Week 3

Question 1

Complete randomisation ensures

Answer 1

We get min variance linear unbiased estimators of parameters and functions of parameters

Question 2

Advantage of blocking

Answer 2

Variance in responses between blocks can be separated from variance between units within blocks

Question 3

Randomised complete block design

Answer 3

Each block has exactly one instance of each treatment which is randomly assigned to a unit (blocks size is equal to number of treatments)

Question 4

Systematic design

Answer 4

Treatments are allocated in ascending order across numbered units

Question 5

What is?

Answer 5

b_i is the average deviation of block i from the mean

e_ij represents the deviation of unit j from block i from the mean of that block

Question 6

Answer 6

1/t

This is allocation of treatment k on unit j in block i

Question 7

Since each treatment can only occur on one unit in block i

Answer 7

0

Since each treatment can only occur on one unit in block i

Question 8

Answer 8

1/(t-1)

Since one treatment has already been allocated in block i

Question 9

ANOVA for RCBD under finite population model

Answer 9

Where

y_ik = μ + b_i + t_k + Σ_j δ_ij^k e_ij

Question 10

Treatment total for treatment k

Answer 10

Sum of responses under treatment K across each block

Question 11

E[T_k] = ?

Answer 11

Question 12

Comparing expectations of treatment totals

Answer 12

Question 13

Variance of treatment total

Answer 13

Question 14

Given a systematic design. What is Randomisation procedure for 2 treatment factors. 4 complete blocks. Each factor has 3 levels

Answer 14

Within each block independently, choose a random permutation of 6 objects and assign it to levels of both factors

Each treatment pair in systematic design should be fixed to ensure each combination is tested