## paired t-test

y1<-c(6,4,6,7,5,6,8,7,8,3,9,4,8,11,12,6,10,3,5,4,6,7,5,6,3,10,5,4,4,7)
y2<-c(4,7,12,10,2,11,9,5,11,8,7,6,8,9,9,8,10,9,8,5,8,7,6,9,3,5,11,7,3,10)
##table 5.1, Imipramine(y1) vs. placebo(y2) to treat depression
## response: depression score. the higher the score, the more severe the dep. 

> mean(y1)
[1] 6.3
> sqrt(var(y1))
[1] 2.394678

> mean(y2)
[1] 7.566667
> sqrt(var(y2))
[1] 2.595531

> mean(y1-y2)
[1] -1.266667
> sqrt(var(y1-y2))
[1] 2.923547

> t.test(y1,y2,paired = T)

        Paired t-test

data:  y1 and y2 
t = -2.3731, df = 29, p-value = 0.02449
alternative hypothesis: true difference in means is not equal to 0 
95 percent confidence interval:
 -2.3583370 -0.1749963 
sample estimates:
mean of the differences 
              -1.266667 

## RBD, class example
conf<-c(1,2,7,6,12,  5,8,9,13,14,  8,14,16,18,17)
block<-rep(1:5,3)
method<-rep(1:3, c(5,5,5))
fit<-lm(conf~factor(method)+factor(block))
> anova(fit)
Analysis of Variance Table

Response: conf

Terms added sequentially (first to last)
               Df Sum of Sq  Mean Sq  F Value       Pr(F) 
factor(method)  2  202.8000 101.4000 33.98883 0.000122918
 factor(block)  4  171.3333  42.8333 14.35754 0.001008124
     Residuals  8   23.8667   2.9833