In all the literature reviewed for this work, researchers measure the performance of their PLS using classification accuracy as follows:

\begin{equation*}
\frac{Sum of Correct Classifications}{Total Number of Instances Tested}
\end{equation*}

However, the results of this method can only be trusted when the class distribution of a data set occur with similar frequencies. In light of this, the performance of both the nearest neighbour classifier (NNC) and MARS was assessed by calculating the probability of detection (pd) and probability of false alarm (pf) \cite{Menzies2007} measures for each data set used in this work. By allowing A, B, C and D to represent true negatives, false negatives, false positives and true positives respectfully, it then follows that pd also known as \emph{recall}, is the result of true positives divided by the sum of false negative and true positives \emph{D / (B + D)}. While pf is the result of: \emph{C / (A + C)}.

In this section the pd and pf values of MARS and NNC are generated for ten (10) standard discrete data sets (See \fig{dsc}) from the UC Irvine machine learning repository 
\cite{UCI2007}. This is done by following the procedure for cross-validation experiments is described in the following section. Next our results are visualized with quartile charts \fig{results}. These charts offer a non-parametric view of the result with no assumptions on the underlying distribution. To further ensure the soundness of our experiments, the Mann-Whitney U test [ref] (a non-parametric test) was applied to our results to see if there was any statistical difference between them.

\begin{figure}[ht]
	\begin{center}
    \begin{tabular}{ | l | l | l | l |}
    \hline
    Data Set      & Attributes & Instances & Labels  \\ \hline \hline
    Lymph         & 18         & 147       & 4       \\ \hline
    Iris          & 4          & 150       & 3       \\ \hline
    Breast Cancer & 9          & 286       & 2       \\ \hline
    Heart         & 13         & 297       & 5       \\ \hline
    Tumor         & 17         & 339       & 2       \\ \hline
    Vote          & 16         & 430       & 2       \\ \hline
    Diabetes      & 8          & 768       & 2       \\ \hline
    Tic-Tac-Toe   & 9          & 958       & 2       \\ \hline
    Sonar         & 60         & 208       & 2       \\ \hline
		Balance Scale & 70         & 226       & 8       \\
    \hline
    \end{tabular}
    \caption{Data Set Characteristics}
		\label{fig:dsc}
	\end{center}
\end{figure}	

\subsection{Experimental Method}
This study used 10 x 10 way cross-validation experiments to evaluate the performance of MARS. The procedure was executed as follows:

\begin{itemize}
\item Shuffle the training data then divide it into N buckets.
\item For each bucket, MARS is trained on nine (9) of the buckets and tested on the remaining bucket.
\item The {A, B, C, D} values for each class are generated from the testing phase and the pds and pfs are calculated.
\item The above is repeated ten (10) times collecting all pd and pf values each time.
\end{itemize}

In the end MARS is trained and tested 100 times.

\subsection{Results}

\fig{results} presents the quartile charts of pd and pf for KNN vs MARS over ten (10) discrete data sets. The pd and pf values are found for each class in the data sets. Although some of the have more than two(2) classes, \fig{results} presents the results of two(2) classes for each data set in column 1 and 2. For the data sets where the number of classes is greater than 2, the majority classes are chosen to be displayed. \fig{class} indicates the classes represented in each column for each data set. The results of performing the Mann-Whitney U test is indicated as (w - win, l -loss and t - tie) in parentheses next to the treatment name. A \emph{w} or \emph{l} signals whether or not the use of MARS is statistically different while \emph{t} shows no difference.

\begin{figure}[ht]
	\begin{center}
    \begin{tabular}{ | l | l | l |}
    \hline
    Data Set      & Column 1 & Column 2  \\ \hline \hline
    Lymph         & 18         & 147          \\ \hline
    Iris          & 4          & 150          \\ \hline
    Breast Cancer & 9          & 286          \\ \hline
    Heart         & 13         & 297          \\ \hline
    Tumor         & 17         & 339          \\ \hline
    Vote          & 16         & 430          \\ \hline
    Diabetes      & 8          & 768          \\ \hline
    Tic-Tac-Toe   & 9          & 958          \\ \hline
    Sonar         & 60         & 208          \\ \hline
		Balance Scale & 70         & 226          \\
    \hline
    \end{tabular}
    \caption{Data Set Classes Used}
		\label{fig:class}
	\end{center}
\end{figure}	

