When plotting quite dissimilar values, it is common to use a logarithmic scale for the Y axis. Let's say, I have the following lists (a and b) of values.
a = [6.43x10^6, 9.42x10^6, 12.7x10^6, 12.9x10^6, 18x10^6, 16.3x10^6]
b= [5.19x10^6, 5.64x10^6, 7.06x10^6, 6.73x10^6]
If I want to compare 'a' and 'b', let's say by using the mean and the standard deviation I have at least two options:
1. I compute the average and the std.dev of each list, but the standard deviation of 'a' will be huge and the 'a' and 'b' means won't be different.
2. I could transform each value in 'a' and 'b' by using Log10 and then calculate the mean and the standard deviation of such logarithms.
1 and 2 produce substantially different results. Intuitively it looks to me that 1 is correct and 2 is not.
What's your opinion?
Hello Juan,
I don't know if the values you've given are typical of what motivated your query, but it seems to me that the simplest solution, given your example, is to: (a) linearly transform each score by dividing all by 10^6; then (b) perform whatever comparison helps to address the specific research question you're trying to address:
A (6.43, 9.42, 12.7, 12.9, 18.0, 16.3)
B (5.19, 5.64, 7.06, 6.73)
The linear transform will not change the shape of either distribution, whereas the log transform will (even if all values have the same characteristic, the incremental changes in mantissa are not equal across the range).
Good luck with your work.
I could find no question. However, you are allowed to report both of them (one of them before transformation and the other after it); It is not an either-or situation.
- Badges
- Science topic
- Similar topics
- Social Psychology
- Attitude