stats

1. Section 1.2: Sampling Methods, p.1
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When you choose a sample you want it to be as similar to the
population as possible. Example: To test of a new painkiller for adults you would
want the sample to include people who are old, young, healthy, not healthy, male,
female, etc.
There are many ways to collect a sample. No method is perfect,
becuz:
• A new sample with different individuals would be different.
• If you were to include one more individual, the sample would change.
This type of randomness is inherent and can’t be avoided.
• But other kinds of errors (biases) can be avoided.
1. Simple random sample – All individuals have an
equal chance of being selected, independently of all
other individuals.
So, every different possible sample of size n has the same chance
of being selected.
Slides by Carey Smith, with content from Kate Kozak, Statistics Using Technology, 2nd
edition, from David Straayer, and elsewhere, as noted.
Licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

2. Simple Random Sample Examples
• Example #1.2.1: Choosing a Simple Random Sample
• Describe how to take a simple random sample from a classroom.
• Solution:
• Give each student in the class a number. Using a random number
generator you could then pick the number of students you want to
pick.
• Example #1.2.2: How Not to Choose a Simple Random Sample
• You want to choose 5 students out of a class of 20. Give some
examples of samples that are not simple random samples:
• Solution:
• Choose 5 students from the front row. The people in the last row
have no chance of being selected.
• Choose the 5 shortest students. The tallest students have no chance
of being selected.
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3. Stratified Sampling
2. Stratified sample – “Strata” are groups of similar individuals, such as men &
women, ethnic, education level, income, and geography groups.
– For elections and other government purposes, the proportion of individuals in selected
in a group of the sample should equal that group’s proportion of the total population.
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https://www.census.gov/quickfacts/fact/table/venturacountycalifornia,ca/RHI125217
2017, US Census Bureau Ventura County California
Black or African American 2.3% 6.5%
American Indian 1.9% 1.6%
Asian 7.8% 15.2%
Pacific Islanders 0.3% 0.5%
Two or More Races 3.5% 3.9%
Hispanic or Latino 42.9% 39.1%
White, not Hispanic or Latino 45.2% 37.2%
Example: Banner Health wants to assess complications after surgery.
One method is to use a stratified sample:
Divide the patients according to type of surgery.
Draw simple random samples from each group.
This may show that some types of surgeries have more complications
than others.

4. Cluster Sampling
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3. Cluster sample
(a) Divide the population into clusters.
e.g. Classes, neighborhoods, businesses
(b) Randomly select clusters
(c) Sample some or all in the selected clusters.
Many people confuse stratified sampling and
cluster sampling.
• Stratified sampling uses all the groups and
some of the members in each group.
Cluster sampling is the other way around.
• Cluster sampling uses some of the groups
and all the members in each group.
Example:
• A school wants to survey a sample of
students.
• It randomly selects 5 classes and surveys
all the students in each class.

5. Systematic Sampling
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Systematic sample
Sample every nth individual or item.
This avoids biases of only wanting to survey
friendly looking people.
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Example: Quality control obtains a
systematic sample of bottles from a factory.
They can start with the 3rd bottle, then
choose every 6th bottle after that.
Example: A business surveys every
3rd customer.

6. 1-6
A Convenience Sample is one in which the individuals in the sample are
easily obtained.
Convenience Samples are usually not representative of the whole population
2 types:
A. Friends and family (including social media)
B. Voluntary Response
• Internet polls
• Radio call-in
• People with strong opinions are more likely to respond than the general
population
Voluntary Poll Question Examples:
• “Is ice skating your favorite sport?”
• Who is most likely to respond?
•A political question
Convenience Sample
Not statistically valid.
End of Section