IQ: Ordinal, Interval, or Ratio?


As with any measurement, it is important to distinquish between the concept and the operational definition. Intelligence Is it Ordinal? Is it Interval?
Fig1. This figure shows the relationship between the numbers assigned to the intelligence of particular individiuals and their actual intelligence if the IQ test measured at the equal-interval level of measurement.

If the measure of intelligence were not at the interval level, that would mean that some 10-IQ point differences marked off larger differences in intelligence than other 10-IQ point differences. One possibility is shown in Fig. 2.

Fig. 2. This figures shows one (of many) possible relationship between the "real" intelligence of particular persons and the IQ score measured from an IQ test if intelligence is NOT measured at an interval level.

Another possiblity is shown in Fig. 3.

Fig. 2. This figures shows one (of many) possible relationship between the "real" intelligence of particular persons and the IQ score measured from an IQ test if intelligence is NOT measured at an interval level.

There's pretty strong evidence that IQs don't measure at the interval level of measurement

    Take 4 people with IQs of 130, 120, 90, and 80. Talk with them. Is the difference in intelligence between the 130 and 120 IQ-people the same difference in intelligence as between the 90 and 80 IQ-people? Most often research of this sort has indicated the differences in intelligence are not the same size even though both pairs differ by the same number of measured IQ points..

Based on your experiences, do you think Fig. 2, Fig. 3, or another Figure best describes the relationship between IQ scores and the person's underlying intelliegence.

Is it Ratio?

  • If its not interval, it can't be ratio.
  • However, for illustrative purposes, assume intelligence were measured at the interval level.
  • Could it be at the ratio level? For a ratio measurement we would have to be able to say that one event has twice (or half, or 6.2571 times) the amount of intelligence as another event. Can we say that one person is 80% as intelligent as another (an IQ of 80 is 80% of an IQ of 100--but that is not the question).
  • It could only be ratio if there were an intelligence you could set to indicate and IQ score of 0 and there is no way no-one could have an intelligence less than the one you have set at 0.

© 2002 by BurrtonWoodruff. All rights reserved. Modified Thursday, March 27, 2003