Question
Is IQ interval or ratio data?
Short answer
IQ is usually treated as interval data, not ratio data. The scale has equal steps (one standard deviation is 15 points everywhere) but no true zero, because 100 is simply the average of a reference group. So an IQ of 140 is not twice as intelligent as 70. Some statisticians argue it is really ordinal.
Want your own number? The test is 25 visual puzzles, about 12 minutes, no sign-up.
The four levels of measurement
- Nominal: categories with no order, such as eye color.
- Ordinal: ordered ranks with unequal or unknown gaps, such as finishing places in a race.
- Interval: ordered with equal gaps, but no true zero, such as temperature in Fahrenheit.
- Ratio: equal gaps and a true zero, such as height or reaction time.
Where IQ fits
A modern IQ is a deviation score. Each age group is scaled to a mean of 100 and a standard deviation of 15 (Wikipedia: Intelligence quotient). That construction gives the scale equal steps in the statistical sense: 115 is one standard deviation above the mean and 130 is two, and the normal curve fixes how many people fall between any two points (the 68-95-99.7 rule). This is why most textbooks and researchers treat IQ as interval data and happily compute means and correlations with it.
What the scale lacks is a true zero. 100 marks the middle of a reference group, not a halfway point between none and double. So statements like "an IQ of 140 is twice an IQ of 70" are meaningless, in the same way that 80 degrees Fahrenheit is not twice as hot as 40.
Try one · Spatial Reasoning
Which option is the same shape, only rotated?
Tap the option you think is right, or show the answer.
Show the answer
Option 2 is the original figure turned a half turn.
How to solve it
- Pick a landmark: the marked cell or the end of the longest arm.
- Turn the figure in your head and watch where that landmark goes, and which side the other cells end up on.
- Turning the figure a half turn gives option 2.
- Each of the other options is a mirror image: flipping it over would match, but no turn does.
That was 1 puzzle. The full test has 25.
The ordinal argument
A stricter view says IQ is ordinal. Raw test scores are turned into IQs by ranking people against norms and mapping those ranks onto a bell curve. The equal steps come from that mapping, so whether ten points near 100 means the same amount of ability as ten points near 140 is a modeling choice rather than an observed fact. Item response models, like the Rasch model IQ Octopus uses, are one attempt to build a scale with equal steps from the items themselves.
Practical answer for a statistics class
Call it interval data, mention that it has no true zero, and note the ordinal objection if you want full marks. For the mechanics, see deviation IQ, z-score, the Rasch model and is an IQ score a percentage.
Sources
- Intelligence quotient. Wikipedia. en.wikipedia.org/wiki/Intelligence_quotient
- 68-95-99.7 rule. Wikipedia. en.wikipedia.org/wiki/68%E2%80%9395%E2%80%9399.7_rule