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sampling

This document defines key terms related to sampling design and methods. It discusses the differences between populations, target populations, and accessible populations. It also defines samples, sampling frames, strata, random selection, and representativeness. The document outlines several probability sampling methods, including simple random sampling, stratified random sampling, cluster sampling, and systematic sampling. It also discusses non-probability sampling methods like convenience sampling, purposive sampling, and quota sampling.

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SAMPLING DESIGN Geethakumary.V.P.
SAMPLING -TERMS  SAMPLING THEORY-is a mathematical method of decision making for determining the most efficient means of selecting a sample that represent the population under study
SAMPLING -TERMS Population : Is a group whose members possess specific attributes that a researcher is interested in studying. Population is the entire aggregation of cases that meet a designed set of criteria. May consist of events, places, objects, animals or individuals
Sampling -terms Target Population : is the population under study / The population to which the researcher wants to generalize the findings. Is the entire set of individuals or elements who meet the sampling criteria. Accessible Population : is that part of target population that is available to the researcher.
SAMPLE  A portion of the population that has been selected by the researcher to represent the population of interest.  Sample consists of a subset of the units that compose the population.  Element : Is a single member of the population under study. (Subject / Participant )
SAMPLING -TERMS  Sampling criteria/eligibility criteria –sampling criteria list the characteristics essential for membership in target population. The criteria that specify characteristics that the people must possess to be included into the sample. Inclusion criteria Exclusion criteria : The criteria that the subjects must not possess.
Sampling criteria/eligibility criteria Reflect considerations other than substantive or theoretical interest  Cost  Practical constraints  Peoples ability to participate in the study  Design considerations
SAMPLING -TERMS  REPRESENTATIVENESS-means that the sample must like the population in as many ways as possible  Representativeness – is how well the sample represents the variables of interest in the target population  Representative sample is one whose key characteristics closely approximate those of population  If sample is not representative ,external validity is at risk
REPRESENTATIVENESS contd  No way make sure that a sample is representative without obtaining information from population.  Certain sampling procedures are less likely to result in biased samples than others ,but representativeness can never be guaranteed.  Minimise error and if possible estimate their magnitude.
SAMPLING -TERMS Sampling frame : A comprehensive list of all the sampling elements in the target population. Strata : A stratum refers to a mutually exclusive segment of a population established by one or more characteristics.
SAMPLING –TERMS contd  Random selection : Is a process of selecting a representative sample of the target population. The purpose of which is to ensure that every element in the target population has an equal, independent non- zero chance of being selected for inclusion in the study.
SAMPLING –TERMS contd  Sampling frame : A comprehensive list of all the sampling elements in the target population  Strata : A stratum refers to a mutually exclusive segment of a population established by one or more characteristics
SAMPLING -TERMS Statistic and parameter information collected from a sample is called statistic information collected from a population is called a parameter Data –data are information collected from a source
SAMPLING -TERMS  Sampling error –is the difference or error between the sample statistic and the population parameter-estimated statistically by calculating the standard error.  Standard error –is the measurement of the standard deviation between a sample measure and a population measure.
SAMPLING -TERMS Standard error random variation –expected difference in value of different subjects from the same sample systematic variation –exclusion criteria tend to increase the systematic bias in sample
SAMPLING -TERMS  Sampling bias –occurs when the researcher shows a preference in selecting one participant over the another. Systematic over representation of segment of the population in terms of a characteristics relevant to the research question.
Sampling Design
Why Sample?  Why not study everyone?  Census vs. sampling
Why sampling?  Sampling reduces demands on resources -finance, manpower, materials.  Reduces duration of study.  Sampling may be the feasible method.  Ethically sampling is the only permitted method  Sometimes increases accuracy(non sampling errors and non response rate can be kept minimal)
Quantitative studies  Seek to select samples that allow them to generalize their results to broader groups  Sampling plan that specifies the number & method of selection, in advance
Qualitative studies  Not concerned with issues of generalizability  Concerned with holistic understanding of the phenomenon of interest  Sampling decisions are based on informational & theoretical needs  Do not develop a formal sampling plan in advance
Sampling plan  Describes the strategies that will be used to obtain a sample for the study  Developed to Enhance representativeness Reduce systematic bias Decrease sampling error  Provides details of the use of a sampling method in a specific study  Must be described in detail for purpose of critique, replication & meta analyses
Types of Sampling Probability Non-Probability
Probability Sampling methods  Random selection in choosing elements  Researcher can specify the probability that each element of the population will be included in the sample  More respected of the two approaches because of greater confidence in their representativeness
Probability Sampling  Is a random method of selecting participants in a research study who are the most representative of the population  Involves a selection process in which each element in the population has an equal, independent chance of being selected
Probability Sampling  Cannot guarantee “representativeness” on all traits of interest  A sampling plan with known statistical properties  Permits statements like: “The probability is .99 that the true population correlation falls between .46 and .56.”
