Mathematical

Mathematical fallacies are those related to the misunderstanding and misapplication of mathematical concepts, especially probability theory and statistics.

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Gambler’s fallacy:

Definition Example
When it is suggested that the likelihood of a random event can be affected by or predicted from other, independent events. The coin flip has resulted in 5 “heads” in a row. I’m overdue for a “tails”.
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Ecological fallacy:

Definition Example
When inferences about the nature of specific individuals are based solely upon aggregate statistics collected for the group to which those individuals belong. Because the average German is taller than me, you won’t find a German who is shorter than me.
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Base rate fallacy:

Mathematical Fallacy
Definition Example
When a probability judgment is made without taking into account known empirical statistics that affect the probability. The rare disease detection device is 99% accurate, and it detected that I have a rare disease. Therefore I almost certainly do have a rare disease.
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Appeal to probability:

Mathematical Fallacy
Definition Example
When it is assumed that, because something could happen, it is inevitable that it will happen. I’m certain to win the lottery if I just keep buying tickets.
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Hasty generalization:

Definition Example
When a conclusion is made about a group when there are insufficient statistics or an insufficient sample size. I drove through the town and counted 20 residents, all of them women. The town probably has only female residents.
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Linearity fallacy:

Definition Example
When it is assumed that a phenomenon functions linearly, overlooking important factors that may produce non-linearity. The mortality rate of cats falling 20 stories will be double that of cats falling 10 stories.
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Conjunction fallacy:

Definition Example
the assumption that an outcome simultaneously satisfying multiple conditions is more probable than an outcome satisfying fewer of those same conditions. Because Susan is young, it is more probable that she is both a student and unmarried than that she is merely a student.
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Regression fallacy:

Definition Example
When the cause of some apparent phenomenon is assumed to be some factor outside statistical noise and artifacts, when natural and expected statistical dynamics may in part or wholly account for the apparent phenomenon. Last year we had 12 car accidents on main street, double the previous year’s figures! The frequency of accidents on Main Street fell to only 6 again after a speed camera was installed early this year. Therefore, the speed camera has improved road safety.
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