Problems averaging fold changes
average, mean
Solution
This is a great question and I've been searching for the answer myself. Here is what I've come up with: 1) take the log of the fold changes (on the 0 to infinity scale); 2) average the log values; 3) calculate the anti-log; 4) then transform to +/- values if necessary
In your second example:
log(0.8) = -0.09691
log(1.25) = 0.09691
average = 0
10^0 = 1 (average fold change of 1)
For your first example with the 6 numbers and using this method I get your average to be 1.214425 fold.
Problem
I work with fold changes as defined in the wikipedia article: http://en.wikipedia.org/wiki/Fold_change I work with fold changes for quite a while now but there was never really the need to calculate an average fold change across all my fold changes. When I did so yesterday I realised it's not a straight forward as it seems by just taking the mean of all fold change values. Here's an example which demonstrates my problem: Let's consider 6 fold changes: ``` A = 1.1635710 B = 0.9284593 C = 1.1688855 D = 1.6400114 E = 1.2073252 F = 1.2830912 ``` What I always do is to transform fold changes below 1 into the -1 format by dividing -1 by the fold change: ``` A = 1.1635710 B = -1.077053 C = 1.1688855 D = 1.6400114 E = 1.2073252 F = 1.2830912 ``` Then to calculate the average fold change I took the mean of all fold change values which results in 0.8976386 suggesting that the average fold change is decreased even though from the values itself it is obvious that the average fold change should be increased as most of them are increased with a even higher magnitude. Then I thought I calculate the average fold change before I transform fold changes below 1 into the minus format. Then I got an average value of 1.231891 which seems much more plausible. However, I doubt that this is correct either. Let's simplify it even more. Let's say we have two fold changes with values of 0.8 (-1.25) and 1.25. Apparently, when looking at -1.25 and 1.25 the average fold change should be 1 so no average change. Which makes sense. But taking the average of 0.8 and 1.25 results in 1.025 so a slight increase. Long story made short, I am not sure of how to best average a list of fold changes to get a representative average fold change.