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# Class Note for STAT 529 at OSU 02

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This 1 page Class Notes was uploaded by an elite notetaker on Friday February 6, 2015. The Class Notes belongs to a course at Ohio State University taught by a professor in Fall. Since its upload, it has received 22 views.

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Date Created: 02/06/15
STAT 529 The standard error of the proportion estimate The computer simulations in Chapter 3 examine the robustness of the pooled t procedures against deviations from normality and equal variance assumptions The tabled values in Display 34 and Display 35 are the percentages of 95 con dence intervals for M1 7 2 in 1000 replications that successfully contained a prespeci ed true value of M1 7 2 using the pooled t Each con dence interval was based on two independent samples from each of the distributions that the authors speci ed If the pooled t procedures were valid7 the proportion of 95 con dence intervals containing the true value of M1 7 2 would be exactly 95 If the actual coverage probability of 95 con dence intervals for each scenario can be mathematically obtained7 any deviation from the nominal level 95 indicates that the procedure is not valid As the exact coverage probabilities are dif cult to get in general7 the authors estimated them by the sample proportions of the con dence intervals successfully containing 1 7 2 out of 1000 replicates Given a xed scenario7 let p be the coverage probability of pooled t 95 con dence intervals Then the number of successful intervals X in 1000 replicates follows the binomial distribution Bnp with n 17 000 and the probability of success7 p By the central limit theorem7 the sample proportion 16 Xn has approximately normal distribution with mean M13 p and standard deviation 03 p1 7 So7 the standard error ofp is 161 7 13 n7 and an approximate 95 con dence interval for p is given by Alii pifd 77 n For example7 the estimate 955 in Display 34 for strongly skewed distribution and n1 n2 5Qws05ifd0 170 LW005i 9 m0 020ampasa 95 con dence interval for p Note that when p 0957 the standard deviation off is 4 0951 7 09517 000 x 00069 Thus7 roughly 095 i 19600069 095 i 0014 09367 0964 is the range ofp values for which H0 1 095 would not be rejected at the signi cance level of 5 In light of this calculation7 we conclude that the pooled t procedure would not be valid for the long tailed distribution across all the sample sizes in Display 34 For departures from the equal variance assumption in Display 357 the success rates for the cases with 0201 74 1 and n1 74 n2 suggest that the coverage probabilities are signi cantly different from the nominal level of 95

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