In previous work done on PLS, the goal has been that the accuracy with the use of a prototype learner is either comparable or greater than that using the entire training data. However, in this work we seek comparable or higher pd values in conjunction with lower pf values for MARS. Most of our results demonstrate

\begin{figure}[ht]
\small
%\begin{center}
\scalebox{0.8}{
\begin{tabular}{  l | r }
\begin{tabular}{l@{~}|l@{~}|r@{~}r@{~}@{~}r@{~}|c}
%\multicolumn{2}{c}{~}&\multicolumn{5}{c}{quartiles}\\\cline{3-5}
%&min& & median & &max\\\cline{3-5}
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{pd}&2nd quartile\\
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{percentiles}&median,\\\cline{3-5}
Lymph&Treatment& 25\%& 50\% & 75\%&Q1 median Q3\\\hline 
pd&MARS (w) & 50& 71& 100&  \boxplot{0.0}{50.0}{71.0}{100.0}{0.0}  \\
 &KNN (l)& 50& 60& 75&  \boxplot{0.0}{50.0}{60.0}{75.0}{25.0}  \\ \hline
pf&MARS (w) & 11& 36& 57&  \boxplot{0.0}{11.1}{36.4}{57.1}{42.9} \\
&KNN (l)& 0& 9& 17&  \boxplot{0.0}{0.0}{9.1}{16.7}{83.3}  \\
\hline
\multicolumn{5}{c}{~}&~~~~~0~~~~~~~~50~~~~100
\end{tabular} &
\begin{tabular}{l@{~}|l@{~}|r@{~}r@{~}@{~}r@{~}|c}
%\multicolumn{2}{c}{~}&\multicolumn{5}{c}{quartiles}\\\cline{3-5}
%&min& & median & &max\\\cline{3-5}
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{pd}&2nd quartile\\
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{percentiles}&median,\\\cline{3-5}
Lymph&Treatment& 25\%& 50\% & 75\%&Q1 median Q3\\\hline 
pd&MARS (l) & 38& 63& 89&  \boxplot{0.0}{37.5}{62.5}{88.9}{11.1}  \\
 &KNN (w)& 89& 100& 100&  \boxplot{0.0}{88.9}{100.0}{100.0}{0.0}  \\ \hline
pf&MARS (l) & 0& 25& 44&  \boxplot{0.0}{0.0}{25.0}{44.4}{55.6} \\
&KNN (w)& 25& 38& 50&  \boxplot{0.0}{25.0}{37.5}{50.0}{50.0}  \\
\hline
\multicolumn{5}{c}{~}&~~~~~0~~~~~~~~50~~~~100
\end{tabular} \\  \hline \hline

