4 About Numerical Values of Mental Ability (p. 29-30)

The Meaning of Numbers

Scores on tests are numerical values. The first important thing to understand about test scores is that, whatever the particular test of mental development used, the resultant numerical value represents a relative position. It does not indicate a dimension of absolute size. Psychological measurement differs in this sense from physical measurement. Consider these examples:

a) Physical Measurement (Arithmetical Ratio Scales)

If a table is measured as being five metres long and another table is measured as being ten metres long, then we can say that one table is twice the size of the other.

b) Psychological Measurement (Arithmetical Interval Scales)

If a child gets a test score of five and another child gets a test score of ten, we cannot say that one child has twice the ability of the other. The key difference between physical and psychological measuring scales is that the latter do not start from a zero value. The starting point for psychological measuring scales is some sort of expected standard against which an individual is measured. The most common standard for assessing mental development in children is the typical level of performance in "most" children of a certain age. The psychological starting, or zero point, is set at this "most" value. Thus, if we expect most children to get a score of between ten and twelve, the scores obtained by individual children will be compared to this expected standard. If a child scores eight, then clearly that child is below the expected standard, but how far below? What is the significance of two or three or four points below the expected standard? In order to answer these questions, it is necessary to understand more about the nature of psychological measurement.

Norm-Referenced Testing

The numerical value derived from a psychological test simply tells us how a specific child stands in relation to a peer group; how close the child’s score is to the majority that occupy a central position (the average) in the group, or how far away it is from the level at which the majority score. In other words, the numerical value is a measure of how much the score deviates from the achieved average range of the sampled group. The sampled group are referred to as the norm group. The norm group is the standard or benchmark against which we compare the performance of an individual child. The choice of norm group is therefore crucial. The norm group must be selected to be representative of whatever category of children we wish to compare the individual child against. For example, if we wish to compare the individual against all children in the UK, then our norm group must include the same range of variables that categorise all children in the UK in a similar percentage to that which exists in the total population. Variables might include age of child, education level of parent, ethnic group and many others. Understanding how the norm group performs on a test is a key part of the development of the test as well as key to subsequent interpretations of the test in practice.