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Talk:PNAS Response to Letter (view source)
Revision as of 19:18, September 20, 2008
, 19:18, September 20, 2008→Data from several experiments
:::::: In other words, the cited paper actually ''supports'' Point 5.--[[User:Aschlafly|Aschlafly]] 09:34, 20 September 2008 (EDT)
:::::: In other words, the cited paper actually ''supports'' Point 5.--[[User:Aschlafly|Aschlafly]] 09:34, 20 September 2008 (EDT)
:::::::Lenski used the weighted method. See note 49 to the paper.--[[User:Toffeeman|Toffeeman]] 14:33, 20 September 2008 (EDT)
:::::::Lenski used the weighted method. See note 49 to the paper and the text around the combination. Of course there is the question of on what basis Lenski weighted the results. Lenski weighted the results on the basis of the Cit+ numbers and we may think it would have been better to weight on the basis of the number of replicates. I have below the calculations (not mine) of combined P-values based on 1) no weighting, 2) weighting on the basis of Cit+ and 3) weighting on the basis of replicates. The weighted Z-transformed = SUM(Weight x Z-score for each run)/SQRT(SUM(Weight^2 for each run))
{| class="wikitable"
|-
! Expt# !! p-value !! z-score !! #Cit+ muts !! #replicates
|-
| 1 || 0.0085 || 2.387 || 4 || 72
|-
| 2 || 0.0007 || 3.195 || 5 || 340
|-
| 3 || 0.0823 || 1.390 || 8 || 2800
|-
|}
Applying the formula described above..
{| class="wikitable"
|-
! Weighting !! Z transformed !! p
|-
| Equal || 4.025 || <0.001
|-
|By total Cit+|| 3.576 || <0.001
|-
|By total replicates|| 1.825 || 0.034
|-
|}
So weighting on the basis of the number of replicates considerably increases the P-value. It remains, however, well within the range of statistical significance (0>P<0.05). If we hold that Lenski should have weighted on the basis of replicates then he should have rejected the null hypothesis and reached exactly the same conclusions that he did. The entire paper would have been exactly the same except the sentence “the result is extremely significant (P<0.0001) whether or not….” Would read “the result is significant (P<0.04) whether or not”. Point 5 establishes one number and an “extremely”. Point 5, therefore, has no weight (excuse the pun).
--[[User:Toffeeman|Toffeeman]] 15:18, 20 September 2008 (EDT)