\begin{tabular}{l@{~}|l@{~}|r@{~}r@{~}@{~}r@{~}|c}
%\multicolumn{2}{c}{~}&\multicolumn{5}{c}{quartiles}\\\cline{3-5}
%&min& & median & &max\\\cline{3-5}
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{pd}&2nd quartile\\
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{percentiles}&median,\\\cline{3-5}
Vote&Treatment& 25\%& 50\% & 75\%&Q1 median Q3\\\hline 
pd&MARS (t) & 33& 80& 100&  \boxplot{0.0}{33.3}{80.0}{100.0}{0.0}  \\
 &KNN (t)& 75& 81& 86&  \boxplot{0.0}{75.0}{81.0}{85.7}{14.3}  \\ \hline
pf&MARS (w) & 8& 38& 100&  \boxplot{0.0}{7.7}{37.5}{100.0}{0.0} \\
&KNN (l)& 14& 20& 27&  \boxplot{0.0}{14.3}{20.0}{27.3}{70.7}  \\
\hline
\multicolumn{5}{c}{~}&~~~~~0~~~~~~~~50~~~~100
\end{tabular} &
\begin{tabular}{l@{~}|l@{~}|r@{~}r@{~}@{~}r@{~}|c}
%\multicolumn{2}{c}{~}&\multicolumn{5}{c}{quartiles}\\\cline{3-5}
%&min& & median & &max\\\cline{3-5}
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{pd}&2nd quartile\\
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{percentiles}&median,\\\cline{3-5}
Vote&Treatment& 25\%& 50\% & 75\%&Q1 median Q3\\\hline 
pd&MARS (l) & 0& 53& 92&  \boxplot{0.0}{.0}{52.9}{91.7}{8.3}  \\
 &KNN (w)& 72& 80& 86&  \boxplot{0.0}{72.2}{80.0}{85.7}{14.3}  \\ \hline
pf&MARS (t) & 0& 18& 63&  \boxplot{0.0}{0.0}{17.9}{63.0}{37.0} \\
&KNN (t) & 14& 19& 25&  \boxplot{0.0}{13.8}{18.5}{25.0}{75.0} \\
\hline
\multicolumn{5}{c}{~}&~~~~~0~~~~~~~~50~~~~100
\end{tabular} \\ \hline \hline

\begin{tabular}{l@{~}|l@{~}|r@{~}r@{~}@{~}r@{~}|c}
%\multicolumn{2}{c}{~}&\multicolumn{5}{c}{quartiles}\\\cline{3-5}
%&min& & median & &max\\\cline{3-5}
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{pd}&2nd quartile\\
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{percentiles}&median,\\\cline{3-5}
Heart&Treatment& 25\%& 50\% & 75\%&Q1 median Q3\\\hline 
pd&MARS (l) & 13& 80& 100&  \boxplot{0.0}{12.5}{80.0}{100.0}{0.0}  \\
&KNN (w)& 100& 100& 100&  \boxplot{0.0}{100.0}{100.0}{100.0}{0.0}  \\ \hline
pf&MARS (t) & 0& 0& 0&  \boxplot{0.0}{0.0}{0.0}{0.0}{100.0} \\
&KNN (t)& 0& 0& 0&  \boxplot{0.0}{0.0}{0.0}{0.0}{100.0} \\
\hline
\multicolumn{5}{c}{~}&~~~~~0~~~~~~~~50~~~~100
\end{tabular} &
\begin{tabular}{l@{~}|l@{~}|r@{~}r@{~}@{~}r@{~}|c}
%\multicolumn{2}{c}{~}&\multicolumn{5}{c}{quartiles}\\\cline{3-5}
%&min& & median & &max\\\cline{3-5}
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{pd}&2nd quartile\\
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{percentiles}&median,\\\cline{3-5}
Heart&Treatment& 25\%& 50\% & 75\%&Q1 median Q3\\\hline 
pd&MARS (l) & 0& 67& 100&  \boxplot{0.0}{0.0}{66.7}{100.0}{0.0}  \\
&KNN (w)& 0& 100& 100&  \boxplot{0.0}{0.0}{100.0}{100.0}{0.0}  \\ \hline
pf&MARS (t) & 0& 0& 0&  \boxplot{0.0}{0.0}{0.0}{0.0}{100.0} \\
&KNN (t)& 0& 0& 0&  \boxplot{0.0}{0.0}{0.0}{0.0}{100.0} \\
\hline
\multicolumn{5}{c}{~}&~~~~~0~~~~~~~~50~~~~100
\end{tabular} \\ \hline \hline

