#Biostatistics 250

#ONE-WAY ANOVA TABLE
#MULTIPLE t-TESTS
ZAR=read.table("ZarEX10.3R.txt")
ZAR
attach(ZAR)
Y=potassium
X=factor(variety)
options(digits=12)
#DESCRIPTIVE STATISTICS:
X1bar=mean(Y[X=="1"])
X1bar
X2bar=mean(Y[X=="2"])
X2bar
X3bar=mean(Y[X=="3"])
X3bar
n1=length(Y[X=="1"])
n1
n2=length(Y[X=="2"])
n2
n3=length(Y[X=="3"])
n3
s1=sqrt(var(Y[X=="1"]))
s1
s2=sqrt(var(Y[X=="2"]))
s2
s3=sqrt(var(Y[X=="3"]))
s3
#GENERATING ANOVA TABLE:
anova(lm(Y~X))

#PAIRWISE COMPARISON OF MEANS:
#MULTIPLE t-TEST/FISHER'S LSD:
pairwise.t.test(Y,X,p.adj="none",alternative="two.sided")

#BONFERRONI COMPARISON OF MEANS:
pairwise.t.test(Y,X,p.adj="bonferroni",alternative="two.sided")

#HOLM COMPARISON OF MEANS:
pairwise.t.test(Y,X,p.adj="holm",alternative="two.sided")

#CALCULATING C FROM THE STUDENTIZED RANGE DISTRIBUTION:
alpha=0.05
N=18
k=3
qtukey(1-alpha,k,N-k)

#CALCULATING P FROM THE STUDENTIZED RANGE DISTRIBUTION:
#q-STATISTICS FROM MATHCAD:
q1=3.053251732725
q2=5.951908441386
q3=9.00516017411

options(digits=12)
#FOR SAMPLE 1 VS 2:
P1=1-ptukey(q1,k,N-k)
P1

#FOR SAMPLE 1 VS 3:
P2=1-ptukey(q2,k,N-k)
P2

#FOR SAMPLE 2 VS 3:
P3=1-ptukey(q3,k,N-k)
P3

#TUKEY HSD TEST:
TukeyHSD(aov(Y~X),conf.level=0.95)