Post Hoc Ergo Proctor Hoc
A small boy accompanies his mum and dad to the railway station every weekday for several years, to wave his dad off to his job in the city. Many years later the son has his own job in the city and is reminiscing about those boyhood visits to the station. He confesses that for most of his childhood he believed that it was a whistle that powered the train. If I had suggested this to my grandson when he was about 5, he would have dragged me off to the front of the train to show me the engine and explain how it worked.
But it’s an easy mistake to make, isn’t it? In fact it is the most common cognitive error we suffer from. Even if you are aware of the hazard it represents you can still fall for it in the heat of the moment. This is a classic example of the consequences of a natural tendency to simplify. It’s easier to assume than it is to check. Of course it’s not too much of a problem to think it was the whistle that powered the train. It’s an innocuous example of the error. However, as we will see, there are many other examples that are much more dangerous.
But first an explanation of the title of this article. “Post hoc, ergo propter hoc” is Latin for “After this, therefore because of this.” In other words if one thing habitually follows another thing then the second thing must be caused by the first thing. The problem is that this is only sometimes true and mostly not, so is there a way of analysing what’s going on?
Well yes there is, by using a simple version of symbolic logic. Symbolic logic is a way to translate the written or spoken word to something resembling algebra. This involves sucking the subject matter out, leaving only the bare bones of the logical argument, which can then be examined for flaws. I don’t propose to use the proper symbols. I’ll leave that for another article.
For the story of the whistle and the train the bare bones look like this.
X happened
Then Y happened
Therefore X caused Y
We know two things for sure
X and Y really did happen
Not all occurrences are cause and effect
So lines 1 and 2 are correct and line 3 is only sometimes correct. This means that there is something missing between the 2nd and 3rd lines. There are several ways that another line can be inserted, provided that it answered the question of whether the apparent cause and effect relationship was in fact just a correlation.
What is a correlation?
The term correlation is widely used, particularly in statistical analysis, to explore the relationship between different variables in a dynamic process, like the weather or society. It can get very mathematical, which we don’t need to dive into here. We simply want to find out whether two things that habitually happen together are associated in any way other than cause and effect. Strictly speaking all such habitual relationships are correlations (they happen together). It’s just that some of them are also cause and effect. The missing lines could look something like this:
X happened
Then Y happened
Alternative explanations to cause and effect checked.
Outcomes
If X is clearly evidenced, then X caused Y
If alternative is clearly evidenced, then X and Y are only correlated.
The key is evidence. Without evidence, cause and effect cannot reasonably be established either way. Even if you have identified all the potential alternative causes you can think of and eliminated them, you can never be sure you have found them all. There is always the possibility that there are some you are not aware of. The only two positive outcomes are solid evidence that X is the cause or solid evidence that its an alternative, otherwise any conclusion is at best speculative.
Using this procedure on the whistle and train scenario is easy. Examination will reveal that the whistle is a station management safety feature designed to tell the driver that it is safe to move off because all the doors are closed and there are no people in any potential danger. Examine the train and you find it has an engine.
You’re probably thinking by this point that you’ve heard enough, but we haven’t got to the fun part yet. Sucking the content out means that you can re-flesh the bones with something else: Same bones, different story.
So lets try a couple.
Regression to the Mean
From its inception in 1954 America’s most popular sports magazine, Sports Illustrated, was deemed to have a jinx. If as a sports person your picture appeared on the front cover of the magazine, disastrous performance would follow. For example in 1957 an American football team with a winning streak of 47 games lost the next one after appearing on the magazine’s cover. Alexander Wolff, a writer for the magazine, Reviewed all 2456 covers in 2002 and found that 37.2% of individuals or teams featured on the cover went downhill afterwards. Belief in this jinx was so pervasive that many sports stars refused to appear on the cover. This story starts off in a very similar way to the shrinking tumour story below: An assumption is made about cause and effect.
We did X (appeared on the cover)
Then Y happened (our performance went down the toilet)
Therefore X caused Y (the magazine has a jinx)
Two investigators decided to look into the whole career of each person, not just the aftermath of being on the cover. They also compared this with the careers of people who didn’t make the cover. The result was quite dramatic, but at the same time almost intuitively correct. To appear on the cover of Sports Illustrated you have to have done something really impressive; something that represents a peak for you, such as a personal best or even better, a world record. It’s at this point that probability kicks in. If you have just hit a peak, it’s more likely you will do less well next time. This is regression to the mean and it is wondrous to behold.
Most things fluctuate. The displayed value of an electric current for example is just the average. The actual current, if looked at in detail, will spend most of it time equally distributed either side of that average, and sports performance is particularly prone to two of these types of fluctuation. At the beginning of a career they are still learning, possibly competing in junior tournaments, with competence increasing throughout a career to a peak, when many people choose to retire while still at their best. We can represent this as the humble sine curve.
Performance also fluctuates over the short term. Some sports, like golf, are prone to big changes in performance from small fluctuations in mental state or minor alterations in technique. This can be represented as a sine curve made of sine curves. So there are plenty of opportunities for peak performances in a career to trigger an opportunity to feature on the front cover of Sports Illustrated.
Healing
There are many stories told from around the world of tumours shrinking away following some form of non-medical healing. This is a classic case of the propter hoc bias in that checking for alternative explanations almost never takes place. On those occasions when it does take place at least half a dozen alternatives are identified. The most common by far is the medical treatment someone with a tumour is inevitably receiving. Whilst some medications might be dealing with peripheral issues, like side effects of main drugs, the most common purpose of a medication is to get rid of the tumour.
Other alternative explanations include:
Regression to the mean: Many medical conditions fluctuate over time and an apparent improvement may not be sustained. Checking this would require a longer-term follow up of the person after healing.
There are well-known remission rates for the various types of cancer that any other intervention would have to improve on. Cancer is the most monitored condition in the world because we are constantly trying to find causes and cures, so we have an accurate idea of survival rates.
The three related phenomenon of biofeedback, placebo and positive thinking techniques. Training in such techniques would be a legitimate alternative approach to consider.
Misdiagnosis. Doctors don’t always get it right.
Spontaneous remission. People get better without any obvious explanation.
Non-medical healing could be more credible if these alternatives were checked for elimination. The reason why it is rarely done may be the avoidance of discovering the real cause. It could equally be deemed unnecessary if confidence in the healing is very high.
There are a lot of different types of cognitive bias, so there will be many more.