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→In Search of the Truth: Who's Better?
In the case of the 508 games played in the four years of cribbage competition, our expected number of wins for each player is 254. We can plug this value and the observed number of wins into the equation to determine the <math>\chi^2</math> value for the analysis:
:<math>\chi^2 = {(264 - 254)^2 \over 254}+{(244 - 254)^2 \over 254}</math>:<math>\chi^2 \approx 0.787401575</math>
We now compare this value of <math>\chi^2</math> to a threshold value of <math>\chi^2</math> in our chi-squared distribution of two degress of freedom. In experiments of this kind, it is customary to take a confidence level of at least 95% as evidence that your data demonstrates a significant trend, however to have a confidence of 95% that one player were better than the other in this case we would need a <math>\chi^2</math> value of '''3.84''' or greater. 0.787... is far too low, corresponding more closely to a confidence of about 40%.
Though it went against the standards of every academic field, including his own basic training in [[Psychology]] statistics, Zach seemed satisfied by this level of confidence. Writing: ''There was a time senior year when a t-squared analysis ''[sic.]'' 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.''
==Cribbage moments==
