An examination of graduate students' statistical judgments: Statistical and fuzzy set approaches

The present study examined how statistical significance levels are treated and interpreted by graduate students who use hypothesis-testing in their sc ientific investigation. To rest underlying psychological aspects of hypothe sis-testing, the idea of fuzzy set theory was employed to identify the unce rtain points in judgments. 34 graduate students in a psychology department made judgments about hypothetical statistical decisions. The results indica ted that (1) the majority of these students treated significance levels on a continuum and rated them according to the magnitude of statistical signif icance; (2) the subjects shifted their decisions based on the types of hypo thetical scenarios but not by the sample sizes; instead, they interpreted a smaller sample size as being less reliable. (3) The subjects frequently ch ose formally used statistical terms, e.g., Significant and Not Significant, more than graduated verbal expressions, e.g., Marginally Significant and B orderline Significant; and (4) the Fuzziness (degree of confidence in decis ion-making) was dependent on individuals and existed more in the critical p oints of transition where judgments are most difficult. The Fuzziness Index illustrated the subtle shifts of human decision-making patterns in statist ical judgments. Underlying decision uncertainties and difficulties can be i llustrated by functions generated from fuzzy set theory, which may more clo sely resemble human psychological mechanism. This integrative study of fuzz y set theory and behavioral measurements appears to provide a technique tha t is more natural for examining and understanding imprecise boundaries of h uman decisions.