FSharp.Stats
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[Feature Request] Missing medianOfRatios normalization documenation
A proper documentation of the medianOfRatios normalization should be added. From a mathematical perspective the calculation of the geometric mean as the nth square root of the product of all values (1) seems odd, but when displayed as mean of the log-transformed data (2) it becomes clear, that the geometric mean is just an outlier-insensitive measure of the mean, which is intuitive to do when dealing with biological data. No prior log-transform has to be applied before normalizing the data with this method. If required a log transform can be applied to the normalized values to restore homoscedasticity.
In short, you determine the (antilog of the (mean of the (values in log space)))!
It may be beneficial to implement a second version of the median of ratios (mor) normalization method, that works on log transformed data. When the data is already log transformed to reduce heteroscedasticity, a normalization does not require a geometric mean, but a standard arithmetic mean.
The additional log transform in the default mor would stabilize the values disproportionately and therefore the resulting differencial normalization would be non-sufficient.
Additionally, it would be great to have access to the applied scaling factors to check the validity of the normalization!