Question

Reasoning You are studying the colors of houses on a highly populated street. Decide whether or not each of the following descriptions is an example of systematic sampling. Use pencil and paper. Explain your reasoning for each decision.
You choose the first and last 12 houses on the street. nothing
You choose every sixth house on the street comma starting with the third. nothing
You list the houses alphabetically by owner's last name comma and choose every eighth house on the list comma starting at the first.
You start at the eighth house and choose the next 20 houses on the street.

Answer 1

1) You choose the first and last 12 houses on the street.
- Not systematic. Systematic sampling selects elements at a fixed interval (every k-th element) through the whole population. Picking the first and last 12 picks two end blocks and not a regular interval; it’s a convenience / boundary sample and can be biased by location.

2) You choose every sixth house on the street, starting with the third.
- Systematic. This is the standard form: a fixed interval k = 6 with a specified start (position 3). (Best practice is to choose the start at random from 1,…,6 to avoid periodic bias, but the selection rule itself is systematic.)

3) You list the houses alphabetically by owner’s last name and choose every eighth house on the list, starting at the first.
- Systematic (with caution). Choosing every 8th on an ordered list is a systematic procedure. Possible caveat: if the alphabetical ordering is related to the trait of interest (house color) it can introduce bias; also a random start between 1 and 8 is usually recommended.

4) You start at the eighth house and choose the next 20 houses on the street.
- Not systematic. This picks a single consecutive block of 20 houses (a cluster or convenience sample) rather than selecting at a regular interval across the whole street, so it is not a systematic sample.