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

2. 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

3. 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

4. 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

5. 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

6. Example 1: Designing a Systematic Sample
A telephone company is planning a marketing survey of its 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?

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

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

9. 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.

10. 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)

11. Age
Race
Hair colour
Gender
Clubs
Etc…

12. 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