I have a question relating to computing confidence intervals that doesn't seem to be correct for my data. I have sales data on a test group and control group that looks something like this (note - the numbers have been made up just to show the kind of data I have):
Date Group1 Control (Group1 - Control) Standardized(Group1 - Control) X-Jan-20XX 123.5 187.2 (123.5-187.2) -0.05 X 200.9 97.8 . . . . . . . . . . . . . . . Xn Yn Tn Dn Sn
I then compute the 95% confidence intervals on the standardized(group1 - control) using the standard method (shown below) to identify the line where we can safely assume the data should fall under.
The problem I have is shown through the image below, as you can see majority of the data falls outside of the confidence interval. It must be noted that my data is not normally distributed, however, when I standardize my data I get mean 0 and standard deviation of 1. Can someone help with solutions on this issue?
What I am suspicious of is the fact that my initial raw data is not normally distributed whilst the methods implemented are for normally distributed data. I believe this is why there are many data points that are not captured under the normal distribution. If this seems to be the problem, can someone suggest solutions?!?