I have two pulses one is a simulation the other is experimental data. I my simulation's voltage outputs are to match the experimental data by 95%. Meaning if the voltage of the experimental is 100 then the corresponding point in the simulation would be between 95-105Volts. I can tweak my simulation as much as I want to get them to match by adding switches and filters in the circuit. But a graph that "looks" like it matches is not the same as it being proven by the data. I ran a t - test and a Mann- Whitney (Wilcoxon) test . I am pretty sure a Chi square is not corrected because that is for discrete variables. I don't think that Correlation test is correct because its not dose/response But I am not even sure that that is the correct tests to choose.

The data looks like it follows a normal distribution. But again I am not really sure. What statistical tests would you choose to verify this assumption. I am including a box plot of the mean and the graph of the voltages . Should I put error on the simulations graph? Is it a problem that the simulation has 30000 observation and the experimental.

This is the output when I run the student t test

Welch Two Sample t-test

data: DS_ks_test and Pulserfile_ks_test

t = -25.909, df = 1117.4, p-value < 2.2e-16

alternative hypothesis: true difference in means is not equal to 0

95 percent confidence interval:

-12057.75 -10360.05

sample estimates:

mean of x mean of y

-15455.722 -4246.824

If you are not sure what I am saying I will do my best to clarify. Any help is much appreciated