Probability Samples  A probability sample is one in which each element of the population has a known non-zero probability of selection.  Not a probability sample if probabilities of selection are not known.
Types of Sampling Probability  Simple Random  Stratified Random  Cluster sampling  Systematic sampling
Types of Sampling Probability  Simple Random  Systematic Random  Stratified Random  Random Cluster  Complex Multi-stage Random (various kinds)  Stratified Cluster
Simple random sampling  The most basic of probability sampling designs  Each element has independent chance for being included in to the study group  Requires complete list of the accessible population  One stage selection process
Steps of simple random sampling
Advantages  The randomness offers the advantage of being the most representative  The only viable method of obtaining representative sample in quantitative studies  Allows for the use of inferential statistics  Allows more accurate generalization to the target population  Allows the researcher to estimate the magnitude of sampling error
Advantages Eliminates researcher bias Requires limited knowledge about the population Provides a means of estimating the sampling error
Stratified random sampling A variant of simple random sampling in which the population is first divided into 2 or more strata or subtypes Used to increase the representativeness of different groups within the population Subdivides the population in to homogenous subjects from which an appropriate number of elements can be selected at random
Stratified Random Sampling-1  Divide population into groups that differ in important ways  Basis for grouping must be known before sampling  Select random sample from within each group
Stratified Random Sampling  For a given sample size, reduces error compared to simple random sampling if the groups are different from each other  Probabilities of selection may be different for different groups, as long as they are known  Over sampling small groups improves inter group comparisons
Proportional stratified random sampling  A method of increasing the representativeness of the variable in the sample  The number of subjects taken from each stratum would be proportional to the number in the population
Advantages More representative Greater accuracy Greater geographic concentration Decreased sampling error, power increased, data collection time reduced
Disadvantages It requires extensive knowledge of the population under study to stratify it accurately A complete list of target population is needed It can quickly become very complex Knowledge of advanced statistical methods & or assistance of a sampling consultant will be needed
Disproportional stratified random sampling Disproportional stratified random sampling In this sampling method the number of subjects in each stratum would not be proportional to the number in the population
Cluster sampling Suitable when the study population is large Takes place in stages –Multistage sampling The researcher begins with the largest most inclusive sampling unit , then progresses to the next most inclusive unit until the final stage i.e.. The stage from which the study subjects are randomly drawn to the sample Involves successive random sampling of
Research Example
Cluster sampling Merits  Economical and time saving  It allows probability sampling for a population that is not listed in the sampling frame  Flexibility in the sampling method-existing divisions/subdivisions can be used
Cluster sampling Limitations  less accurate  possibility of sampling error in each stage
Systematic Sampling Can be a probability or non-probability sampling To be a probability sampling design, the elements in the sampling frame need to be listed randomly Involves the selection of every kth from the sampling frame The sampling interval, k= N/n Where N is the accessible population & n is the sample size
Systematic Random Sampling  Each element has an equal probability of selection, but combinations of elements have different probabilities. Population size N, desired sample size n, sampling interval k=N/n.  Randomly select a number j between 1and k, sample element j and then every kth element thereafter, j+k, j+2k, etc.  Example: N=64, n=8, k=64/8=8. Random j=3.
Systematic Random Sampling  Each element has an equal probability of selection, but combinations of elements have different probabilities. Population size N, desired sample size n, sampling interval k=N/n.  Randomly select a number j between 1and k, sample element j and then every kth element thereafter, j+k, j+2k, etc.  Example: N=64, n=8, k=64/8=8. Random j=3.
Systematic Random Sampling  Has same error rate as simple random sample if the list is in random or haphazard order  Provides the benefits of implicit stratification if the list is grouped
Systematic Random Sampling  Runs the risk of error if periodicity in the list matches the sampling interval  This is rare.  In this example, every 4thelement is red, and red never gets sampled. If j had been 4or 8, ONLY reds would be sampled.