\begin{tabular}{l@{~}|l@{~}|r@{~}r@{~}@{~}r@{~}|c}
%\multicolumn{2}{c}{~}&\multicolumn{5}{c}{quartiles}\\\cline{3-5}
%&min& & median & &max\\\cline{3-5}
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{pd}&2nd quartile\\
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{percentiles}&median,\\\cline{3-5}
Breast Cancer&Treatment& 25\%& 50\% & 75\%&Q1 median Q3\\\hline 
pd&MARS (l) & 36& 91& 100&  \boxplot{0.0}{36.4}{90.9}{100.0}{0.0}  \\
 &KNN (w)& 91& 95& 100&  \boxplot{0.0}{90.5}{94.7}{100.0}{0.0}  \\ \hline
pf&MARS (t) & 17& 86& 100&  \boxplot{0.0}{16.7}{85.7}{100.0}{0.0} \\
&KNN (t)& 67& 73& 80&  \boxplot{0.0}{66.7}{72.7}{80.0}{20.0}  \\
\hline
\multicolumn{5}{c}{~}&~~~~~0~~~~~~~~50~~~~100
\end{tabular} &
\begin{tabular}{l@{~}|l@{~}|r@{~}r@{~}@{~}r@{~}|c}
%\multicolumn{2}{c}{~}&\multicolumn{5}{c}{quartiles}\\\cline{3-5}
%&min& & median & &max\\\cline{3-5}
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{pd}&2nd quartile\\
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{percentiles}&median,\\\cline{3-5}
Breast Cancer&Treatment& 25\%& 50\% & 75\%&Q1 median Q3\\\hline 
pd&MARS (t) & 0& 14& 83&  \boxplot{0.0}{0.0}{14.3}{83.3}{16.7}  \\
 &KNN (t)& 18& 25& 33&  \boxplot{0.0}{18.2}{25.0}{33.3}{66.7}  \\ \hline
pf&MARS (w) & 0& 6& 61&  \boxplot{0.0}{0.0}{6.2}{61.1}{38.9} \\
&KNN (l)& 0& 5& 10&  \boxplot{0.0}{0.0}{5.3}{9.5}{90.5}  \\
\hline
\multicolumn{5}{c}{~}&~~~~~0~~~~~~~~50~~~~100
\end{tabular} \\ \hline \hline

\begin{tabular}{l@{~}|l@{~}|r@{~}r@{~}@{~}r@{~}|c}
%\multicolumn{2}{c}{~}&\multicolumn{5}{c}{quartiles}\\\cline{3-5}
%&min& & median & &max\\\cline{3-5}
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{pd}&2nd quartile\\
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{percentiles}&median,\\\cline{3-5}
Tumor&Treatment& 25\%& 50\% & 75\%&Q1 median Q3\\\hline 
pd&MARS (t) & 16& 90& 100&  \boxplot{0.0}{15.8}{90.0}{100.0}{0.0}  \\
&KNN (t)& 80& 85& 91&  \boxplot{0.0}{80.0}{85.2}{90.9}{9.1}  \\ \hline
pf&MARS (w) & 0& 83& 100&  \boxplot{0.0}{0.0}{83.3}{100.0}{0.0} \\
&KNN (l)& 40& 50& 60&  \boxplot{0.0}{40.0}{50.0}{60.0}{40.0}  \\
\hline
\multicolumn{5}{c}{~}&~~~~~0~~~~~~~~50~~~~100
\end{tabular} &
\begin{tabular}{l@{~}|l@{~}|r@{~}r@{~}@{~}r@{~}|c}
%\multicolumn{2}{c}{~}&\multicolumn{5}{c}{quartiles}\\\cline{3-5}
%&min& & median & &max\\\cline{3-5}
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{pd}&2nd quartile\\
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{percentiles}&median,\\\cline{3-5}
Tumor&Treatment& 25\%& 50\% & 75\%&Q1 median Q3\\\hline 
pd&MARS (l) & 0& 11& 100&  \boxplot{0.0}{0.0}{11.1}{100.0}{0.0}  \\
 &KNN (w)& 40& 50& 60&  \boxplot{0.0}{40.0}{50.0}{60.0}{40.0}  \\ \hline
pf&MARS (t) & 0& 10& 82&  \boxplot{0.0}{0.0}{9.5}{81.8}{18.2} \\
&KNN (t)& 9& 14& 20&  \boxplot{0.0}{9.1}{14.3}{20.0}{80.0}  \\
\hline
\multicolumn{5}{c}{~}&~~~~~0~~~~~~~~50~~~~100
\end{tabular} \\ \hline \hline

