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h6 - Matched Pair Design

Course: STAT 201, Fall 2003
School: Simon Fraser
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Word Count: 350

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Title Page No 1 of 4 Matched Pair Design by Example Goal: To compare IQ's of 1st borns (FB) and 2nd borns (SB). Population of N pairs of siblings: Pop'n of FB's Pop'n of SB's Pop'n of diff's pop'n mean pop'n var In particular, we ask Q: Are first borns more intelligent than their second born siblings? Answering the question via computing a 100(1- )% C.I. for : A sample of n pairs of siblings are selected...

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Title Page No 1 of 4 Matched Pair Design by Example Goal: To compare IQ's of 1st borns (FB) and 2nd borns (SB). Population of N pairs of siblings: Pop'n of FB's Pop'n of SB's Pop'n of diff's pop'n mean pop'n var In particular, we ask Q: Are first borns more intelligent than their second born siblings? Answering the question via computing a 100(1- )% C.I. for : A sample of n pairs of siblings are selected from the population of N pairs: where Now, define http://www.stat.sfu.ca/~sgchiu/Grace/S330/handouts/paired/ 3/26/2011 No Title Page 2 of 4 Di = Xi - Yi so that Di> 0 is some indication that the first born of the ith selected pair is more intelligent. Note that due to common characteristics shared by siblings within each ith pair, Xi and Yi are dependent variables, even though one pair is independent of another pair because of random selection. In this case, Xi and Yi are likely to be positively correlated (increase or decrease together). Then Note that estimates : http://www.stat.sfu.ca/~sgchiu/Grace/S330/handouts/paired/ 3/26/2011 No 3 Title Page of 4 From here on out, we don't worry about the original Xi's and Yi's! All we need are the Di's. (Of course, for the sake of computing sD2 if , simply take . However, the Di's are still needed for EDA and for computing is unknown.) So, a 100(1- )% C.I. for is depending on whether is known? is normal? (CLT?) Di's are normal? Q: How to check normality in practice??? FACT: http://www.stat.sfu.ca/~sgchiu/Grace/S330/handouts/paired/ 3/26/2011 No Title Page 4 of 4 Making conclusions: If the 100(1different (i.e. )% C.I. for does not contain 0, then we are quite confident that the siblings' IQ's are 0). Depending on wether 0 is to the left or right of the C.I., we get a sense of which sibling is more intelligent. A formal one-sided hypothesis test can be conducted to determine if the first borns have higher IQ's than their second born siblings. Grace Chiu 2000-08-17 http://www.stat.sfu.ca/~sgchiu/Grace/S330/handouts/paired/ 3/26/2011
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