Confidence Interval Plot

Table of Contents

  1. Introduction
  2. How to Use
  3. Behavior

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

Both the average spectrum and standard deviation values are calculated via the same methods as in the “Average Plot with Original Spectra” feature discussed previously. See related documentation here.

  • Confidence interval: The bounds of the light blue region are calculated by adding/subtracting the standard deviation to/from the average spectrum. Mathematically speaking, the upper bound line $U(x)$ is determined by $U(x)=\overline{I}(x)+\sigma(x)$, and the lower bound line $L(x)$ is determined by $L(x)=\overline{I}(x)-\sigma(x)$, where $\overline{I}(x)$ is the average intensity of the spectra at Raman shift $x$ $[{cm}^{-1}]$, and $\sigma(x)$ is the standard deviation.