Changes

6. It was error to include generations of the E. coli already known to contain trace Cit+ variants. The highly improbable occurrence of four Cit+ variants from the 32,000th generation in the Second Experiment suggests an origin from undetected, pre-existing Cit+ variants.

6. It was error to include generations of the E. coli already known to contain trace Cit+ variants. The highly improbable occurrence of four Cit+ variants from the 32,000th generation in the Second Experiment suggests an origin from undetected, pre-existing Cit+ variants.

7. The Third Experiment was erroneously combined with the other two experiments based on outcome rather than sample size, thereby yielding a false claim of overall statistical significance.

7. The Third Experiment was erroneously combined with the other two experiments based on outcome rather than sample size, thereby yielding a false claim of overall statistical significance.  Lenski's paper applied the Whitlock Z-transformation incorrectly, perhaps intentionally so, in making a claim that Lenski's results were "extremely significant": "We also used the Z-transformation method to combine the probabilities from our three experiments, and '''the result is extremely significant (P < 0.0001) whether or not''' the experiments are weighted by the number of independent Cit+ mutants observed in each one."<ref>Lenski paper at 7902 (citation to Whitlock paper omitted, emphasis added).</ref>  Lenski's "whether or not" refers to two incorrect applications of the Whitlock technique, obscuring how the straightforward, correct weighting based on sample size was ''not'' used.  A reader could conclude that the Lenski paper deliberately conceals the misapplication.

8.  Lenski's paper is not clear in explaining how the results of his largest experiment (Third Experiment) failed to confirm his hypothesis with statistical significance, even with the incorrect inclusion of the Cit⁺ variant generations.  Instead, his paper refers to his largest experiment as "marginally ... significant," which serves to obscure its statistical insignificance.  Other works published in PNAS are clear in defining statistical significance in the traditional way, which Lenski's Third Experiment (even with incorrect inclusion of the above-referenced generations) failed to satisfy.<ref>See, e.g., [http://www.pnas.org/cgi/content/full/0701990104 Cholera toxin induces malignant glioma cell differentiation]</ref>

8.  Lenski's paper is not clear in explaining how the results of his largest experiment (Third Experiment) failed to confirm his hypothesis with statistical significance, even with the incorrect inclusion of the Cit⁺ variant generations.  Instead, his paper refers to his largest experiment as "marginally ... significant," which serves to obscure its statistical insignificance.  Other works published in PNAS are clear in defining statistical significance in the traditional way, which Lenski's Third Experiment (even with incorrect inclusion of the above-referenced generations) failed to satisfy.<ref>See, e.g., [http://www.pnas.org/cgi/content/full/0701990104 Cholera toxin induces malignant glioma cell differentiation]</ref>

12.  The p-value computed for experiment two was incorrectly listed as 0.0007 instead of 0.0006 in [http://www.pnas.org/content/105/23/7899.full.pdf]. These p-values are meaningless because the paper used a flawed test statistic (see: [[Significance of E. Coli Evolution Experiments#Test Statistics]]). However, the error illustrates the need to use enough random realizations when using Monte Carlo methods to measure p-values.

12.  The p-value computed for experiment two was incorrectly listed as 0.0007 instead of 0.0006 in [http://www.pnas.org/content/105/23/7899.full.pdf]. These p-values are meaningless because the paper used a flawed test statistic (see: [[Significance of E. Coli Evolution Experiments#Test Statistics]]). However, the error illustrates the need to use enough random realizations when using Monte Carlo methods to measure p-values.

== References ==

== References ==