S tatistik fo r M P H : 5 F ra d en 4 . u g es statistik u n d erv isn in g : F ...
S tatistik fo r M P H : 5 F ra d en 4 . u g es statistik u n d erv isn in g : F ...
S tatistik fo r M P H : 5 F ra d en 4 . u g es statistik u n d erv isn in g : F ...
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The Mantel-Ha<strong>en</strong>szel <strong>es</strong>timator.In each table, we may <strong>es</strong>timate the <strong>ra</strong>te <strong>ra</strong>tio bya 1 /y 1a 2 /y 2= a 1y 2a 2 y 1= a 1y 2 /ya 2 y 1 /yA common <strong>ra</strong>te <strong>ra</strong>tio <strong>fo</strong>r all st<strong>ra</strong>ta may be <strong>es</strong>timated by theMantel-Ha<strong>en</strong>szel <strong>es</strong>timator (Weighted ave<strong>ra</strong>ge of sepa<strong>ra</strong>teRR-<strong>es</strong>timat<strong>es</strong>):P a1 y 2yP a2 y 1y= RR MH .In example: RR MH =39·67344009355500+ 266·23260002707520+ 315·1164400127639079·26211009355500+ 1037·3815202707520+ 2352·1119901276390= 1.45.23The Mantel-Ha<strong>en</strong>szel t<strong>es</strong>t.In each st<strong>ra</strong>tum, we can calculate:OBS<strong>erv</strong>ed = a 1EXPected = a · y1y= (a 1 + a 2 )y 1 +y 2= E(a 1 )√ √Standard Deviation = a y 1 y 2yy y= (a 1 + a 2 ) 1 y 2(y 1 +y 2 )= SD(a 2 1 )The comb<strong>in</strong>ed Mantel-Ha<strong>en</strong>szel t<strong>es</strong>t statistic is:( ∑ a 1 − ∑ E(a 1 )) 2∑ (SD(a1 )) 2 = X 2 MH ∼ χ 2 1 under H 0y 1X 2 MH =((39 + 266 + 315) −(11826211009355500+ 13033815202707520))111990 2+ 26671276390118 2621100·6734400(9355500)+ 1303 381520·23260002 (2707520)+ 2667 111990·11644002 (1276390) 2= (169.33) 2 /395.00 = 72.59 ∼ χ 2 1, P < 0.001.24
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