Z Score Values Used and Interpretation

Question

I have been working on a time series-like data set from using calcium indicators (waveform data). A script I was given transforms the voltages (x values) into Z-scores. However, the mean and standard deviation used in calculating these scores are from a baseline period before the trial, which makes it look something like this:

$$ x_{trial} - \mu_{baseline} \over \sigma_{baseline} $$

I know that the "x - mu" represents the difference between voltages during the trial and mean voltages at baseline, but how would using a baseline standard deviation affect the interpretation? Similarly, how would using a mu value from the trial and sigma value from the baseline period be interpreted?

Thanks in advance!

Answer 1

This can be interpreted from the hypothesis testing point of view. The null hypothesis is to assume that your x follows the same normal distribution as your baseline (given $\mu$ and $\sigma$). The z-score tells how many standard deviations your observation deviates from the assumed mean. From it you can estimate the probability of observing such a great deviation if your null assumption was true. However, you may also use z-score just to scale the result and see if you observation is like baseline (near 0 or maybe in range [-2,2]) or exceptional.

It is hard to see what you could test if you assumed the null distribution with the observed mean but the baseline standard deviation.