Upload
lekiet
View
219
Download
2
Embed Size (px)
Citation preview
!"#$%&'()*&+$,-&.'
/0,#"('12#%&3'
!/4/!'556'
7,-&.'
78.&9&:;'<2%%'='<2%%')('>"%(&?'
'
• @<2%%')('>"%(&A')('<,;'(2B:)&<;%3'$.&:)(&'– <&&C'&<,2D0')<>,.#"E,<';,':,#$2;&';0&'C)(;.)F2E,<',>';0&'$GH"%2&I'
– ;.&";#&<;'&J&:;'
– <2)("<:&'$"."#&;&.('8H".)"<:&K':,..&%"E,<K'&;:?'
LJ&:;'()*&'
• 7,-&.'(0,2%C'F&'0)D0'>,.';0&'(#"%%&(;'&J&:;'()*&';0";')(')#$,.;"<;';,'C&;&:;'– <,;';0&'M;.2&'&J&:;AK'-0):0')('<,;'N<,-<'
• O(2"%%3'2(&>2%';,':,#$2;&'$,-&.'>,.'"'."<D&',>'&J&:;'()*&('– PQR'$,-&.'>,.'"'6G>,%C'.&C2:E,<'#"3'(,2<C'"::&$;"F%&'
– 6QR'$,-&.'>,.'"'SG>,%C'.&C2:E,<'<,;'(,'#2:0'
• LH&.3,<&';.)&(';,'#"N&';.)"%(';,,'(#"%%I'T,<A;I'
U,#$2;"E,<'
• VW'$,-&.I;I;&(;8?K'$,-&.I$.,$I;&(;8?'• V'$-.'$":N"D&'• 1,;(',>'>.&&':"%:2%";,.(',<';0&'-&F'
• !)#2%"E,<K'>,.'#,.&':,#$%):";&C'(&X<D(I'
'
'
Y,.#2%"('P(significant) =1!!P(test statistic > Z1!" /2 ) =1!!
P differencescale / n
> Z1!" /2
"
#$
%
&'=1!!
differencescale / n
! Z1!" /2
"
#$
%
&'= Z1!!
difference = scalen
Z1!! + Z1!" /2( )
n =Z1!! + Z1!" /2( )
2
difference / scale( )2 =Z1!! /2 ! Z"( )
2
difference / scale( )2
-2 0 2 4 6 8
0.0
0.1
0.2
0.3
0.4
Z =µ1 ! µ2
! n
Density
P(Z > 1.96, H1) = 0.85P(Z > 1.96, H0) = 0.05
H0 : µ1 = µ2 H1 : µ1 = µ2 + !
Y,.#2%"'
T)J&.&<:&')<'#&"<(W'
'
'
'
Z"():"%%3'("#&'>,.#2%"'>,.',;0&.',2;:,#&('– :0"<D&'C&[<)E,<',>'\K']'(,';0";'S]S+<')(';0&'H".)"<:&',>';0&'&(E#";&',>'\'
2! sample size =2(Z1"! /2 " Z" )2
# 2 / 2$ 2
L^"#$%&W'
_"*".C'."E,'`')<'(2.H)H"%'
'
'
'a".)"<:&',>'%,D'0"*".C'."E,')('.,2D0%3'S+<I&H&<;('
total number of events =2! (Z! " Z" /2 )2
(log#)2 / 2
b2)("<:&'$"."#&;&.('
• U,#$".)<D'#&"<'– ',<%3'<&&C'(;"<C".C'C&H)"E,<(K'.&D".C%&((',>'C)(;.)F2E,<',.'>,.#',>':0"<D&'
• !2.H)H"%'"<"%3()(W'– '<&&C'.";&')<':,<;.,%(';,':,<H&.;'<2#F&.',>'&H&<;(')<;,'("#$%&'()*&'
– >,.#2%"'"((2#&(':,<(;"<;'0"*".C'."E,'
• U,#$".)<D'#&C)"<('– <&&C';,'N<,-'C)(;.)F2E,<'2<C&.'F,;0';.&";#&<;(I''
V&".."<D&#&<;('
T&;&:;"F%&'C)J&.&<:&')<'#&"<(W'
'
' 2! sample size =2(Z1"! /2 " Z! )2
" 2 / 2# 2
" =2# n
Z1"! /2 " Z!
=" ntotalZ1"! /2 " Z!
Power =#"1(1"!) =# "#
n2" Z1"! /2
$
%&
'
()
L^"#$%&'
• V&C2:E,<',>'cQ##_D')<'F%,,C'$.&((2.&'– deR'$,-&.'– (C'f'SQ##_D'
– 8gcGh+SGgi?S''f'c6'– <'f'S^c6+8cQ+SQ?S'f'cQj')<'&":0'".#'
Y,.'"'e##_D'.&C2:E,<K''
''''''''''''''''''''''$,-&.')(',<%3'
'
'
!520
1042
"1.96#
$%
&
'(= 0.44
L^"#$%&'
• !2$$,(&'Z7'.&C2:E,<'.&C2:&('0&".;'"k":N('F3'SQR'"<C'-&'-"<;';0&'("#&'$,-&.'
