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Ch12_Outline

# Ch12_Outline - Chapter 12 Outline Introduction In Chapter...

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Chapter 12 Outline Introduction In Chapter 11 we developed methods to determine whether there is a difference between two population means. What if we wanted to compare more than two population means? The two- sample tests used in Chapter 11 require that the population means be compared two at a time. This would be very time consuming, but more importantly there would be a build-up of Type I error. That is, the total value of α would become quite large as the number of comparisons increased. In this chapter, we will describe a technique that is efficient when simultaneously comparing several sample means to determine if they come from the same or equal populations. This technique is known as Analysis of Variance (ANOVA). Analysis of Variance (ANOVA ). A statistical technique for testing whether several populations have the same mean. A second test compares two sample variances to determine if the populations are equal. This test is particularly useful for validating a requirement of the two-sample t test presented in Chapter 11. This test assumed that the population standard deviations were equal but unknown (see text formulas [11-5] and [11-6]). The F Distribution The F distribution can be used to test whether two samples are from populations having equal variances. It can also be used to compare several population means simultaneously ( ANOVA ). F Distribution . A continuous probability distribution where F is always 0 or positive. The distribution is positively skewed. It is based on two parameters, the number of degrees of freedom in the numerator and the number of degrees of freedom in the denominator. The major characteristics of the F distribution are: 1. There is a family of F distributions . A particular member of the family is determined by two parameters: the degrees of freedom in the numerator and the degrees of freedom in the denominator. 2. The F distribution is continuous. This means that it can assume an infinite number of values between 0 and plus infinity. 3. The F distribution cannot be negative. The smallest value F can assume is 0. 4. It is positively skewed. The long tail of the distribution is to the right-hand side. As the number of degrees of freedom increases in both the numerator and denominator, the distribution approaches a normal distribution. 5. It is asymptotic . As the values of X increase, the F curve approaches the X -axis but never touches it. This is similar to the behavior of the normal distribution described in Chapter 7. Comparing Two Populations Variances The F distribution is used to test the hypothesis that the variance of one normal population equals the variance of another normal population. The F distribution can also be used to validate

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assumptions with respect to certain statistical tests. Regardless of whether we want to determine if one population has more variation than another population does or validate an assumption with respect to a statistical test, we still use the usual five-step hypothesis testing procedure. The value of the test statistic is determined using text formula [12-1].
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Ch12_Outline - Chapter 12 Outline Introduction In Chapter...

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