# Power

• ### Why Do We Need to Compute the Power of a Test?

When performing a hypothesis test about the population mean, a possible reason for the failure of rejection of the null hypothesis is that there's an insufficient sample size to achieve a powerful test. Using a small data set, Minitab is used to check for normality of the data, to perform a 1-Sample t test, and to compute Power and Sample Size for 1-Sample t.

• ### Game: Statistically Grounded

A game to aid in the active learning of significance testing including power and the limitations of p-values. Statistically Grounded is an on-line game that introduces multivariate issues in a simplified game environment. Students are asked to serve as a consultant for their friend, Joe. Joe is starting his own coffee company and students help him design a study to determine whether factors, such as location, time of day, price, type of music, or some combination of these influence sales. The on-line game allows students to design a study, sample data, and make suggestions on how Joe's business should be run. The game then simulates several months of business based on student's suggestions. The goal is to design a plan that will earn the most sales and make the largest amount of profits. The TigetSTAT labs handouts were created by Rod Sturdivant (Ohio State University) and John Jackson (West Point) as part of the Stat2Labs collection at Grinnell College
• ### Joke: The Cost of a Bigger n

A joke for use with discussions about the relationship between sample size and power or in discussing the large sample caution in significance testing.
• ### Quote: Rudnick on Statisticians

...statisticians are the new sexy vampires, only even more pasty. A quote by American playwright, columnist, and humorist Paul M. Rudnick (1957 - ) from his November 19, 2012 essay "A Date with Nate" in "The New Yorker". The essay arose after the correct prediction of the winner of the presidential race in all 50 states in 2012 by statistician Nate Silver

• ### Quote: Acton on Power

Power tends to corrupt, and absolute power corrupts absolutely. is a famous quote of English historian Sir John Dalberg-Acton (1834 - 1902). Of course, Lord Acton was not referring to statistical hypothesis testing when he made the remark in an April 1887 letter to Mandell Creighton. However, the widespread knowledge of the quote by students makes it an interesting way to cover the idea that statistical significance is not the same as practical significance.
• ### Quote: Machol on Coincidences

Most accidents in well-designed systems involve two or more events of low probability occurring in the worst possible combination. is a quote by American systems engineering expert Robert E. Machol (1917 - 1998). The quote is found in his 1975 column "Principles of Operations Research" for the journal "Interfaces" vol. 5, pages 53-54 (this column was titled "The Titanic Coincidence."
• ### Analysis Tool: T-Distribution Table

This page provides a t-table with degrees of freedom 1-30, 60, 120, and infinity and seven levels of alpha from .1 to .0005.

• ### Power Simulation JAVA Applet

This applet demonstrates the concept of power. Users select the hypothesized mean, the alternative mean, the sample size, and the number of samples. The applet shows the hypothesized histogram and the alternative histogram. Users then select either the level of significance and set alpha or the rejection region and set the test statistic. The applet then shows the p-value (in red) and power (in green). User can also determine the direction of the test by clicking the inequality sign.

• ### Statistics at Square One: Differences Between Percentages and Paired Alternatives

This topic from an online textbook discusses standard error, confidence interval, and significance testing for a difference in percentages or proportions. It also covers paired alternatives and standard error of a total. Exercises and answers are also provided.
• ### Power of a Hypothesis Test

This applet performs a hypothesis test for the mean of a single normal population, variance known. Users set the hypothesized mean, true mean, variance, and appropriate alternative hypothesis. The applet plots a representative distribution under the given values with power shaded in blue and significance level shaded in red.