Survey sampling Many of our behaviours and action are based on samples (could be of size one), for incidence, our like or dislike of a foreign dish. Would such a sample be representative of the whole population? How many should we try /samples to be drawn? Sample design determines the precision of estimates. It consists of both a sample selection plan and an estimation procedure. Population: The entire set of persons, objects, or events, which the researcher intends to study. Must specify the inclusion and exclusion criteria that define a pop s characteristics Sample: A subset of the pop, serves as the ref group for drawing inference about pop e.g. for quality control: a sample of items from the entire inventory In a survey: a sample of households Sampling: involves the selection of the sample from the population A good sample reflects the relevant characteristics and variations of the population No guarantee that a sample represents the pop Probability sampling procedures minimize bias and error in choosing a representative sample Sampling Theory Concepts population Target Population: The universe of interest, or reference population e.g. all learning disabled Accessible/experimental Population A population very close to the target population and can be assessed e.g. learning-disabled in a given city s school system Validity of the accessible pop is not readily testable, require good judgement and expertise Elements of a Population Individual units of a population When elements are persons, they are referred to as subjects 1
Sampling Criteria Characteristics essential for membership in the target population Representativeness An objective plan of selection, minimize bias Drop out Non-response Sampling Error Discrepancy between the true population parameter and the sample statistic. Random Variation Differences are due to chance, not human bias Systematic Variation Sampling bias occurs when individuals selected for a sample overrepresent or under-represent the population attributes that are related to the phenomenon under study, e.g. random sampling at the corner of a street (unconscious bias: haphazard sample) Randomization Obtain samples to represent the population Permits valid generalization of the findings of an investigation to the population (external validity : population validity) or other situations/settings (external validity : ecological validity) Random sample affords the greatest possible confidence in the sample s validity because in the long run, it will produce samples that most accurately reflect the population s characteristics Sampling Frame A listing of all members in the target (accessible) pop Subjects are selected from the sampling frame using a sampling plan Accessible population is usually defined according to available listing(s) Sampling Plans Define the process / strategies of making a sample selection 2
Sampling techniques Probability sampling methods Samples are created through a process of random selection Every element has a chance to be selected The sample is considered representative of the population Provides a mechanism to estimate sampling distribution and error Nonprobability sampling methods Degree of sampling error cannot be estimated Probability (Random) Sampling Methods / Schemes Simple random sampling Sampling without replacement Each selection is independent Each possible sample of a specified size of the population has equal chance of being selected The accessible pop is organized as a finite, pre-numbered list Blind draw, use of dice, random numbers Systematic sampling 1. Divide the total number of elements in the accessible pop by the number of elements to be selected: sampling interval (n) 2. Determine a starting point on the list at random 3. Now pick every n th element on the list from this starting point Considered equivalent to random sampling, as long as no recurring pattern or particular order exists in the listing Stratified random sampling Identify relevant population characteristics, then Partition members of a population into homogeneous non-overlapping strata (subsets) based on the identified characteristics Random or systematic samples are then drawn from each stratum Proportional stratified samples could be drawn to reflect pop composition Stratification increases the precision of estimates only when the stratification variable is closely related to the variables of experimental / study interest 3
Disproportional sampling Select random samples of adequate size from each category (for comparison) This may lead to over-representation of the characteristics of one group (stratum) in the pop Control this error by calculating proportional weights for strata Cluster sampling If it is impractical or impossible to obtain a complete listing of a large dispersed pop, then use cluster / multi-stage sampling For example, a random selection of province; within selected province, random selection of hospitals; within each selected hospital, a random selection of therapists Advantages: convenience and efficiency (time-wise) Price paid: increased sampling error because of the number of samples drawn, each subjected to error Examples used in survey: Area probability sampling (sampled geographically-> districts->households) Random-digit dialing (sample area-code->telephone exchanges); bias: can only reach those with phones; timing of calls Nonprobability (Nonrandom) Sampling Methods Generalization of data collected from nonrandom samples must be made with caution Keppel suggests that researchers can distinguish between o statistical (require random sampling and based on the validity of representativeness) and o nonstatistical generalization (justified on the basis of knowledge of the research topic, the logic of the study, and consistency in replicated outcomes). Convenience (Accidental) sampling Chosen on the basis of availability Potential bias of self-selection Not possible to assess the attributes that are present in those who offer themselves Unclear how these attributes affect the ability to generalize the study /experimental outcomes 4
Quota sampling A convenience sample with added feature: maintain a balance of specific characteristics For example: maintain a certain proportion of each gender Purposive sampling Researcher handpicks subjects OR use of groups of elements as sampling unit on the basis of specific criteria Generalization of results is limited to those who have these characteristics Snowball / Network sampling 1. When subjects with specific characteristics are hard to locate, a few subjects are identified 2. Interview /test the few subjects 3. These subjects further id others who have the requisite characteristics 4. A chain referral / snowballing / network referral until an adequate sample is obtained 5. Researcher must verify the eligibility of each respondent to ensure a representative group Sample Surveys Descriptive: For example, study the proportion of pop watching a certain TV program Analytical: for example, compare groups and employ stat techniques in order to estimate pop parameters Factors influencing Sample Sizes Sampling technique Estimation procedure Measurement sensitivity: precision Effect size: the extent of the presence of a phenomenon Study design influences power Number of variables Data analysis techniques (Chi-square test on association between categorical variables have weak power) Significance level 5
Conducting a Survey (from the perspective of sampling for estimation with specified precision) 1. Make a clear statement of objectives 2. Define the population to be sampled 3. List the relevant data to be collected 4. Specify the required precision of estimates 5. Determine well-defined sampling units (The list of sampling units is called a frame) 6. Determine the sampling scheme method of selecting the sample 7. Plan ahead how to handle non-response 8. Collect data 9. Summarize the data a. Take into consideration if there was large non-response b. If sample size is large, may apply central limit theorems c. If sample size is small, may wish to apply distribution free techniques 10. Proceed with sample estimation procedure (if appropriate) 11. Identify mistakes in the present survey for the benefit of future work. Reference: Govindarajulu, Zakkula (1999), Elements of Sampling Theory and Methods, Prentice-Hall, New Jersey. 6