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### 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.

Question

- One of the most visible uses of survey sampling lies in _____________.
- political polling
- probability sampling
- core sampling
- 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.
- snowball
- quota
- purposive
- 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.

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.
- exclusion
- probability sampling
- EPSEM
- representativeness
- 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.

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.

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

- Findings based on a sample represent only the aggregation of elements that compose the sampling frame.
- Sampling frames do not include all the elements their names might imply. Omissions are inevitable.
- 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.
- confidence level
- confidence interval
- sampling frame
- systematic sample
- 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.

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.

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.

1. Political polling rests on _____________.

- subtle innuendos
- field research
- observations
- 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.

- snowball
- quota
- purposive
- 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.

- nonprobability analyses
- correlation coefficients
- probability sampling
- 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.

- theoretical
- small
- large
- concept
- 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.

- True
- False

Answer: True

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

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