From: Ted Harding <ted.harding_at_wlandres.net>

Date: Thu, 12 May 2011 17:37:48 +0100 (BST)

> [1] 600

*>
*

> [1] 316.2278

*>
*

*> What I am doing wrong to get the different values
*

E-Mail: (Ted Harding) <ted.harding_at_wlandres.net> Fax-to-email: +44 (0)870 094 0861

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Received on Thu 12 May 2011 - 16:40:15 GMT

Date: Thu, 12 May 2011 17:37:48 +0100 (BST)

On 12-May-11 15:15:00, 1Rnwb wrote:

> I have question about log2 transformation and performing mean

*> on log2 data. I am doing analysis for ELISA data. the OD values
**> and the concentration values for the standards were log2
**> transformed before performing the lm. the OD values for samples
**> were log2 transformed and coefficients of lm were applied to get
**> the log2 concentration values. I then backtransformed these
**> log2 concentrations and the trouble started. when i take the
**> mean of log2 concentrations the value is different than the
**> backtransformed concentrations.
**>
*

>> 100+1000/2

> [1] 600

>> 2^( ( log2(100)+log2(1000) )/2 )

> [1] 316.2278

Apart from the fact that I think your first line should be

(100+1000)/2

# [1] 550

you are doing nothing whatever wrong! The difference is an inevitable result of the fact that, for any set of positive numbers X = c(x1,x2,...,xn), not all equal,

mean(log(X)) < log(mean(X))

This is because the curve of y = log(x) lies below the tangent to the curve at any given point. If that point is mean(X), and the tangent is y = a + b*x, then

mean(log(X)) < mean(a + b*X) = a + b*mean(X) = log(mean(X))

since y = a + b*x is tangent to y = log(x) at x = mean(X). This is a special case of a general result called Jensen's Inequality.

Your second line is

2^mean(log2(X)) < 2^log2(mean(X)) = mean(X).

where X = c(100,1000).

Ted.

E-Mail: (Ted Harding) <ted.harding_at_wlandres.net> Fax-to-email: +44 (0)870 094 0861

Date: 12-May-11 Time: 17:37:45 ------------------------------ XFMail ------------------------------ ______________________________________________R-help_at_r-project.org mailing list

https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. Received on Thu 12 May 2011 - 16:40:15 GMT

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