In popular language, when talking about aspects related to intelligence and cognitive abilities in general, it is common to hear the expressions IQ and IQ used as if they were synonyms.

It is not uncommon to find people, both those who specialize in psychology and those who have studied medicine and other fields, who use both terms indiscriminately. Even books that address this topic use both words interchangeably.

The aim of this article is to explain which is the appropriate term, as well as to clarify the difference between quotient and coefficient , giving some examples related to their definitions and addressing this debate from a historical perspective.

Quotient or IQ: what difference does it make?

Using the dictionary of the Royal Spanish Academy (RAE), we can find the definitions for “quotient” and “coefficient”.

According to the SAR, the word quotient refers to the result obtained when dividing one quantity by another, while the word coefficient has among its meanings the term used to refer to a numerical expression of a property or characteristic, which is generally expressed as the ratio between two magnitudes. Although the SAR gives different definitions for “quotient” and “coefficient”, the fact is that exemplifies them with a similar expression: coefficient/intellectual quotient .

This same case occurs in another institution specialized in clarifying linguistic doubts: the Fundéu BBVA. In fact, this organisation has an entry on its website dealing with the “quotient” vs “IQ” debate, indicating that, in essence, they are the same, and that both expressions are correct.

Therefore, starting from the given definitions and resorting to the world of mathematics, we are going to exemplify with formulas what exactly the terms “quotient” and “coefficient” are . To do so, we will leave aside their relationship with the intelligence construct, to return to it later.

Basic definitions

A coefficient is essentially a factor, i.e. something that multiplies something else, such as a linear function: y = ax + b. In this formula, a is the coefficient of x, because it multiplies it.

Also with coefficient, in scientific fields such as physics, reference is made to a formula with which it is intended to discern the value of the property of a certain element , such as the “dilatation coefficient which relates the length of an object to its increase in temperature:ΔL = α Δt, where ΔL is the increase in length, α is the coefficient of expansion and Δt is the increase in temperature.

A ratio is basically dividing something by something. A clear example of this is how IQ was calculated in the beginning, by psychologists such as Alfred Binet and William Stern. They basically divided mental age by chronological age and multiplied it by 100 to remove decimal values. Some might think that this is really a coefficient because it is multiplied by 100, but the truth is that it is not because this value is not always the same, and it does not multiply to a variable value.

As can be seen, in institutions specialising in language, such as the RAE or the Fundéu BBVA, sometimes the specialised opinion of professionals in a given field, such as psychologists and educationalists, is not taken into account.

These institutions focus on how language is used in society and how it evolves. For this reason, in recent years, terms such as “toballa” or “cocreta” have been accepted in dictionaries, although they specify that their use is not formal, but reflects linguistic reality.

Although we psychologists and other professionals specializing in health and social sciences respect the criteria and professionalism of linguists, philologists and other specialists in humanities and letters, we do claim that the only correct expression is “IQ”.

Historical background

The first person to use the expression “IQ” was the German psychologist William Stern , in 1912, creating the German word “intelligenzquotient”. This term refers to the relative intellectual capacity of a person at the time of being evaluated. This is evaluated by means of the results obtained in psychometric tests, and comparing them with the rest of the people in the same age group. The IQ is distributed in the population in the form of a Gaussian bell, with a central value of 100 and standard deviation of 15.

Alfred Binet, another leading psychologist from Nice, France, calculated the IQ of the children who came to his office by dividing it: the person’s mental age divided by their chronological age, and multiplying the result by 100.

As we have already said, the original term came from the German “intelligenzquotient”, and when translated into English it became literally “intelligence quotient”. On the other hand, in Spanish speakers, whether specialized or not, are still hesitant today, especially if the institutions of the language treat both “quotient” and “coefficient” as if they were synonyms in practice .

Although today the calculation of IQ has changed and alternatives to the tests used by Binet and Stern, among other psychologists of the time, have been proposed, the truth is that the appropriate expression is still “IQ” .

However, as we have indicated before, there are many, both those who specialize in psychology and those who do not, who still use the expression “IQ”. On the basis of this article and the explanations given in it, there is no longer any reason to fall into error.

Bibliographic references:

  • Quotient. (2018.). In Diccionario de la Real Academia Española (23ª edición). Retrieved from https://dle.rae.es/?w=cociente
  • Coefficient. (2018). In Diccionario de la Real Academia Española (23rd edition). Retrieved from https://dle.rae.es/?id=9e8d8Dc