The Thought Refuse

A Virtual Repository for the Mind

The Problem of Correlation As Causation

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The confusion of supplanting correlation for causation is one of the most common logical fallacies we make.  This is the fallacy of correlation.  The basic premise is that you will attribute a connection between two experiences as the root cause of one experience being the cause of the other.

While it’s one of the easiest logical fallacies to spot, we continually fall for the trap of the fallacy of correlation.  It does require a minor exertion in mental analysis to catch ourselves spiraling down it’s pitfalls, but it’s shouldn’t be too much to ask a person to invest that energy into their own line of thinking.  None-the-less, it’s a logical fallacy which pervades everyday thinking, and, regretfully, even scientific research.

As a general schematic, think of the fallacy of correlation to be as follows:

  • Event A occurs synchronously or chronologically to Event B‘s occurrence, therefore
  • Event A is the cause of Event B.

The possibilities of the relationship between Event A and Event B are too numerous to conclude A caused B.  Some of these include:

  1. A is the cause of B;
  2. A is the cause of B, and B is the cause of A (or both events sharing a circular causation);
  3. an unknown Event C is cause for either A or B, or both;
  4. the incidence of A and B share no relationship other then temporal occurrence.

It is rare for Case 1 to be true, yet far too often we prefer it from the other possible Cases.  This is often the outcome when a layer of plausibility exists within our empirical history interconnects two events(Hume’s definition of causation).  Plainly stated, if I have been witness to two events occurring in the past, I am likely to make a connection between these two events when the happen again in the future.  They are believable.

The negation for a layer of plausibility would be to say:

  • I wore a red hat today;
  • On my way to work, I was involved in a car accident;
  • The red hat caused my car accident.

The premise that my red hat was the cause of my car accident is absurd because there is no past relationship in our minds between hats and accidents.  We have no empirical past evidence to create a connection between the two, otherwise, unrelated events.

This is not to say that simply because two events are not covered in a layer of plausibility that no relationship actually exists between the two, only that we cannot know if one exists.  It’s possible, with a low probability, that my hat caused my accident, but we prefer a cause holding greater probability, which translates to one that we have past experience observing.

If I was to remove the red hat, and replace it with;

  • It was snowing outside.

we easily make the causal connection between snow and a possible accident.  You have, first hand, experienced an accident in bad weather, or you know someone who has, or, at the very least, you’ve watched the Weather Channel enough times to have been warned of dangerous road conditions.

Our path towards confusing correlation with causation is, therefore, rooted in our tendency for inductive logic.  A non-inductive evaluation of the car accident should state, “The snow holds a greater probability of being the cause for accident, then the wearing of a red hat.  However, I cannot completely discount the possibility the red hat was, indeed, the cause.”  At some later point, we just might discover that the color red is a mental distraction, and causes other drivers take their attention away from the road.

Some examples of the fallacy of correlation in action would be useful.

Ex. 1 – Joining the military made me a disciplined and strong person(this is similar to the US Army’s recruiting slogan “Strength For Now, Strength For Later”).

The implication is that, through military training and service, one will become a stronger person.  What this statement misses is that all the weak individuals are weeded out during the training process.  The underlying logic here, is that every graduate that enters military service must be strong.  The weak are either removed from the sample during the interview process prior to formal training, or are eliminated from the pool during their many months in attendance at military training school.

It is not uncommon to find, within the fallacy of correlation, to have a failure to realize that the sample pool your drawing from towards possible causation’s, does not contain anything but a singular outcome within it’s total aggregate.  You can’t help but draw the conclusion that the Army made you strong when you wouldn’t have been in the Army had you not been strong to begin with.

Ex. 2 -The Community Reinvestment Act caused the recent home mortgage meltdown, as well as the subsequent economic recession.

This is a particular favorite of Rush Limbaugh and conservative ideologues, who extrapolate the above statement to direct the lion’s share of the blame on Democrats.

Putting aside the complexity of causes behind the economic collapse in the United States, the premise that the CRA caused the home mortgage disaster illustrates the problem of correlation, which becomes pronounced when the statistical impact CRA sub-prime loans had on the aggregate of all sub-prime loans outstanding, alongside the chronological life of the CRA.

I have examined the share of CRA home loans compared to the total value of outstanding loans previously, and need not delve into details here.  The CRA was passed in 1977.  Sub-prime home mortgages never accounted for more then a sliver of the aggregate until more then 20 years later.  It is difficult to attribute a casual link between a piece of legislation enacted two decades previous to developments within private lending institutions, and stands as a mere correlative link at best.

Despite being a convenient finger pointing apparatus for conservatives, this particular example is a clear indication of the fallacy of correlation at work, cleverly shaped for partisan, political gain.  It is a common trap to latch onto and find casual evidence when two events share a single commonality, but especially insidious when intentionally exploited.

There are countless other examples that could be given, but these two should suffice to show that a single link between two independent events does not necessitate causality.  We make these common mistakes daily without subjecting our conclusions to critical examination.  It’s much easier to identify a commonality and cry “A caused B” then to go deeper into the relationship between A and B.  A fair amount of mental energy needs to be expended to explore deeper, and that’s not an exercise we seem to be built for.  As it concerns mental expenditures, we tend to follow the path of least resistance(all the more energy efficient when correlation fits neatly into our preexisting notions, beliefs, or ideologies).

A good first step for avoiding this fallacy is to not rely our your past experiences so fully – do not take your empirical knowledge quite so seriously.  This can be illustrated by Hume’s black swan example(previous to the discovery of Australia is was said, with empirical certainty, that all swans are white).

Necessarily subsequent to the move away from empirical experience, is an analytical openness to a wide range of possible causalities.  As illustrated in Case 3, an unknown Event C might, and often times is, the actual cause of Event A or B, or both.  While not disavowing either Case 1 or 2, it is critical to incorporate, the more probable, Case 3 and 4.

Case 3 is, fundamentally, saying that we have to account for the unknown, or for what we do not know.  The history of knowledge has consistently shown that it is ever expanding.  With a perceived infinite epistemology, the breadth of potential unknowns, of what we might learn in the future, cannot be sufficiently quantified, at least not in terms of probabilistic value, enough to ever reach a definitive conclusion where we can say – Event A caused Event B.

Neither can we ever conclusively say – an unknown Event C caused Event A or B, or both.  All we can ever say, as Popper properly showed in his fight against induction, that one Case is more probable then another Case.  This is what we must be satisfied with when we search for causality.

Through extensive logical criticism, a sometimes mind numbing process, that takes into account, both empirical knowledge and unknown possibilities, one can avoid the trap of the fallacy of correlation.

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Written by huxbux

February 4, 2009 at 7:25 pm

Posted in Logic, Philosophy

Tagged with , ,

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