# Limit Theorems

• ### Chi Square Test of Deviations from Expected Frequencies

The applet allows users to sample from a normal distribution or from a uniform distribution. It shows the expected values and the observed values and computes the deviation. Then, a chi-square test shows if the deviations are significant for both the normal and uniform distributions.
• ### 2 x 2 Contingency Tables

This applet simulates experiments using 2 x 2 contingency tables. You specify the population proportions and the sample size and examine the effects on the probability of rejecting the null hypothesis.
• ### Dataset Example: Reliability and Regression Analysis

This applet demonstrates how the reliability of X and Y affect various aspects of the regression of Y on X.
• ### JAVA Comparing distributions

This simulation shows recorded response times on a simple motor task under two conditions. Various statistics and graphs used to compare the distributions are presented.
• ### Unequal n ANOVA and Types of Sums of Squares

This simulation illustrates types of sums of squares in a 2 x 3 ANOVA.
• ### Video: Against All Odds: 23. Control Charts

In this free online video program, "the successes of casino owners and the manufacturing industry are used to demonstrate the use of the central limit theorem. One example shows how control charts allow us to effectively monitor random variation in business and industry. Students will learn how to create x-bar charts and the definitions of control limits and out-of-control limits."
• ### **Normal Approximation to the Binomial Distribution

This demonstration allows you to view the binomial distribution and the normal approximation to it as a function of the probability of a success on a given trial and the number of trials. It can be used to compute binomial probabilities and normal approximations of those probabilities.
• ### Sampling SIM Program: P-values and Standard Distributions

This webpage provides instructions for teaching p-values and standard distributions using Sampling SIM software. It includes information regarding prerequisite knowledge, common misconceptions, and objectives, as well as links to an activity and a pre/post-test.
• ### Sampling SIM program: Confidence Intervals

This webpage provides instructions for teaching confidence intervals using Sampling SIM software. It includes information regarding prerequisite knowledge, common misconceptions, and objectives, as well as links to an activity and a pre/post-test.
• ### Stattucino Statistical Analysis

Stattucino is a free Java-based system for data analysis. This service is available as a Java applet or application. Some statistics are provided by a web-based interface as servlets. The applet and the application have a spreadsheet type interface for entering data, whereas the servlets use a html form for entering data. The output produced by the servlets, the applet and the application are in html.