\section{Statistics of saccade targets}
%on ``THE LIST`` this was called ``Next Fixation Statistics``
This section characterizes saccades with respect to the properties of the respective target location. 

\begin{figure}[!htb]
\label{nextfixation}
\centering
\fbox{ \begin{minipage}{\textwidth}\begin{tabular}{cc}
\input{nextfixhumans.tex} & \input{nextfixmonkeys.tex}
\end{tabular}
\caption{\textit{Next fixation} statistics for humans and monkeys}
%description of figure
All saccades, as defined by magnitude and directions plotted with respect to the center of a coordinate system of double the size an image. All points are averaged (means). 
\end{minipage} }
\end{figure}

In fig. \ref{nextfixation} the direction of all saccades are plotted with respect to the origin.\footnote{function nextfixation.m \ref{ssec:.:nextfixation}.}{} Fewer saccades lead to a slightly clustered image in monkeys. Human saccades show a tendency towards moving more horizontally than vertically and more upwards than downwards as compared to monkeys. 

\begin{table}[!htbp]
	\label{marginalxy}
\fbox{ \begin{minipage}{\textwidth}
	\begin{tabular}{cc}
		\begin{tabular}{lcc}
			\multicolumn{3}{c}{ increase of x- and y-movement } \\
			 {} & monkeys & humans \\
			{   } correlations  &  0.1622  &  0.2463  \\ 
			{   } p-values  &  0.0000  &  0.0000  \\ 
			KW & \multicolumn{2}{c}{ p= 0.0802 } \\ 
			slope\footnote{\textsc{Matlab} function robustfit}{} & 0.1162 & 0.1105 \\ 
			% median  84.5000 ,  47.0000 
			% std 101.8333 ,  87.4388 
		\end{tabular} &
		\begin{minipage}{4cm}
			\center{      absolute ordinate and abscissa movement} \\
			\input{xyradius.tex}
		\end{minipage} \\
	\end{tabular}
	\begin{tabular}{lcclcc}
		& \multicolumn{5}{c} {  } \\        
		& \multicolumn{5}{c} { marginal probabilities of movements on ordinate and abscissa } \\
		& \multicolumn{2}{c} { abscissa movements } & & \multicolumn{2}{c} { ordinate movements } \\
		& monkeys & humans & & monkeys & humans\\
		right & 0.4789 & 0.5012 & up & 0.5090 & 0.4756 \\
		left & 0.5183 & 0.4941 & down & 0.4865 & 0.5168 \\
		none & 0.0028 & 0.0047 & none & 0.0045 & 0.0077 \\
	\end{tabular}
	\caption{Correlation of absolute ordinate and abscissa movement}
The figure plots absolute movement on the x-axis against absolute movement of the y-axis and the table right to it correlations of x/y and a signed-test of the two lines. The table below lists the marginal probabilities of eye movements along the four main directions. 
	\end{minipage} }
\end{table}

In order to understand correlations of feature effects and eye movement, we needed a different concept of controls. Controls were defined as feature contrast on an image at fixation points by the same participant on different images. However, as can be seen exemplarily in fig. \ref{eccentricitysaccadelength}, many eye movements change with eccentricity (cf. table \ref{eccentricitytable}). Therefore, taking the usual definition of controls, we will have biased correlations, e.g. we would erroneously find that short fixations have increased influences of feature contrasts. This would be wrong, as short saccades are more in the center. \cite{Tatler2006} correlated saccade length and feature contrasts and controls were defined by saccade length. We defined controls straightforwardly as average feature contrast over all images. We argue that this removes central biases at fixation points, and with large data sizes, false alarms and misses get averaged out (which can be deduced from the standard errors in the figure). As can be seen in fig. \ref{eccentricitysaccadelength}, saccade length and eccentricity are related, but our definition removes all bias instead of only some parts of it as by Tatler et al.'s  definition. Tables \ref{eyemovementlctable}, \ref{eyemovementtctable}, and \ref{eyemovementbarnesstable} show the effect sizes of features for different eye movements according to this definition.\footnote{restricted to Osnabr\"uck/Montana. 20 bin edges on the abscissa}{} The tables show corresponding correlations and p-values. Our definition of controls had a considerable impact on effect sizes, but we hold that thorough examination with different controls will reveal that our correlations give a correct picture of the interrelations. 

