Random sampling

What is random sampling?

When each sampling unit in the sample frame has an equal chance of being chosen

What are the three types of random sampling?

Simple random sampling, systematic sampling and stratified sampling

What is simple random sampling?

Every sampling unit in the sampling frame has an equal chance of being selected

How do you carry out simple random sampling?

In the sampling frame, give each item an identifying number. Then use a random number generator

What are the two advantages of simple random sampling?

• Free of bias.

• Easy and cheap to implement for small populations and small samples.

What are the two disadvantages of simple random sampling?

• Not suitable when population size is large

• Sampling frame is needed

ESQ: There are 64 girls and 56 boys in a school. Explain briefly how you could take a random sample of 15 students using a simple random sample. (3)

Allocate a number between 1 and 120 to each student. (1)

Use a computer to select 15 different numbers between 1 and 120. (1)

The pupils corresponding to these numbers become the sample. (1)

What is systematic sampling?

Required elements are chosen at regular intervals in an ordered list.

How do you carry out systematic sampling?

What are two advantages of systematic sampling?

• Simple and quick to use.

• Suitable for large samples and large populations.

What are two disadvantages of systematic sampling?

• A sampling frame is needed.

• It can introduce bias if the sampling frame is not random.

EQS: A telephone directory contains 50,000 names. A researcher wishes to select a systematic sample of 100 names from the directory. Explain in detail how the researcher should obtain such a sample? (2)

k = 50,000/100 = every 500th element,

• Randomly select a number between 1 and 500. (1)

• Then select every 500th person following. (1)

What is stratified sampling?

The population is divided into strata and a simple random sample is carried out

What are strata?

Distinct groups the population is divided into

When is stratified sampling used?

When a sample is large and the population naturally divides into groups

How do you carry out a stratified sample?

Same proportion for each stratum - sample size (n) / population size (N) sampled from each strata

What are the advantages of stratified sampling?

• Reflects population structure.

• Guarantees proportional representation of groups within population.

What are the disadvantages of stratified sampling?

• Population must be clearly classified into distinct strata.

• Selection within each stratum suffers from same disadvantages as simple random sampling