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Field Research Methods. Lecture 4: Sampling & Sampling Error. Edmund Malesky, Ph.D., UCSD. Probability Sampling. Each element has a known, nonzero chance of being included in the sample. Selection bias is avoided

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Field Research Methods

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## Field Research Methods

Lecture 4:

Sampling & Sampling Error

Edmund Malesky, Ph.D., UCSD

### Probability Sampling

• Each element has a known, nonzero chance of being included in the sample.

• Selection bias is avoided

• Statistical theory can be used to derive properties of the survey estimators.

• Alternative is non-probability sampling (volunteers, convenience, expert selection)

• Highly subjective, precluding a theoretical framework for analysis.

### Organization

• The Sampling Frame

• Types of Sampling

• Sample Size

• Sampling Error

### 1. Tools

• A Definition of the Population you wish to study (i.e. households, firms, customers, foreign policy elites…)

• The sampling frame: More or less, a complete list of the individuals in the population to be studied.

• Lists can be obtained through census bureaus, tax offices, or other agencies.

• If a list does not exist, you will need to create one. This usually necessitates performing your own census or a a multi-stage research design, where the first stage is identification of the population.

• Sometimes the sampling frame will be individuals who went somewhere or did something, allowing them to be sampled (visits to the hospital, meeting attendance).

• In this case, be wary of selection bias. These individuals did not arrive in your population accidentally. They selected themselves into it (North Korean refugees in China, UCSD students….).

### Types of Sampling

• Simple Random Sampling – Each individual has the same probability of being selected.

### Types of Sampling

• Systematic Sampling – Divide the desired sample size by the population size (s/p). This will give you a selection ratio (100/8,500 = 1/85). Thus, 1 out of every 85 people should be selected. Select a starting point on the list and begin.

• Warning: If there is any pattern to the ordering of the list (age, name…), this will not work.

### Types of Sampling

• Stratified Random Sampling- Used when you are worried normal sampling variation will lead to unrepresentative sub-groups.

### Stratified Sampling

Simple Random Sampling: Will give me the percentage balls of a certain color (plus/minus 3%)

If I want to be more certain, I stratify and randomly sample within category

15% Yellow

10% Green

50% Blue

25% Red

=

### Type of Sampling

• Area (Cluster) Probability Sampling: Representative sample of geographical units, then individuals within unit.

• Two-Stage: Like clustering, except for random sample within group.

### Determining Sample Size

• In a Simple Random Sampling Design, we only need to know three things;

• The population size

• The variability of the parameter

• The desired level of precision & confidence

If you are interested in a proportion of the population substitute P(1-P) for S.

### Example (Iarossi, p. 100)

• Population = 650,000

• We are willing to accept a margin of error of 3%

• We decide we would like a 95% confidence interval.

• We assume that the residents are equally split between supporters and opponents.

• How to?

• More detail

### The Mystery of Margin Error

A joke from Joe Klein: “Prime Minister Ehud Olmert is testing the limits of the possible: in a recent poll by a local television station, he had a favorable rating of 3%. Given the poll's margin of error, it was possible Olmert had no support beyond his extended family."

### Sampling Error

• The potential variation due to measuring a sample rather than the entire population.

• The margin of error equals the confidence interval (usually produced by a 95% confidence level).

### Sampling Error

• Notice: Sampling Error Decreases when:

• Sample Size Increases

• The Estimated Proportion approaches 0 or 100% (usually assumed to be 50%)

• The Confidence Interval Gets Smaller

• Also Notice:

• Margin of Error is not a measure of other types of error (bias, non-response, measurement) – only sampling error.

• When comparing two candidates, the margin of error applies to both numbers.

### Remember

• With a 95% confidence interval, 1 out of every 20 times, our mean value will be outside the confidence interval.

• It is impossible to determine if the actual population results fall within the CI for the results of a particular survey.

• Blind roulette: Imagine a roulette wheel, where 95% of the slots are red. Each time we spin we know we have a 95% chance of hitting red. The problem with a survey is that we cannot see the colors.