7-1 Chapter Seven SAMPLING DESIGN

7-2 Selection of Elements Population Element the individual subject on which the measurement is taken; e.g., the population unit, case, or record. Population is the total collection of elements about which we wish to make some inferences. Sampling the process of selecting some elements from a population to represent the population as a whole Census a count of all the elements in a population.

7-3 Why Sample? Lower Cost Greater Accuracy of Results Deming suggests, “Sampling possesses the possibility of better interviewing (testing), more thorough investigation of missing, wrong, or suspicious information, better supervision, and better processing than is possible with complete coverage.” Greater Speed of Data Collection Availability of Population Element test the breaking strength of materials the population is infinite A census is (1) feasible when the population is small and (2) necessary when the elements are quite different from each other

7-4 What is a Good Sample? Validity of a sample depends on two considerations: accuracy and precision Accurate: absence of bias one of the considerations in determining sample validity: the degree to which bias is absent from the sample--the underestimators and the overestimators are balanced among members of the sample (i.e. no systematic variance). e.g., homes on the corner, 1936 Literary Digest Precise estimate: sampling error one of the considerations in determining sample validity: the degree to which estimates from the sample reflect the measure taken by a census; measured by the standard error of the estimate--the smaller the error, the greater the precision of the estimate.

7-5 Sampling Design within the Research Process Exhibit 7-1. Sampling Design within the Research Process Exhibit 7-2 Types of Sampling Designs

7-6 Types of Sampling Designs Representation Probability sampling: based on the concept of random selection – a controlled procedure that assures that each population element is given a known nonzero chance of selection Nonprobability sampling: arbitrary (nonrandom) and subjective Element Selection Unrestricted: select individually and directly from the population Restricted: select with additional control Exhibit 7-2 Types of Sampling Designs

7-7 Steps in Sampling Design What is the relevant population Good operational definitions are critical in choosing the relevant population. What are the parameters of interest? Population parameters are summary descriptors of variables (e.g. incidence, mean, variance) of interest in the population. Sample statistics are descriptors of the relevant variables computed from sample data. Sample statistics are used as estimators of population parameters The sample statistics are the basis of our inferences about the population. Exhibit 7-4.

7-8 Steps in Sampling Design What is the sampling frame? a list of elements in the population from which the sample is actually drawn. What is the type of sample? probability sample or nonprobability sample What size sample is needed? how large a sample should be a function of the variation in the population parameters under study and the estimating precision needed by the researcher. How much will it cost?

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7-10 Probability Sampling Designs Simple random sampling Systematic sampling ( 系統抽樣法 ) a complex probability sampling technique in which the population (N) is divided by the desired sample (n) to obtain a skip pattern (k). Using a random start between 1 - k, each k th element is chosen from the sample frame.

7-11 Probability Sampling Designs Stratified sampling ( 分層抽樣法 ) a probability sampling technique where the sample is constrained to include elements from each of the mutually exclusive segments or strata within a population –Proportionate a probability sampling technique in which each stratum is properly represented so the sample drawn from it is proportionate to the stratum's share of the population; higher statistical efficiency than a simple random sample –Disproportionate A probability sampling technique in which each stratum's size is not proportionate to the stratum's share of the population; allocation is usually based on variability of measures expected from the stratum, cost of sampling from a given stratum, and size of the various strata.

7-12 Probability Sampling Designs Cluster sampling ( 集群抽樣法 ) a sampling plan that involves dividing the population into clusters or subgroups of elements with some groups randomly selected for study. area sampling :a type of cluster sampling usually applied to a population with well-defined political or natural boundaries but without a detailed sample frame; population is divided into homogeneous clusters from which a single-stage or multistage sample is drawn.

7-13 Designing Cluster Samples How homogeneous are the clusters? Shall we seek equal or unequal clusters? How large a cluster shall we take? Shall we use a single-stage or multistage cluster? How large a sample is needed?

7-14 Probability Sampling Designs Double sampling ( 雙重抽樣法 ) a procedure for selecting a subsample from a sample for further study; i.e., sequential sampling or multiphase sampling. Exhibit 7-6

7-15 Nonprobability Sampling Reasons to use Procedure satisfactorily meets the sampling objectives Lower Cost Limited Time Not as much human error as selecting a completely random sample Total list population not available

7-16 Nonprobability Sampling Convenience Sampling a low-cost but less reliable nonprobability sample where element selection is unrestricted or left to those elements easily accessible by the researcher.

7-17 Nonprobability Sampling Purposive Sampling –Judgment Sampling a type of purposive sampling in which the researcher arbitrarily selects elements to conform to some criterion. –Quota Sampling a type of purposive sampling in which relevant characteristics are used to stratify the sample in an attempt to improve the representativeness of the sample. Snowball Sampling

7-18 Nonprobability Sampling Snowball Sampling a nonprobability sampling procedure in which initial sample elements, which may or may not have been chosen by probability techniques, refer to additional sample elements based on similar characteristics