\section{Evaluation}
The object of the experiment was to obtain some empirical data on the rate of information flow that humans find tolerable when scrolling rapidly.

\subsection{Participants}
Twelve volunteer participants (ten male, two female) took part in the experiment. Eleven were Computer Science students and one was a Computer Science lecturer.

\subsection{Apparatus}
The evaluation was done using a basic document display interface written in OpenGL/C which was capable of rendering the document at different magnifications and providing a high frame rate ($>300$ frames per second).
The experiment was conducted on a 2.4 GHz Intel Pentium 4 computer with 512Mb RAM and a Geforce 4 MX Video card. The 19-inch display was set to 1280x1024 pixels, though the interface only took up 690x810 pixels. The software ran under Redhat Linux 8.

\subsection{User interface}
Initially the document was displayed stationary with page-one showing. Pressing pg-down caused the document to begin scrolling slowly to wards the end. Further pressing of pg-down caused the scrolling of the document to speed up, while pressing pg-up reduced the scrolling speed. The up- and down-arrows could also be used to fine-tune the scrolling speed, with each arrow having only a tenth of the effect of the pg-buttons. The pg-buttons provided sufficiently fine adjustments ($\approx$0.074 pages/s) that most participants found the use of the arrows largely unnecessary. When the end of the document was reached, the document started scrolling from the beginning again.

\begin{figure}[!tbh]
\begin{center}
\includegraphics[width=0.5\textwidth]{graphs/dv.eps}
\caption{The user interface displaying a document at one-third magnification.}
\label{dv}
\end{center}
\end{figure}

The document could be scrolled in one direction only (from top to bottom). Thus, continual pressing of pg-up or the up-arrow eventually reduced the scrolling to a halt, and further pressing of these keys had no effect.

Once an appropriate speed had been acquired, pressing the escape key recorded the speed and moved on to the next condition.

\subsection{Experimental design}
The experiment was a 2x2 within participants design. The dependent measure was scrolling velocity. (This scrolling velocity will be reported in terms of both document speed and viewer speed.) The two factors were as follows:
\begin{itemize}
\item \emph{Magnification}. The levels of this factor were full magnification (one document page on the screen at once) and one-third magnification (three pages on the screen at once).
\item \emph{Task Type}. The two levels of this factor were ``most comfortable'' and ``maximum tolerable''.
\end{itemize}

Participants were order-balanced in their exposure to the four conditions, using a Latin square, to avoid order effects.

The document used was a report \cite{js:1} with blank pages removed, which resulted in it being a 28 page document (see figure \ref{dv}).

\begin{figure*}[!t]
\begin{center}
\subfigure[Mean Document Speed versus Magnification.]{
\label{DSGraph}
\includegraphics[width=0.45\textwidth]{graphs/DSGraph.eps}
}
\subfigure[Mean Viewer Speed versus Magnification.]{
\label{VSGraph}
\includegraphics[width=0.45\textwidth]{graphs/VSGraph.eps}
}
\caption{Results.}
\label{Graphs}
%note that this actually gets put on the next page
\end{center}
\end{figure*}

\subsection{Procedure}
An important part of the experiment lay in the participants' understanding of the meaning of the two different task types. Participants were advised to consider the task of scrolling through a familiar document with the goal of target acquisition in mind. They were instructed not to try and read the body text, but rather look for the locations of significant features such as pictures and section headings. They were asked to imagine they were scrolling through the document with the intention of navigating to a known heading or image.

The ``most comfortable'' speed was defined to be the speed at which they felt provided the optimal trade-off between acquiring the target quickly and maintaining an understanding of their location in the document. It was emphasized that this speed was to be the one at which they were most subjectively happy using to scroll through the document. They were advised to consider the question that ``If this was your document and you were scrolling through it to get to another part of it, how fast would you go?''

The ``maximum tolerable'' speed was explained as the speed at which any faster was considered to be ``too fast''. Participants were told that this was the point at which they considered that if the document was scrolled any faster, they would no longer be able to see their target as it went by.

Each participant was questioned after the explanation of these two terms in order to ensure that they had fully understood the ideas behind them. (All participants had done so accurately.) Results indicated that all participants correctly indicated their ``most comfortable'' speed at a given magnification was less than their ``maximum tolerable'' speed.

Participants were strongly advised to rest their eyes regularly and were informed that there was no time limit. Most participants completed the four conditions in about five minutes. Three complained of eye strain, one commenting ``my eyes hurt''. Though another added, after expressing a similar complaint, ``but if you look away for a bit, it's okay.''

\section{Results and discussion}
We first present the results of the evaluation in terms of both viewer speed and document speed. We then discuss the practical applications of these results and their limitations.

\subsection{Document speed}

A summary of the data obtained for document speed is given in table \ref{DSTable} and shown in figure \ref{DSGraph}.

\begin{table}[!b]
\begin{center}
\begin{tabular}{|l|l|r|r|}
\hline
Magnification & Task type & Mean & SD\\\hline
full & max & 2.6753 & 1.1649\\\hline
full & comfort & 1.5160 & 0.9893\\\hline
third & max & 5.2574 & 2.0945\\\hline
third & comfort & 2.6963 & 1.6941\\\hline
\end{tabular}
\caption{Document Speed (pages/s).}
\label{DSTable}
\end{center}
\end{table}

An analysis of variance revealed a significant main effect for magnification ($F_{1,11}=54.5, p<0.001$). The effect of magnification on document speed is good news for SDAZ. It indicates (see figure \ref{DSGraph}) that reducing the magnification allows for much more rapid navigation through the document space while maintaining the same level of user comfort.

