# Significance Testing Principles

• ### Selective Attention: Gorilla Video

This video is an example of what is known in psychology as selective attention. When a person is instructed to only focus on the number of times a ball is passed between players wearing a white shirt it is sometimes difficult to see what else is going on.
• ### The Probability of Penalizing the Innocent Due to Bad Test Results

This is an example of "growing" a decision tree to analyze two possible outcomes. The tree's branches examine the two possible conditions of employee drug use with corresponding probabilities. This example looks at the final outcome probabilities of being correctly and incorrectly identified versus testing accuracy.

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.
• ### Racing Game with One Die

This applet allows the user to simulate a race where the results are based on the roll of a die. For each outcome of the die, the user chooses which player moves forward. Then that car moves forward the given number of spaces. Users can experiment with the race by determining which player will win more often based on the rules that they specify.

• ### Testosterone and Antisocial Behavior

This set of exercises asks students to model relationships and test them based on the chi-square distribution. The data used is based on testosterone levels and delinquency rate of American military men.
• ### Star Library: Rectangularity

This article describes an interactive activity illustrating sampling distributions for means, properties of confidence intervals, properties of hypothesis testing, confidence intervals for means, and hypothesis tests for means. Students generate and analyze data and through simulation explore these concepts. The activity is completed in three parts. The three parts of the activity can be used in sequence or they can be used individually as "stand alone" activities. This allows the educator flexibility in utilizing the activity. Part I illustrates the sampling distribution of the sample mean. Part II illustrates confidence intervals for the population mean. Part III illustrates hypothesis tests for the population mean. This activity is appropriate for use in an introductory college or high school AP statistics course. Key words: sampling distribution of a sample mean, confidence interval for a mean, hypothesis test on a mean, simulation, random rectangles
• ### 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

• ### Which Paper Towel is More Absorbent? (Star Library)

This group activity focuses on conducting an experiment to determine which of two brands of paper towels are more absorbent by measuring the amount of water absorbed. A two-sample t-test can be used to analyze the data, or simple graphics and descriptive statistics can be used as an exploratory analysis. Students are asked to think about design issues, and to write a short report stating their results and conclusions, along with an evaluation of the experimental design. Key words: Two-sample t-test

• ### Age Discrimination?

In this handout, students are asked to compare the ages of terminated employees to the ages of retained employees. Students will use the comparison to decide if the data supports the conclusion of age discrimination.