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Sampling . The Statistical Adventure Begins. Populations. Def: Census Sample Which is better? census? sample?. Step 1: Define the Target Population. Must be very specific: What is a user? What demographics matter? Are there geographic boundaries? What is the relevant time period?

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sampling

Sampling

The Statistical Adventure Begins

populations
Populations

Def:

Census

Sample

Which is better?

census?

sample?

step 1 define the target population
Step 1: Define the Target Population

Must be very specific:

What is a user?

What demographics matter?

Are there geographic boundaries?

What is the relevant time period?

What is an element?

step 2 specify a sampling frame
Step 2: Specify a Sampling Frame

Def:

Where can you get a sampling frame?

sample frame error
Sample Frame Error

List may not match the target population

over-registration

under-registration

step 3 selecting a sampling method
Step 3: Selecting a Sampling Method

Probability samples

example:

Non-probability samples

example:

what s the big deal
What’s the Big Deal?

Probability samples let us estimate _________

We can calculate a confidence interval

So, probability samples are more representative than non-probability samples.

true false

simple random sampling
Simple Random Sampling

Probability sample

Number each unit in the sampling frame

Pick ___ units using a random numbers table

NOT haphazard

take a simple random sample srs of n 3
Take a Simple Random Sample (SRS) of n=3

Element Attitude toward Motel 6

Natasha 6

Scotty 7

Kalie 4

Lynn 2

Gregory 8

Paul 4

John 7

stratified sample
Stratified Sample

Decide on stratification variable

Homogeneity with respect to the dependent variable w/in the group

Divide population into a few mutually exclusive and exhaustive strata

Take a SRS from each strata

proportionate stratified sample
Proportionate Stratified Sample

Choose sample from strata in same proportion as they are in the population

NOTE: Use when you have equal variance within the strata

Population Sample

Strata proportion proportion n=200

Fresh

Soph

Junior

Senior

disproportionate stratified sample
Disproportionate Stratified Sample

Take a larger sample from the strata with ________ variance

What is variance?

Exercise: Develop two populations with 8 elements each.

Population 1: high variance, low mean

Population 2: low variance, high mean

disproportionate stratified sample13
Disproportionate Stratified Sample

Population Sample

Strata Variance proportion proportion

Fresh

Soph

Junior

Seniors

why use stratified samples
Why use Stratified Samples?

Make sure that you include certain subgroups

More precise, IF we use the right stratification variable

margin of error is ___________

sampling distribution is __________

confidence intervals are __________

What is the right variable?

cluster sampling
Cluster Sampling

Divide population into lots of heterogeneous clusters

Take a SRS of clusters

Either:

Single stage: sample all elements in the selected clusters

OR

Multi-stage: take a SRS of elements in the selected clusters

why use cluster samples
Why use Cluster Samples

Cheap

Easy

Likely to be the way the sampling frame is set up

Problem

not precise, lacks statistical efficiency

non probability sample cannot estimate margin of error
Non-probability Sample: Cannot estimate margin of error

Convenience or accidental sample: select subjects because they are the most convenient or readily available

If the sample size is really large, we know we have a representative sample

true false

judgment or purposive sample
Judgment or Purposive Sample

Elements selected because they can serve the research purpose--they are believed to be representative

Snowball sample

quota sample
Quota Sample

Attempts to be representative by sampling characteristics in the same proportion as the population

Interviewer chooses sample

Are these representative? _____

step 4 determine the sample size
Step 4: Determine the Sample Size

Must take into consideration:

cost

time

industry standards

statistical precision

Discuss this in detail in the next chapter

step 5 select elements
Step 5: Select Elements

Actually collect the data

Clean-up the data - Editing

Put the data into the computer

characteristics of interest
Characteristics of Interest

Population

N

U (mu)

2 (sigma squared)

(sigma)

Sample

n

X (x bar)

Sx2

Sx

# of elements

Mean

Variance

Standard Deviation

step 6 estimate the characteristics of interest
Step 6: Estimate the Characteristics of Interest

Sample mean:

sum of the sample elements

X= number of elements in sample

Sample variance = Sx2

sum of deviations around the mean squared

sample size minus 1

sample standard deviation
Sample Standard Deviation

The square root of the sample variance = sx

Has a specific meaning

Think Chebychev’s Theorem

sampling error
Sampling Error

The difference between the :

population parameter

and the sample statistic

We look at confidence intervals to estimate this but not until the next chapter

non sampling error

Non-sampling Error

(i.e., all other kinds of errors except for sampling error!)

types of non sampling error
Sampling frame

Poor questions

Poor branching

Item non-response

Non-response

Interviewer bias

Interviewer cheating

Coding and editing problems

Types of Non-Sampling Error
which is the larger problem and why
Which is the Larger Problem? (and why)

Sampling error

Non-sampling error