Chapter 7

The Logic Of Sampling

Chapter Outline Introduction A Brief History of Sampling Nonprobability Sampling The Theory and Logic of Probability

Sampling

Chapter Outline Populations and Sampling Frames Types of Sampling Designs Multistage Cluster Sampling Probability Sampling in Review

Political Polls and Survey Sampling In the 2004 Presidential election, pollsters

generally agreed that the election was “too close to call”.

To gather this information, they interviewed fewer than 2,000 people.

Election Eve Polls - U.S. Presidential Candidates, 2004

Date Begun

Agency Bush Kerry

10/28 Fox/OpinDynamics 50 50

10/28 TIPP 53 47

10/28 CBS/NYT 52 48

10/28 ARG 50 50

10/28 ABC 51 49

10/29 Fox/OpinDynamics 49 51

Election Eve Polls - U.S. Presidential Candidates, 2004

Date Begun

Agency Bush Kerry

10/29 Gallup/CNN/USA 51

10/29 NBC/WSJ 51 49

10/29 TIPP 51 49

10/29 Harris 52 48

10/29 Democracy Crops 49 51

10/29 CBS 51 49

Election Eve Polls - U.S. Presidential Candidates, 2004

Date Begun

Agency Bush Kerry

10/30 Fox/OpinDynamics 49 52

10/30 TIPP 51 49

10/31 Marist 50 50

10/31GWU Battleground

200452 48

11/2 Actual Vote 52 48

Bush Approval: Raw Poll Data

Question One of the most visible uses of survey

sampling lies in _____________.

A. political polling

B. probability sampling

C. core sampling

D. traditional polling

Answer: A One of the most visible uses of survey

sampling lies in political polling.

Observation and Sampling Polls and other forms of social research

rest on observations. The task of researchers is to select the

key aspects to observe (sample). Generalizing from a sample to a larger

population is called probability sampling and involves random selection.

Nonprobability Sampling Technique in which samples are selected

in a way that is not suggested by probability theory.

Examples include reliance on available subjects as well as purposive (judgmental), quota, and snowball sampling.

Types of Nonprobability Sampling Reliance on available subjects:

• Only justified if less risky sampling methods are not possible.

• Researchers must exercise caution in generalizing from their data when this method is used.

Types of Nonprobability Sampling Purposive or judgmental sampling

• Selecting a sample based on knowledge of a population, its elements, and the purpose of the study.

• Used when field researchers are interested in studying cases that don’t fit into regular patterns of attitudes and behaviors ( 非常態的態度與行為 )

Types of Nonprobability Sampling Snowball sampling

• Appropriate when members of a population are difficult to locate.

• Researcher collects data on members of the target population she can locate, then asks them to help locate other members of that population.

Types of Nonprobability Sampling Quota sampling

Begin with a matrix of the population. Data is collected from people with the

characteristics of a given cell. Each group is assigned a weight appropriate

to their portion of the population. Data should represent the total population.

Question ______________sampling occurs when

units are selected on the basis of prespecified characteristics.

A. snowball

B. quota

C. purposive

D. probability

Answer: B Quota sampling occurs when units are

selected on the basis of prespecified characteristics.

Informant Someone who is well versed in the social

phenomenon that you wish to study and who is willing to tell you what he or she knows about it.

Probability Sampling Used when researchers want precise,

statistical descriptions of large populations. 研究結果要能以精確統計描述母體。

A sample of individuals from a population must contain the same variations that exist in the population. 樣本的內在變異必須與母體相同。

Populations and Sampling Frames Findings based on a sample represent the

aggregation of elements that compose the sampling frame. 研究發現代表抽樣架構的元素集合。

Sampling frames do not always include all the elements their names imply. 遺漏的可能？

All elements must have equal representation in the frame. 所有元素在架構內具相等的代表性。

A Population of 100 Folks Sampling aims to

reflect the characteristics and dynamics of large populations.

Let’s assume our total population only has 100 members.

Sample of Convenience: Easy but Not Representative

Types of Sampling Designs Simple random sampling (SRS) Systematic sampling Stratified sampling

Representativeness Representativeness - Quality of a

sample having the same distribution of characteristics as the population from which it was selected. 諸特質在樣本中與母體具同樣分佈。

EPSEM - Equal probability of selection method. A sample design in which each member of a population has the same chance of being selected into the sample.

Question ______________describes a sample whose

aggregate characteristics closely approximate the aggregate characteristics of the population.

A. exclusionB. probability samplingC. EPSEMD. representativenessE. none of these choices

Answer: D Representativeness describes a sample

whose aggregate characteristics closely approximate the aggregate characteristics of the population.

Population The theoretically specified aggregation of

study elements. Study population - Aggregation of

elements from which the sample is actually selected.

Element - Unit about which information is collected and that provides the basis of analysis.

Random selection Each element has an equal chance of

selection independent of any other event in the selection process.

Sampling unit Element or set of elements considered for

selection in some stage of sampling.

Parameter Summary description of a given variable

in a population.

