1. 4.1 (Day 2)

2. Other Sampling Methods
Last week we talked about simple random samples
Simplest way to eliminate bias
Sometimes, however, there are factors that make more complex sampling methods more appealing
Taking an SRS is too difficult/expensive
We are not convinced that an SRS will actually give is a representative sample

3. Stratified Random Sample
Probably the most commonly used sampling method
Instead of sampling from the entire population, you divide the population into sub-groups (“strata”)
You then randomly sample from each of these strata
Combine these “sub-samples” together to form your overall sample

4. Stratified Random Sampling
Taking an SRS is too difficult/expensive
We are not convinced that an SRS will actually give is a representative sample
Which of these problems is Stratified Random Sampling fixing?

5. Stratified Random Sampling
Taking an SRS is too difficult/expensive
We are not convinced that an SRS will actually give is a representative sample
Which of these problems is Stratified Random Sampling fixing? #2
Sidenote: do NOT abbreviate stratified random sampling as SRS
SRS always means simple random sample

6. Stratified Random Sampling
When is it most commonly used?
Commonly used to make sure that important groups are all represented
Income
Race/ethnicity
Gender
Age
Etc.

7. Downsides to Stratified Random Sampling

8. Downsides to Stratified Random Sampling
Harder/more expensive than SRS
You have to know in advance who falls into which strata
You have to know how many to sample from each strata to make it representative

9. Cluster Sampling
Cluster sampling is a solution to the other problem: that SRS can be expensive/difficult
Particularly if your population is large and/or very spread out, it is difficult to use SRS or stratified random sampling
These methods are also very difficult to use if you cannot easily identify each individual in your population
Think of the trees in the forest

10. Cluster Sampling to the Rescue
The procedure for carrying out a cluster sample is similar to a stratified random sample
First divide the population into smaller groups (or “clusters”)
So far this sounds exactly like stratified random sampling
But now we are not dividing into different groups to try to make it representative, but instead we are dividing into groups that can be readily found together
Homerooms
Neighborhoods
50x50 sections of the forest

11. Cluster Sampling to the Rescue
But now we are not dividing into different groups to try to make it representative, but instead we are dividing into groups that can be readily found together
Homerooms
Neighborhoods
50x50 sections of the forest
Then we randomly select which clusters to sample
Typically, once a cluster is selected, ALL individuals in the cluster are included in the sample
Occasionally you may choose to then take an SRS within each cluster

12. Cluster Sampling
As with stratified random sampling, we then combine the clusters back together to form our overall sample
So cluster sampling is NOT necessarily making our sample more representative than an SRS
But it is, in some cases, making it easier to perform and more cost/time effective

13. The Stratified/Cluster Sample Hybrid
On a test, a given method will clearly be an SRS, a stratified random sample, or a cluster sample
But in practice, there is some overlap between cluster samples and stratified random samples
You may even use such a hybrid later this semester

14. The Stratified/Cluster Sample Hybrid
But in practice, there is some overlap between cluster samples and stratified random samples
You may even use such a hybrid later this semester
For example, if my population is citizens of the United States, it would be too difficult to take an SRS
So I decide to use a cluster sample to make it easier
But I want to make sure that people in both smaller cities/towns (under 40,000 people) and bigger cities (over 40,000 people) are represented

15. The Stratified/Cluster Sample Hybrid
For example, if my population is citizens of the United States, it would be too difficult to take an SRS
So I decide to use a cluster sample to make it easier
But I want to make sure that people in both smaller cities/towns (under 40,000 people) and bigger cities (over 40,000 people) are represented
So I decide to randomly sample individual from 10 big cities, and 5 smaller cities

16. The Stratified/Cluster Sample Hybrid
So I decide to randomly sample individual from 10 big cities, and 5 smaller cities
Notice that I have clustered by city
But also stratified by size of the city
So this is not a pure stratified random sample, and not a pure cluster sample—it is a hybrid
Your book (as far as I know) does not really talk about this, but I just wanted you to be aware of it

18. Inference Why random sampling? Let’s do an activity
I have 3 decks of cards
One at a time, come shuffle a deck, then pick 5 cards from a deck
Then put them back in the deck
Then record on the (left) dotplot what percentage were red
What does it look like?

19. Inference Why random sampling? Let’s do an activity
I have 3 decks of cards
Now pick 10 cards
Then record on the (middle) dotplot what percentage were red
What does it look like?

20. Inference Why random sampling? Let’s do an activity
I have 3 decks of cards
Now pick 20 cards
Then record on the (right) dotplot what percentage were red
What does it look like?

21. Inference What did this activity tell us?
What does it imply for random sampling?

22. Random Sampling
Random sampling works so well because each individual is equally likely to be chosen
Each card was equally likely to be chosen
As the sample gets larger, it comes closer and closer to representing the entire population

23. Margin of Error Each sample has a margin of error
Sets bounds for the likely potential range of the true population value based on the sample

24. Sample Surveys: What Can Go Wrong?
Undercoverage occurs when some groups in the population
are left out of the process of choosing the sample.
Nonresponse occurs when an individual chosen for the sample
can’t be contacted or refuses to participate.
A systematic pattern of incorrect responses in a sample survey
leads to response bias.
The wording of questions is the most important influence on
the answers given to a sample survey.

25. Wording of the Question
“Since they are breaking the law, should illegal immigrants be deported?”
“Should illegal immigrants be deported?”
“Despite holding jobs and helping the US economy, should illegal immigrants be deported?”

26. Order of the Questions
A series of two questions were asked to college students as part of a larger survey. The order of the two questions was randomly assigned
Order #1:
“How happy are you with your life in general? (on a scale of 1 to 5)”
“How many dates have you been on in the past month?”
This order found almost no correlated between happiness and number of dates

27. Order of the Questions Order #2:
“How many dates have you been on in the past month?”
“How happy are you with your life in general? (on a scale of 1 to 5)”
This order found a moderately strong positive correlation between happiness and number of dates
Sometimes the answer to one question changes the answer to another—so even the order can matter

28. Surveys Moral of the story:
There are lots of ways to create bias in a survey
You will explore these in the first semester project
In general, if you want unbiased results:
Be careful with your wording—make sure that the questions are as neutral as possible
Try not to put questions near each other that would affect the answer to the other
Make your sample as representative as possible
It is HARD to know for sure that you’re not getting bias—but you can take precautions
It is EASY to intentionally create bias
But this makes it more PROPAGANDA than statistics

29. The End