Random Cluster Sampling  Done correctly, this is a form of random sampling  Population is divided into groups, usually geographic or organizational  Some of the groups are randomly chosen  In pure cluster sampling, whole cluster is sampled.  In simple multistage cluster, there is random sampling within each randomly chosen cluster
Random Cluster Sampling  Population is divided into groups  Some of the groups are randomly selected  For given sample size, a cluster sample has more error than a simple random sample  Cost savings of clustering may permit larger sample  Error is smaller if the clusters are similar to each other
Random Cluster Sampling -  Cluster sampling has very high error if the clusters are different from each other  Cluster sampling is NOT desirable if the clusters are different  It IS random sampling: you randomly choose the clusters  But you will tend to omit some kinds of subjects
Stratified Cluster Sampling  Reduce the error in cluster sampling by creating strata of clusters  Sample one cluster from each stratum  The cost-savings of clustering with the error reduction of stratification
Stratification vs. Clustering Stratification  Divide population into groups different from each other: sexes, races, ages  Sample randomly from each group  Less error compared to simple random  More expensive to obtain stratification information before sampling Clustering  Divide population into comparable groups :schools, cities  Randomly sample some of the groups  More error compared to simple random  Reduces costs to sample only some areas or organizations
Stratified Cluster Sampling  Combines elements of stratification and clusteringFirst you define the clusters  Then you group the clusters into strata of clusters,putting similar clusters together in a stratum  Then you randomly pick one (or more) clusterfrom each of the strata of clusters  Then you sample the subjects within the sampledclusters (either all the subjects, or a simple random sample of them)
Multi-stage Probability Samples  Large national probability samples involve several stages of stratified cluster sampling  The whole country is divided into geographic clusters, metropolitan and rural  Some large metropolitan areas are selected with certainty (certainty is a non-zero probability!)  Other areas are formed into strata of areas (e.g. middle-sized cities, rural counties); clusters are selected randomly from these strata
 Within each sampled area, the clusters are defined, and the process is repeated, perhaps several times, until blocks or telephone exchanges are selected  At the last step, households and individuals within household are randomly selected  Random samples make multiple call- backs to people not at home.
Non-probability Sampling An alternative approach to probability sampling Each element in this study does not have an independent chance of being included in the study
Non Probability Sampling methods  Elements are selected by non random method  No way to estimate the probability that each element has of being included  Every element usually does not have a chance for inclusion  Less likely to produce accurate & representative sample
Non-probability Samples  • Convenience  • Purposive  • Quota
Convenience Sampling Uses participants who are easily accessible to the researcher & who meet the criteria of the study Entails the use of the most conveniently available people / objects as subjects in a study Also known as Accidental sampling
Convenience Sampling Also called CHUNK refers to fraction of the population being investigated which is selected neither by probability nor by judgement but by convenience .
Convenience Sample  Subjects selected because it is easy to access them.  No reason tied to purposes of research.  Students in your class, people on State Street, friends
Convenience Sampling Advantages: Easy, Saves money & time Disadvantages: Potential for sampling bias, Limited generalizability of the results
Purposive Samples  Subjects selected for a good reason tied to purposes of research  Small samples < 30, not large enough for power of probability sampling.  Nature of research requires small sample  Choose subjects with appropriate variability in what you are studying  Hard-to-get populations that cannot be found through screening general population
Quota Sampling  Pre-plan number of subjects in specified categories (e.g. 100 men, 100 women)  In uncontrolled quota sampling, the subjects chosen for those categories are a convenience sample, selected any way the interviewer chooses  In controlled quota sampling, restrictions are imposed to limit interviewer’s choice  No call-backs or other features to eliminate convenience factors in sample selection
Quota Vs Stratified Sampling  In Stratified Sampling, selection of subject is random. Call-backs are used to get that particular subject.  Stratified sampling without call-backs may not, in practice, be much different from quota sampling.  In Quota Sampling, interviewer selects first available subject who meets criteria: is a convenience sample.  Highly controlled quota sampling uses probability sampling down to the last block or telephone exchange •But you should know the difference for the test!!