A Population of 10 People with $0–$9

The Sampling Distribution of Samples of 1 In this example, the

mean amount of money these people have is $4.50 ($45/10).

If we picked 10 different samples of 1 person each, our “estimates” of the mean would range all across the board.

Sampling Distributions

Sampling Distributions

Sampling Distributions

Sampling Distributions

Range of Possible Sample Study Results

Shifting to a more realistic example, let’s assume that we want to sample student attitudes concerning a proposed conduct code. ( 如學生行為守則 )

Let’s assume 50% of the student body approves and 50% disapproves - though the researcher doesn’t know that.

Results Produced by Three Hypothetical Studies

Assuming a large student body, let’s suppose we selected three different samples, each of substantial size.( 例如，三個樣本數都是 80 位學生 )

We would not expect those samples to perfectly reflect attitudes in the whole student body, but they should come close.( 平均值應該都相當接近 )

Statistic Summary description of a variable in a

sample. Parameter: Summary description of a

given variable in a population.

Sampling Error The degree of error to be expected of a

given sample design. 樣本統計偏離母群體母數的程度。

Confidence Level The estimated probability that a population

parameter lies within a given confidence interval.

Thus, we might be 95% confident(±1.96se) that between 35 and 45% of all voters favor Candidate A.

Confidence interval - The range of values within which a population parameter is estimated to lie.

Sampling Frame That list or quasi list of units composing a

population from which a sample is selected.

If the sample is to be representative of the population, it is essential that the sampling frame include all (or nearly all) members of the population.

The Sampling Distribution If we were to select a

large number of good samples, we would expect them to cluster around the true value (50%), but given enough such samples, a few would fall far from the mark.

Review of Populations and Sampling Frames: Guidelines

1. Findings based on a sample represent only the aggregation of elements that compose the sampling frame.

2. Sampling frames do not include all the elements their names might imply. Omissions are inevitable.

3. To be generalized, all elements must have equal representation in the frame.

Question A _______________ is the list or quasi list of

elements from which a probability sample is selected.

A. confidence levelB. confidence intervalC. sampling frameD. systematic sampleE. none of these choices

Answer: C A sampling frame is the list or quasi list of

elements from which a probability sample is selected.

Simple Random Sampling Feasible only with the simplest sampling

frame. Not the most accurate method available.

A Simple Random Sample

Systematic Sampling Slightly more accurate than simple

random sampling. Arrangement of elements in the list can

result in a biased sample.

Sampling ratio Proportion of elements in the population

that are selected.

Stratification Grouping of units composing a population into

homogenous groups before sampling. 抽樣前，將研究母群依據某分層的標準區分成同質的組別，如依據性別、年級將母體先分成同性別與同年級的組別。 ( 母體愈同質，抽樣誤差愈小 )

This procedure, which may be used in conjunction with simple random, systematic, or cluster sampling, improves the representativeness of a sample, at least in terms of the stratification variables.

Stratified Sampling Rather than selecting sample for

population at large, researcher draws from homogenous subsets of the population. 然後，依各同質的組別在母體中的比例，從中隨機抽出同比例的樣本。

Results in a greater degree of representativeness by decreasing the probable sampling error.

A Stratified, Systematic Sample with a Random Start.

Cluster Sampling A multistage sampling in which natural

groups ( 如村、里 ) are sampled initially with the members of each selected group being subsampled afterward.

Multistage Cluster Sampling Used when it‘s not possible or practical to

create a list of all the elements that compose the target population. 沒有所有樣本個體的名冊，但可以取得次群體的名冊；抽取次群體之後，可以取得次群體中的個體樣本名冊。

Involves repetition of two basic steps: listing and sampling.

Highly efficient but less accurate.

Probability Proportionate to Size (PPS) Sampling Sophisticated form of cluster sampling. Used in many large scale survey

sampling projects.

Weighting Giving some cases more weight than

others.

Probability Sampling Most effective method for selection of

study elements. Avoids researchers biases in element

selection. Permits estimates of sampling error.

Quick Quiz

1. Political polling rests on _____________.

A. subtle innuendos

B. field research

C. observations

D. none of these choices

Answer: C Political polling rests on observations.

2. _____________ sampling is often employed in field research whereby each person interviewed may be asked to suggest additional people for interviewing.

A. snowball

B. quota

C. purposive

D. probability

Answer: A Snowball sampling is often employed in

field research whereby each person interviewed may be asked to suggest additional people for interviewing.

3. ______________ is the general term for samples selected in accord with probability theory.

A. nonprobability analyses

B. correlation coefficients

C. probability sampling

D. none of these choices

Answer: C Probability sampling is the general

term for samples selected in accord with probability theory.

4. A____________ population is that aggregation of elements from which a sample is actually selected.

A. theoretical

B. small

C. large

D. concept

E. study

Answer: E• A study population is that aggregation of

elements from which a sample is actually selected.

Question

5. Cluster sampling may be used when it is impossible to compile an exhaustive list of the elements composing the target population.

A. True

B. False

Answer: True• Cluster sampling may be used when it is

impossible to compile an exhaustive list of the elements composing the target.