Section 1.4

Other Effective Sampling Methods

SRS is the gold standard, but it's not always practical. Learn the specialized tools statisticians use to conquer massive populations.

1

Stratified Sampling

Method

Divide the population into non-overlapping groups called Strata (singular: Stratum) and obtain a simple random sample from each stratum.

LogicLens: The Representation Guarantee

Why SRS isn't enough: In a purely random sample of the US, you might accidentally get 0 people from Wyoming.

Stratified vs. SRS Outcome:
  • SRS: "I hope we get enough diverse opinions." (Luck)
  • Stratified: "I will take exactly 50 Democrats, 50 Republicans, and 50 Independents." (Guaranteed)

Key Feature: Strata are internally homogeneous (everyone in the group is similar in some way).

2

Systematic Sampling

The k-Interval Method
  1. Determine population size and sample size .
  2. Calculate the interval (round down).
  3. Pick a random starting number between 1 and .
  4. Select every th individual thereafter:
LogicLens: The Pattern Trap

Systematic sampling fails if the list has a hidden cycle.

Example: Inspecting every 10th item on a conveyor belt.

If the machine has a flaw that occurs exactly every 10 items, you might inspect ONLY flawed items (or miss them entirely).
3

Cluster Sampling

Defining "Clusters"

Divide the population into groups and select all individuals from a randomly selected set of groups.

Stratified
Some from All

Strata are Homogeneous (Same).
Ex: 50 Freshmen, 50 Sophomores...

Cluster
All from Some

Clusters are Heterogeneous (Diverse/Mini-pop).
Ex: All students in Classroom 101 and 104.

4

The Warning: Convenience Sampling

Not Probability Based

Selecting individuals who are easily accessible. This is not a scientific method. The results are strictly anecdotal and cannot be generalized to the population.

Example: Interviewing people walking past a library.
Bias: You only get people who like books/studying. You miss everyone else.
5

Multistage Sampling

The Professional Approach

Most large-scale surveys (Gallup, Nielsen, Government Census) combine these methods in layers.

Stage 1: Stratify by State
Stage 2: Cluster by Counties
Stage 3: SRS of Households
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