What is log transformation formula?
For example, the mean of the log-transformed observations (log yi), μ ^ L T = ( 1 / n ) * ∑ i = 1 n log y i is often used to estimate the population mean of the original data by applying the anti-log (i.e., exponential) function to obtain exp( μ ^ L T ).
How do you calculate log transformation?
Recall the general form of a logarithmic function is: f(x)=k+alogb(x−h) where a, b, k, and h are real numbers such that b is a positive number ≠ 1, and x – h > 0. A logarithmic function is transformed into the equation: f(x)=4+3log(x−5).
How is the standard deviation of a log transformed variable calculated?
Keep the standard deviation as a percent variation or coefficient of variation (CV). Calculate this CV in the same way as for differences or changes in the variable: if SD is the standard deviation of the log-transformed variable, the approximate CV is simply 100SD, and the exact CV is 100 (e SD – 1).
How to convert the mean of a log transformation to raw units?
Convert the mean of the log-transformed variable back to raw units using the back-transformation Y = e mean (if your transformation was Z = logY) or Y = e mean/100 (if you used Z = 100logY). Keep the standard deviation as a percent variation or coefficient of variation (CV).
How is the antilog of the log transformed data measured?
The antilog of the standard deviation, however, is not measured in mmol/l. Calculation of the standard deviation of the log transformed data requires taking the difference between each log observation and the log geometric mean.
When to use a logarithmic transformation in statistics?
A logarithmic transformation is often useful for data which have positive skewness like this, and here the approximation to a normal distribution is greatly improved. For the untransformed data the mean is 0.51 mmol/l and the standard deviation 0.22 mmol/l. The mean of the log10 transformed data is -0.33 and the standard deviation is 0.17.