Snowball Sampling A particular type of convenience sampling Useful for studies in which the criteria for inclusion in the study specify a specific trait i.e. difficult to find by ordinary means In this early members are asked to identify & refer other people who meet the eligibility criteria Also known as Network sampling
Non-probability Sampling Advantages: Less complicated, less expensive& allows the researcher to be more spontaneous when research situation arises Disadvantages: Sample may not be a representative of the population, Cannot be generalized beyond the study sample & sampling error can not be estimated
STEPS IN SAMPLING  IDENTIFY THE POPULATION –IDENTIFY THE POPULATION – TARGET,ACCESSIBLETARGET,ACCESSIBLE  SPECIFY THE INCLUSION ANDSPECIFY THE INCLUSION AND EXCLUSION CRITERIAEXCLUSION CRITERIA  SPECIFY THE SAMPLING PLAN –SPECIFY THE SAMPLING PLAN – METHOD,SIZE.METHOD,SIZE.  IDENTIFY THE ELEMENTIDENTIFY THE ELEMENT
STEPS IN SAMPLING-Contd  RECRUIT THE SAMPLERECRUIT THE SAMPLE USE A SCREENING INSTRUMENTUSE A SCREENING INSTRUMENT IDENTIFY ELIGIBLE CANDIDATESIDENTIFY ELIGIBLE CANDIDATES GAIN COOPERATIONGAIN COOPERATION EnjoyableEnjoyable worthwhileworthwhile convenientconvenient pleasantpleasant nonthreateningnonthreatening
STEPS IN SAMPLING-Contd  RECRUIT THE SAMPLERECRUIT THE SAMPLE  RECRUITMENT METHODRECRUITMENT METHOD face to face more effectiveface to face more effective CourtesyCourtesy PersistencePersistence IncentivesIncentives Research benefitsResearch benefits Sharing resultsSharing results Endorsements, confidentiality assuranceEndorsements, confidentiality assurance
STEPS IN SAMPLING-Contd  RETAINING SUBJECTS get contact details reimbursement for participation bonus payment Use subjects time preciously Do not take for granted nurture subjects-refreshment, surrounding Maintain a pleasant climate
STEPS IN SAMPLING-Contd ENSURE THESE DO NOT INFLUENCE THE DATA
SAMPLE SIZE  No simple formula  Use the largest sample  Larger the sample more representative it is likely to be  Smaller sample tend to produce less accurate estimates than larger ones  Larger the sample smaller the sampling error
SAMPLE SIZE -contd  Size increases probability of deviant sample diminishes  Larger sample provide opportunity to counter balance atypical value  Larger sample are no assurance of accuracy  Large sample can harbor extensive bias
HOW TO ESTIMATE SAMPLE SIZE ? CONSIDER Main research question, outcome measure statistical procedure statistical and clinical assumption type 1,type 2 error- less; more subjects level of significance-high; more subjects precision - high ;more subjects one sides/two sides
HOW TO ESTIMATE SAMPLE SIZE ? CONSIDER  study constraints Availability of resources- finance material, manpower, logistic support, Time, Ethical consideration  level of significance, power and effect size
HOW TO ESTIMATE SAMPLE SIZE ? LEVEL OF SIGNIFICANCE –the more stringent the greater the necessary sample size POWER - is the capacity of the study to detect differences or relationships that actually exist in the population -is the capacity to correctly reject a null hypothesis
HOW TO ESTIMATE SAMPLE SIZE ? EFFECT SIZE Effect is the presence of a phenomenon  If a phenomenon exists;it exist to some degree  Effect size is the extent of the presence of a phenomenon
HOW TO ESTIMATE SAMPLE SIZE ?  It is easier to detect large difference  Smaller sample can detect large difference  Smaller effect size require large sample  Effect size is smaller with small samples and thus more difficult to detect  Increasing sample size increase effect size making it more likely that the effect will be detected  Extremely small effect size may not be
Factors determining sample size  Size of population  The resource available  The degree of accuracy or precision desired  Homogeneity / heterogeneity of population  Nature of the study  Sampling plan adopted
Factors determining sample size  Nature of respondent/attrition  Effect size –strength of relationship between variables  Subgroup analysis  Sensitivity of measures
Type of study  Qualitative & case studies: use very small samples, comparisons are not being made and sampling error & generalizations have little relevance
Type of study  Descriptive studies using survey questionnaires & correlational studies often require very large samples  Multiple variables are examined, extraneous variables
Type of study  Quasi & experimental studies must use sample size sufficient to achieve an acceptable level of power (.08) to reduce the risk of Type II error  These studies use controls & refined instruments, thus improving precision
Type of study  The study design influences power, but the design with the greatest power may not always be the most valid design to use
Number of variables  If the variables are highly correlated with the DV, the effect size will increase & sample size can be reduced  Therefore the variables in a study must be carefully selected  They should be essential to the question  Or should have a documented strong relationship with the DV
Measurement Sensitivity  As variance in instrument scores increases, the sample size needed to gain an accurate understanding of the phenomenon under study increases
Data analysis techniques  Large samples must be used when the power of the planned statistical analysis is low  For some procedures having equal group size increases power, because the effect size is maximized  The more unequal the group sizes are, the smaller the effect size. Therefore, in unequal groups the total sample size must be larger
Attrition  Number of subjects decline over time  More likely if time lag between data collection points is great  Mobile population, difficult to trace  Vulnerable or ‘at risk’ population  Anticipate loss of subjects over time
Sample Size  Heterogeneity: need larger sample to study more diverse population  Desired precision: need larger sample to get smaller error  Sampling design: smaller if stratified, larger if cluster  Nature of analysis: complex multivariate statistics need larger samples  Accuracy of sample depends upon sample size, not ratio of sample to population
Sampling in Practice  Often a non-random selection of basic sampling frame (city, organization etc.)  Fit between sampling frame and research goals must be evaluated  Sampling frame as a concept is relevant to all kinds of research (including non probability)  Non probability sampling means you cannot generalize beyond the sample  Probability sampling means you can generalize to the population defined by the sampling frame