Cum Hoc, Ergo Propter Hoc

Taxonomy: Logical Fallacy > Informal Fallacy > Non Causa Pro Causa > Cum Hoc, Ergo Propter Hoc1

Sibling Fallacy: Post Hoc, Ergo Propter Hoc

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.2

…Unquote

Forms
Events C and E both happened at the same time.
Therefore, C caused E.		 Events of type C have always been accompanied by events of type E.
Therefore, events of type C cause events of type E.

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."3

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.4

Exposure:

Mere correlation between two variables is not enough to rationally conclude that one causes the other. To avoid committing the Cum Hoc fallacy, rule out other possible explanations for the correlation:

  1. Coincidence: Statistical lore is filled with examples of coincidental correlations, for example see the Quote-Unquote, above.
  2. Confounding Causation: This occurs when a third event or type of event causes the correlation. For instance, consider the Counter-Example, above: 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.
  3. Reverse Causation: This happens when the supposed effect is the actual cause and vice versa. 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 distinguishes Cum Hoc from its better-known big brother Post Hoc―see the Sibling Fallacy, above. 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.

Context of the Example:

Bauer uses specious statistical studies to discredit the welfare system. … But this study by two Ohio State University sociologists overlooked the fact that median income declined or was flat in the ten states where welfare costs and child poverty rose, while income rose substantially in nine of the ten states where welfare payments and poverty showed the least increase. The data showed that economic decline caused an increase in both welfare and child poverty.

Notes:

  1. Translation: "With this, therefore because of this", Latin.
  2. David Hackett Fischer, Historians' Fallacies: Toward a Logic of Historical Thought (Harper & Row, 1970), pp. 167-169.
  3. John B. Judis, "The Mouse That Roars", The New Republic, 8/3/1987, p. 25.
  4. Few writers on fallacies bother to distinguish between the Cum Hoc and Post Hoc fallacies, with most preferring the latter. For exceptions, see Fischer's Historians' Fallacies―see note 2, above―and Madsen Pirie's How to Win Every Argument: The Use and Abuse of Logic (2013).