h6 - Matched Pair Design

h6 - Matched Pair Design - From here on out, we don't worry...

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Matched Pair Design by Example Goal: To compare IQ's of 1st borns (FB) and 2nd borns (SB). Population of N pairs of siblings: 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 Pop'n of FB's Pop'n of SB's Pop'n of diff's pop'n mean pop'n var Page 1 of 4 No Title 3/26/2011 http://www.stat.sfu.ca/~sgchiu/Grace/S330/handouts/paired/
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D i = X i - Y i so that D i > 0 is some indication that the first born of the i th selected pair is more intelligent. Note that due to common characteristics shared by siblings within each i th pair, X i and Y i are dependent variables, even though one pair is independent of another pair because of random selection. In this case, X i and Y i are likely to be positively correlated (increase or decrease together). Then Note that estimates : Page 2 of 4 No Title 3/26/2011 http://www.stat.sfu.ca/~sgchiu/Grace/S330/handouts/paired/
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Unformatted text preview: From here on out, we don't worry about the original X i 's and Y i 's! All we need are the D i 's. (Of course, for the sake of computing , simply take . However, the D i 's are still needed for EDA and for computing s D 2 if is unknown.) So, a 100(1-)% C.I. for is depending on whether z is known? z is normal? (CLT?) z D i 's are normal? Q: How to check normality in practice??? FACT: Page 3 of 4 No Title 3/26/2011 http://www.stat.sfu.ca/~sgchiu/Grace/S330/handouts/paired/ Making conclusions: If the 100(1-)% C.I. for does not contain 0, then we are quite confident that the siblings' IQ's are different (i.e. 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 Page 4 of 4 No Title 3/26/2011 http://www.stat.sfu.ca/~sgchiu/Grace/S330/handouts/paired/...
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This note was uploaded on 01/23/2012 for the course STAT 201 taught by Professor Staff during the Fall '03 term at Simon Fraser.

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h6 - Matched Pair Design - From here on out, we don't worry...

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