\documentclass[10pt,letterpaper, final]{report} % \documentclass{} required in all files

\usepackage{../preamble/myWEPS} % This is now our single preamble file inclusion (it assumes a “.sty” file extension)

\begin{document}
The WEPS Confidence Interval Report screen (\cref{fig:WEPS_Confidence_Interval_Report})
contains a statistical summarization
of the estimated erosion loss from the field in terms of a “confidence interval”
and reports the non-linearity of the erosion data in terms of quartiles.
A \textbf{Final Cycle Gross Loss Confidence Interval} box and whisker graph is shown in the first section.
In the middle section, a \textbf{Cycle Gross Loss Confidence Interval} graph
of the gross average soil for each rotation cycle,
the gross soil loss upper and lower 90$\%$ confidence intervals
and the running average soil loss are plotted against the rotation cycles.
There is also an \textbf{Annual Gross Loss Quartile Distribution} box and whisker graph
that plots the “Mean”, Median” and “Extreme-Outlier annual soil loss data against erosion loss.
In addition, there is a table starting on page 2 displaying the individual rotation cycle values
reporting the annual soil loss for the individual cycle,
a running average annual soil loss,
and the upper and lower  confidence 90$\%$ interval values through each rotation cycle.

\textbf{Final Cycle Gross Loss Confidence Interva}l:
A box and whisker graph
providing a statistical picture of the final minimum, maximum and median annual erosion values,
the annual average (mean) erosion total and 90$\%$ confidence interval values are shown.
Each data point is the average of the individual year values for each rotation cycle,
e.g. a 3-year cycle would be the average of the 3 individual yearly average values.
The whiskers show the maximum and minimum values for the cycles.
The box ends indicate the upper and lower values of the 90$\%$ confidence interval
and the box itself representing the confidence interval range.
The black dot is placed at the mean value and the black vertical bar at the median value.

\textbf{Cycle Gross Loss Confidence Interval Plot}:
Each value of the annual erosion total is averaged over each rotation cycle (blue line),
and the running average mean (red line) and confidence interval (green line/fill region) values
are calculated as each cycle is added.
When fewer cycles have been simulated, the mean and confidence interval values
can change dramatically when a large cycle erosion value is included in the calculation.
As more years are simulated, the mean and confidence interval become more stable,
even when large cycle erosion values occur.
The final results at the end of the plot are presented more clearly
in the previous box and whisker graph. 
Note that the auto-scaling is based upon the maximum average annual erosion value,
so the upper 90$\%$ CI values are truncated if they exceed that maximum Y-axis plot limit.

\textbf{Annual Gross Loss Quartile Distribution}:
A box and whisker graph providing a statistical picture of total erosion for each year,
irrespective of the cycles, is shown.
The lower quartile is the 25$\%$ of values which are below the lower end of the red bar.
When at least 25$\%$ of the years have no erosion, then the lower end of the red bar would be at zero,
signifying a zero erosion amount.
The second quartile is the 25$\%$ of values which are between the lower end of the red bar
and the median (as shown by the black vertical bar).
The third quartile are the 25$\%$ of values which are between the median and the upper end of the red bar.
The fourth quartile is all values above the upper end of the red bar.
The inter-quartile range is the distance
between the lower and upper ends of the red bar (represented by the red box).
The lower and upper “fences” are shown by the lower and upper whiskers,
which are the values which are 1.5 times the inter-quartile range below the lower end of the red bar,
or 1.5 times the inter-quartile range above the upper end of the red bar.
All values below the lower whisker or above the upper whisker
are considered to be extreme outliers and are plotted with a blue × symbol.
Note that this graph is plotting the individual yearly erosion values
and not the individual rotation cycle average values.


\begin{figure}[H]
\centering
	\includegraphics[scale=0.75]{images/Reports/confidence_interval_report_1.jpg}
\caption{WEPS Confidence Interval Report.}
\label{fig:WEPS_Confidence_Interval_Report} 
\end{figure}

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