#Biostatistics 130

#POWER & SAMPLE SIZE CALCULATIONS
#FOR ONE SAMPLE

#ESTIMATING SAMPLE SIZE FOR CI
#ZAR EXAMPLE 7.3
ZAR=read.table("ZarEX7.3.txt")
ZAR
attach(ZAR)
X=wtchg
s=sqrt(var(X))  #sample variance
#SET THE FOLLOWING VALUES AS DESIRED:
d=0.25
N0=40
alpha=0.05
#ITERATE THE FOLLOWING UNTIL N IS STABILIZED:
N1=(s^2*(qt(alpha/2,N0-1))^2)/d^2
N1
N2=(s^2*(qt(alpha/2,N1-1))^2)/d^2
N2
N3=(s^2*(qt(alpha/2,N2-1))^2)/d^2
N3
N4=(s^2*(qt(alpha/2,N3-1))^2)/d^2
N4
N5=(s^2*(qt(alpha/2,N4-1))^2)/d^2
N5

#ESTIMATING SAMPLE SIZE FOR ONE SAMPLE T-TEST
#ZAR EXAMPLE 7.2
ZAR=read.table("ZarEX7.2.txt")
ZAR
attach(ZAR)
X=RATwtchg
s=sqrt(var(X))
#SET THE FOLLOWING VALUES AS DESIRED:
delta=1.0
alpha=0.05
beta=0.10
N0=20
#ITERATE THE FOLLOWING UNTIL N IS STABILIZED:
N1=(s^2/delta^2)*(qt(alpha/2,N0-1)+qt(beta,N0-1))^2
N1
N2=(s^2/delta^2)*(qt(alpha/2,N1-1)+qt(beta,N1-1))^2
N2
N3=(s^2/delta^2)*(qt(alpha/2,N2-1)+qt(beta,N2-1))^2
N3
N4=(s^2/delta^2)*(qt(alpha/2,N3-1)+qt(beta,N3-1))^2
N4
N5=(s^2/delta^2)*(qt(alpha/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=25
alpha=0.05
beta=0.10

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

#ESTIMATING POWER OF ONE SAMPLE t-TEST
#SET THE FOLLOWING VALUES AS DESIRED:
N=12
delta=1.0
alpha=0.05

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