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1918 andrew gelman stats-2013-06-29-Going negative


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Introduction: Troels Ring writes: I have measured total phosphorus, TP, on a number of dialysis patients, and also measured conventional phosphate, Pi. Now P is exchanged with the environment as Pi, so in principle a correlation between TP and Pi could perhaps be expected. I’m really most interested in the fraction of TP which is not Pi, that is TP-Pi. I would also expect that to be positively correlated with Pi. However, looking at the data using a mixed model an insignificant negative correlation is obtained. Then I thought, that since TP-Pi is bound to be small if Pi is large a negative correlation is almost dictated by the math even if the biology would have it otherwise in so far as the the TP-Pi, likely organic P, must someday have been Pi. Hence I thought about correcting the slight negative correlation between TP-Pi and Pi for the expected large negative correlation due to the math – to eventually recover what I came from: a positive correlation. People seems to agree that this thinki


Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 Troels Ring writes: I have measured total phosphorus, TP, on a number of dialysis patients, and also measured conventional phosphate, Pi. [sent-1, score-0.384]

2 Now P is exchanged with the environment as Pi, so in principle a correlation between TP and Pi could perhaps be expected. [sent-2, score-0.472]

3 I’m really most interested in the fraction of TP which is not Pi, that is TP-Pi. [sent-3, score-0.064]

4 I would also expect that to be positively correlated with Pi. [sent-4, score-0.125]

5 However, looking at the data using a mixed model an insignificant negative correlation is obtained. [sent-5, score-0.628]

6 Then I thought, that since TP-Pi is bound to be small if Pi is large a negative correlation is almost dictated by the math even if the biology would have it otherwise in so far as the the TP-Pi, likely organic P, must someday have been Pi. [sent-6, score-0.995]

7 Hence I thought about correcting the slight negative correlation between TP-Pi and Pi for the expected large negative correlation due to the math – to eventually recover what I came from: a positive correlation. [sent-7, score-1.514]

8 People seems to agree that this thinking is nonsense. [sent-8, score-0.059]

9 They say I can just keep to the analysis and forget about RTM. [sent-9, score-0.055]

10 I cannot help thinking that if I could measure TP-Pi by a method not requiring me to subtract Pi, I would get at least a cleaner result. [sent-10, score-0.281]

11 My reply: I’m getting confused on the details here, but, yes, it is typical that if you have two variables A and B measured on a common scale, that A-B has a negative correlation with B. [sent-11, score-0.768]

12 This comes up, for example, in adjusting for pretest scores in education. [sent-12, score-0.388]

13 People often have the intuition that they should be analyzing posttest – pretest, but it typically makes more sense to look at posttest – 0. [sent-13, score-0.482]

14 Ultimately I suppose the solution is to go beyond correlations and to have a generative model for the joint distribution of TP and Pi. [sent-16, score-0.184]


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