Wilcoxon Test.

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