Spectrum error analysis
Contents
Intensity Spectrum error analysis
Peak heights with partially replicated spectra
When spectra are replicated, the variance for a single spin at a single replicated spectra set is calculated by the formula $$ \sigma^2 = \frac{\sum( I_i - I_{av} )}{n -1 } $$ where $\sigma^2$ is the variance, $\sigma$ is the standard deviation, $n$ is the size of the replicated spectra set with i being the corresponding index, $I_i$ is the peak intensity for spectrum $i$ , and $I_{av}$ is the mean over all spectra i .e. the sum of all peak intensities divided by $n$.
As the value of $n$ in the above equation is always very low since normally only a couple of spectra are collected per replicated spectra set, the variance of all spins is averaged for a single replicated spectra set.
Although this results in all spins having the same error, the accuracy of the error estimate is significantly improved.
If there are in addition to the replicated spectra loaded peak intensities which only consist of a single spectrum, i .e. not all spectra are replicated, then the variances of replicated replicated spectra sets will be averaged.
This will be used for the entire experiment so that there will be only a single error value for all spins and for all spectra.
Peak heights with all spectra replicated
If all spectra are collected in duplicate (triplicate or higher number of spectra are supported), the each replicated spectra set will have its own error estimate.
The error for a single peak is calculated as when partially replicated spectra are collected, and these are again averaged to give a single error per replicated spectra set.
However as all replicated spectra sets will have their own error estimate, variance averaging across all spectra sets will not be performed.
