Sampling Methods

Learn simple random samples, systematic sampling, stratified sampling.

Lesson 1 of 33 parts Practice Flashcards

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Simple Random Samples

Objective: Explain simple random samples, apply the stated method, and check its conditions.

A simple random sample of size n without replacement makes every size-n subset of a finite population equally likely. Each unit then has inclusion probability n/N. Equal individual chances alone do not define every possible sampling design as a simple random sample. Equal individual inclusion probabilities alone do not establish a simple random sample.

Formulas

Individual inclusion probability=n/N

Worked examples

Try itA simple random sample selects 42 people without replacement from 700 people. What is one given person’s inclusion probability?Show answer

Step 1: In a simple random sample of size n from N, each person has inclusion probability n/N. Step 2: Use 42/700. Step 3: The inclusion probability is 3/50; all size-n subsets are equally likely.

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Simple Random Samples

Objective: Explain simple random samples, apply the stated method, and check its conditions.

Formulas

Individual inclusion probability=n/N

Worked examples

Try itA simple random sample selects 42 people without replacement from 700 people. What is one given person’s inclusion probability?Show answer

Step 1: In a simple random sample of size n from N, each person has inclusion probability n/N. Step 2: Use 42/700. Step 3: The inclusion probability is 3/50; all size-n subsets are equally likely.

Systematic Sampling

Objective: Explain systematic sampling, apply the stated method, and check its conditions.

Systematic sampling selects a random starting point and then a fixed interval along a list. Its validity depends on list coverage and on avoiding ordering patterns that align with the sampling interval. It is not the same as independently selecting every unit. Periodicity in list order can bias a systematic sample.

Formulas

Random start + fixed interval k

Worked examples

Try itA synthetic sampling list has 42 entries. After a random start, every 6th entry is selected with exactly 7 selections. How many units are sampled?Show answer

Step 1: Systematic sampling uses a fixed interval after a random start. Step 2: The prompt states there are 7 selected entries. Step 3: The sample size is 7; check that list order does not introduce periodic bias.

Stratified Sampling

Objective: Explain stratified sampling, apply the stated method, and check its conditions.

Stratified sampling divides a population into nonoverlapping groups and selects a sample within each. Proportional allocation samples the same fraction from every stratum. This differs from cluster sampling, which selects groups and then includes or samples units within selected clusters. Sampling within every stratum is different from selecting only some clusters.

Formulas

Total sample size = sum of stratum sample sizes

Worked examples

Try itTwo strata contain 84 and 98 people. Sample half of each stratum. Find the total sample size.Show answer

Step 1: A stratified design samples within each group. Step 2: Half the combined count is (84+98)/2. Step 3: The sample size is 91; counts in this example are even when sampling requires whole people.

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