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Experiments were performed in duplicate, and the error bars are the sample standard deviation.
Fleiss, J. L., Cohen, J. & Everitt, B. S. Large sample standard errors of kappa and weighted kappa.
The catch is that assumptions come first, not the sample standard deviation for estimating error (or sigma) of unknown distribution.
Instead of sample standard deviation, use absolute mean deviation (simple mean residual, Eddington's words) to quantify uncertainty.
When the population standard deviation, σ, is unknown, the sample standard deviation is used to estimate σ in the confidence interval formula.
The synthetic chart is a combination of the sample standard deviation (S) chart and the conforming run length (CRL) chart.
We also know the asymptotic efficiency of sample standard deviation when the probability density function satisfies more general regularity conditions than the Gaussian density.
Commonly cited statistical methods in astronomy, like chi square methods, are built on Gaussianity assumption from which sample standard deviation is used for σ, the scale parameter of the normal distribution that is mapped to 68% coverage and multiple of the sample standard deviation correspond to well known percentiles as given in Numerical Recipes.
(b) Sample standard deviation.
The transparent envelopes indicate the sample standard deviation.
The sample standard deviation was calculated using the expression.
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