ABSTRACT
This chapter introduces uses of probability spaces as models for common research designs. It starts with the conceptually simple that is, modeling measurement error and then progresses to a study design that may defy the usefulness of probability spaces as a modeling paradigm that is, modeling natural data generating processes for observational data. Perhaps the simplest scientific use of a probability space is to model the variability associated with measurement in the context of a fully controlled experiment of a deterministic process. Another use of probability spaces is to model uncertainty associated with random assignment of research subjects to experimental conditions. Consequently, multiple experiments with random variables having the same distribution are typically used so that statistics are available to estimate desired quantities. The chapter begins by specifying the population as the outcome set, the power set as the event set, and a probability modeling nature's selecting of individuals.