• 4;'0&".;G"k":N'.)(N',>'SR'$&.'$&.(,<'$&.'3&".';0)(')('cele+QIQS'$&.(,<G3&".('– 5PSeQ'$&.(,<G3&".('– 4F,2;'clQQQ'$&,$%&'>,.'[H&'3&".(I'– PeR'$,-&.'.&C2:&(';,'ccQQQ'$&,$%&'>,.'[H&'3&".('
number of heart attacks = 2! (13)(log1.2)2 / 2
=1565
T.,$,2;+:.,((,H&.'
• !,#&'$&,$%&'-,<A;'D&;';0&'"(()D<&C';.&";#&<;'– ,<&G-"3'C.,$,2;';,'<,';.&";#&<;'
– ;-,G-"3':.,((,H&.'– ;0.&&G-"3':.,((,H&.'m'C.,$,2;'
• Y,.'$,-&.':"%:2%"E,<(K'"((2#&'&J&:;')('F"(&C',<';.&";#&<;'.&:&)H&C'– >").%3':,<(&.H"EH&'
L^"#$%&'
• n"<;';,'C&;&:;'C)J&.&<:&')<'#&"<',>'cQ##_D'• !2$$,(&'– cQR'."<C,#)*&C';,'":EH&';.&";#&<;'D&;'<,';.&";#&<;'– eR'."<C,#)*&C';,'<,';.&";#&<;'D&;'":EH&';.&";#&<;'
'
• o<:.&"(&')<'("#$%&'()*&')('8cQ+PIe?SfcI6P'>,%C'• o>'<,<G:,#$%)"<:&')('(#"%%K''8c+8cG^??SpcmS^'
– >,.'&":0'<,<G:,#$%)&.K'<&&C';,'"CC'";'%&"(;';-,'#,.&'$&,$%&'– C,&(<A;'C,'"<3;0)<D';,'[^';0&'F)"(K',<%3';0&'$.&:)(),<I'
E[difference]= 0.9!10+ 0.1!0( )" 0.95!0+ 0.05!10( ) = 8.5
V2<G)<'
• q"3'F&'"F%&';,'.&C2:&'<,<G:,#$%)"<:&'-);0'.2<G)<'– (;".;'&H&.3,<&',J',<';0&'("#&';.&";#&<;'
– "r&.'"'>&-'-&&N(K'."<C,#)*&',<%3';0&'$&,$%&'-0,'0"H&'F&&<':,#$%3)<D'
• s<%3'>,.'%,<DG;&.#'(;2C)&('
• b&&C('"((&((#&<;',>':,#$%)"<:&I'
a".)"E,<('
n0";')>';.&";#&<;')<:.&"(&('H".)"F)%);3'"('-&%%'"('.&C2:)<D'#&"<t'
'b&&C';,'.&$%":&'S]S+<'F3';0&'H".)"<:&',>';0&'&(E#";&',>'\'
/-,'(;"<C".C'C&H)"E,<(W'(cK'(S''H".)"<:&',>'C)J&.&<:&')<'#&"<')(''
'
2! sample size =2(Z1"! /2 " Z" )2
# 2 / 2$ 2
(s12 + s2
2 ) / n
2! sample size =2(Z1"! /2 " Z" )2
# 2 / (s12 + s2
2 )
a".)"E,<('
n0";')>'C)J&.&<;'<2#F&.('".&')<';0&';-,';.&";#&<;(t'
'b&&C';,'.&$%":&'S]S+<'F3';0&'H".)"<:&',>';0&'&(E#";&',>'\'
/-,'(;"<C".C'C&H)"E,<(''H".)"<:&',>'C)J&.&<:&')<'#&"<')('
',.'-.);&'<cf$<K'<Sf8cG$?<''
'
2! sample size =2(Z1"! /2 " Z" )2
# 2 / 2$ 2
! 2 1 / n1 +1/ n2( )
1n1!1 + n2
!1 =2(Z1!! /2 ! Z" )
2
# 2 /$ 2
n1n2n1 + n2
=2(Z1!! /2 ! Z" )
2
# 2 /$ 2
p(1! p)n =2(Z1!! /2 ! Z" )
2
# 2 /$ 2
n =2(Z1!! /2 ! Z" )
2
p(1! p)# 2 /$ 2
7,-&.')('%,-&.')>'."<C,#)("E,<')('<,;'&H&<'
!)#2%"E,<'
• Y,.'#,.&':,#$%&^'(:&<".),(K'2(&';0&'C&[<)E,<',>'$,-&.';,':,#$2;&'F3'()#2%"E,<'
