meana15 <- mean(c(7,7,15,11,9))
meanb20 <- mean(c(12,17,12,18,18))
meanc25 <- mean(c(14,19,19,18,18))
meand30 <- mean(c(19,25,22,19,23))
meane35 <- mean(c(7,10,11,15,11))#meana15=9.8, meanb20=15.4, meanc20=17.6, meand25=21.6, meane30=10.8
grandmean <- mean(c(meana15,meanb20,meanc25,meand30,meane35))sse_15 <- sum((a15-meana15)^2)
sse_20 <- sum((b20-meanb20)^2)
sse_25 <- sum((c25-meanc25)^2)
sse_30 <- sum((d30-meand30)^2)
sse_35 <- sum((e35-meane35)^2)
sse <- sum(sse_15,sse_20,sse_25,sse_30,sse_35)
MSE <- sse/20#sse_15=44.8 #sse_20=39.2 #sse_25=17.2 #sse_30=27.2 #sse_35=32.8 #sse=161.2 #MSE=8.06
sstr_15 <- sum((meana15-grandmean)^2*5)
sstr_20 <- sum((meanb20-grandmean)^2*5)
sstr_25 <- sum((meanc25-grandmean)^2*5)
sstr_30 <- sum((meand30-grandmean)^2*5)
sstr_35 <- sum((meane35-grandmean)^2*5)
sstr <- sum(sstr_15,sstr_20,sstr_25,sstr_30,sstr_35)
mstr <- sstr/4#sstr_15=137.2 #sstr_20=0.64 #sstr_25=32.768 #sstr_30=215.16 #sstr_35=89.8 #sstr=475.76 #mstr=118.94
F <- mstr/MSE
qf(0.95,4,20)## [1] 2.866081#f=14.75 #2.86 is the critical value less than the f statistic we reject the null hypothesis #there is evidance toto support cotton content affects the meantensile strength.
a15 <- c(7,7,15,11,9)
b20 <- c(12,17,12,18,18)
c25 <- c(14,19,19,18,18)
d30 <- c(19,25,22,19,23)
e35 <- c(7,10,11,15,11)
meana15 <- mean(c(7,7,15,11,9))
meanb20 <- mean(c(12,17,12,18,18))
meanc25 <- mean(c(14,19,19,18,18))
meand30 <- mean(c(19,25,22,19,23))
meane35 <- mean(c(7,10,11,15,11))
grandmean <- mean(c(meana15,meanb20,meanc25,meand30,meane35))
sse_15 <- sum((a15-meana15)^2)
sse_20 <- sum((b20-meanb20)^2)
sse_25 <- sum((c25-meanc25)^2)
sse_30 <- sum((d30-meand30)^2)
sse_35 <- sum((e35-meane35)^2)
sse <- sum(sse_15,sse_20,sse_25,sse_30,sse_35)
MSE <- sse/20
sstr_15 <- sum((meana15-grandmean)^2*5)
sstr_20 <- sum((meanb20-grandmean)^2*5)
sstr_25 <- sum((meanc25-grandmean)^2*5)
sstr_30 <- sum((meand30-grandmean)^2*5)
sstr_35 <- sum((meane35-grandmean)^2*5)
sstr <- sum(sstr_15,sstr_20,sstr_25,sstr_30,sstr_35)
mstr <- sstr/4
F <- mstr/MSE
qf(0.95,4,20)