\label{expresults}
\section{Fitts' Law Models of the Systems}
Figure \ref{IoDGraph} shows the mean times for each scrolling system plotted against the Indexes of Difficulty (IoD) tested, and the data itself is shown in Table \ref{IoDTable}.

According to the information theoretic basis of Fitts' Law, it is optimal to have a 4.13\% error in the results \cite{macfitts:2}. If the error level differs significantly from this, the IoDs can be adjusted statistically to account for it. Users in our evaluation made errors 3.95\% of the time so we have not used any adjustments in our results.

Table \ref{EqnTable} shows the equations of the lines of best fit for the three systems according to the Fitts' Law model (see Section \ref{fittslaw} for a description of Fitts' Law). The high $R^{2}$ values are typical of Fitts' Law which is well known for $R^{2}$ values of 0.9 or above \cite{macfitts:2}.

\begin{figure}[!b]
\begin{center}
\includegraphics[width=1.0\textwidth]{resu/IoDGraph.eps}
\caption{The performance of the three scrolling systems at different indexes of difficulty}
\label{IoDGraph}
\end{center}
\end{figure}

\begin{table}[!t]
\begin{center}
\begin{tabular}{l|l|l}
System & Equation & Pearson's $R^{2}$\\[1mm]
\hline
 & & \\[-2mm]
Scrollbar & $y=0.71x + 0.67$ & $R^{2} = 0.843$\\[2mm]
SDAZ & $y=1.51x - 0.19$ & $R^{2} = 0.996$\\[2mm]
RateBased & $y=1.69x - 0.08$ & $R^{2} = 0.971$\\
\end{tabular}
\end{center}
\caption{The equations of the lines of best fit}
\label{EqnTable}
\end{table}

\begin{table}[!b]
\begin{center}
\begin{tabular}{lrrrr}
Scroll-Type & IoD & Mean Time (ms)& SD & SE\\
\hline
 &     1.32 & 2051 &  1019 & 263\\
 &     2.00 & 3250 &  1150 & 297\\
Rate-Based &     2.58 & 3572 &  1131 & 292\\
 &     2.58 & 4978 & 1801 & 465\\
 &     4.39 & 8088 & 2473 & 638\\
 &     5.17 & 8052 &  2687 & 694\\
\hline
 &   1.32 & 1767 &  624 & 161\\
 &   2.00 & 2861 &  1180 & 305\\
SDAZ &   2.58 & 3263 &  1254 & 324\\
 &   2.58 & 4094 &  2119 & 547\\
 &   4.39 & 6691 &  2754 & 711\\
 &   5.16 & 7414 &  2626 & 678\\
\hline
 &     1.32 & 1191 &  429 & 111\\
 &     2.00 & 1997 &  647 & 167\\
Scrollbar &     2.58 & 2446 &  609 & 157\\
 &     2.58 & 3118 &  1255 & 324\\
 & 4.39 & 4339 &  1933 & 499\\
 & 5.17 & 3727 &  1273 & 329\\
\hline
\end{tabular}
\end{center}
\caption{The data for scrolling system vs IoD}
\label{IoDTable}
\end{table}

Notable is the way in which the fifth point drops off for all three curves. This suggests that the target set was easier than the rest for users to spot. That particular target set was the introduction and conclusion headings of the document --- both of which were followed by a small amount of text with a page or so of whitespace on either side, hence making these targets visually obvious.

The vast superiority of scrollbars over the other two systems raises questions. Were \citename{cs:1} wrong when they found SDAZ to be faster than scrollbars? We believe the answer lies in the nature of the task. Based on our taxonomy given in Chapter \ref{TaxChapter} the task in a Fitts' Law reciprocal tapping task is a Reacquire action. As we mention in that discussion, position control devices such as scrolling are known to be especially efficient at Reacquire actions. Our findings clearly support that thesis. Some of our participants commented that they were simply remembering where abouts on the scrollbar the thumb needed to be located rather than actually looking for the target within the document. Thus, they were performing a Spatial-Locate task rather than a Visual Search one.

Therefore, to some extent, the experimental paradigm of modelling a scrolling system using Fitts' law tapping tasks is not universally valid. More specifically, comparison between a rate-control system and a position control system is unfairly biased in favour of the position control system. We can still, of course, draw results between rate-based systems though and conclude that our results show SDAZ to be faster than a standard rate-based system for performing Reacquire tasks. Hence we see no conflict between our results and those of \citename{cs:1}. \citename{cs:1} used Visual Search tasks in their evaluation, which we believe to be the strength of SDAZ.

