490 CHAPTER 9 Inferences from Two Samples Key Concept The preceding sections of this chapter included methods for testing claims about two proportions, two independent means, means of differences from matched pairs, and two standard deviations (or variances). Those methods have certain requirements that limit the situations in which they can be used. When some of the requirements are not satisfied, we can often use resampling methods of bootstrapping or randomization. Even when requirements are satisfied, resampling methods can be used in addition to other methods to provide an additional perspective and insight into the data. These methods typically require the use of software such as Statdisk (www.statdisk.com). For this section, here are key differences between bootstrap resampling and randomization: ■ Bootstrap: Construct a confidence interval by resampling with replacement. ■ Randomization: Test a claim by resampling without replacement. Bootstrapping with Two Samples The basic concept of bootstrap resampling with one sample was introduced in Section 7-4. The procedure for Bootstrapping with two samples is similar but requires some additional steps based on the claims being tested. These steps are summarized in this section and are also illustrated with examples. Randomization with Two Samples Randomization for one sample was introduced in Section 8-5, and we now introduce the randomization method for two samples. 9-5 Resampling: Using Technology for Inferences DEFINITION Randomization of sample data from two samples occurs when we randomly reassign the data to the two samples without replacement. The following example is designed to illustrate this central concept of randomization with two samples: If there is no difference between two groups, any individual sample value is just as likely to be in one group as in the other group. How Many Times to Resample? It would be wise to repeat a resampling at least 1000 times. Professional statisticians commonly resample 10,000 or more times. It is obviously impractical to resample that many times using any manual procedure, so the use of software such as Statdisk is very strongly recommended. Randomization with Two Samples EXAMPLE 1 Illustrated below is a randomization of income data (thousands of dollars) from two samples of college students arranged according to gender. See that the data have been randomly reallocated between the two samples, and the random selections were made without replacement. Also note that the original sample sizes of 3 and 4 are the same in the randomization.
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