7: The Logic of Sampling

Introduction• Nobody can observe everything• Critical to decide what to observe• Sampling

– Process of selecting observations• Probability sampling vs.

nonprobability sampling

History of Sampling• Developed hand in hand with

political polling• 1936: Literary Digest poll

– 10 million ballots were sent to people in telephone directories and automobile owner lists

– 2 million responded: 57% for Alf Landon, 43% for FDR

– Actual results: 61% for FDR

Nonprobability Sampling• Used when probability samples

can’t be selected• Four types:

1. Reliance on available subjects2. Purposive or judgmental sampling3. Snowball sampling4. Quota sampling

Reliance on Available Subjects

• Extremely risky - be cautious in generalizing

• Used frequently• Justified if:

– Want to study people passing the sampling point at a specified time

– Less risky methods are not feasible

Purposive or Judgmental Sampling

• May be appropriate to select sample based on judgment and purpose of study

• Used for pretests• Used to study a small subset of a

larger population• Used to study deviant cases

Snowball Sampling• Accidental sampling• Common in qualitative field

research• Appropriate when members of

special populations are hard to locate

• Collect data on a few members and then ask if they know others

• Used primarily for exploratory purposes

Quota Sampling• Addresses the issue of

representativeness• Matrix- describe characteristics of

population• Collect data from people having

characteristics of a given cell• Several problems

– Quota frame must be accurate– Biases may exist

Selecting Informants• Respondents

– People who provide information about themselves

• Informants – Members of the group who can talk

directly about the group• Select informants who are typical

of the groups

The Logic of Probability Sampling

• If everyone was the same…• But humans are quite different• Sample must contain same

variations that exist in the population

• Isn’t that simple and there are ways researchers mess up

Conscious and Unconscious Sampling

Bias• What happens when you select

people who are convenient for study?

• Personal leanings may affect the sample– May consciously or unconsciously

avoid interviewing certain people• Bias

– Those selected are not “typical” or “representative” of the larger population

Representativeness and Probability of Selection

• Sample is representative if…• Samples don’t have to be

representative in all respects: just to those characteristics relevant to the study

• EPSEM• Seldom perfectly represent the

population• Two advantages of probability

sampling1. More representative2. Permits us to estimate the accuracy of the

sample

Probability Sampling Theory

• The ultimate purpose of sampling• Probability sampling enhances

likelihood• Random selection

Sampling Distribution

Sampling Distribution• Sample size = 1

Sampling Distribution• Sample size = 2

Sampling Distribution• Sample size = 3 & 4

Sampling Distribution• Sample size = 5 & 6

Sampling Distribution

Sampling Distribution

Sampling Distribution• s= P x Q n• Contains 3 factors:

1. The population parameters (P & Q)2. The sample size (n)3. The standard error (s)

Sampling Distribution

Populations and Sampling Frames

• Less than perfect conditions exist in the field for sampling

• Sampling frame• Where can you get a list?• Omissions are inevitable

Types of Sampling Designs• Seldom choose simple random

sampling• Two reasons

1. Not feasible2. May not be most accurate method

Simple Random Sampling• Basic sampling method• Single number is assigned • Table of random numbers or

computer program

Systematic Sampling• Every kth element is chosen• First element selected at random

– Systematic sample with a random start

• Sampling interval• Sampling ratio• Virtually identical to SRS• Pay attention to the arrangement

of elements in the list

Stratified Sampling• Modification of two previous methods• Obtain a greater degree of

representativeness• Homogeneous subsets• Select number from each• Two methods of stratification

1. Sort into groups, select based on proportion of population

2. Put groups in continuous list, select systematic sample

Multistage Cluster Sampling

• Lists may not be available• Listing and sampling• Makes impossible studies possible• Highly efficient but less accurate

sample– Two sampling errors

• Stratification can be used• Probability proportionate to size

(PPS)• Disproportionate sampling and

weighting

Probability Sampling in Review

• Most effective method for the selection of study elements

• Avoids biases• Permits estimates of sampling

error