Anecdotal evidence
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Anecdotal evidence is unreliable evidence based on personal experience that has not been empirically tested, and which is often used in an argument as if it had been scientifically or statistically proven. The person using anecdotal evidence may or may not be aware of the fact that, by doing so, they are generalizing.
For example, someone who is not a physician or other kind of expert might argue that eating crushed garlic and drinking one glass of red wine per day will prolong your life, just because their own neighbour indulged in that habit and died aged 90. It becomes clear that in this case any form of inductive reasoning lacks a broad empirical basis.
Similarly, a politician might publicly demand better teacher training facilities just because their own son or daughter happens to have a spectacularly incompetent teacher, or conversely, might insist that public schools are in fine shape just because their own son or daughter happens to have a singularly wonderful teacher.
This is not to say that anecdotal evidence is fallacious per se; it just depends on how it is used. In many cases, it can be the starting point rather than the result of scientific investigation.