1. Chapter 7
Systematic sampling

2. Why systematic sampling a useful alternative?
Easier to perform in the field (possibly less subject to selection errors by fieldworkers, especially if a good frame is not available)
More information per unit cost than simple or stratified sampling

3. How to select a systematic sample
Need to determine k (systematic sampling is a 1-in-k sampling strategy)
If we know N, then k should be chosen such that is does NOT exceed N/n (N=number in population and n=desired sample size)
If don’t know N, choose a reasonable k
Randomly choose the first individual among the first k elements, then choose every kth element after that until desired sample size is obtained.

4. Estimates and bounds for mean and total
m-hatSY = Siyi/n
Estimated variance of m-hatSY is
(1-n/N)s2/n (if N is unknown, do not worry about the fpc)
t-hatSY = NSiyi/n (or N*ybarSY)
Estimated variance of t-hatSY is
N2(1-n/N)s2/n (Notice that N needs to be known)

5. Definitions A population is random if the elements are in random order
A population is ordered if the elements of a population have values that trend upward or downward when they are listed
A population is periodic if the elements have values that tend to cycle in a regular pattern

6. Random

7. Ordered

8. Periodic

9. Examples
7.16

10. Chapter 7.4 Population proportion: phatSY = ybarSY = Siyi/n
Estimated variance of phatSY =
(1-n/N)phatSYqhatSY/(n-1)
(where yi = 0 or 1)
Ignore fpc when N is unknown or very large

11. Chapter 7.5 Sample size for m and t: n = Ns2/( (N-1)D + s2)
where D = B2/4 for m and D = B2/(4N2) for t
if s2 is unknown, can estimate it with s2 or (range/4)2
Sample size for p
n = Npq/( (N-1)D +pq)
where D = B2/4

12. Classroom examples
7.4, 7.5, 7.6, 7.7, 7.11, 7.12 (just estimate n)