\section{SDAZ vs Rate-Based}
As Figure \ref{IoDGraph} shows, SDAZ was faster than rate-based, on average, for every distance tested. An ANOVA run across the data of the three systems revealed a significant difference between the three scrolling systems ($F_{2,28}=30.2, p<0.001$). A paired t-test showed a statistical difference ($t_{538}=17.8, p<0.0001$) between SDAZ and rate-based. The overall means for the three systems are shown in Table \ref{OverallTable}. It can be seen that SDAZ was 13\% faster than rate-based on average for these tasks.

\begin{figure}[!t]
\begin{center}
\includegraphics[width=0.9\textwidth]{resu/SEgraph.eps}
\caption{The NASA TLX subjective evaluation results.}
\label{NASATLX}
\end{center}
\end{figure}

\begin{table}[!b]
\begin{center}
\begin{tabular}{l|c|r|r}
System & Mean Time (ms) & SD & SE\\
\hline
Rate-Based & 4998 & 1455 & 376\\
SDAZ & 4348 & 1570 & 405\\
Scrollbar & 2803 & 875 & 226\\
\end{tabular}
\end{center}
\caption{The overall results for the systems}
\label{OverallTable}
\end{table}

From the participants comments, they clearly preferred SDAZ to rate-based scrolling. Three participants said something similar to ``It [rate-based] was horrible''. Some of the participants did not feel comfortable with any form of rate-based scrolling, as it was new to them.

Four participants made comments to the effect that SDAZ in general was better than rate-based scrolling because it gave them more time to see what was coming and made it easier to locate images because of this.

In the subjective ranking of the three systems, 67\% of participants preferred SDAZ to rate-based scrolling. 60\% of the participants ranked rate-based as the worst of all three systems, while only 13\% ranked SDAZ as worst. (60\% ranked scrollbars as best of all, but as has already been discussed, scrollbars were particularly useful in this evaluation).

The NASA Task Load Index subjective evaluation (see Figure \ref{NASATLX}) revealed no clear differences between rate-based and SDAZ systems. In the NASA TLX test participants rank each system from one (best) to five (worst) in six different categories.

\section{The Accuracy of the Earlier Calibration}

One of our interests in this experiment was feedback about how our calibration of SDAZ seemed to perform in a real target acquisition task --- rather than simply playing with the system as our earlier participants had done (see Chapter \ref{calSD}).

One participant wrote that the SDAZ system was ``Too hard to stop without middle clicking'' by which we understand him to mean that he found the null-speed region too small. This was something we had already identified as a potential problem --- see Section \ref{calStoppingInstantly}. However the problem may just have been that this participant clicked the mouse rather than dragged with it.

One participant felt that SDAZ zoomed out the document too far and would have preferred a maximum magnification of about five pages. This surprised us as when we use the system ourselves we encounter the problem that our maximum magnification of ten pages seems too low. It may be that greater familiarity with the document means that a higher maximum magnification is appropriate. Alternatively, this could be an indication that our Document Speed $\to$ Magnification mapping is incorrect. The participant wanted to go faster on a lower magnification, while we want the system to reach higher magnifications. A linear mapping with a higher maximum magnification would seem to fit both of these requirements.

Two participants reported difficulties in changing the direction when they had overshot the target. They commented on the difficulty of changing direction and on the difficulty caused by the system zooming in as they reversed direction. We believed we had corrected the problem of the zoom-in on direction change (see Section \ref{calHuntingEffect}) but our solution was apparently not sufficient for these users. The issue of a quick direction change we have already identified (see Section \ref{calStoppingInstantly}) but is not one we could find an adequate solution to.

One participant commented that SDAZ was annoying when scrolling really short distances (presumably because the zoom-out seemed counterintuitive when travelling such short distances). However two users made comments to the opposite effect --- that they found SDAZ easier for short distance scrolling than they did over longer distances.

One participant complained that the speed control was oversensitive. This suggests that the slope of line mapping Displacement $\to$ DS was too steep (see Section \ref{calZoomFormula} and Table \ref{calsettingstable}). We had not so carefully investigated the calibration of this formula, as we believed the settings used by \citename{cs:1} were adequate.

\section{The Use of Modal vs Dragging mouse interaction}

To use the Rate-Based and SDAZ systems, participants were told to ``use the middle mouse button''. Both systems could be operated by either holding down the middle mouse button and dragging the mouse and releasing it to end scrolling, or by clicking the middle mouse button and then moving the mouse and clicking again to end scrolling. We decided to investigate this because the Windows implementation of rate-based scrolling provides for both functionalities we were unsure during our calibration of SDAZ which functionality was better.

Ten participants dragged with the mouse, and five participants used the modal operation. Only one of the fifteen users discovered both methods of using the mouse --- he then chose to drag. There was no significant difference ($F_{1,13}=0.01, p=0.91$) between the performance of those who dragged ($mean=4.78s$) and those who use the modal interface ($mean=4.88s$). Neither was there a significant interaction ($F_{4,52}=0.25, p=0.91$) between the Index of Difficulty of the targets and the method of mouse interaction being used. There was also no significant difference ($F_{1,13}=1.14, p=0.31$) between the scrolling system used (SDAZ or rate-based) and the method of mouse interaction used (dragging or modal). This last however, is moderately close to being significant and its lack of statistical significance may be due to our small sample size. Our data shows SDAZ performs better when dragging is used (a mean of 4.34 rather than 4.77s) and rate-based performs better when the mouse is used modally (a mean of 4.98 rather than 5.22s).

