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In the book "Causal Inference In Statistics" by Pearl et al., there is the following problem (study question 1.2.2.)

A baseball batter Tim has a better batting average than his teammate Frank. However, someone notices that Frank has a better batting average than Tim against both right-handed and left-handed pitchers. How can this happen? (Present your answer in a table.)

This is basically an example of the Simpson's paradox. The following table of proportions is used in the solution

enter image description here

And, apparently, the "casual story" would be

  • left-handed batters, on average, hit better than their right-handed counterparts
  • Frank met significantly more left-handed than Tim

And the solution is then "left-handed batters is a common cause of meeting the player and failure", thus we should look at the segregated data, that is, we should compare Frank and Time with left-hand and right-hand batters separately.

I am not fully understanding this "causal story". It is clear that Frank met more left-handed than Tim, according to the table. But how can we solve this problem if we do not know that "left-handed batters, on average, hit better than their right-handed counterparts". Where does this information come from? Or is this just a supposition in order to draw a conclusion? For example, could we have supposed that right-handed batters are better than left-handed? Then what? Furthermore, how can we come up with these tables?

In general, how do we know whether to draw some conclusions based on the segregated or aggregated data?

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"left-handed batters, on average, hit better than their right-handed counterparts" is drawn from a long-held belief in many sports that lefties are more gifted than right-handed athletes. This example shows that when making the decision between aggregate and segregate data, it is important to consider the intricacies of the domain you are studying.

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  • $\begingroup$ It is a social belief like in football, tennis and almost all sports. Left-handed players are believed to be more gifted than their right-handed counterparts mainly because they are harder to come by. Here is a link which explains how baseball favors lefties : livescience.com/2665-baseball-rigged-lefties.html. Please let me know if I need to improve my answer. $\endgroup$ – Salma Bouzid Jan 19 '19 at 15:45
  • $\begingroup$ Yes, this how domain knowledge comes in handy. That's why you need to know the intricacies of the field you are studying before presenting conclusions. $\endgroup$ – Salma Bouzid Jan 19 '19 at 15:50

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