Talk:Significance of E. Coli Evolution Experiments

SJohnson, your assessment, while good in the utilization of the chi-squared test is unfortunately incorrect. The Monte Carlo resampling gives a more accurate p-value than the chi-squared. You may research the literature (i.e. publications in statistical mathematics, many pubs actualy compare Monte Carlo vs Chi Squared) to discover that this method is commonly used in advance statistical work and how it is more accurate than the chi-squared test.--Able806 17:00, 4 March 2009 (EST)

It doesn’t make sense to compare the chi-square test, which is a specific statistical hypothesis test, to Monte Carlo methods, which can be used for anything from fluid motion modeling to p-value computations. You can use Monte Carlo methods to compute the p-values of the chi-square test!

Monte Carlo methods involve the generation of random realizations. Your broad claim the Monte Carlo methods are “more accurate” than the chi-square test is obviously incorrect because the accuracy of Monte Carlo methods always depends on the number of random realizations generated. When p-values are small, Monte Carlo methods are notoriously inaccurate unless the number of realizations generated is enormous.

Which publications compare Monte Carlo to chi-square and show that the former is more accurate? Could you provide specific examples? Thanks. SJohnson 18:50, 4 March 2009 (EST)

In furtherance of SJohnson's remarks with respect to rarely occurring events, the use of the basic Monte Carlo method is plainly incorrect for modeling a rarely occurring event, as the Lenski paper did. This has long been pointed out in Flaws in Richard Lenski Study. I know evolutionists will never admit a flaw in anything promoting their pet theory, but this (and other) flaws in that paper is undeniable.

Watch how evolutionists defended obvious errors in the Lenski paper, and then realize why the Piltdown Man fraud was taught for 40 years without evolutionists admitting it was a hoax.--Andy Schlafly 09:55, 5 March 2009 (EST)

Andy, how exactly is the Monte Carlo method incorrect to use in this case? I have seen it used in publications with much smaller datasets.--Able806 10:29, 5 March 2009 (EST)

Sjohnson, I believe you just proved my point. In the literature of mean and covariance structure analysis, non-central chi-square distribution is commonly used to describe the behavior of the likelihood ratio statistic under alternative hypothesis; it is widely believed that the non-central chi-square distribution is justified by statistical theory. Actually, when the null hypothesis is not trivially violated, the non-central chi-square distribution cannot describe the LR statistic well even when data are normally distributed and the sample size is large. Monte Carlo results compare the strength of the normal distribution against that of the non-central chi-square distribution. In an association analysis comparing cases and controls with respect to allele frequencies at a highly polymorphic locus, a potential problem is that the conventional chi-squared test may not be valid for a large, sparse contingency table. Reliance on statistics with known asymptotic distribution is unnecessary, as Monte Carlo simulations can be performed to estimate the significance level of the test statistic.

Here is a link to a great page the provides an interactive example as to why the Chi Squared test would provide poor results compared to the Monte Carlo in relation to the Lenski data workup.

Something you may have overlooked was that the data set is actually too small to use the chi square method correctly. It is often accepted that is any of the analyzed data falls under 10 for a particular cell of the data set then the Yates correction needs to be applied; unfortunately the Yates correction can over correct thus skewing the p-value. Lenksi seemed to understand this by supporting his Monte Carlo p-value results with the Fisher z-transformation p-value.

I hope this helps.--Able806 10:27, 5 March 2009 (EST)

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Quick question for SJohnson: How many degrees of freedom did you choose when calculating the p-value? I'd like to know upon what condition you base that number. Thanks.--Argon 11:05, 5 March 2009 (EST)