In addition to direct measurement, data is frequently obtained through survey. This generally means that individual persons will be queried for information that represents that individual as a member within the population Surveys and Sampling

Example: You want to run for class valedictorian. What can you do to increase your chances of being elected? If you were to conduct a survey, what would you ask, and who would you ask?

Sampling For large or infinite populations, it is normally only feasible to sample the population when collecting data for analysis If done correctly, the sample will represent the population

Populations A population is ALL of the data elements, whether measured or not, that belong to the present study A population may be: – Finite and small (eg the set of marks for this class) – Finite and large (eg global birthrates by country) – Infinite (eg the roll values of a pair of dice) Do not confuse a data population with a population of persons – it doesn’t have to be!

Identify the Population: Who will you vote for in the next election? What is the average diameter of a manufacturing run of pistons? Who should be named NHL MVP? What is the calorie content of a donut? Do you prefer contact lenses or glasses? What is the atmospheric CO 2 level?

Sampling Frame The sampling frame is those elements of the population that could be chosen for a sample. The sampling frame is often driven by the type of sample (or sampling method)

Simple Random Sample Members of the population are chosen at random. Note that “random” does not happen by accident.

Systematic Sample Members of population are selected on a systematic interval. Interval Size = (Population Size) ÷(Sample Size)

Systematic Sample Example: A telephone company is going to do a marketing survey of its customers. A sample size of 250 is considered. What is the sampling interval? What does it mean? What drives the cost of such a survey?

Stratified Sample Used where the population has certain segments (eg age, gender, education level) with common characteristics, and that should be proportionally represented in the sample.

Stratified Sample Example: Design a sample of 10% of this school’s population that is stratified by grade. Example: Design a sample of 10% of this school’s population that is stratified by gender.

Cluster Sample Used where an obviously isolated group is representative of the entire population. Example: Surveying patrons at one Tim Horton’s location in the GTA rather than surveying patrons at all Tim Horton’s locations in the GTA

Multi-Stage Sample Used to add several layers of random selection to a sample Example: If the population is all households in Ontario, then select cities at random, and then select households within the selected cities at random.

Voluntary Response Sampling Used where members of the population must actively choose to be sampled. Examples: Call-in radio shows (eg AC-DC vs Led-Z) or mail-in surveys Beware of bias!

Convenience Sample Where the sample is selected on the basis of convenience Example: Using the students in this class to represent the whole school or all teenagers or all cellphone users.

Primary Data: Data that you measure or survey specifically for your purpose. Secondary Data: Data that has been collected by others, and you make use of in your study. A couple of data types that could appear, whether measured or surveyed: