Lesson 11

Simple Random Sampling (SRS)

A simple random sample (SRS) of size n consists of n individuals from the population chosen in such a way that every set of n individuals has equal chance of being selected

Sampling Frame

• In order to perform random sampling we need a record of the entire population. The sampling frame is the list of individuals in the population from which a sample is drawn.

• Might not necessarily be the same as population

  • Example: Want to sample businesses in Toronto and use Yellow Pages as sampling frame; but not all businesses are necessarily listed!

• Try to use sampling frame that is as close as possible to population of interest

Stratified Sampling

• Sometimes population is divided into groups of similar individuals, called strata

• Example: Student population w/ 40% males and 60% females

  • With SRS you could end up with all female sample

  • Could be a problem, especially if strata are very different from each other (in terms of parameter)

• To ensure more representative sample, use Stratified random sampling

• Stratified Random Sampling: Select separate SRS’s within each stratum (w/ separate sample sizes relative to stratum sizes), and combine them to get stratified sample

  ▶ Example: Total size n = 5

  ▶ Males: n ×0.4 = 2

  ▶ Females: n ×0.6 = 3

Cluster Sampling

• SRS can sometimes be impractical

• Example: SRS of n Torontonians −→might have to visit n different households

• If population is divided in clusters, by geography or other boundaries, it is easier to perform SRS of clusters, i.e. cluster sampling

• Example: SRS of Toronto households (clusters)

Multistage Sampling

• Population might be divided into a hierarchy of clusters

  • Example: Province > City > Neighborhood > Household

• Multistage sampling: use SRS within each stage of hierarchy to collect sample

• Note: Cluster/Multistage sampling is mainly used for convenience, unlike stratified sampling which is used for improving accuracy

Systematic Sample

• Individuals in population are often ordered

  • Example: Students in alphabetical list, customers exiting store, etc

• If order is not associated with response, can use systematic sampling: sample every i-th individual, starting at random

  • Example: Sample every 5th customer

What Can Go Wrong?

• Mistake 1: Sample Volunteers

  • The resulting voluntary response bias invalidates the survey. More likely to leave store review if you didn’t like the service provided.

• Mistake 2: Sample Conveniently

  • In convenience sampling we simply include the individuals who are convenient for us to sample.

  • Unfortunately, this group may not be representative of the population.

• Mistake 3: Use a Bad Sampling Frame

  • An SRS from an incomplete sampling frame introduces bias

• Mistake 4: Undercoverage

  • In many survey designs, some portion of the population is not sampled at all or has a smaller representation in the sample than it has in the population.

Non response bias

• a significant portion of those who are selected for the sample do not respond to the survey or study.

• People who do not respond to a survey or study differ in important ways from those who do.

• Imagine a survey sent to 1,000 university students asking about mental health:

  • Only 400 students respond.

  • Most responses come from students already engaged with mental health services.

  • If students not struggling or those too busy to respond are underrepresented, the results may overestimate the prevalence of mental health issues.

response bias

• favoring certain answer in way question is asked

• Make sure wording is neutral; use pilot (trial) study

• Participants give inaccurate or untruthful answers, often in a systematic way that skews the data, usually to be more socially desirable

Difference between cluster and stratified sampling

In cluster sampling, the population is divided into groups (clusters), and then entire clusters are randomly selected for inclusion in the sample. In stratified sampling, the population is divided into subgroups (strata) based on shared characteristics, and then individuals are randomly sampled from each stratum