Biostatistics 190

#POWER & SAMPLE SIZE CALCULATIONS
#FOR TWO SAMPLES

#ZAR EXAMPLE 8.1
ZAR=read.table("ZarEX8.1R.txt")
ZAR
attach(ZAR)
X1=data[group=="gpB"]
X2=data[group=="gpG"]
n1=length(X1)
n1
n2=length(X2)
n2
s1=sqrt(var(X1))
s2=sqrt(var(X2))
#POOLED VARIANCE:
sp=sqrt(((n1-1)*s1^2+(n2-1)*s2^2)/(n1+n2-2))
sp
sp^2

#ESTIMATING SAMPLE SIZE FOR CI
#SET THE FOLLOWING VALUES AS DESIRED:
d=0.5
N0=50
alpha=0.05
#ITERATE THE FOLLOWING UNTIL N IS STABILIZED:
N1=(2*sp^2*(qt(1-alpha/2,2*(N0-1)))^2)/d^2
N1
N2=(2*sp^2*(qt(1-alpha/2,2*(N1-1)))^2)/d^2
N2
N3=(2*sp^2*(qt(1-alpha/2,2*(N2-1)))^2)/d^2
N3
N4=(2*sp^2*(qt(1-alpha/2,2*(N3-1)))^2)/d^2
N4
N5=(2*sp^2*(qt(1-alpha/2,2*(N4-1)))^2)/d^2
N5

#ESTIMATING SAMPLE SIZE FOR TWO SAMPLE T-TEST
#SET THE FOLLOWING VALUES AS DESIRED:
delta=0.5
alpha=0.05
beta=0.10
N0=100
#ITERATE THE FOLLOWING UNTIL N IS STABILIZED:
N1=(2*sp^2/delta^2)*(qt(alpha/2,2*(N0-1))+qt(beta,N0-1))^2
N1
N2=(2*sp^2/delta^2)*(qt(alpha/2,2*(N1-1))+qt(beta,N1-1))^2
N2
N3=(2*sp^2/delta^2)*(qt(alpha/2,2*(N2-1))+qt(beta,N2-1))^2
N3
N4=(2*sp^2/delta^2)*(qt(alpha/2,2*(N3-1))+qt(beta,N3-1))^2
N4
N5=(2*sp^2/delta^2)*(qt(alpha/2,2*(N4-1))+qt(beta,N4-1))^2
N5

#ESTIMATING DETECTABLE DIFFERENCE GIVEN N 
#FOR ONE SAMPLE t-TEST
#SET THE FOLLOWING VALUES AS DESIRED:
N=20
alpha=0.05
beta=0.10

delta=sqrt(2*sp^2/N)*(qt(alpha/2,2*(N-1))+qt(beta,2*(N-1)))
delta

#ESTIMATING POWER OF TWO SAMPLE t-TEST
#SET THE FOLLOWING VALUES AS DESIRED:
N=15
delta=1.0
alpha=0.05

B=(delta/sqrt(2*sp^2/N))-abs(qt(alpha/2,2*(N-1)))
B
POWER=pt(B,2*(N-1))
POWER
POWERN=pnorm(B,0,1)
POWERN