Simply put, anecdotal evidence fallacy is invoked when a story is used as proof for your argument. This is the classic “I know what you are saying but the exact opposite happened to me/someone I know/someone I heard about. Therefore your claim is false”  argument. At the surface you might look at this and wonder, how is this a fallacy at all? Isn’t this how most lawsuits are settled? One person gives the account of the incident as their “story”, others give theirs, and then the court tests the stories against laws to give a decision. But then, you would be wrong. The mistake you did there is getting evidence and proof confused. An anecdote can be used as evidence (a data point) to prove a point but not as the proof itself. Anecdotal evidence fallacy is invoked when a small biased sample is used to do a hasty generalization. Let us look at an example;
Smoking isn’t harmful even though scientists say it causes you to die young. Bob’s grandfather smoked a pack a day and lived until 97 [1, 2, 4]
As you can see, in this example, an implicit generalization is drawn from a single data point. In simpler words, it says; “Bob’s grandfather lived long even-though he smoked a lot. Therefore smoking will not have an effect on anyone that smokes“. So we observe one instance and then generalize it over the entire data set. This goes according to the following form ;
- P1: X happened once when Y.
- P2: (unstated) Things that happen once will happen every time.
- C1: X happens every time when Y.
This form is very famously followed by pseudoscience pundits such as David Wolfe and Food Babe. It is not so hard to see how outrageously stupid these claims are when you try to transform them into a different claim but with the same way of formalization. Consider the following example ;
- P1: Abby choked once when she ate some goat meat.
- P2: (unstated) Things that happen once will happen every time.
- C1: Everyone will choke when they eat goat meat.
Even an average person will see the absurdity of this claim about goat meat but the same people will be more than willing to take the claim “A certain child had an allergic reaction to a vaccine. Therefore kids should not be given vaccines“. The above is the basis on which the anti-vaxxer plague is based on.
The second platform that anti-vaxxer plague uses is the autism claim. It goes like this; “A certain child who got a vaccine was later discovered to be suffering from autism. Therefore kids should not be given vaccines“. Now this anti-vaxxer basis is something that needs to be discussed separately with references to a fraudulent research paper that initiated all this mess. But here I am only interested in showing how this second claim also falls under the anecdotal evidence fallacy. This time, it falls under the second form of the fallacy ;
- P1: Horatio started drinking orange juice after being diagnosed with cancer and then his cancer went into remission.
- P2: (unstated) There is no other plausible explanation for Horatio’s cancer going into omission than the drinking of orange juice.
- C1: Orange juice can cure cancer.
In this form, a single data point where the supposed premise and supposed consequent co-occurs is used as proof to claim that the supposed premise and nothing else is the cause to bring about the supposed consequent. Note that this is even worse than the classical correlation-and-causation assumption. In that classical case at least the faulty causation conclusion is derived after observing a high correlation of variables across multiple data points. Here, a single or a few data point(s) is used to claim causation.
As you may have deduced by now, the fallacy resides in the unstated premise in both of the above forms. In form one, it generalizes that just because X happened once it will happen always. The fault here is the fact that the singular happening of X only proves that the probability of X happening is larger than zero (i.e.: It is possible for X to happen). Not that the probability of X happening is near or equal to one (i.e.: X always happens). In form two, it generalizes that the happening of X is the reason for the conclusion. This too is not true. What we can logically derive from this is only that the conclusion happened in a certain instance when X was true. It is very likely that the existence of X was independent or highly irrelevant to the final outcome.
The biggest danger of anecdotal evidence fallacy is its susceptibility to confirmation bias especially at the hands of people who are aware that this is a fallacy. When such a person sees an anecdote that does not fit their viewpoint, they are the first to reject it citing anecdotal evidence fallacy, but when the same person sees an anecdote that fits that person’s viewpoint, they take it as a perfect example that works in the real world .
An example of how dangerous the anecdotal evidence fallacy is, is shown in Fig. 3. The implication of this meme is that the successful businessmen in the image are dropouts thus it is good or better to be a dropout or not attain an education at all. But what the meme is missing is the fact that all these three individuals are anomalous data points. Out of hundreds of thousands of people who give up on education, only a handful become successful businessmen. The wide majority of the uneducated masses either stagnate on the social level they were included in the beginning or fall further down. In contrast to that, those who do obtain an education, tend to improve their social standing in a higher probability.
The popularity of the anecdotal evidence fallacy comes from the innate characteristic of humans where it is much easier to believe someone’s testimony as opposed to understanding complex data and variation across a continuum. While it is generally understood that quantitative scientific measures are almost always more accurate than personal perceptions and experiences, the overwhelming inclination in humans is to believe something that is tangible or the word of a “trustworthy” individual over the abstract reality of statistics . This is exactly how religious miracles and faith healings take root in people’s minds. No matter the existence of thousands of examples of people praying to God and not winning the lottery, the one that get sensationalized and remembered by the common people is the story of that one poor person who won the lottery who also, coincidentally, prayed to God the previous day.
The process of the populace accepting a case of anecdotal evidence as proof is fueled by the availability heuristic which then leads to an overestimation of prevalence. In cases on miracles and such where “a cause can be easily linked to an effect, people overestimate the likelihood of the cause having that effect (availability)“. This is why especially religious anecdotes are widely accepted by the gullible masses. Due to the availability heuristic vivid, emotionally charged anecdotes seem more plausible to the simple minded. Thus they give them greater weight  than the more “boring” normal incidents.
As I always say, what is a rule without exceptions? There is a number of instances where what seems like anecdotal evidence fallacy is in fact not the fallacy. The first is when the anecdote is offered as a data point and not as proof. This is when the opponent have other rational arguments to counter your position successfully and the anecdote is just used as a data point in that process. Basically, s/he does not say “Here is a story that disagrees with you. Therefore you are wrong”.
Second instance is when a statistically significant number of consistent anecdotes are presented. In that case, the argument shifts from anecdotal evidence to statistical evidence. Unlike anecdotal evidence, statistical evidence is acceptable as a logical proof to establish a point. It is also called inductive reasoning. In fact, refusing to come to a conclusion at the face of consistent and repeated anecdotes is by itself another fallacy named slothful induction fallacy. “When Lucy pulls the football away from Charlie Brown again and again, but he keeps trusting her, he isn’t avoiding the anecdotal fallacy; he’s being a fool”.
The third instance is when the anecdote is used to counter a universal claim as a counter-example. This is a valid form of proof named proof by counter-example. The point to note here is the fact that this works only when there is a universal claim . For example, the universal claim “All numbers are either positive or negative” can be disproved by the single example “0” (Zero). The universal claim “all musical arrangements have sounds” can be disproved by John Cage’s 4’33”. The take away on this point is that “one counterexample is all it takes to prove a universal rule false” . (The inverse of this is proving an existential rule true. But to avoid confusion, I shall not describe it here.) Note that once you refute a universal claim with a counter example, your opponent might invoke the “No True Scotsman Fallacy“. You can read more about that by following the provided link above.