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# Peer Review

## Simulating Binomial Distribution

by Beth Chance , Allan Rossman

## Ratings

### Overall Rating:

Content Quality:
Effectiveness:
Ease of Use:
 Reviewed: Feb 22, 2007 by Statistics Editorial Board Overview: This applet simulates drawing samples from a binomial distribution. Users set the population proportion of success (pi), sample size (n), and number of samples. By clicking Draw Samples, the applet will draw a sample and display the corresponding sample histogram. Each new sample drawn is added to the previous ones unless the user clicks Reset between samples. Users can choose to display the number and proportion of successes above or below a certain value (tail probabilities) by entering a value in the Num Successes box and clicking Count. The portion of the distribution that meets the condition is highlighted in red, and the proportion of success is given at the bottom of the page. Clicking the inequality sign changes its direction. Clicking Theo Values displays the theoretical distribution in green on top of the empirical. Instructions and an activity for this applet can be found in the textbook Investigating Statistical Concepts, Applications, and Methods (ISCAM) in Lesson 3.2.2 on page 205. Learning Goals: The goal of the applets is to help students develop an understanding of the binomial distribution by examining the relationship between the population proportion of success, the sample size, simulated binomial results, and theoretical binomial results. Target Student Population: This applet could be appropriate for any level of introductory statistics students or any statistics class that is going to discuss the binomial distribution. Prerequisite Knowledge or Skills: An understanding of the properties of the binomial distribution and an introduction to sampling distributions is needed to best use this applet. Type of Material: Java Applet Recommended Uses: This applet could be used as part of a class demonstration or lecture to compare simulation to theory or to examine the effect of changing population parameters. Instructors who have the associated ISCAM textbook could assign the module as homework; otherwise, teachers will need to give their own instructions for assigned activities. Technical Requirements: Java enabled web browser

### Content Quality

Rating:
 Strengths: This applet gives an excellent visual presentation of the binomial distribution, which is useful for examining simulated and theoretical results. The shape of the binomial distribution is accurately displayed, and the ability to change parameters, sample multiple times, count successes, and see tail probabilities is quite nice. The associated ISCAM textbook provides some excellent investigative, problem-solving questions that are designed to use this applet on page 205. Concerns: There are no instructions on how to use the applet within the web page itself for those who do not have the ISCAM text.

### Potential Effectiveness as a Teaching Tool

Rating:
 Strengths: The ability to make adjustments in the parameters and visuals provided should enable students to deepen their understanding of the binomial distribution. The applet allows students to see how the binomial distribution works without the need to understand the theoretical formulas. Concerns: Teachers without the ISCAM text will have to create their own materials and instructions for students to use this applet independently.

### Ease of Use for Both Students and Faculty

Rating:
 Strengths: Because this applet focuses only on the binomial distribution, students should be able to manipulate the parameters and run the applet (with some instructions provided by the instructor). The applet is fairly straight-forward, intuitive, and easy to use. Concerns: Due to the absence of any guidance on the page, students who are able to run the applet may not know what to look for in terms of understanding. Also, users may have to experiment to figure out what the buttons do (e.g. clicking on the inequality sign changes its direction, a running total of samples is kept unless Reset is clicked, etc.). Teachers without the ISCAM textbook will have to write lesson plans for this applet.

Other Issues and Comments: This applet provides a useful visual representation of sampling from the binomial distribution, which can help enhance students understanding of the binomial. Teachers without the ISCAM textbook will have to spend some time preparing materials and activities for students to get the most benefit from this applet.
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