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→In Search of the Truth: Who's Better?: chi-sq
Of the 508 games of cribbage played between Fall 2001 and [[Commencement]] 2005, Zach was victorious in 264 games, Jonathan in 244. However, only 31 of Zach's victories were skunks, to Jonathan's 36. This accounts for the smaller margin of difference in the final score: Zach 295, Jonathan 280.
As [[Psychology]] majors, Jonathan and Zach were eventually enriched by a knowledge of basic statistical tests, and from the point of learning the chi-squared analysis -- the statistical test with the power to determine, statistically, which of the two was a better player.
Interpreting data by a chi-square analysis is done using the formula:
<math>\sum_{i=1}^k \left(\frac{X_i-\mu_i}{\sigma_i}\right)^2</math>
Where <math>X_i</math> is the observed value, <math>mu_i</math> is the expected value, and <math>sigma_i</math> is again the expected value, but with different Greek letter representing it to be cute.
There was a time senior year when a t-squared analysis on the number of victories each showed that Zach was, statistically, a superior cribbage player to Jonathan. Once that point was reached, Zach felt his point was proven and lowered his level of play, allowing Jonathan to win a few games and regain a bit of dignity... at least statistically speaking.
