# Z Score Values Used and Interpretation

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?

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.