By Larry Lutsky, PhD. firstname.lastname@example.org
Your friend from out of town tells you that he has a ticket for a ball game tonight, but he is worried because there is rain in the forecast.Â If there is any rain at all the game will be canceled.Â The next day you hear on the radio that the game was canceled.Â Can you conclude that it rained the night before at the ball park?Â It may seem so, but a momentâ€™s reflection will suggest there may be other reasons why a game can be canceled e.g., hurricane, lightening, electrical blackout, etc.Â For the same reason, it canâ€™t be concluded that the game will be played even if it doesnâ€™t rain.Â You can conclude with certainty, however, that if the game was played it did not rain.Â Mathematicians would say that statements of the form
(1) if A then B
must have the same truth value as
(2) If not B then not A
That is, if (1) is true then (2) must be true as well.Â Studies have shown that people have an easier time looking for evidence in the form of (1) to confirm an hypothesis, than looking for evidence in the form of (2) to disconfirm an hypothesis.Â This has been called the confirmation bias.Â Good critical thinking skills require one to be aware of the trap of confirmation bias by seeking evidence that would possibly disconfirm an hypothesis as well as evidence that would confirm it.