CONCEPT OF A RELATION

Saying things are related means that one thing can be expressed in terms of the other thing. For example, saying that behavior of parent and child are related means that either one’s behavior can be expressed in terms of the other’s behavior. Similarly, saying that product price and product sales are related means price can be expressed in terms of sales, and, likewise, sales can be expressed in terms of price.

MATHEMATICAL MODELLING OF RELATION

Mathematically, relationships are modelled as equations.

For instance, IQ (intelligence quotient) = mental age/physical age.

IQ = mental age/physical age. So,
mental age = IQ x physical age, and
physical age = mental age/ IQ

See? Each can be expressed in terms of the other. So they are all related.

Similarly, in physics, we learn about the equation, f = ma i.e. force = mass x acceleration due to gravity.

f = ma. So,
m = f/a, and
a = f/m

So, again, “f”, “m” and “a” are related to each other.

CONCEPT OF CORRELATION

The prefix “co” usually connotes “togetherness” in a relation.

“Cooperation,” for instance, implies that people should work together, not that one should work, while the other does nothing.  Similarly, men and women “coexisting” in the world means they should work together to address conflict and keep the peace, not that one should make all the effort while the other makes no effort at all.

In the same way, correlation between two data items is about how both the data items change together.

Equations and correlation

Equations do give us information about correlation. Consider one of the previous examples:

IQ = mental age/physical age. This can be interpreted as follows:

IQ is high if the mental age is high despite physical age being low. For example, if one’s physical age is only 6 years old, but mentally they operate like a 23 year old, then their IQ is exceptionally high.

Thus, IQ and mental age change in the same direction, whereas IQ and physical age change in opposite directions. These “directions” tell us how IQ and mental age change together and, similarly, how IQ and physical age change together. Thus, these directions describe correlation.

Thus, in every equation, there is some information about the correlation between the variables of the equation.

Distinction between equation (simple relation) and correlation

It can get confusing at times. So, we’ll make a clear distinction using all of the above examples.

Example 1

Equation (relation): Behavior of parents and their children are related
Possible Correlation(s): As parents become nicer, children get more spoiled.  Or, as parents become stricter, children become less confident.

Example 2

Equation (relation): Price of a product and sales of the product are related.
Possible Correlation(s): As price increases, sales decrease. Or, as price decreases, sales increase.

Example 3

Equation (relation): IQ = mental age/physical age
Possible Correlation(s): As mental age increases and physical age decreases, IQ increases.

Example 4

Equation (relation): f = ma
Possible Correlation(s): As mass increases, so does force.

In the end, equations or relations are about capturing the nature of a relationship i.e how one variable can be expressed in terms of the other. Whereas, correlation is about capturing how much “togetherness” there is when the variables change i.e. whether two variables change in the same direction, or change in opposite directions.

Positive and negative correlation

If the variables change in the same direction, then they are positively correlated. For example, as weight decreases, so does risk of heart disease. Thus, both weight and heart disease change in the same direction, constituting a positive correlation. As another example, as weight increases, energy level decreases. Thus weight and energy level change in opposite directions, which means that they are negatively correlated.

Other examples:

1. As age increases, so does experience – Positive correlation
2. As effort increases, so does performance – Positive correlation
3. As activity decreases, so does capability – Positive correlation
4. As activity decreases, laziness increases – Negative correlation
5. With every increase in personal space, there is a decrease in stress level – Negative correlation

CORRELATION IS THE BEGINNING OF SCIENCE

The objective of science is to answer “why?” questions. Why does the Earth spin? Why do people get angry? Why do dogs lick their balls? So on and so forth. Whatever your observation, science is about explaining the cause behind it. It is about determining causality.

Correlation and causality

How did psychologists figure out that an unmet need causes anger? They saw, for a large group of people, that the more unmet needs there were, the more their anger increased. They saw a positive correlation between the number of unmet needs and anger. Next thing they did was calculate the strength of the correlation, which turned about to be big. Owing to that strong correlation, they inferred that there must be a causal relationship between anger and unmet needs.

In this way, correlations, depending on their strength, eventually lead to the establishment or dismissal of a causal relationship between the variables being examined. Thus, causality is inferred from stronger correlations.

Strong correlation does not always establish a cause

Even though it is very likely that a strongly correlated variable is involved in causality, it’s not always the case. For example, the data collected from your life may show that every time Uranus tilts in its orbit, a bad luck event happens to you on Earth. That would mean that there is a strong correlation between Uranus’ tilt and your bad luck events. So does that mean Uranus is causing the bad luck events?

No, it does not. Such a correlation is probably just a freakish coincidence. Therefore, it is always advised to get data that makes logical sense before examining the variables for correlations. Otherwise, you would be establishing causalities from strong correlations even if they are completely ridiculous.

Coming up in Correlation – II — How to calculate the strength of a correlation. Thank you for reading.