Problem 1
(a)(b)
It
’
s a paired t-test.
According to (3.1), we can get:
t = -3.08, p = 0.027
Since t
5, 0.05/2
= 2.571 < |t|, we reject the null hypothesis
R code:
> x1=c(8,14,16,19,18,12)
> x2=c(11,16,20,18,20,15)
> N=length(x1)
> d = x1-x2
> s_d=sd(d)
> t=sqrt(N)*mean(d)/s_d
> t
[1] -3.081296
> t.test(x1,x2,paired=TRUE)
Paired t-test
data:
x1 and x2
t = -3.0813, df = 5, p-value = 0.02743
…
Problem 2
Zero sum:
τ
i
is the offset between the expected treatment i response and the average
treatment response.
α
i
is the offset between the expected block j effect and the
average block effect.
Baseline:
τ
i
is the offset between the expected treatment i response and treatment 1.
α
i
is the offset between the expected block j effect and the block 1 effect.
Problem 3
For tukey
’
s method, we have: 1/sqrt(2) *q
4,24,0.01
= 3.47
The t-values are in table 3.7
We
can see all pairs except
A
vs C have t-value greater than 3.47.
The conclusion is different from the one made at 0.05 level
Problem 4
>y=c(25.66,29.15,35.73,28.00,35.09,39.56,20.65,29.79,35.66)
>
X=rep(c(40,50,60),3)
>
p1=((X-50)/10)/sqrt(2)
>
p2=(3*(((X-50)/10)^2-2/3))/sqrt(6)
>
X2=rep(c(0,1,2),each=3)
>
s1=((X2-1)/1)/sqrt(2)
>
s2=(3*(((X2-1)/1)^2-2/3))/sqrt(6)
>