General introduction

Abstract

Research workers in the behavioural sciences often seek a better understanding of the relationship between two observed variables, by trying to discover whether the relationship can be explained by a third variable, in the sense that it disappears when this third variable is held constant. For example, it is very likely that in a sample of psychiatrically disturbed children, a positive correlation would be found between the amount of slow-wave activity in their EEGs and a measure of their hyperactivity. Here the obvious third variable which might account for this relationship is the age of the child, since it is well known that both the amount of slow-wave activity and the amount of hyperactivity decrease with increasing age. As a further example consider the data shown in Table 1.1, which relates survival of infants to amount of pre-natal care received. The usual chi-squared statistic for this table takes the value 5.26 which with 1 degree of freedom is significant beyond the 5% level, indicating that survival is related to the amount of care received. However, these data originally arose from two separate clinics as shown in Table 1.2. Analysing, firstly, only the data for clinic A we find that the chi-squared statistic is almost zero. Similarly, for the data from Clinic B, chi-squared is also approximately zero.