\begin{tabular}{l@{~}|l@{~}|r@{~}r@{~}@{~}r@{~}|c}
%\multicolumn{2}{c}{~}&\multicolumn{5}{c}{quartiles}\\\cline{3-5}
%&min& & median & &max\\\cline{3-5}
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{pd}&2nd quartile\\
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{percentiles}&median,\\\cline{3-5}
Tic-Tac-Toe&Treatment& 25\%& 50\% & 75\%&Q1 median Q3\\\hline 
pd&MARS (w) & 0& 72& 100&  \boxplot{0.0}{0.0}{71.8}{100.0}{0.0}  \\
 &KNN (l)& 0& 14& 19&  \boxplot{0.0}{0.0}{13.5}{18.6}{81.4}  \\ \hline
pf&MARS (w) & 0& 77& 100&  \boxplot{0.0}{0.0}{77.2}{100.0}{0.0} \\
&KNN (l)& 0& 5& 9&  \boxplot{0.0}{0.0}{4.9}{8.5}{91.5}  \\
\hline
\multicolumn{5}{c}{~}&~~~~~0~~~~~~~~50~~~~100
\end{tabular} &
\begin{tabular}{l@{~}|l@{~}|r@{~}r@{~}@{~}r@{~}|c}
%\multicolumn{2}{c}{~}&\multicolumn{5}{c}{quartiles}\\\cline{3-5}
%&min& & median & &max\\\cline{3-5}
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{pd}&2nd quartile\\
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{percentiles}&median,\\\cline{3-5}
Tic-Tac-Toe&Treatment& 25\%& 50\% & 75\%&Q1 median Q3\\\hline 
pd&MARS (l) & 0& 21& 100&  \boxplot{0.0}{0.0}{21.0}{100.0}{0.0}  \\
 &KNN (w)& 0& 92& 100&  \boxplot{0.0}{91.5}{94.9}{100.0}{0.0}  \\ \hline
pf&MARS (l) & 0& 28& 100&  \boxplot{0.0}{0.0}{27.6}{100.0}{0.0} \\
&KNN (w)& 80& 86& 100&  \boxplot{0.0}{80.0}{86.4}{100.0}{0.0}  \\
\hline
\multicolumn{5}{c}{~}&~~~~~0~~~~~~~~50~~~~100
\end{tabular} \\ \hline \hline

\begin{tabular}{l@{~}|l@{~}|r@{~}r@{~}@{~}r@{~}|c}
%\multicolumn{2}{c}{~}&\multicolumn{5}{c}{quartiles}\\\cline{3-5}
%&min& & median & &max\\\cline{3-5}
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{pd}&2nd quartile\\
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{percentiles}&median,\\\cline{3-5}
Iris&Treatment& 25\%& 50\% & 75\%&Q1 median Q3\\\hline 
pd&MARS (t) & 100& 100& 100&  \boxplot{0.0}{100.0}{100.0}{100.0}{0.0}  \\
 &KNN (t)& 86& 100& 100&  \boxplot{0.0}{85.7}{100.0}{100.0}{0.0}  \\ \hline
pf&MARS (w) & 0& 11& 25&  \boxplot{0.0}{11.1}{25.0}{69.2}{30.8} \\
&KNN (l)& 0& 0& 0&  \boxplot{0.0}{0.0}{0.0}{0.0}{100.0}  \\
\hline
\multicolumn{5}{c}{~}&~~~~~0~~~~~~~~50~~~~100
\end{tabular} &
\begin{tabular}{l@{~}|l@{~}|r@{~}r@{~}@{~}r@{~}|c}
%\multicolumn{2}{c}{~}&\multicolumn{5}{c}{quartiles}\\\cline{3-5}
%&min& & median & &max\\\cline{3-5}
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{pd}&2nd quartile\\
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{percentiles}&median,\\\cline{3-5}
Iris&Treatment& 25\%& 50\% & 75\%&Q1 median Q3\\\hline 
pd&MARS (l) & 50& 80& 100&  \boxplot{0.0}{50.0}{80.0}{100.0}{0.0}  \\
&KNN (w)& 100& 100& 100&  \boxplot{0.0}{100.0}{100.0}{100.0}{0.0}  \\ \hline
pf&MARS (t) & 0& 0& 8&  \boxplot{0.0}{0.0}{0.0}{8.3}{91.7} \\
&KNN (t)& 0& 0& 0&  \boxplot{0.0}{0.0}{0.0}{0.0}{100.0}  \\
\hline
\multicolumn{5}{c}{~}&~~~~~0~~~~~~~~50~~~~100
\end{tabular} \\ \hline \hline

