Probability Sampling

  • Gideon J. MellenberghEmail author


A sampling method has four main elements. First, defining the population of interest (the target population). Second, constructing a list of the units of the target population (the sampling frame). Usually, the units of behavioral studies are humans. Third, sampling of units. A distinction is made between probability and nonprobability sampling. Fourth, obtaining participation of selected units. Incorrect definitions of the target population, incorrect lists of units, and nonparticipation of selected units are systematic errors that bias the study results. Procedures are described to increase the participation rate of selected persons. Probability sampling methods select units from the target population by a random procedure. Sample statistics (e.g., means, variances, and correlations) are computed to estimate corresponding population parameters. The estimation is affected by random errors, but is based on sound statistical theory. The precision of the estimates depends on the sample size and the sampling method. Methods to determine the sample size that is needed for a prespecified precision are discussed. A simple random sample is obtained by randomly selecting units without replacement from the target population. A stratified random sample is obtained by dividing the target population into subpopulations and randomly selecting units without replacement from each of the subpopulations. In practice, it is often more convenient and less expensive to select groups of units (clusters) instead of individual units. A cluster sample is obtained by randomly selecting clusters without replacement. A stratified random sample often increases the estimation precision compared to a simple random sample of the same size, whereas a cluster sample decreases the precision.


Cluster sample Intraclass correlation Missingness Post hoc stratification Proportional allocation Simple random sample Stratified random sample 


  1. Barnett, V. (1974). Elements of sampling theory. London, UK: The English University Press.Google Scholar
  2. Bethlehem, J. (1999). Cross-sectional research. In H. J. Adèr & G. J. Mellenbergh (Eds.), Research methodology in the social, behavioural & life sciences (pp. 110–142). London, UK: Sage.CrossRefGoogle Scholar
  3. Bethlehem, J. G. (2009). Applied survey methods: A statistical perspective. Hoboken, NJ: Wiley.CrossRefGoogle Scholar
  4. Czaja, R., & Blair, J. (2005). Designing surveys: A guide to decisions and procedures. Thousand Oaks, CA: Pine Forge Press.CrossRefGoogle Scholar
  5. Dillman, D. A. (1978). Mail and telephone surveys: The total design method. New York, NY: Wiley.Google Scholar
  6. Dillman, D. A., Smyth, J. D., & Christian, L. M. (2009). Internet, mail, and mixed-mode surveys: The tailored design method (3rd ed.). Hoboken, NJ: Wiley.Google Scholar
  7. Lynn, P. (2008). The problem of nonresponse. In E. D. de Leeuw, J. J. Hox, & D. A. Dillman (Eds.), International handbook of survey methodology (pp. 35–55). New York, NY: Erlbaum.Google Scholar
  8. Seaman, J. W., Jr., & Odell, P. L. (1988). Variance, upper bounds. In S. Kotz & N. L. Johson (Eds.), Encyclopedia of statistical sciences (Vol. 9, pp. 480–484). New York, NY: Wiley.Google Scholar
  9. Snedecor, G. W., & Cochran, W. G. (1967). Statistical methods (6th ed.). Ames, IA: The Iowa State University Press.Google Scholar
  10. Snijders, T. A. B., & Bosker, R. J. (1999). Multilevel analysis. London, UK: Sage.Google Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Emeritus Professor Psychological Methods, Department of PsychologyUniversity of AmsterdamAmsterdamThe Netherlands

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