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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 + !

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2! sample size =2(Z1"! /2 " Z" )2

# 2 / 2$ 2

L^"#$%&W'

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total number of events =2! (Z! " Z" /2 )2

(log#)2 / 2

b2)("<:&'$"."#&;&.('

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' 2! sample size =2(Z1"! /2 " Z! )2

" 2 / 2# 2

" =2# n

Z1"! /2 " Z!

=" ntotalZ1"! /2 " Z!

Power =#"1(1"!) =# "#

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number of heart attacks = 2! (13)(log1.2)2 / 2

=1565

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E[difference]= 0.9!10+ 0.1!0( )" 0.95!0+ 0.05!10( ) = 8.5

V2<G)<'

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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

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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

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