Choosing and implementing sampling methods

What you’ll learn

• Implement simple random, stratified and systematic sampling.
• Compare probability sampling with quota sampling.
• Identify frame, non-response and periodicity problems.

Understand the idea

In a simple random sample of fixed size, each possible subset has the same selection probability. Number the complete population and select distinct random labels, rejecting labels outside the range and repeats. This requires a suitable frame and does not guarantee balanced subgroup counts in a small sample.

A stratified sample divides the population into non-overlapping groups and randomly samples within each. Proportional allocation keeps the sample shares close to population shares. A systematic sample selects a random start and then every kth unit; it is easy to implement but can be distorted by a repeating pattern in the ordered frame.

Quota sampling fills specified subgroup totals using non-random selection within groups. It can be convenient without a full frame, but interviewer choices can bias results. No method automatically removes non-response or inaccurate measurement, so justify the method using the actual setting.

Key formulae

$$n_h\approx n\frac{N_h}{N}$$

$$k=\frac{N}{n}$$

$$r,\ r+k,\ r+2k,\ldots,\ r+(n-1)k$$

Worked example

A club has 180 junior and 120 senior members. Design a proportional stratified random sample of 25 members.

1. The population total is $N=180+120=300$.
2. Allocate $25(180/300)=15$ places to juniors and $25(120/300)=10$ to seniors.
3. Create separate numbered lists for the two strata and choose 15 distinct junior labels and 10 distinct senior labels at random.
4. Use the selected members rather than replacing inconvenient responses with volunteers.

Answer: Randomly select 15 juniors and 10 seniors from their respective complete lists.