Classification and Assessment of Error

I put this topic from Marketing Research, Methodological Foundations, 5th edition, The Dryden Press International Edition, author Gilbert A. Churchill, Jr. The idea in measurement is to generate a score that reflects true differences in the characteristic one is attempting to measure and nothing else. What we in fact obtain, is something else. A measurement, call it X0, for what is observed can be written as a function of several components:

X0 = Xt + Xs + Xr;

Where:
Xt = the true score of the characteristic being measured
Xs = systematic error
Xr = random error
The total error of measurement is given, by the sum of Xs and Xr.

Xs is systematic error, systematic error is also known as constant error, because it affects the measurement in a constant way. An example would be the measurement of a man’s height with a poorly calibrated wooden yardstick. Differences in other stable characteristic of the individual, which affect the person score, are a source of systematic error.

Xr is random error, random error is not constant error but, rather, is use to transient aspects of the person or measurement situation. A random error manifest itself in the lack of consistency of repeated or equivalent measurements when the measurement are made on the same object or person. An example would be the use of an elastic ruler to measure a man’s height. It is unlikely that on two successive measurements of observer would stretch the elastic ruler to the same degree of tautness and therefore, the two measures would not agree although the man’s height had not changed. Differences resulting from transient personal factors are an example of this type of error in psychological measurement.

The distinction between systematic error and random error is critical because of the way the validity of measure is assessed. Validity is synonymous with accuracy or correctness. The validity of measurement is defined as “the extent to which differences in scores on it reflects true differences among individuals on the characteristic we seek to measure, rather than constant or random errors. When a measurement is valid, X0 = Xt, since there is no error.

The problem is to develop measures in which the score we observe and record actually represents the true score of the object on the characteristic we are attempting to measure. This is much harder to do than to say. It is not accomplished by simply making up a set of question or statements to measure. This relationship between measured score and true score is never established unequivocally but is always inferred. The bases for inferences are two:
1. Direct assessment employing validity
2. Indirect assessment via reliability