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Chapter 7

Chapter 7. Systematic sampling. 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.

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Chapter 7

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  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)

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