\begin{figure}[!htb]
\label{eccentricitysaccadelength}
\centering
\fbox{ \begin{minipage}{\textwidth}\begin{tabular}{cc}
\input{abscissaeccentricitysaccadelength.tex} & \input{ordinateeccentricitysaccadelength.tex}
\end{tabular}
\caption{Eccentricity and saccade length}
Correlation of eccentricity and saccadelength. Included are only experiments 1 and 2. Refer to table \ref{eccentricitytable} for correlations of other eye movements with eccentricity.  
\end{minipage} }
\end{figure}


\begin{figure}[p]
\label{eyemovementfeatures}
\centering
\fbox{ \begin{minipage}{\textwidth}\begin{tabular}{cccc}
& saccade duration & saccade length & fixation duration \\
\begin{rotate}{90} luminance contrast \end{rotate} & \input{saccadedurationlc.tex} & \input{saccadelengthlc.tex} & \input{fixationdurationlc.tex} \\
\begin{rotate}{90} texture contrast \end{rotate} & \input{saccadedurationtc.tex} & \input{saccadelengthtc.tex} & \input{fixationdurationtc.tex} \\
\begin{rotate}{90} {           barness } \end{rotate} & \input{saccadedurationbarness.tex} & \input{saccadelengthbarness.tex} & \input{fixationdurationbarness.tex} \\
\end{tabular}
\caption{Effect sizes of image features for eye movements}
The idea was to get all feature values at saccade targets and take the median actuals. For this purpose it was practical to redefine controls. We read out controls from averages feature maps based on the locations of fixations. Effect sizes were were calculated as actual feature contrast - control feature contrast over control feature contrast. See also tables \ref{eyemovementlctable}, {eyemovementlctable}, and {eyemovementbarnesstable}. 
\end{minipage} }
\end{figure}

\begin{singlespacing}  
\begin{table}[p]
\label{eyemovementlctable}
\centering
\fbox{ \begin{minipage} {\textwidth}
\begin{tabular}{lcc}
\multicolumn{3}{c}{ saccade duration } \\
 {} & monkeys & humans \\
{   } correlations  &  -0.0563  &  -0.1438  \\ 
{   } p-values  &  0.0030  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.0000 } \\ 
\end{tabular}
% median  0.0185 ,  1.2211 
% std 0.8841 ,  0.9384 
\begin{tabular}{lcc}
\multicolumn{3}{c}{ saccade speed } \\
 {} & monkeys & humans \\
{   } correlations  &  -0.0153  &  -0.1305  \\ 
{   } p-values  &  0.4172  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.0000 } \\ 
\end{tabular}
% median  0.0159 ,  1.2223 
% std 0.8814 ,  0.9396 
\begin{tabular}{lcc}
\hline
\multicolumn{3}{c}{ saccade length } \\
 {} & monkeys & humans \\
{   } correlations  &  -0.0400  &  -0.1503  \\ 
{   } p-values  &  0.0326  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.0000 } \\ 
\end{tabular}
% median  0.0149 ,  1.2224 
% std 0.8817 ,  0.9397 
\begin{tabular}{lcc}
\hline
\multicolumn{3}{c}{ fixation duration } \\
 {} & monkeys & humans \\
{   } correlations  &  -0.0359  &  0.0996  \\ 
{   } p-values  &  0.0456  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.0000 } \\ 
\end{tabular}
% median  0.0140 ,  1.2197 
% std 0.8864 ,  0.9364 
\caption{Influence of luminance contrast on eye movements}
These effect sizes, corresponding to fig. \ref{eyemovementfeatures} were computed according to the re-definition of controls (see above). Medians of effect sizes of luminance contrast were 0.015 (std=0.88) for monkeys and 1.22 (0.94) for humans. 
\end{minipage} }
\end{table}
\end{singlespacing}  % double line spacing

