Why quoting percentages of I.Q.'s betrays incompetence

Percentages only meaningful on a ratio scale

Computing a percentage is a form of the arithmetical manipulations called "division" and "multiplication". Such calculations only give meaningful results on a so-called "ratio scale"; that is, a scale that fulfils both of the following requirements:

1. The scale has a true and absolute "zero" that really means zero, rather than a zero that is randomly assigned to one of many possible values;
2. The scale is intervallic, that is, each unit step has the same size as every other unit step on the scale.

Examples of scales that meet these demands are distance, mass, time, and the Kelvin temperature scale. Scales that do not qualify are for instance the Celsius and Fahrenheit temperature scales; their zeros have been assigned to particular values and do not reflect true zeros.

The I.Q. scale has a zero that simply means "6 2/3 standard deviations below the mean". It is therefore not a true zero, and I.Q. is therefore not a ratio scale. The question whether or not it is an intervallic scale is not relevant at this point, as the absence of an absolute zero suffices to disqualify it as a ratio scale.

It follows that multiplication and division, and therewith the computation of percentages, do not give true and meaningful outcomes when applied to I.Q.'s. This insight is useful when encountering claims such as:

• Playing this brain game for a mere five minutes each day will increase your overall mental alertness and raise you I.Q. by 10 % !
• After 25 years as a professional test taker, the the high I.Q. genius Ribbert Brozzel has improved his I.Q. by 33 % and is now on par 33 % is is now on par with historical geniuses like Einstein and Newton!
• Exposure to a full-blown vuvuzela at close range may temporarily reduce one's I.Q. by 25 %, while the I.Q. of the player is in any case as good as halved permanently.
• Double-blind placebo-controlled clinical trials have shown this product to elevate your I.Q. by 3.45 % in three months (p < 0.001).
• For the first time in a century of testing, women are scoring higher than men on I.Q. examinations. Until recently, women's scores lagged behind men's by as much as five percent, leading some scientists to claim that men were inherently more intelligent than women. Over the decades, men's and women's scores have both improved, but women's have surged more dramatically.

Such pseudoscientific ignorance betrays deep incompetence in the field the claimant is speaking about. Be assured that nothing from such a person or found in such a publication needs to be taken seriously.