Lecture 6 Who are we talking about? Populations and samples. Overview. Defining a populationTaking a simple random sampleHow similar is the sample to the population?. Population and Samples. Population All the cases (individuals, objects, or groups) in which the researcher is interested.Sample A relatively small subset from a population.ExampleThe US population: ~300 million peopleThe General Social Survey (GSS): a sample of the US populationabout 3,000 peopleStudent version of the GS273
1. Assignment After this lecture, start Assignment #3.
It’s in the course binder.
2. About 10 minutes short. Enough time for students to work an example.About 10 minutes short. Enough time for students to work an example.
3. Overview Defining a population
Taking a simple random sample
How similar is the sample to the population?
4. Population and Samples Population
All the cases (individuals, objects, or groups) in which the researcher is interested.
A relatively small subset from a population.
The US population: ~300 million people
The General Social Survey (GSS):
a sample of the US population
about 3,000 people
Student version of the GSS:
a sample from the GSS
about 1,500 people
5. The sampling problem We care about populations.
We can only afford to look at samples.
How do we know our sample is relevant?
6. Simple random sampling: Definition Define the population
label every person
Sample the labels
so everyone in the population has the same probability of being sampled
7. Simple random sampling: Example Define the population: this class=52 people
label every person: Give everyone a playing card
Sample the labels: Draw 5 cards from a second deck
randomly: after shuffling
so everyone in the population has the same probability of being sampled: Everyone’s card appears once in the deck.
8. Sampling: Bad examples Define the population: This class=52 people
label every person: Put everyone in a seat
Sample the labels: Choose 5 people from first row.
not everyone has the same probability
only first row has any chance
Sample the labels: Choose 5 volunteers.
not everyone has the same probability
Sample the labels: Choose 5 people without a system
Is it random?
9. Sampling: Presidential election, 1936 Literary Digest poll
Sampled 10 million names from lists of car and phone owners
Mailed 10 million questionnaires
Got 2.3 million responses
Results: 57% favor Landon (R), 43% favor Roosevelt (D)
What went wrong?
10. Myth: Simple random samples are “representative” Actually can be quite different from population
we can usually place bounds on the difference
13. Sampling error for a mean
14. Sampling variation
15. Conceptual definitions Sampling error – The sample mean is probably not the same as the population mean
Sampling variation – Take a different sample, get a different sample mean.
16. Technical definitions Sampling error – The difference between the sample mean and the population mean.
Sampling variation – The variation of the sample mean from one sample to another.
17. Repeated sampling
18. Sampling distribution Sampling distribution of the mean— The distribution of sample means over all possible samples.
19. Mean of the sampling distribution
20. Variation of the sampling distribution
21. Standard error: Definition
22. Standard error shrinks with sample size
23. Sample mean usually within 2 SE’s of pop. mean
24. Summary: Sampling distribution of the mean Across all possible samples
and standard deviation
a.k.a. standard error
sample mean usually within 2 SEs of pop. mean
In newspapers, +/- 2 SEs is often called “margin of error”
larger samples have smaller SEs
25. Summary: More general If we take a simple random sample
from a well-defined population
that the sample mean
is “probably” “close” to the population mean
By “close” we mean “within 2 standard errors”
Larger samples have smaller standard errors.
Next time we’ll say what me mean by “probably”