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Unformatted text preview: Some housekeeping Formulae will be provided in the midterm test Simple calculations Short answers No admission after 4:35 pm Standard error of a proportion ( 29 = = n i i n x x x Variance 1 2 1 ) ( For continuous data: And SE = SD / n If we score a success as 1, and a failure as 0, then applying the formula above (with n, rather than n1, in the denominator of the variance formula) gives SE ( ) = SD = Standard Deviation = V a r ia n c e n )  (1 Approximation of binomial distribution to the normal distribution It was noted that the approximation could be applied when np > 5 or nq > 5 This is because the approximation is not very good otherwise Similar to the idea that the distribution of sample means is a good approximation to the normal distribution when the size of a sample is 30 or more Effect size We have looked at the general principles for computing sample sizes For comparing two groups with the ttest, the formula is: But often we dont know in advance One way round this is to look at effect size, which is essentially / This can be used directly in the formula Click to edit Master subtitle style Problem set 7: Comparing more than two groups Harry Shannon What this problem will cover How do we avoid multiple testing when comparing several groups Oneway ANOVA ANOVA tables Ftests Degrees of freedom Do SunScreens Save your Skin? In the previous problem set, we analysed the data as both an unmatched and matched design using t tests. However, there is more to sunscreens than addressed by the simple question of "Does it work?" All screens prominently display a SPF code (Sun Protection Factor) which is defined as the ratio of time to burn with sunscreen on to time to burn with no sunscreen Is there any difference among sunscreens? Can we establish whether there really is a doseresponse relationship? We might proceed by taking three samples of Bronzetone off the shelf, with SPF ratings of 2, 8, and 15 for the sake of argument (staying within one brand name for consistency). For six subjects in each group, the degree of burning scores might look like this: SPF2 SPF8 SPF15 Subject Score Subject Score Subject Score 1 10 7 7 13 4 2 11 8 5 14 5 3 12 9 12 15 6 4 4 10 2 16 3 5 5 11 5 17 2 6 6 12 5 18 4 Mean 8.0 Mean 6.0 Mean 4.0 Once again, we ask the statistical question: Are these SPFspecific results statistically different from each other? How do we compare the means of more than two groups? In our example we have 3 groups. We could simply do 3 ttests between each pair of means: 1 vs 2; 1 vs 3; 2 vs 3 Or more generally compare the means of all pairs of groups Number of comparisons = n(n1)/2 No. Groups No. Comparisons 3 3 4 6 6 15 9 36 This messes with the pvalue: Whats the probability of getting at least one pair significantly different under all the possible hypotheses like H0 : r = s Prob (at least 1 diff) = 1  Prob(no diff) = 1  (1  & )k No groups Prob (1 or more sig) 3 .15 4 .27 Pascals triangle...
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This note was uploaded on 06/23/2011 for the course HTH SCI 2A03 taught by Professor Shannon during the Winter '11 term at McMaster University.
 Winter '11
 SHannon

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