\begin{tabular}{l@{~}|l@{~}|r@{~}r@{~}@{~}r@{~}|c}
%\multicolumn{2}{c}{~}&\multicolumn{5}{c}{quartiles}\\\cline{3-5}
%&min& & median & &max\\\cline{3-5}
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{pd}&2nd quartile\\
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{percentiles}&median,\\\cline{3-5}
Sonar&Treatment& 25\%& 50\% & 75\%&Q1 median Q3\\\hline 
pd&MARS (t) & 36& 73& 100&  \boxplot{0.0}{36.4}{72.7}{100.0}{0.0}  \\
 &KNN (t)& 67& 75& 85&  \boxplot{0.0}{66.7}{75.0}{84.6}{15.4}  \\ \hline
pf&MARS (w) & 20& 58& 100&  \boxplot{0.0}{20.0}{58.3}{100.0}{0.0} \\
&KNN (l)& 30& 46& 55&  \boxplot{0.0}{30.0}{45.5}{54.5}{45.5}  \\
\hline
\multicolumn{5}{c}{~}&~~~~~0~~~~~~~~50~~~~100
\end{tabular} &
\begin{tabular}{l@{~}|l@{~}|r@{~}r@{~}@{~}r@{~}|c}
%\multicolumn{2}{c}{~}&\multicolumn{5}{c}{quartiles}\\\cline{3-5}
%&min& & median & &max\\\cline{3-5}
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{pd}&2nd quartile\\
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{percentiles}&median,\\\cline{3-5}
Sonar&Treatment& 25\%& 50\% & 75\%&Q1 median Q3\\\hline 
pd&MARS (l) & 0& 40& 78&  \boxplot{0.0}{0.0}{40.0}{77.8}{22.2}  \\
 &KNN (w)& 44& 54& 67&  \boxplot{0.0}{44.4}{53.9}{66.7}{33.3}  \\ \hline
pf&MARS (t) & 0& 25& 64&  \boxplot{0.0}{0.0}{25.0}{63.6}{36.4} \\
&KNN (t)& 15& 25& 33&  \boxplot{0.0}{15.4}{25.0}{33.3}{66.7}  \\
\hline
\multicolumn{5}{c}{~}&~~~~~0~~~~~~~~50~~~~100
\end{tabular} \\ \hline \hline

