Transcript Chapter 21
Chapter 21 Type I & Type II Errors And Power • We have talked some about α (alpha) levels. An alpha level is like a “line in the sand”. It identifies for us up front, how extreme we think the sample statistics must be, in order to be considered “significant”. The most common levels of alpha are .10, .05, and .01. We choose an alpha based on the consequences of an incorrect conclusion. Those incorrect conclusions are… Type I and Type II Errors “The Truth” Ho is true Ho is false “My Decision” Fail to reject Ho Reject Ho • The power of a test is defined as the probability to correctly reject a false null hypothesis. • The distance between the null hypothesis value po and the true p is called the effect size. • Ideally we would like to reduce the probability we make type I and type II errors while at the same time having a powerful test. Unfortunately it’s not that simple. As we alter one, we often have an effect on the other. Here are some things you should know about Type I, Type II, and Power… We can increase power by: – *Increasing the sample size (which decreases the variability) – *Increasing the effect size – *Increasing alpha (α) Anything that increases the power (1 - β ) will automatically decrease the Type II error (β). • It’s a balancing act between all of these!! There are no guarantees for a correct decision. • On the AP Test you do not have to calculate power. You must understand power conceptually and understand how changing other values effects power. Example 1 • The marketing department for a computer company must determine the selling price for a new model of personal computer. In order to make a reasonable profit, the company would like the computer to sell for $3200. If more than 30% of the potential customers would be willing to pay this price, the company will adopt it. A survey of potential customers is to be carried out; it will include a question asking the maximum amount that the respondent would be willing to pay for a computer with the features of the new model. Let p denote the proportion of all potential customers who would be willing to pay $3200 or more. Then the hypotheses to be tested are • Ho: p = .3 • Ha: p > .3. • In the context of this example, describe type I and type II errors. Discuss the possible consequences of each type of error. Example 2 • Occasionally, warning flares of the type contained in most automobile emergency kits fail to ignite. A consumer advocacy group is to investigate a claim against a manufacturer of flares brought by a person who claims that the proportion of defectives is much higher than the value of .1 claimed by the manufacturer. A large number of flares will be tested and the results used to decide between • Ho: p = .1 • Ha: p > .1, • where p represents the true proportion of defectives for flares made by this manufacturer. If Ho is rejected, charges of false advertising will be filed against the manufacturer. • In this context, describe type I and type II errors and discuss the consequences of each. Example 3 • Medical researchers now believe there may be a link between baldness and heart attacks in men. • A) State the null and alternative hypotheses for a study used to investigate whether or not there is such a relationship. Since there are no numbers given, you will have to state verbal hypotheses. • B) In the context of this situation, what would a Type I error be and what would be a consequence of that decision? • C) In the context of this situation, what would a Type II error be and what would be a consequence of that decision?