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where 2 is the assumed common variance, this technical dif culty is avoided. Cohen (1977) de ned a large effect as something that is visible to the naked eye and concluded that for two normal distributions having a common variance, small, medium, and large effect sizes correspond to = .2, = .5, and = .8, respectively. Given that the probability of a Type I error is , Cohen provides tables for determining the required sample sizes (also see Kraemer & Thiemann, 1987). For example, with n 1 = n 2 = 20, = .8, and = .05, power is .68. Rather than specify a value for , one can plot a so-called power curve where power is plotted versus , given the sample sizes and . An advantage of this approach is that it provides a more global sense of how power is related to based on the sample sizes used. (For software, see Bornstein, 2000; Elashoff, 2000; O Brien, 1998.) An extension of this standard power analysis to more than two groups, still assuming normality and homoscedasticity, has been derived. That is, given , the sample sizes corresponding to J groups, and a difference among the means deemed to be important, power can be computed. Assuming equal sample sizes, now the difference among the means is typically measured with 1 (
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For Identifier, enter an ID for the movie clip. If you don t want the movie clip or sound to load before the first frame, deselect the Export in First Frame option. Click OK.
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symbol of X (i.e., Px (a) = N (a|x)/n for all a X, where N (a|x) is the number of times the symbol a occurs in the sequence x X n ). The type of a sequence x is denoted as Px . It is a probability mass function on X. (Note that in this chapter, we will use capital letters to denote types and distributions. We also loosely use the word distribution to mean a probability mass function.) De nition The probability simplex in Rm is the set of points x = (x1 , x2 , . . . , xm ) Rm such that xi 0, m xi = 1. i=1 The probability simplex is an (m 1)-dimensional manifold in m-dimensional space. When m = 3, the probability simplex is the set of points {(x1 , x2 , x3 ) : x1 0, x2 0, x3 0, x1 + x2 + x3 = 1} (Figure 11.1). Since this is a triangular two-dimensional at in R3 , we use a triangle to represent the probability simplex in later sections of this chapter. De nition Let Pn denote the set of types with denominator n. For example, if X = {0, 1}, the set of possible types with denominator n is
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(IGP) and Exterior Gateway Protocols (EGP). An IGP is a routing protocol that propagates information inside one autonomous system. An EGP is a routing protocol that propagates information between autonomous systems. In order for data to be moved across an internet, information on the location of the networks must be propagated throughout the network. This is the introduction to the difference between a routing protocol and a routable protocol. IP is a routable protocol. Propagating information throughout the network as to the location of the networks is known as a routing protocol. Don t confuse the two. I know that I keep using the term autonomous system (AS). Yes, it is defined as a network that is under a single administrative control, but let s define that a little and yes, it does get a little blurry. Before the plethora of ISPs, anyone connected to the Internet was assigned an address and used a special protocol (then known as EGP) to connect to the Internet. Therefore, that connection became known as an autonomous system, and routes for that network were known on the Internet using EGP (yes, the acronym for the protocol is the same one used for the definition of the protocol). Autonomous
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