The Silver Linings Chi-Square Playbook

Author: Michael A. Lewis

Star of Silver Linings Playbook Jennifer Lawrence at the Oscars in 2011.

Star of Silver Linings Playbook Jennifer

Lawrence at the Oscars in 2011.

Image by Mingle MediaTV/Wikimedia.

Lately Jennifer Lawrence seems to have a knack for appearing in movies where mathematics is part of the action. This was quite obvious in the Hunger Games, a young adult novel-turned-blockbuster movie that featured lessons in probability and game theory. Lawrence’s latest lesson in mathematics is provided by the Oscar-nominated (for best Picture) Silver Linings Playbook.

Silver Linings Playbook, on the surface, is a deftly acted and compelling look at mental illness. It stars Bradley Cooper as Pat a former teacher who is suffering from Bipolar disorder, Robert De Niro as Pat’s obsessive compulsive father Pat Sr., and Jennifer Lawrence as Pat’s companion (for lack of a better term) Tiffany. Much of the drama and humor in the film comes from Pat and his father’s odd relationship.

Pat Sr. is a big fan of the Philadelphia Eagles and thinks that the Eagles do better when Pat watches the game with him. The problem is that Pat has been spending a lot of time with Tiffany and, therefore, hasn’t been around to help the Eagles win by watching the game with his father. At one point, Pat Sr. confronts Tiffany about this and Tiffany fights back claiming that the Eagles have actually done better when Pat has been with her. As I watched this very hilarious scene, I couldn’t help thinking about the Chi-Square Test.

The Chi-Square Test is a statistical test that is used to see if two variables are related to each other, where the variables in question are nominal or ordinal. Nominal means that the categories of the variable are simply labels with no quantitative meaning, such as black or non-black for the variable race. Ordinal means that the categories of the variable do have a quantitative meaning but this quantitative aspect amounts to a mere ranking - one category can be higher or lower than another but the differences between rankings have no meaning. Level of assent with a statement in a survey where the options are “disagree”, “agree”, or “strongly agree” would be an example of an ordinal variable. The logic of the Chi-Square Test works is as follows:

Suppose we have two variables A and B. The categories of A are A1 and A2 and those of B are B1 and B2. If A and B are unrelated to each other, or independent of one another in statistical jargon, we’d expect a certain number of cases in each of the cells of the following table:

B1

B2

A1

Expected Number1 1

Expected Number1 2

A2

Expected Number2 1

Expected Number2 2

If the actual numbers in these cells depart enough from the expected ones this is taken as evidence that variables A and B are related.

In terms of the Chi-Square Test Jennifer Lawrence’s character Tiffany was making the case that the Tiffany Factor (variable A) and Eagle’s Success (variable B) are related. More specifically, she was arguing that the Eagles are more likely to win when Pat is with her. Here is the table for this application of the Chi-Square Test:

Eagles Win

Eagles Lose

Pat with Tiffany

Expected Numberwith win

Expected Numberwith lose

Pat not with Tiffany

Expected Numbernot with win

Expected Numbernot with lose

What Tiffany was contending is that the Pat with Tiffany/Eagles Win and the Pat not with Tiffany/Eagles Lose cells of the table would have bigger numbers than the expected ones for those two cells. This would mean that the with Tiffany and Eagles winning and the not with Tiffany and Eagles losing combinations are the more likely outcomes.

So Silver Linings Playbook isn’t just a sometimes funny, sometimes heartbreaking, and always well acted film. It’s also a statistics lesson in disguise.

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Comments

D L McArthur

The claim "that the Eagles have actually done better when Pat has been with her" might also be expressed as an odds ratio and its accompanying confidence interval, addressing the problem somewhat more explicitly than the chi-square test.

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