• 7,-&.')(';0&'$.,$,.E,<',>'.&$&";&C'.2<(',>';0&'(;2C3';0";'-)%%'0"H&'$GH"%2&uQIQe'
• n.);&':,C&';0";'C,&('.&$&";&C'.2<(',>';0&'(;2C3'"<C':,2<;';0&'$GH"%2&('uQIQe'
• 4C92(;';0&'$"."#&;&.(';,'(&&'0,-'$,-&.'H".)&('
L^"#$%&W'2<&v2"%'H".)"<:&'
!"#$%&'()*+,'"-&.!"/012032%12%32"45666666)&7&*+7"!70/"260126%14666666)-&78*+7"!70/"260326%34666666&$&#%&/)&7&2)-&7849:$;<8'#6=668!&%$!,$%&'(.#%6*+67#:8.-<&#/1>>>>2666 6 6 6 6 6!"#$%&'()/1>>211>23>2?>21>>446
0#<"/8!&%$!,$%&'(.#%6*6>$>@466A1B6>$CDEC66
4C"$EH&'."<C,#)*"E,<'
oC&"'
!"#$%&'()*()+,)&*-,)*.)/,)-"#$%)0*1,)(2,)+,3,4)(4,5(6,&()(")6"4,)7,"7$,8)45(2,4)(25&)9:;9:<)
• O(&':2..&<;')<>,.#"E,<'>.,#';0&';.)"%';,'C&:)C&'-0):0';.&";#&<;';,'D)H&';0&'<&^;'$&.(,<'
7%"3G;0&G-)<<&.'
4((2#&';0";';.&";#&<;'(2::&((':"<'F&',F(&.H&C')##&C)";&%3I'• o>';.&";#&<;')('(2::&((>2%K'2(&';0&'("#&';.&";#&<;',<';0&'<&^;'$"E&<;'
• o>';.&";#&<;')('2<(2::&((>2%K'2(&';0&',;0&.';.&";#&<;',<';0&'<&^;'$"E&<;I'
'o##&C)";&'$.,F%&#W'C&;&.#)<)(E:'"<C'$.&C):;"F%&K'(,'C,:;,.'N<,-('-0):0';.&";#&<;'-)%%'F&'D)H&<';,';0&'<&^;'$"E&<;I''
V"<C,#)*&C'7;n'
• V"<C,#%3'C."-';.&";#&<;('>.,#'"'0";'– )>';0&';.&";#&<;')('(2::&((>2%K'$2;'#,.&'E:N&;('>,.';0&'("#&';.&";#&<;')<';0&'0";'
– o>');')('2<(2::&((>2%K'$2;'#,.&'E:N&;('>,.';0&',;0&.';.&";#&<;')<';0&'0";I'
• /0&'F&(;';.&";#&<;'D&;('0)D0&.'$.,F"F)%);3',H&.'E#&K'F2;'."<C,#)("E,<')('"%-"3('2<$.&C):;"F%&I'
7.,F%&#('
• s<%3'F&<&[;('$"E&<;(')<';0&';.)"%K'>").%3'&".%3'– $"E&<;(',2;()C&';0&';.)"%'".&'0".#&CK'()<:&';0&';.)"%';"N&('%,<D&.'
– q"N)<D';0&';.)"%'.2<'%,<D&.'"%(,'(%,-('C,-<';0&'(;".;',>';0&'<&^;';.)"%'
• o;A(';,,':,#$%):";&CI''
L^"#$%&W'LUqs'
• L^;.":,.$,.&"%'#&#F."<&',^3D&<"E,<'– M0&".;G%2<D'#":0)<&A'>,.'$.&#";2.&'F"F)&('– #"9,.'(2.D&.3K'F2;'$,;&<E"%%3'#"9,.'F&<&[;'
• Y).(;';.)"%'2(&C'."<C,#)*&C'$%"3G;0&G-)<<&.'– [.(;'F"F3'D,;'LUqsK'(2.H)H&C'– (&:,<C'D,;':,<;.,%K'C)&C'– .&#")<)<D'&)D0;'D,;'LUqs'"<C'(2.H)H&C'
• o(';0)(':,<H)<:)<Dt'– #"9,.'(;"E(E:"%':,<;.,H&.(3K')<:%2C)<D'C)(:2((),<'$"$&.')<'=(5>?>-5$)=-*,&-,)
L^"#$%&W'LUqs'
• !&:,<C';.)"%'2(&C':,<H&<E,<"%'F%,:N'."<C,#)*"E,<'– 8j+cQ?'C&";0(')<':,<;.,%K'8Q+d?')<'LUqs'
• L"()&.';,'2<C&.(;"<CK'#,.&':,<H)<:)<D'