Four of the fifteen users suffered ``modal confusion'' at some point where they attempted to use the mouse in one way and accidentally used it the other way. For example, a user that operated the system by dragging, would click the button accidentally (or the system would interpret a very short dragging motion as a click) and then get stuck in scrolling mode until they clicked again. Users appeared to attribute this functionality to a bug rather than realising the system supported both types of interaction.

The scrollbar, like typical scrollbars, provided three methods of interaction. The user could click and drag the scroll thumb, click the arrows to scroll one line, or click outside the scroll thumb to move one page. Four participants actively discovered all three uses of the scrollbar (not including the one participant who discovered both methods of using rate-based and SDAZ scrolling) --- though we assume that many of the others were aware of the alternate ways to use a scrollbar from their previous experience of them. All but one participants operated the scrollbar in the experiment purely by dragging the scroll thumb.

\section{The Effects of Previous Experience}

Six of the fifteen participants had previous experience with SDAZ. Unsurprisingly these people were significantly faster ($F_{1,13}=6.4, p<0.03$) at all types of scrolling ($mean=3.26s$) than the inexperienced people ($mean=4.58s$). There was also a significant interaction ($F_{2,26}=6.2, p<0.01$) between previous experience with SDAZ and the scrolling system used. Figure \ref{prevexpGraph} shows a plot of this and Table \ref{prevexpTable} gives the data.

%\begin{wrapfigure}{r}{10cm}
\begin{figure}[!t]
\begin{center}
\includegraphics[width=0.65\textwidth]{resu/prevExpGraph.eps}
\caption{The effect of previous experience with SDAZ}
\label{prevexpGraph}
\end{center}
\end{figure}
%\end{wrapfigure}

\begin{table}[!b]
\begin{center}
\begin{tabular}{clcrr}
SDAZ Experience & Interface & Mean Time (ms) & SD & SE\\
\hline
 &   rate-based&   3771 &  971 &  396\\
Yes &   SDAZ      &   3392 &  572 &  233\\
 &   scrollbar &   2609 &  396 &  162\\
\hline
 &   rate-based&   5817 & 1109 &  370\\
No &   SDAZ      &   4986 & 1723 &  574\\
 &   scrollbar &   2933 & 1093 &  364\\
\hline
\end{tabular}
\end{center}
\caption{Previous experience with SDAZ }
\label{prevexpTable}
\end{table}

Eight of the fifteen participants said they regularly played computer games which involved rapid information flow. There was almost a significant main effect for game playing ($F_{1,13}=4.3, p=0.06$) and no significant interaction with the scrolling system ($F_{2,26}=2.6, p=0.10$).

Nine of the participants were computer-science majors. There was a significant difference ($F_{1,13}=5.5, p<0.04$) between those majoring in computer science ($mean=3.54s$) and those not ($mean=4.80s$). There was almost a significant interaction between computer science major and scrolling system ($F_{2,26}=3.3, p=0.052$). The difference at using scrollbars between those majoring in computer science and those not was quite small (means of 2.6 and 3.1), whereas the difference at using SDAZ between those majoring in computer science and those not was comparatively large (means of 3.6 and 5.5). This is very similar to the data obtained for condition of the previous experience with SDAZ. Together they suggest that experience benifits users of SDAZ more than it does users of scrollbars. This means that scrollbars are easier to learn to use effectively than SDAZ. This is unsurprising since scrollbars are relatively simple compared to SDAZ.

\section{The IoD tested on both documents}

Users scrolled a distance of five pages on both the larger and smaller documents. It was hoped that this would give some indication as to how a larger size document affected the different scrolling systems.

We thought that the scrollbar might perform worse on the large document than the smaller one as the larger document would require the scroll thumb to be positioned more accurately. Figure \ref{SameIoDGraph} shows a plot of the data for this IoD. This shows there is no such interaction occurring. The larger document was slightly slower in all systems, but suggests it is likely the case that the target pair used in the larger document was more difficult to acquire than the shorter document target pair was. We have already seen (with the example of the target pair with an IoD of 5.1) that target context can have a large effect on the acquisition time.

Perhaps the reason that the performance of the scrollbar didn't degenerate on our large document was our high screen resolution. Because of this the use would have had a margin of error of about 20 pixels in which to position the scroll thumb.

%\begin{wrapfigure}{r}{10cm}
\begin{figure}[!t]
\begin{center}
\includegraphics[width=0.7\textwidth]{resu/SameIoDGraph.eps}
\caption{The performance of the three scrolling systems on the two different documents when scrolling five pages}
\label{SameIoDGraph}
\end{center}
\end{figure}
%\end{wrapfigure}
