Why is my "basic ratio" & "Z-score difference" different?!
I have 2 sets of data, 300 plots in each set.
I plot the basic ratio of the 300 data points, (ie: one divided by the other). This is fine.
But if I standardize both sets individually by calculating their Z-scores (using their mean and standard deviation) and then go on to plot the DIFFERENCE of these 2 Z-score sets, I thought the relative output should be the same as simply plotting the ratio (but on a difference absolute scale, of course).
What I mean is, these 2 final plots (ratio and Z-score difference) I thought should make exactly the same "moves" relative to themselves when plotted as graphs, and so be equals with their relative highs and lows. But they are not.
They are VERY similar, each high and low point can be spotted on both outputs in the same place on the X axis, but they do not actually match in terms of relative movement (for example, 3 peaks in a row on the ratio chart may be slightly ascending with each new peak, but the same 3 peaks on the Z-score difference chart are slightly descending, or flat).
Please could you answer me 2 questions regarding this:
1 - why are they slightly different?
2 - which one is "correct" in terms of plotting the TRUE relative fluctuations of the data sets?
I’m guessing because the ratio is “untouched” then that should be the true output of the differences between the 2 sets. Also, I think (although am probably wrong!!) that because the data sets are NOT normally distributed the Z-scores calculations are slightly “wrong” (for want of a better word) and this could be leading to the slight differences in the 2 final outputs.