There was also a significant main effect for task-type ($F_{1,11}=43.6, p<0.001$) and a significant interaction ($F_{1,11}=13.1, p<0.005$). These will be discussed later.

\begin{table}[!b]
\begin{center}
\begin{tabular}{|l|l|r|r|}
\hline
Magnification & Task type & Mean & SD\\\hline
full & max & 0.4426 & 0.1835\\\hline
full & comfort & 0.9277 & 0.5502\\\hline
third & max & 0.6532 & 0.2451\\\hline
third & comfort & 1.5208 & 0.8047\\\hline
\end{tabular}
\caption{Viewer Speed (screen time, in seconds).}
\label{VSTable}
\end{center}
\end{table}

\begin{table*}[!bt]
% Note that this actually lives on the next page...
\begin{center}
\begin{tabular}{|c|c|c|c|}
\hline
Magnification & Mean comfort time & 1st percentile for maximum & Recommended screen time\\\hline
full & 0.93 & 0.87 & 0.9 \\\hline
third & 1.52 & 1.22 & 1.4 \\\hline
\end{tabular}
\caption{Recommended calibration values (screen time in seconds).}
\label{RVTable}
\end{center}
\end{table*}

\subsection{Viewer speed}

A summary of the data obtained for viewer speed is given in table \ref{VSTable} and shown in figure \ref{VSGraph}.

We had hoped there would be no main effect of magnification on viewer speed. This would have meant SDAZ systems could be implemented using the simple method used by \citename{cs:1} in which viewer speed is kept constant over all magnifications. However, we found a significant main effect for magnification ($F_{1,11}=36.0, p<0.001$), which implies a more complex relationship. We hypothesize two possible causes for this interrelationship:
\begin{itemize}
\item The reduced text size decreases reading rate, subsequently increasing the amount of time required to read the headings.
\item The lower magnification results in more information being on the screen at once, which means the user is being presented with more data to process, thus requiring more time.
\end{itemize}

There was also a significant main effect for task type ($F_{1,11}=24.4, p<0.005$) and a significant interaction ($F_{1,11}=8.7, p<0.05$). These will be discussed in the next section.

\subsection{Task types}
Our theoretical estimation suggested that 450--950ms would be an appropriate length of time for the information to remain on the screen. Our results at full magnification agreed strongly with this estimation. However, our results at one-third magnification did not.

In both result sets there was a significant main effect for task type. This was contrary to our theoretical estimation which took no account of the magnification and thus predicted results independent of magnification.

The main effect for task type makes application of the results more difficult. It shows that viewer comfort begins to degrade prior to the point at which maximum performance is reached. Any calibration of a scrolling system will therefore have to consider the trade-offs being made between viewer comfort and performance.

The significant interactions measured also serve to reemphasize this point by showing that viewer comfort and maximum performance degrade differently with magnification. This makes the task of calibration difficult, because even if an optimal speed is found at one level of magnification, there is no easy way to determine the optimal speed at other magnifications.

\subsection{Practical values}

We have already expressed concerned about the difficulty of recommending exact values for general use. However, concentrating on the application of SDAZ it should be possible to make some general suggestions.

In an SDAZ system it is desirable to zoom-out sooner rather than later as the zoom-out allows a higher document speed while maintaining the same level of user comfort. Also, if the zoom-out does not trigger soon enough, then some users will find the visual flow too much. On the other hand, invoking the zoom-out too soon could upset users who are only attempting to scroll short distances (one page, for example) and who do not want to trigger a zoom-out. We therefore suggest that a zoom out should not be triggered until the viewer speed is in excess of the mean comfortable speed.

Since it is strongly desirable that it is not ``too fast'' for any users, we also suggest that the viewer speed exceed the maximum speed of, at most, 1\% of users. That is, viewer speed should be less than what 99\% of people indicated was their their maximum tolerable speed. (In calculating this, we assumed a normal distribution applied.)

This data is displayed in table \ref{RVTable}, along with our recommended values which we obtained by selecting a value in the middle of the range given by the two suggestions.

\subsection{Confounding factors}
We identified four potentially problematic factors in our evaluation:
\begin{enumerate}
\item All except one of the participants were reasonably young (early twenties) and all were experienced computer users. As such, they could be expected to be better at scrolling and more able to tolerate high rates of information flow than the general population.
\item Our experiment only involved document scrolling in one direction (top to bottom). Given that humans are used to reading from top to bottom it is entirely possible that different results would be obtained if we had examined scrolling in the other direction.
\item We only used one document for the experiment. Perhaps if different documents were used (especially if they contained a different amount of graphics, different font sizes or different amounts of white-space) differing results would be obtained.
\item We asked participants to \emph{imagine} they were scrolling through a document rather than having them perform the actual task of scrolling. It is possible that this caused a systematic error as participants may not have accurately estimated their scrolling speeds.
\end{enumerate}
