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Write the start and interval
In a fictional ordered list of eight units, choose start 1 or 2 with equal probability and take every second unit. The possible samples are positions 1,3,5,7 and 2,4,6,8. Each position is selected with probability 1/2.
Compare the restricted sample sets
The design has two possible samples of four units. A size-four simple random sample from eight units has 70 possible subsets. Equal unit chances do not make the two designs identical.
Investigate recurring patterns
If odd positions all carry value 10 and even positions all carry value 30, the systematic mean is either 10 or 30. The population mean is 20. Random start keeps the estimator centered at 20 across repetitions, but does not prevent large realized errors.
Keep the ordering in the research record
| Field | Why it matters |
|---|---|
| Ordering rule | May align with periodic values |
| Start distribution | Defines the randomization |
| Sampling interval | Defines the selected positions |
| Endpoint handling | Avoids an unstated rule for leftover units |