Using these visualizations:

These apps are intended to be used in a number of ways:

• As a visual aid during lectures
• As an open-ended learning tool for active learning
• As a guided learning experience, using either the built-in tutorials or an instructor-written set of instructions.

All of the apps can be used in a demo mode in which all the functionality is enabled. The apps start in this mode, designed for use in lecture or in open-ended discovery by students. Most of the apps have a button labeled “TUTORIAL”, which begins a series of guided exploration, asking the users simple questions and giving commentary on the topic at hand. In the tutorial mode, the functions (i.e., buttons) are constrained to only respond to the next appropriate actions for the guided experience.

Notes about each visualization:

Sampling from a normal distribution -- This app demonstrates the concept of a sampling distribution of an estimate, using the example of a mean of a normally distributed variable. It also reinforces the idea of a histogram.

Learning objectives:

• Visualize the meaning of the sampling distribution of the estimate of the mean.
• Understand that the distribution of sample means has the same mean as the mean of the population.
• Predict the relationship between sample size and the standard error.

Confidence intervals for the mean -- This app shows the meaning of a confidence interval, calculating confidence intervals of the means of repeated samples.

Learning objectives:

• Understand the meaning of a confidence interval.
• Predict the effects of changing sample size on confidence intervals.

Central limit theorem -- This app explores the sampling distribution of the mean when the data do not necessarily follow a normal distribution.

This app is designed to be used after the students are familiar with the general principles of sampling. The “Sampling from a normal distribution” app should perhaps be used first to introduce some of the basic concepts and the visual metaphors used here.

Learning objectives:

• Understand when the sample means of large samples will follow a normal sampling distribution, even when the variable is not normally distributed.
• Predict the effect of increasing or decreasing sample size on the normal approximation of the sample mean distribution.

χ² contingency analysis -- This app simulates samples of a 2x2 contingency analysis. It demonstrates that the χ² test statistic follows a χ² distribution and illustrates the meaning of the P-value. It may be most useful as a demonstration of the meaning of Type I error and power. This app has no tutorial version.

Learning objectives:

• Illustrate the meaning of the P-value associated with a contingency analysis (both with true and false null hypotheses).
• Demonstrate the meaning of Type I error.
• Show the meaning of power.
• Investigate the effects of sample size on power.

The visualizations were created at the University of British Columbia with financial support from UBC's Teaching and Learning Enhancement Fund. They were created by many fine people. Please send us your comments and suggestions.

These pages and their code are released on a Creative Commons Zero agreement, meaning that it is freely available for use, re-use, and modification. We request that you give us credit, when possible. This work is in the public domain.