Confidence Interval Plot

Table of Contents

1. Introduction
2. How to use
3. Behavior
4. Method
5. References

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Introduction

The confidence interval plot is a concise way to view both the mean intensities and standard deviations all at once. This feature creates a plot of the average spectrum and includes a light blue region around the line representing a spread of one standard deviation from the mean. This is useful for visualizing which Raman shifts result in the most or least variation (potentially noise) between the selected spectra.

How to use

1. In the analytics page, after processing your data, select “Confidence Interval Plot” from the drop-down menu on the left sidebar.
2. The bold blue line represents the average spectrum, and the light blue region represents values within one standard deviation from the mean.

Behavior

The page shows the mean spectrum with an uncertainty band. In Confidence Interval mode, the band estimates uncertainty in the mean using the selected confidence level. In Standard Deviation mode, the band shows spread among individual spectra using the selected number of standard deviations.

Method

Confidence interval mode uses:

\[CI(x)=\bar{I}(x)\pm t_{\alpha/2,n-1}\frac{s(x)}{\sqrt{n}}\]

Standard deviation mode uses:

\[B(x)=\bar{I}(x)\pm k\,s(x)\]

Parameter	Tunable or fixed	Implementation
Interval Method	Tunable	Confidence Interval or Standard Deviation
Confidence Level	Tunable	90, 95, or 99; default 95
Number of Standard Deviations	Tunable	1, 2, or 3; default 1
Output	Fixed	Mean spectrum with an uncertainty band

References

1. Student. (1908). The probable error of a mean. Biometrika, 6(1), 1-25. https://doi.org/10.1093/biomet/6.1.1
2. SciPy Developers. Statistical functions. https://docs.scipy.org/doc/scipy/reference/stats.html