# Power

• ### **Type I and Type II Errors - Making Mistakes in the Justice System

This webpage uses the criminal trials in the US Justice system to illustrate hypothesis testing, type I error, and type II error. An applet allows the user to examine the probability of type I errors and type II errors under various conditions. An applet allows users to visualize p-values and the power of a test. Keywords: type I error, type II error, type one error, type two error, type 1 error, type 2 error

This lesson plan uses the Birthday Paradox to introduce basic concepts of probability. Students run a Monte Carlo simulation using the TI-83 graphing calculator to generate random dates, and then search for matching pairs. Students also perform a graphical analysis of the birthday-problem function. Key Words: Permutations; Explicit Function; Recursive Function; Modeling.
• ### Star Library: What is the Significance of a Kiss?

This article describes an interactive activity illustrating general properties of hypothesis testing and hypothesis tests for proportions. Students generate, collect, and analyze data. Through simulation, students explore hypothesis testing concepts. Concepts illustrated are: interpretation of p-values, type I error rate, type II error rate, power, and the relationship between type I and type II error rates and power. This activity is appropriate for use in an introductory college or high school statistics course. Key words: hypothesis test on a proportion, type I and II errors, power, p-values, simulation
• ### Simulating Size and Power Using a 10-Sided Die (Star Library)

This group activity illustrates the concepts of size and power of a test through simulation. Students simulate binomial data by repeatedly rolling a ten-sided die, and they use their simulated data to estimate the size of a binomial test. They carry out further simulations to estimate the power of the test. After pooling their data with that of other groups, they construct a power curve. A theoretical power curve is also constructed, and the students discuss why there are differences between the expected and estimated curves. Key words: Power, size, hypothesis testing, binomial distribution

• ### **Java Applets for Power and Sample Size

This collection of free, interactive Java applets provides a graphical interface for studying the power of the most commonly encountered experimental designs. Intended to be useful in planning statistical studies, these applets cover confidence intervals for means or proportions, one and two sample hypothesis tests for means or proportions, linear regression, balanced ANOVA designs, and tests of multiple correlation, Chi-square, and Poisson. Each applet opens in its own window with sliders, which are convertible to number-entry fields, for manipulating associated parameters. Controlling for the other parameters, users can change sample size, standard deviation, type I error (alpha) and effect size one at a time to see how each affects power. Conversely, users can manipulate the power for the test to determine the necessary sample size or margin of error. Additional features include a graph option by which the program plots a dependent variable (i.e. power) over a range of parameter values; the graph is automatically updated as the parameters are changed. Each dialog window also offers a Help menu which provides instructions for using the applet. The applets can be used over the Internet or downloaded onto the user's own computer.
• ### Likelihood Ratio Test

This site focuses on using the LRT to compare two competing models.
• ### HyperStat Online: Ch. 11 Power

This site defines power and explains what factors may affect it, such as significance level, sample size and variance.

• ### Power Applet

The applets in this section of Statistical Java address Power. Users can perform one or two tailed tests for proportions or means for one or two samples. Set the parameters and drag the mouse across the graph to see how effect size affects power. An article and an alternative source for this applet can be found at http://www.amstat.org/publications/jse/v11n3/java/power/ This page was formerly located at http://www.stat.vt.edu/~sundar/java/applets/Power.html
• ### Chance

This site contains materials to help teach a Chance course. It includes a newsletter, videos and audios, teaching aids, and other related Internet sources.
• ### Robin Lock's Page

This resource is a collection of links for students and teachers of statistics. For students, it includes links to find statistical data. For teachers, it includes links to assist in statistics instruction.