Week 3

Question 1

4 remarks about systematic sampling

Answer 1

1. Simple to implement
2. When k=N/n step is an integer, ysbar is an unbiased estimator of yUbar
3. Depends on ORDER of POP. LISTING -> can affect variance
4. Can ‘balance’ sample according to variables used to order list

Question 2

How to do stratified sampling?
+ 4 remarks

Answer 2

1. Divide pop. into strata (non-overlapping groups)
   - stratum = a subset of pop. that shares at least 1 common characteristic, eg. F vs M
2. Take a SRS within each stratum
   - select the no. of elements to be selected from each stratum according to an allocation method

• homogeneous within, heterogeneous between
• must know stratification variable for all pop. units

Remarks
1. Can obtain unbiased estimation
2. Can improve precision if there is homogeneity within strata (& if increase no. of clusters sampled)
3. Improve representativeness of sample
4. Costly design b/c need to know stratification factor first

Question 3

How to do cluster sampling?
+ 3 remarks

Answer 3

1. Divide pop. into N clusters (groups)
2. Take a SRS of n clusters
3. If single stage, select ALL units in clusters & examine

• heterogeneous within, homogeneous between

Remarks
1. Can achieve unbiased estimation
2. Tends to lower precision, unless clusters are very heterogeneous within

Question 4

What p to use when p is unknown, and why?

Answer 4

Set p=0.5 so that p(1-p) is as big as possible at 0.25

This is to be conservative about what n would be & give the largest sample size.