#Biostatistics 140

#TEST OF VARIANCE FOR A NORMAL DISTRIBUTION

#ZAR EXAMPLE 7.4
ZAR=read.table("ZarEX7.4.txt")
ZAR
attach(ZAR)
X=distime
n=length(X)
s=sqrt(var(X))

#SET THE FOLLOWING AS DESIRED:
alpha=0.05
sigma0=sqrt(1.5)

#CALCULATING BY HAND:
#CHI SQUARE STATISTIC:
Xsq=((n-1)*s^2)/sigma0^2
Xsq

#CRITICAL VALUES:
C1=qchisq(alpha/2,n-1)
C1
C2=qchisq(1-alpha/2,n-1)
C2
C3=qchisq(alpha,n-1)
C3
C4=qchisq(1-alpha,n-1)
C4

#PROBABILITY:
P=2*(1-pchisq(Xsq,n-1))  # two sided case
P
P=pchisq(Xsq,n-1)          #one sided case lower tail
P
P=1-pchisq(Xsq,n-1)        #one sided case upper tail
P

#CONFIDENCE INTERVALS:

#TWO SIDED CASE:
CIL=((n-1)*s^2)/C2
CIL
CIU=((n-1)*s^2)/C1
CIU

#ONE SIDED CASE LOWER TAIL:
CIL=((n-1)*s^2)/C3
CIL

#ONE SIDED CASE UPPER TAIL:
CIU=((n-1)*s^2)/C4
CIU

#USING FUNCTION varTest() in {EnvStats}:
library(EnvStats)
varTest(X,sigma.squared = 1.5,alternative="two.sided",conf.level=0.95)