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:::Able806, I'm interested in looking at the publications you mentioned that use Monte Carlo methods to analyze small data sets. Could you provide some examples? Thanks. [[User:SJohnson|SJohnson]] 16:41, 5 March 2009 (EST)

:::Able806, I'm interested in looking at the publications you mentioned that use Monte Carlo methods to analyze small data sets. Could you provide some examples? Thanks. [[User:SJohnson|SJohnson]] 16:41, 5 March 2009 (EST)

:::Able806, you still seem to miss the point about how inappropriate the Monte Carlo method (as used in the Lenski paper) is for evaluating rarely occurring events.  You need to open your mind to be productive.  If you simply cling to a view that Lenski (who I don't think has any meaningful education in statistics) must somehow be right, then you're not going to make any progress in understanding the flaws.--[[User:Aschlafly|Andy Schlafly]] 17:07, 5 March 2009 (EST)

:::Able806, you still seem to miss the point about how inappropriate the Monte Carlo method (as used in the Lenski paper) is for evaluating rarely occurring events.  You need to open your mind to be productive.  If you simply cling to a view that Lenski (who I don't think has any meaningful education in statistics) must somehow be right, then you're not going to make any progress in understanding the flaws.--[[User:Aschlafly|Andy Schlafly]] 17:07, 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.

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.

:I’m still waiting to hear which literature says that “Monte Carlo resampling” is “more accurate than the chi-squared test”. The page mentioned above [http://faculty.vassar.edu/lowry/chi_beta.html] is a discussion of why statisticians “fail to reject the null” rather than “accepting the null” when the p-value is above 0.05 or so. The page says nothing about superiority of Monte Carlo methods. Why were alternate hypothesis distributions mentioned? Only the null hypothesis distribution is used to calculate a p-value. Yates’s correction is for 2x2 contingency tables [http://en.wikipedia.org/wiki/Yates%27_correction_for_continuity]. It doesn’t apply in this case. Finally, what the heck do “covariance structure analysis” and “allele frequencies at a highly polymorphic locus” have to do with this problem? [[User:SJohnson|SJohnson]] 16:38, 5 March 2009 (EST)

:I’m still waiting to hear which literature says that “Monte Carlo resampling” is “more accurate than the chi-squared test”. The page mentioned above [http://faculty.vassar.edu/lowry/chi_beta.html] is a discussion of why statisticians “fail to reject the null” rather than “accepting the null” when the p-value is above 0.05 or so. The page says nothing about superiority of Monte Carlo methods. Why were alternate hypothesis distributions mentioned? Only the null hypothesis distribution is used to calculate a p-value. Yates’s correction is for 2x2 contingency tables [http://en.wikipedia.org/wiki/Yates%27_correction_for_continuity]. It doesn’t apply in this case. Finally, what the heck do “covariance structure analysis” and “allele frequencies at a highly polymorphic locus” have to do with this problem? [[User:SJohnson|SJohnson]] 16:38, 5 March 2009 (EST)

:Regarding the "Fisher z-transformation p-value" from the paper, garbage in garbage out. If the p-values were bad to begin with, then why would a combination of them be meaningful? [[User:SJohnson|SJohnson]] 10:49, 9 March 2009 (EDT)

:Regarding the "Fisher z-transformation p-value" from the paper, garbage in garbage out. If the p-values were bad to begin with, then why would a combination of them be meaningful? [[User:SJohnson|SJohnson]] 10:49, 9 March 2009 (EDT)

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:::My biology-degreed wife assures me that mutation does not necessarily mean that evolution occurred. What the paper claimed is that evolution (a “key innovation”) occurred in the lab. The key innovation supposedly increased the mutation rate. In the experiments, the observed mutation rate increased after generation 31,000, but not enough to make a statistically significant claim that the rate is not constant. The analysis in the paper was similar to flipping a coin ten times, counting six heads and claiming that the coin must be biased against tails. In reality, there’s nothing surprising about a fair coin producing slightly more of one outcome than the other. Just like there's nothing surprising about there being slightly more mutations in later generations than early generations given the null hypothesis (constant mutation rate). [[User:SJohnson|SJohnson]] 10:46, 9 March 2009 (EDT)

:::My biology-degreed wife assures me that mutation does not necessarily mean that evolution occurred. What the paper claimed is that evolution (a “key innovation”) occurred in the lab. The key innovation supposedly increased the mutation rate. In the experiments, the observed mutation rate increased after generation 31,000, but not enough to make a statistically significant claim that the rate is not constant. The analysis in the paper was similar to flipping a coin ten times, counting six heads and claiming that the coin must be biased against tails. In reality, there’s nothing surprising about a fair coin producing slightly more of one outcome than the other. Just like there's nothing surprising about there being slightly more mutations in later generations than early generations given the null hypothesis (constant mutation rate). [[User:SJohnson|SJohnson]] 10:46, 9 March 2009 (EDT)

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