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Unformatted text preview: CHAPTER 14 STATISTICAL INFERENCE: OTHER TWO-SAMPLE TEST STATISTICS 14.1 Introduction Learning about the F statistic and F sampling distribution that are used to test hypotheses about 2 variances and how to use a z statistic to test hypotheses about 2 population proportions 14.2 Two-Sample F Test and Confidence Interval for Variances Using Independent Samples F Test for 2 Variances (Independent Samples) Researcher might want to see if 2 populations differ in dispersion or they might want to test one of the assumptions of the t test for independent samples that the 2 unknown population variances are equal F statistic for testing the hypotheses is where and denote, respectively, the larger and smaller sample variance and each sample variance is computed using . The degrees of freedom for the numerator and denominator are, respectively, and . Sampling distribution of the F derived by Ronald A. Fisher and G.W. Snedecor named it after him. Like the t distr., is a family of distributions whose shape depends on its d.f. Unlike the z and t distributions that are symmetrical, the F distribution is positively skewed Shape of the F distribution approaches the normal for large values of and . F is a ratio of non-negative numbers so it can take on values from 0 to . Values around 1 are expected if the null hypothesis that is true Assumptions for the F to test a null hypothesis: 1. Independent samples 2. Populations are normally distributed 3. Participants are random samples from the populations of interest or the participants have been randomly assigned to the conditions in the experiment. F is not robust to violation of the normality assumption like the t is regardless of how large your sample is. So, unless the normality assumption is fulfilled, the probability of making a Type 1 error will not equal the preselected value of . Do NOT use the F unless you have good reason to believe the 2 variables and are normal. is the critical value of F that cuts off the upper region of the sampling distribution for degrees of freedom. The first denotes the df for the numerator of the F and the second denotes the df for the denominator of the F....
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This note was uploaded on 04/30/2008 for the course STATS 2402-04 taught by Professor Kirk during the Spring '08 term at Baylor.

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