%%%%%%%%%%%%%%% barness
\begin{singlespacing}  
\begin{table}[p]
\label{eyemovementbarnesstable}
\centering
\fbox{ \begin{minipage} {\textwidth}
\begin{tabular}{lcc}
\multicolumn{3}{c}{ saccade duration } \\
 {} & monkeys & humans \\
{   } correlations  &  -0.0412  &  -0.0264  \\ 
{   } p-values  &  0.0316  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.8519 } \\ 
\end{tabular}
% median  0.0318 ,  0.0132 
% std 0.5203 ,  0.4365 
\begin{tabular}{lcc}
\multicolumn{3}{c}{ saccade speed } \\
 {} & monkeys & humans \\
{   } correlations  &  -0.0387  &  -0.0171  \\ 
{   } p-values  &  0.0415  &  0.0003  \\ 
KW & \multicolumn{2}{c}{ p= 0.5411 } \\
\end{tabular}
% median  0.0321 ,  0.0132 
% std 0.5197 ,  0.4363 
\begin{tabular}{lcc}
\hline
\multicolumn{3}{c}{ saccade length } \\
 {} & monkeys & humans \\
{   } correlations  &  -0.0384  &  -0.0253  \\ 
{   } p-values  &  0.0420  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.4264 } \\ 
\end{tabular}
% median  0.0316 ,  0.0128 
% std 0.5195 ,  0.4356 
\begin{tabular}{lcc}
\hline
\multicolumn{3}{c}{ fixation duration } \\
 {} & monkeys & humans \\
{   } correlations  &  -0.0742  &  0.0151  \\ 
{   } p-values  &  0.0000  &  0.0013  \\ 
KW & \multicolumn{2}{c}{ p= 0.3147 } \\ 
\end{tabular}
% median  0.0346 ,  0.0117 
% std 0.5222 ,  0.4386 
\caption{Influence of barness on eye movements}
These effect sizes, corresponding to fig. \ref{eyemovementfeatures} were computed according to the re-definition of controls (see above). Medians of effect sizes of barness were 0.032 (std=0.52) for monkeys and 0.013 (0.44) for humans. 
\end{minipage} }
\end{table}
\end{singlespacing}  % double line spacing



\begin{singlespacing}  
\begin{table}[p]
\label{eyemovementtctable}
\centering
\fbox{ \begin{minipage} {\textwidth}
\begin{tabular}{lcc}
\multicolumn{3}{c}{ saccade duration } \\
 {} & monkeys & humans \\
{   } correlations  &  -0.0721  &  -0.0938  \\ 
{   } p-values  &  0.0003  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.0088 } \\
\end{tabular}
% median  -0.0715 ,  0.0872 
% std 0.9484 ,  0.9489 
\begin{tabular}{lcc}
\multicolumn{3}{c}{ saccade speed } \\
 {} & monkeys & humans \\
{   } correlations  &  -0.0268  &  -0.0959  \\ 
{   } p-values  &  0.1722  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.0002 } \\ 
\end{tabular}
% median  -0.0704 ,  0.0879 
% std 0.9401 ,  0.9471 
\begin{tabular}{lcc}
\hline
\multicolumn{3}{c}{ saccade length } \\
 {} & monkeys & humans \\
{   } correlations  &  -0.0453  &  -0.1088  \\ 
{   } p-values  &  0.0199  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.0094 } \\ 
\end{tabular}
% median  -0.0705 ,  0.0877 
% std 0.9476 ,  0.9480 
\begin{tabular}{lcc}
\hline
\multicolumn{3}{c}{ fixation duration } \\
 {} & monkeys & humans \\
{   } correlations  &  -0.0714  &  0.0425  \\ 
{   } p-values  &  0.0001  &  0.0000  \\ 
KW & \multicolumn{2}{c}{ p= 0.0000 } \\
\end{tabular}
% median  -0.0681 ,  0.0858 
% std 0.9223 ,  0.9441 
\caption{Influence of texture contrast on eye movements}
\end{minipage} }
\end{table}
\end{singlespacing}  % double line spacing


%discussion: more refined definition of controls needed for nextfixation!
