Cum Hoc, Ergo Propter Hoc

Type: Non Causa Pro Causa

Quote…

Near-perfect correlations exist between the death rate in Hyderabad, India, from 1911 to 1919, and variations in the membership of the International Association of Machinists during the same period. Nobody seriously believes that there is anything more than a coincidence in that odd and insignificant fact.

…Unquote

Source: David Hackett Fischer, Historians' Fallacies: Toward a Logic of Historical Thought (Harper & Row, 1970), pp. 168-169.

Example:

Charging that welfare causes child poverty, [Gary Bauer] cites a study showing that "the highest increases in the rate of child poverty in recent years have occurred in those states which pay the highest welfare benefits. The lowest increases—or actual decreases—in child poverty have occurred in states which restrain the level of AFDC payments."

Context

Counter-Example:

The bigger a child's shoe size, the better the child's handwriting.
Therefore, having big feet makes it easier to write.

Exposition:

Cum Hoc is the fallacy committed when one jumps to a conclusion about causation based on a correlation between two events, or types of event, which occur simultaneously. In order to avoid this fallacy, one needs to rule out other possible explanations for the correlation:

• A third event—or type of event—is the cause of the correlation.

  For instance, consider the Counter-Example: Children's shoe sizes will be positively correlated with many developmental changes, because they are the common effects of growth. As children grow, so do their feet, and their shoe sizes increase, their handwriting improves, and they develop in many other ways. So, growth is the common cause of both increased shoe size and improved handwriting in children.

• The direction of causation may be the reverse of that in the conclusion.

  For instance, suppose that statistics show a positive correlation between gun ownership and violent crime, namely, the higher number of guns owned, the higher the rate of violent crime. It would be tempting to jump to the conclusion that gun ownership causes violent crime, but the causal relationship may be the exact reverse. High rates of violent crime may cause fearful citizens to purchase guns for protection.

  This type of error is what distinguishes cum hoc from its better known sibling post hoc. In a post hoc fallacy, the supposed cause temporally precedes the alleged effect, so there is no possibility that the causal relationship is the reverse.

• The correlation may simply be coincidence.

  Statistical lore is filled with examples of coincidental correlations, for example see the Quote-Unquote.

Source:

David Hackett Fischer, Historians' Fallacies: Toward a Logic of Historical Thought (Harper & Row, 1970), pp. 167-169.

Context of the Example: