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#### Presentation Transcript

**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.
Sample
A relatively small subset from a population.
Example
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
randomly
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.
Problems
not random
not everyone has the same probability
only first row has any chance
Sample the labels: Choose 5 volunteers.
Problem
not everyone has the same probability
favors extroverts
Sample the labels: Choose 5 people without a system
Problem
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)
Election result
What went wrong?

**10. **Myth: Simple random samples are “representative” Actually can be quite different from population
But
we can usually place bounds on the difference

**11. **Notation

**12. **Population

**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
has
mean
and standard deviation
a.k.a. standard error
Implications
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
we expect
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”