5.3.2 Collecting Samples Sampling Methods For student handout, print out only slides 1-6

Simple Random Sampling Lotto 6/49 Picking names out of a hat Bingo Very easy and straightforward Quick The standard by which other methods are judged Description Advantages All selections equally likely Combinations of selections equally likely Sample is chosen entirely at random Selection of one individual doesn’t affect chance of any other individual Might need to know entire population ahead of time Might not be representative of entire population by chance Disadvantages Simple Random Sampling Examples Card Sample Lotto 6/49 Picking names out of a hat Bingo Non-text example

Systematic Random Sampling I = N/n where I is the sampling interval Description Everyone has equally likely chance of being chosen Not likely to get clusters (of opinion, bad cakes, etc.) Advantages I = N/n where I is the sampling interval N is the population size n is the sample size Randomly choose the starting point between 1 and I Choose every Ith person Disadvantages If you want a fixed sample size, need to know size of entire population ahead of time Systematic Random Sampling Examples Card Sample Testing products on production line Surveying every 10th household Dealing cards

Stratified Random Sampling Description Advantages Resulting sample will have responses from each group The sample taken from each group can be proportional to the size of the group Break population into groups (strata) that have common feature Ex: by age, location, gender, religion, marital status Draw a random sample from each stratum Some strata may be overrepresented if the sample is not proportional to the size of the stratum Disadvantages Stratified Random Sampling Examples Card Sample Break the country into provinces and take a sample of 1% of the population of each province

Cluster/Multi-stage Sampling Can reduce costs Description Advantages Break population into clusters (usually already existing) Each cluster is representative of population, we hope Select a number of clusters randomly and survey everyone in the cluster Multi-stage: break the selected clusters down into smaller sub-clusters and survey everyone in the sub-cluster At least two stages Can reduce costs More convenient administration Lower accuracy due to higher sampling variance than for same size simple random sample Disadvantages Cluster/Multi-stage Sampling Examples Card Sample Want to know students’ opinions: Choose 100 schools and ask all students at each school Multistage: ask only a sample of classes from each of the 100 schools

Example 1: Designing a Systematic Sample A telephone company is planning a marketing survey of its 760 000 customers. For budget reasons, the company wants a sample size of about 250. Suggest a method for selecting a systematic sample. What expense is most likely to limit the sample size?

a) First, determine the sampling interval, I. Randomly choose one of the first 3040 customers, then choose every 3040th customer from that point on.

b) The expense most likely to limit the sample size is the salary of the employees to call and ask questions

Example 2: Designing a Stratified Sample Before booking bands for the school dances, the students’ council at Statsville High School wants to survey the music preferences of the student body. The table on the following slide shows the enrollment at the school. Design a stratified sample for a survey of 25% of the student body. Suggest other ways to stratify this sample.

a) Take 25% from each grade. Number of Students 9 255 10 232 11 208 12 190 Total 885 Number Surveyed 255(0.25) = 63.75 232(0.25) 208(0.25) 190(0.25) 855(0.25)

Age Race Hair colour Gender Clubs Etc…

Sampling Assignment Choose 3 different sampling methods Use each method to create a sample of 10 students from the class Your samples should not include you Explain how you developed each sample List the students (by number) in each sample Discuss the advantages and disadvantages of each sample (how representative it is of the population) Due Thursday at the beginning of class