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 > > What I am doing wrong to get the different values
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.hard...@wlandres.net> Fax-to-email: +44 (0)870 094 0861 Date: 12-May-11 Time: 17:37:45 ------------------------------ XFMail ------------------------------ ______________________________________________ R-help@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.