\begin{tabular}{l@{~}|l@{~}|r@{~}r@{~}@{~}r@{~}|c}
%\multicolumn{2}{c}{~}&\multicolumn{5}{c}{quartiles}\\\cline{3-5}
%&min& & median & &max\\\cline{3-5}
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{pd}&2nd quartile\\
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{percentiles}&median,\\\cline{3-5}
Diabetes&Treatment& 25\%& 50\% & 75\%&Q1 median Q3\\\hline 
pd&MARS (w) & 2& 100& 100&  \boxplot{0.0}{1.9}{100.0}{100.0}{0.0}  \\
 &KNN (l)& 86& 89& 91&  \boxplot{0.0}{85.7}{88.5}{91.1}{8.9}  \\ \hline
pf&MARS (w) & 0& 100& 100&  \boxplot{0.0}{0.0}{100.0}{100.0}{0.0} \\
&KNN (l)& 45& 50& 58&  \boxplot{0.0}{44.8}{50.0}{58.3}{41.7}  \\
\hline
\multicolumn{5}{c}{~}&~~~~~0~~~~~~~~50~~~~100
\end{tabular} &
\begin{tabular}{l@{~}|l@{~}|r@{~}r@{~}@{~}r@{~}|c}
%\multicolumn{2}{c}{~}&\multicolumn{5}{c}{quartiles}\\\cline{3-5}
%&min& & median & &max\\\cline{3-5}
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{pd}&2nd quartile\\
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{percentiles}&median,\\\cline{3-5}
Diabetes&Treatment& 25\%& 50\% & 75\%&Q1 median Q3\\\hline 
pd&MARS (l) & 0& 0& 100&  \boxplot{0.0}{0.0}{0.0}{100.0}{0.0}  \\
&KNN (w)& 41& 50& 55&  \boxplot{0.0}{41.4}{50.0}{55.2}{25.0}  \\ \hline
pf&MARS (l) & 0& 0& 98.2&  \boxplot{0.0}{0.0}{0.0}{98.2}{42.9} \\
&KNN (w)& 9& 12& 14&  \boxplot{0.0}{8.8}{11.5}{14.3}{83.3}  \\
\hline
\multicolumn{5}{c}{~}&~~~~~0~~~~~~~~50~~~~100
\end{tabular} \\ \hline \hline

\begin{tabular}{l@{~}|l@{~}|r@{~}r@{~}@{~}r@{~}|c}
%\multicolumn{2}{c}{~}&\multicolumn{5}{c}{quartiles}\\\cline{3-5}
%&min& & median & &max\\\cline{3-5}
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{pd}&2nd quartile\\
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{percentiles}&median,\\\cline{3-5}
Balance Scale&Treatment& 25\%& 50\% & 75\%&Q1 median Q3\\\hline 
pd&MARS (l) & 0& 19& 36&  \boxplot{0.0}{0.0}{19.4}{36.4}{63.6}  \\
 &KNN (w)& 53& 59& 69&  \boxplot{0.0}{52.9}{59.4}{69.0}{31.0}  \\ \hline
pf&MARS (l) & 0& 8& 24&  \boxplot{0.0}{0.0}{7.7}{23.8}{76.2} \\
&KNN (w)& 18& 24& 34&  \boxplot{0.0}{18.2}{24.2}{34.2}{65.8}  \\
\hline
\multicolumn{5}{c}{~}&~~~~~0~~~~~~~~50~~~~100
\end{tabular} &
\begin{tabular}{l@{~}|l@{~}|r@{~}r@{~}@{~}r@{~}|c}
%\multicolumn{2}{c}{~}&\multicolumn{5}{c}{quartiles}\\\cline{3-5}
%&min& & median & &max\\\cline{3-5}
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{pd}&2nd quartile\\
%\multicolumn{2}{c}{~}&\multicolumn{3}{c}{percentiles}&median,\\\cline{3-5}
Balance Scale&Treatment& 25\%& 50\% & 75\%&Q1 median Q3\\\hline 
pd&MARS (l) & 10& 33& 58&  \boxplot{0.0}{10.0}{33.3}{58.3}{41.7}  \\
 &KNN (w)& 70& 77& 85&  \boxplot{0.0}{69.6}{76.7}{84.8}{15.2}  \\ \hline
pf&MARS (t) & 13& 44& 67&  \boxplot{0.0}{12.5}{44.4}{66.7}{33.3} \\
&KNN t)& 32& 43& 49&  \boxplot{0.0}{32.3}{43.3}{48.5}{51.5}  \\
\hline
\multicolumn{5}{c}{~}&~~~~~0~~~~~~~~50~~~~100
\end{tabular} 
\end{tabular}}
%\end{center}
\caption{Probability of Detection (PD) and Probability of False Alarm (PF)results}
\label{fig:results}
\end{figure}
