The post hoc fallacy is the assumption that because one event preceded another event, they must be causally related. In other words, the first event must have caused the second. However, the chronological order of two events does not prove a cause and effect relationship between them.
Cause
The post hoc error occurs when we draw a conclusion causal without sufficient evidence to support it. “Post hoc” is a shortened version of the Latin phrase “post hoc ergo propter hoc,” meaning “after this, therefore because of that.” Post hoc errors are made when one argues that because B occurred immediately after A, A must be the cause of B. The problem is not that there cannot be a causal connection between A and B, but rather that there is no adequate evidence. for the conclusion.
The post hoc fallacy leads to misconceptions about the causes of various phenomena. It is at the heart of many pseudoscientific arguments, the most notable and persistent being the false belief that certain types of vaccines cause autism in children.
The post hoc fallacy can also lead to magical thinking: the belief that unrelated events are causally related despite the absence of any plausible connection (e.g., believing that inner thoughts can influence the external world without action). Superstitions (for example, attributing misfortune to an “unlucky” event such as walking under a ladder) follow the same pattern.
Sometimes people make a logical leap into hindsight when they believe they can eliminate a problem by eliminating its (alleged) cause.
This is often reflected in how politicians interpret unemployment statistics or crime reduction. In this case, the post hoc fallacy (A caused B) is combined with antecedent negation, another fallacy that goes even further by assuming that "if A caused B, avoiding A will prevent B."
People often make the post hoc fallacy without realizing it, simply because of the way the human mind evolved: it extracts causality from coincidences. For this reason, people confuse the temporal order of events with a true causal connection. Chronological order is a necessary but not sufficient condition for a cause and effect relationship.
A number of cognitive biases can also fuel people's tendency to get caught in the hindsight fallacy trap. For example, jumping to conclusions bias (making decisions without enough information) can cause people to infer causality.
Likewise, confirmation bias can cause people to seek out or interpret information in a way that confirms their pre-existing belief that a cause-and-effect relationship exists.
Example
In research, post hoc error occurs when researchers do not carefully examine the relationship between variables.
Researchers sought to determine whether taking baths could reduce the risk of cardiovascular disease. Their analysis shows that people who took baths regularly were less likely to suffer from cardiovascular disease or stroke. Researchers conclude that baths have a beneficial effect on cardiovascular health.
The media picks up results research and disseminate them widely with titles like “Taking a bath is good for the heart”.
However, without a controlled experiment in which participants are randomly assigned to a control group or a treatment group, it is difficult to know whether this relationship is causal. For example, an alternative explanation could be that those who bathe regularly have more time and are generally less stressed.
Claiming that bathing is the cause of lower rates of heart disease among people who bathe regularly is a form of post hoc fallacy.
How to avoid a post hoc error?
Correlation does not imply causation (the converse can also be true). Be careful to always talk about correlation or hypothesis and not to put everything under the term causality.
EN 
FR