1. Sampling

2. Sampling Probability Sampling Non-probability sampling
Based on random selection
Non-probability sampling
Based on convenience

3. Sampling Miscues: Alf Landon for President (1936)
Literary Digest: post cards to voters in 6 states
Correctly predicting elections from
Names selected from telephone directories and automobile registrations
In 1936, they sent out 10 million post cards
Results pick Landon 57% to Roosevelt 43%
Election: Roosevelt in the largest landslide
Roosevelt 61% of the vote and in Elect. Col.
Why so inaccurate?: Poor sampling frame
Leads to selection of wealthy respondents

4. Sampling Miscues: Thomas E. Dewey for President (1948)
Gallup uses quota sampling to pick winner
Quota sampling:
matches sample characteristics to characteristics of population
Gallup quota samples on the basis of income
In 1948, Gallup picked Dewey to defeat Truman
Reasons:
1. Most pollsters quit polling in October
2. Undecided voters went for Truman
3. Unrepresentative samples—WWII changed society since census

5. Non-probability Sampling
In situations where sampling frame for randomization doesn’t exist
Types of non-probability samples:
1. Reliance on available subjects
convenience sampling
2. Purposive or judgmental sampling
3. Snowball sampling
4. Quota sampling

6. Reliance on Available Subjects
Person on the street, easily accessible
Examples:
Mall intercepts, college students, person on the street
Frequently used, but usually biased
Notoriously inaccurate
Especially in making inferences about larger population

7. Purposive or Judgmental Sampling
Dictated by the purpose of the study
Situational judgments about what individuals should be surveyed to make for a useful or representative sample
E.g., Using college students to study third-person effects regarding rap and metal music
3pe: Others are more affected by exposure than self
Assessing effects on self and others
Using college students makes for homogeneity of self

8. Snowball Sampling
Used when population of interest is difficult to locate
E.g., homeless people
Research collects data from of few people in the targeted group
Initially surveyed individuals asked to name other people to contact
Good for exploration
Bad for generalizability

9. Quota Sampling
Begins with a table of relevant characteristics of the population
Proportions of Gender, Age, Education, Ethnicity from census data
Selecting a sample to match those proportions
Problems:
1. Quota frame must be accurate
2. Sample is not random

10. Probability Sampling Goal: Representativeness Random selection
Sample resembles larger population
Random selection
Enhancing likelihood of representative sample
Each unit of the population has an equal chance of being selected into the sample

11. Population Parameters
Parameter: Summary statistic for the population
E.g., Mean age of the population
Sample is used to make parameter estimates
E.g., Mean age of the sample
Used as an estimate of the population parameter

12. Sampling Error
Every time you draw a sample from the population, the parameter estimate will fluctuate slightly
E.g.:
Sample 1: Mean age = 37.2
Sample 2: Mean age = 36.4
Sample 3: Mean age = 38.1
If you draw lots of samples, you would get a normal curve of values

13. Normal Curve of Sample Estimates
Frequency of estimated means
from multiple samples
Likely population
parameter
Estimated Mean

14. Standard Error
The average distance of sample estimates from the population parameter
68% of sample estimates will fall within in one standard error of the population parameter

15. Normal Curve of Sample Estimates
Frequency of estimated means
from multiple samples
Population
parameter
1 standard
error unit
Estimated Mean

16. Normal Curve of Sample Estimates
2/3 of samples
Frequency of estimated means
from multiple samples
Population
parameter
1 standard
error unit
Estimated Mean

17. Standard Error Estimates and Sample Size
As the sample size increases:
The standard error decreases
In other words, are sample estimate is likely to be closer to the population parameter
As the sample size increases, we get more confident in our parameter estimate

18. Confidence Levels
Two thirds of samples will fall within the standard error of the population parameter
Therefore: a single sample has a 68% chance of being within the standard error
Confidence levels:
68% sure estimate is within 1 s.e. of parameter
95% sure estimate is within 2 s.e. of parameter
99% sure estimate is within 3 s.e. of parameter

19. Confidence Interval
Interval width at which we are 95% confident contains the population parameter
For example, we predict that Candidate X will receive 45% of the vote with a 3% confidence interval
We are 95% sure the parameter will be between:
42% and 48%
Confidence interval shrinks as:
Standard error is smaller
Sample size is larger

21. Sample Size & Confidence Interval
How precise does the estimate have to be?
More precise: larger sample size
Larger samples increase precision
But at a diminishing rate
Each unit you add to your sample contributes to the accuracy of your estimate
But the amount it adds shrinks with additional unit added

22. 95% Confidence Intervals
Sample Size
% split
N = 100
N = 200
N = 300
N = 400
N = 500
N = 700
N = 1000
N = 1500
50/50
10.0
7.1
5.8
5.0
4.5
3.8
3.2
2.6
70/30
9.2
6.5
5.3
4.6
4.1
3.5
2.9
2.4
90/10
6.8
4.2
3.0
2.7
2.3
1.9
1.5

23. Sampling Frame List of units from which sample is drawn
Defines your population
E.g., List of members of organization or community
Ideally you’d like to list all members of your population as your sampling frame
Randomly select your sample from that list
Often impractical to list entire population

24. Sampling Frames for Surveys
Limitations of the telephone book:
Misses unlisted numbers
Class bias:
Poor people may not have phone
Less likely to have multiple phone lines
Most studies use a technique such as Random Digit Dialing as a surrogate for a sampling frame

25. Types of Sampling Designs
Simple Random Sampling
Systematic Sampling
Stratified Sampling
Multi-stage Cluster Sampling

26. Simple Random Sampling
Establish a sampling frame
A number is assigned to each element
Numbers are randomly selected into the sample

27. Systematic Sampling Establish sampling frame
Select every kth element with random start
E.g., 1000 on the list, choosing every 10th name yields a sample size of 100
Sampling interval: standard distance between units on the sampling frame
Sampling interval = population size / sample size
Sampling ratio: proportion of population that are selected
Sampling ratio = sample size / population size

28. Stratified Sampling
Modification used to reduce potential for sampling error
Research ensures that certain groups are represented proportionately in the sample
E.g., If the population is 60% female, stratified sample selects 60% females into the sample
E.g., Stratifying by region of the country to make sure that each region is proportionately represented

29. Two Methods of Stratification
1. Sort population in groups
Randomly select within groups in proportion to relative group size
2. Sort population into groups
Systemically select within groups using random start
Disproportionate stratification:
Some stratification groups can be over-sampled for sub- group analysis
Samples are then weighted to restore population proportions

30. Cluster Sampling
Frequently, there is no convenient way of listing the population for sampling purposes
E.g., Sample of Dane County or Wisconsin
Hard to get a list of the population members
Cluster sample
Sample of census blocks
List of people for selected census block
Select sub-sample of people living on each block

31. Multi-stage Cluster Sample
Cluster sampling done in a series of stages:
List, then sample within
Example:
Stage 1: Listing zip codes
Randomly selecting zip codes
Stage 2: List census blocks within selected zip codes
Randomly select census blocks
Stage 3: List households on selected census blocks
Randomly select households
Stage 4: List residents of selected households
Randomly select person to interview

32. Multi-stage Sampling and Sampling Error
Error is introduced at each stage
One solution is to use stratification at each stage to try to reduce sampling error