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# Peer Review

## P-Value of a Test of Significance

by David Moore , William Notz

## Ratings

### Overall Rating:

Content Quality:
Effectiveness:
Ease of Use:
 Reviewed: Jan 04, 2010 by Statistics Editorial Board Overview: This activity illustrates the concept of p-value. The p-value is calculated for tests of hypotheses concerning the mean of a normal distribution for which the value of sigma is known. For the applet activity, the user enters the hypotheses being tested, the value of sigma, and the sample size. In addition, either the value of the sample mean or the true value of the population mean is entered. If the sample mean is provided, the p-value is computed. If the population mean is provided, a click on generate sample, will provide a sample, the sample mean and p-value. This activity is appropriate for students in an introductory level statistics course. Students in an intermediate level course who need a review of the z-test and p-values should also find it helpful. Learning Goals: To understand the concept of p-value. To understand the relationship between p-value, alpha and Type I error. To illustrate the relationship between the true value of the population mean and the p-value. To illustrate the relationship between the sample size and the p-value. Target Student Population: Introductory statistics students Prerequisite Knowledge or Skills: Students should have an understanding of the standard normal distribution and how to obtain probabilities from this distribution. They should also have seen a z-test for testing the mean of a population when sigma is known. Type of Material: JAVA applet Recommended Uses: This activity should be used to reinforce the concepts after teaching the z-test and how to find the p-value for the test. This can be used in a lecture introducing the concept of p-value in class. Instructors might also give the link to students who miss a particular class or need extra help. Technical Requirements: Web browser, JAVA

### Content Quality

Rating:
 Strengths: This activity illustrates important content. I really like the blue arrow under the normal curve. It changes direction depending on the alternate hypothesis, and the text points this out to the user. I also like the fact that the user can change the actual value of mu, to see what happens when the null hypothesis is true and what happens when it is false. Concerns: 1. Vocabulary/wording: at least that far away from "mu" in the direction of the arrow 2. Use of what or which 3. p-value is printed over the center of the graph which may suggest the incorrect area (This may be hard to fix due to programming issues). 4. I'd like there to be some comment about how the p-value is used in deciding between the hypotheses. Perhaps even a count of how often the null hypothesis is rejected for a given alpha value.

### Potential Effectiveness as a Teaching Tool

Rating:
 Strengths: The shading of under the curve, along with the blue arrow, does a good job of explaining visually how a p-value is calculated. In fact, I will be trying this with my next class, because I've had a difficult time explaining this in the past. The material can easily be integrated into statistics curriculum. It also promotes active engagement. Concerns: The introduction refers to Section 6.2 of IPS. Since I'm looking at this page as a stand-alone, I do not know what this is referring to.

### Ease of Use for Both Students and Faculty

Rating:
 Strengths: This is easy to use and has clear instructions. It is limited to those with an internet connection but I don't think that is a real concern. There are not too many buttons and choices. The one thing that was confusing to me at first glance (Show P vs. generate a sample) was explained in the text. Concerns: When I changed the value of sigma from 1 to 2 while leaving the value of n unchanged, I got a reasonable curve. But if I entered 2 for sigma while changing n to 50, the curve was too skinny.
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