Definition of Post Hoc Ergo Propter Hoc
Post hoc ergo propter hoc is the fallacy of thinking that an event which precedes another event must have caused the other event. It comes from the Latin for “after this, therefore because of this”.
Examples of the Fallacy
Suppose you have a minor illness, such as a cold. You take an experimental supplement, and the cold gets better. It would be a fallacy to think that the cold got better specifically because you took the supplement. The cold might have got better of its own accord whether you took the supplement or not.
Belief in superstition can be an example of the post hoc ergo propter hoc fallacy. If you break a mirror and then suffer bad luck, you might think the bad luck was caused by breaking the mirror. Similarly, if you find a four-leafed clover and then experience good luck, you might think the good luck was caused by finding the four-leafed clover.
Another example is that people in the Middle Ages used to think body lice were good for health. This was because they noticed that soon after lice left a person’s body, the person would usually become sick – so they assumed that the lice helped to prevent disease and that people would get ill in the absence of lice. In fact, lice are sensitive to small changes in body temperature, so people’s temperature would rise when they first caught an illness, before they began to show symptoms, and the higher temperature would drive the lice away.
Correlation and Causation
Correlation is when two things vary in a related way. For example, children’s height correlates with their weight, because, in general, taller children will be heavier and shorter children will be lighter. Of course there are exceptions (some short, heavy children and some tall, light children), but there is a general pattern that children’s weight and height correlate with each other. Similarly, children’s weight and height both correlate with their age. Other examples of correlations are between people’s education level and their income, or between the size of their hands and their feet.
There is an important principle in science that correlation does not imply causation. This means that, just because two things correlate, it doesn’t mean one causes the other. Perhaps some third factor causes both, or perhaps the apparent correlation comes from random noise or measurement error and doesn’t reflect any real relationship. Mistakenly thinking that correlation implies causation is another example of the post hoc ergo propter hoc fallacy.
A memorable example is that ice cream sales correlate with deaths from drowning. It would clearly be fallacious to think that ice cream sales cause drowning, or that drowning causes ice cream sales. A much more likely explanation is that both are caused by a third factor: high temperatures, which drive ice cream sales, and which lead to more people swimming (particularly in seas, rivers and lakes), and hence more drownings.
As a subtler example, you might notice a correlation between children’s reading ability and the number of books in their home. If you assume correlation implies causation, you might conclude that having a lot of books causes children to be good at reading. But there are other potential explanations. It could be that parents who value reading help their children to become good at reading (either by passing on genes for being good at reading, or by regularly reading with their children, or both), and those parents also buy a lot of books for their children. In that case, the children’s reading ability and book ownership would both be caused by a third factor (having parents who value reading), rather than one causing the other. This matters because, if you committed the fallacy of thinking book ownership caused reading ability, you might try to improve reading abilities nationally by giving children books, and this might not make a difference if the important factor is parents regularly reading with their children. The parents who never read with their children might still never read with them even if they are given more books. A more effective intervention might be to work with parents to encourage them to read with their children more often.
Avoiding the Fallacy
If you notice a correlation between two variables, or two events that frequently occur together, there are ways you can tell whether there’s a causal relationship or not.
If it is practical and ethical to do so, you can conduct a controlled experiment, where you deliberately vary one of the events and see whether the other follows, rather than just passively observing that they tend to occur together.
For example, you may have noticed that you often suffer indigestion after eating dairy products. If you automatically assume you have a dairy intolerance, you are committing the post hoc ergo propter hoc fallacy. Instead, you could randomly assign in advance which days over the coming few weeks you’ll eat dairy and which days you’ll avoid it, and keep records of which days you suffer indigestion. You should also try to keep your diet the same in other respects between the dairy and non-dairy days. It may turn out that you sometimes suffer indigestion because of an entirely different factor, and you only noticed the times it follows eating dairy, and not the times it doesn’t.
There are some research questions where it is not practical or ethical to conduct a controlled experiment. For example, a researcher may have noticed that mothers who drink a lot of alcohol during pregnancy are more likely to have babies with developmental delays. It would be fallacious to conclude from this that drinking alcohol in pregnancy causes developmental delays (even if it actually does – it’s possible for fallacious reasoning to lead to a conclusion that happens to be true!) But it would be unethical to recruit a large group of pregnant women and randomly assign some of them to drink a lot of alcohol during pregnancy and some of them to abstain. The best you can do here is conduct more, larger and better-controlled observational studies. More and larger studies will help to rule out the relationship being coincidental, and controlling for more variables will help to rule out the possibility that drinking during pregnancy and developmental delays are both caused by a third factor.