Changeset 20936 in project
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 10/22/10 07:30:05 (11 years ago)
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wiki/eggref/4/randomtest
r20933 r20936 71 71 are the number of experiments which resulted in each possible outcome, 72 72 and probabilities of each outcome {{p1, p2,... pk}}, is given as: 73 \chi^{2} = \sum_{1 <= i <= k}{\frac{(Y_{i}  m p_{i})^{2}}{np_{i}}} 73 [[image:randomtest.fig1.png]] 74 75 \chi^{2} = \sum_{1 <= i <= k}{\frac{(Y_{i}  m p_{i})^{2}}{np_{i}}} 74 76 75 77 {{\Chi^2}} will grow larger as the measured results diverge from those … … 77 79 calculated for an experiment with d degrees of freedom (where 78 80 {{d=k1}}, one less the number of possible outcomes) is due to chance 79 is: 81 is: [[image:randomtest.fig2.png]] 80 82 81 83 Q(\Chi^2,d) = [2^{d/2} * \Gamma(d/2)]^{1} * \int_{\Chi^2}^{\infty}(t)^{d/21} * exp(t/2) * dt 82 84 83 85 Where Gamma is the generalization of the factorial function to real and complex arguments: 86 [[image:randomtest.fig3.png]] 84 87 85 88 \Gamma(x) = \int_{0}^{\infty} t^{x1} * exp(t) * dt
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