Statistical approaches to the assessment of necessary and sufficient conditions in the analysis of psychological data

If an outcome cannot occur unless a particular condition is present, then the condition is necessary for the outcome. If an outcome always occurs when a particular condition is present, then the condition is sufficient for the outcome. Given that the concepts of necessity and sufficiency pertain to unique kinds of relationships, it might be expected that the concepts would be used frequently in psychological research. A study of current research practice undertaken here, however, indicates that the terms necessity and sufficiency are used infrequently. In addition, an empirical study shows that subjects often have difficulty making inferences about necessary relationships and sufficient relationships. Psychological researchers usually examine relationships between continuous variables and may not be concerned with necessity and sufficiency because these concepts, traditionally, are defined in terms of dichotomous variables. It is argued, however, that the concepts of necessity and sufficiency can be defined in a way that makes the concepts applicable to continuous variables. A theoretical examination of several different data patterns suggest the following definitions. Let x...