This item compares the concepts of hypothesis testing (including Type I and Type II errors) to the American judicial system. There is also an applet which allows students to examine the Type I and Type II errors based on the evidence against the null hypothesis (the z-score) and the actual truth--sliders let students explore how Type I and Type II errors work together.
Type of Material:
Text introduction with graphics and Java applet.
This material could be used as a lecture example using the applet as part of a demonstration. It could also be used in a laboratory or out of class for students to explore the relationships between type I and type II errors and power.
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Identify Major Learning Goals:
Major learning goals are: 1) give students a good way to attach the jargon of hypothesis testing to the more familar jargon of a trial; and 2) allow students to explore relationships between Type I and Type II errors together through the use of an applet.
Target Student Population:
The target student population is most likely students in introductory statistics courses. However, this could also be used as a refresher for students in any discipline who need to be reminded about the logic of hypothesis testing.
Prerequisite Knowledge or Skills:
Students need to know about the normal distribution and that z-scores represent the number of standard deviations away from the mean. Students should also have been introduced to hypothesis testing so that they have a brief background of the material.
Evaluation and Observation
The text illustration of this item is nicely written and fun to read. It uses an easily understood analogy of a criminal trial. Additionally, the applet is very helpful for understanding the relationship between Type I and Type II errors. This is done by allowing the user to move the location of the true distribution relative to the distribution under the null hypothesis.
1. The text description here sometimes discusses an error and the probability of an error interchangably. These are distinct concepts, and the instructor needs to help students understand this. 2. The authors incorrectly state that alpha is "equal to the p-value." Most statisticians would agree that alpha is the significance level. 3. The authors don't make it explicit that alpha and beta are inversely related only if the amount of information is assumed constant. In fact, if more information is gathered, then it is possible to reduce both probabilities because the relevant sampling distributions become less variable. 4. The false notion that researchers always want to evaluate the alternative hypothesis is perpetuated. 5. In this applet only greater than alternatives are allowed. The instructor should be sure to explain to students that other alternatives are available.
Potential Effectiveness as a Teaching Tool
The applet is useful for visually and dynamically illustrating the connection between alpha and beta when the amount of information is held constant. The applet could be helpful if a series of guided questions were written to accompany this material, or if the instructor used it in class where he/she could ask the questions and explain.
The text explanation is quite similar to a textbook explanation. The included applet will need specific questions for the student to help them explore the relationship. The instructor may also want to supplement this applet with connections to real world examples other than the trial analogy.
Ease of Use for Both Students and Faculty
Very easy to use. The applet layout is uncluttered and intuitive (no pun with the URL intended).
Other Issues and Comments:
The trial analogy is good for definining and differentiating between Type I and Type II errors; however, the analogy becomes awkward and labored as it continues to be used to define and illustrate the probabilities of these errors. It is probably better to switch to an actual statistical hypothesis test (a familiar one from a homework assignment) to explain and illustrate alpha and beta.