I have a dataset that I normalize so that the average equals 1. If I then log2 transform the dataset, should the average of the log2 data equal 0?
1, 1, 1. The average of the dataset is equal to 1. If I log2 transform the data, the new set is: 0; 0; 0;. The new average is 0.
So, why does this not work when I start using different numbers? For example:
Data set: 1, 2, 3. Average = 2. I normalize the data set by dividing by the mean (2).
Normalized data set: 0.5, 1, 1.5. Average = 1. I then log2 transform the dataset.
Log2 transformed: -1, 0, 0.58496. Average = -0.13835.
Why does the average of the log2 dataset not equal 0 if the normalized average equals 1? I feel like I'm losing my mind in my inability to understand why this does not work.
Can someone explain to me how to transform my data so that the mean of the log2 transformed data equals zero? I could graph the log2 of the ratio, but I want to plot individual values for a control and experimental group in log2(ratio) format.