The Determination of the Optimal Sample Size for Reliability Scales in Social Sciences

In many areas of research, the precise measurement of hypothesized processes or variables (theoretical constructs, latent variables) poses a challenge by itself. In social sciences, unreliable measurements of people’s beliefs or intentions obviously hamper efforts to predict their behavior. Each measurement (response to an item) reflects to some extent the true score for the intended concept and to some extent esoteric, random error. It can be expressed in an equation as: ε τ + = Χ , where Χ refers to the respective actual measurement, that is subject’s response to a particular item, τ is commonly used to refer to the true score and ε refers to the random error component in the measurement. An index of reliability can be defined in terms of the proportion of true score variability that is captured across subjects or respondents, relative to the total observed variability. This can be written as follows: 2 ) ( 2 ) ( / Re observed total score true liability σ σ = . Α measurement is reliable if it reflects mostly true score, relative to the error. The most widely used estimator of the above mentioned index is provided by Cronbach’s alpha [Cronbach (1951)]. The aim of this study is the determination of the optimal sample size to estimate the probability that Cronbach’s alpha exceeds a prespecified desirable level of accuracy. The Bayesian point of view is employed.