Sampling Method — Definition, Formula & Examples
A sampling method is the rule you follow to decide which members of a population end up in your sample. The method you choose determines whether your sample is likely to represent the whole group fairly.
A sampling method (or sampling design) is a procedure that specifies how units are selected from a sampling frame. In a probability sampling method, every unit has a known, nonzero chance of selection, chosen by a random mechanism. A nonprobability method, such as convenience or voluntary response sampling, does not have known selection chances.
How It Works
Start by listing the population you want to study. Then pick a design that fits how that population is organized. Simple random sampling gives every possible group of size the same chance of being chosen. Stratified sampling splits the population into similar groups (strata) and randomly samples within each one. Cluster sampling randomly selects whole groups and surveys everyone in them. Systematic sampling picks every th unit after a random start.
Worked Example
Problem: A school has 1,000 students: 400 freshmen, 300 sophomores, 200 juniors, and 100 seniors. You want a stratified sample of 50 students in which each grade's share of the sample matches its share of the school. How many students should you randomly select from each grade?
Step 1: Find the fraction of the population that will be sampled.
Step 2: Multiply each grade's size by that fraction.
Step 3: Check that the counts add up to the planned sample size. Then use a random number generator to choose the students within each grade.
Answer: Select 20 freshmen, 15 sophomores, 10 juniors, and 5 seniors at random.
Why It Matters
In AP Statistics, you must identify sampling methods and explain how a poor design causes bias. Political pollsters and medical researchers rely on stratified and cluster designs to draw conclusions about millions of people from only a few thousand responses.
Common Mistakes
Mistake: Believing that a very large sample makes up for a biased method, such as an online poll that anyone can answer.
Correction: A bigger sample reduces random variation, but it does not remove bias. If the method keeps favoring certain people, more responses repeat the same error. Fix the selection method first, then choose the sample size.