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:where <math>n_{i,j}</math> is the observed value and <math>E\left[n_{i,j}\right]</math> is the expected null hypothesis value. So if you have MS Excel, another way to arrive at the p-value of 0.19 is to type “=CHIDIST(14.82,11)” into a cell. Cheers! [[User:SJohnson|SJohnson]] 16:38, 5 March 2009 (EST)
 
:where <math>n_{i,j}</math> is the observed value and <math>E\left[n_{i,j}\right]</math> is the expected null hypothesis value. So if you have MS Excel, another way to arrive at the p-value of 0.19 is to type “=CHIDIST(14.82,11)” into a cell. Cheers! [[User:SJohnson|SJohnson]] 16:38, 5 March 2009 (EST)
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::OK, thanks for the info. From what I'd calculated and looked up in tables, the numbers seemed close to a df=11 for a chi-square of ~14. (Aside: With terms having 17/3 in the denominator in the figures above, were you using the test of independence? I was using Pearson's test for [http://en.wikipedia.org/wiki/Pearson%27s_chi-square_test#Test_for_fit_of_a_distribution fit of a distribution] which returns a chi-squared value of 14 and roughly matched the p-values you reported, assuming the df was 11).
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::Also, the first sentence of the article reads: "Blount, Borland, and Lenski[1] claimed that a key evolutionary innovation was observed during a laboratory experiment. That claim is false." There were several claims in the paper. The 'key evolution innovation' was acquisition of the ability to utilize citrate as a food source. That claim was demonstrated multiple times. The claim, which pertains to this statistics discussion was that the Cit+ phenotype arose in a multi-step process, first requiring a rare, pre-adaptive mutation before additional mutation(s) lead to the subsequent development of citrate utilization.--[[User:Argon|Argon]] 20:46, 5 March 2009 (EST)
    
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