I have a series of simulation results and I would like to demonstrate how the confidence interval for the mean and standard deviation decrease as the number of results increases.
I have done this for the mean using the inbuilt MeanCI function as shown below (I've replaced my simulation results with random data).
Needs["HypothesisTesting`"]
data = Table[RandomReal[{-1, 1}], {i, 1, 100}];
movingData = Table[data[[1 ;; i]], {i, 2, Length[data]}];
meanCI = MeanCI[#, ConfidenceLevel -> .80] & /@ movingData;
ListPlot[Transpose[meanCI]]
What I would like to do is create a similar chart showing how the standard deviation confidence interval decreases. There isn't a standard function for StandardDeviationCI but is there a way to use the tools inside the HypothesisTesting package to get a similar result?