\chapter{Experiment I }\label{kapitel:ExperimentI}

\section{Introduction: Aims and Hypotheses}


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\section{Methods}

\subsection{Participants}

Altogether 26 right-handed subjects (13 female, 13 male)
participated in this study. 24 of them were college students from
the University of Dortmund, while 2 worked at the Institute for
Occupational Physiology at the University of Dortmund.
Participants received 10 euro or class credits for taking part.
Data from three female participants from each group had to be
excluded from further analysis because of incorrect task handling.
13 male and 7 female subjects (mean age 24.2 yrs, SD 2.74 yrs, age
range: 20-29 yrs) were able to complete the task correctly. Group
''Explicit Knowledge`` consisted of 7 male and 3 female persons
(mean age 23.9 yrs, SD 2.69 yrs, age range: 20-29 yrs), while
group ``No Explicit Knowledge'' was formed by 6 male and 4 female
participants (mean age 24.4 yrs, SD 2.91 yrs, age range: 20-29
yrs). There was no significant difference between the two groups
concerning age (\emph{t}(18) = -.399, \emph{p} > .1) and gender
(Pearson $\\chiČ$(1) = .639, p > .1).

\subsection{Apparatus}

All experimental sessions took place at the Institute for
Occupational Physiology at the University of Dortmund.
Participants were seated in front of a 17-inch flat screen (EIZO
FlexScan) with a resolution of 1280 x 1024 pixels an a refreshing
rate of 60 Hz. One cm on the screen contained 37.9 pixels. The
distance between subjects and the screen was 60 cm. Between the
screen and the participant a writing pad (SummaSketch III
Professional) with a size of 18 x 12 inches and a resolution of
500 lines per inch was positioned. Participants used a pen to draw
on the writing pad with their right hand. An attached cover
prevented participants from seeing their hand while drawing. To
prevent participants from resting their right arm on the writing
pad during drawing, the height of the table with the writing pad
on it was only ??? cm. One lamp illuminating the wall behind the
monitor and another light source on the ceiling were the only
light sources to prevent reflections on the monitor. OHM???

%\begin{figure}[htbp]
%\begin{center}
%\includegraphics[width=8cm]{kapitel/graphiken/LaborEWAT1}
%\caption{.} \label{LaborEWAT1}
%\end{center}
%\end{figure}


\subsection{Task and procedure}

The experiment started with an introduction phase in which both
groups were informed about the course of the task. Group
``Explicit Knowledge`` was also informed about the occurrence of
changes in visuomotor coupling which was indicated by a colour
change of the cursor during the trials. Participants of this group
were also told to adapt their movements when visuomotor coupling
was changed. Group ''No Explicit Knowledge`` did not get any
information about changes in transformation. Also the colour of
the cursor did not change during the experiment for this group.
The original introductions can be found
in appendix \ref{IntroductionEWAT1} . \\
After the instruction phase participants completed a training
phase to get used to working with the writing pad. A white circle
with an eccentricity of 9° of visual angle and therefor a radius
of 4.72 cm became visible in the center of the monitor.
Participants were asked to move the cursor around this circle in
continuous circles. The cursor was visualized by a white dot with
a radius of 0.21 cm. Participants were told to draw circles of
about the size of the white circle in a comfortable way (see
figure \ref{uebungEWAT1}. If drawing was too slow (less than 1.1
seconds per circle) or too fast (more than 2.5 ??? seconds per
circle) training phase was repeated until a proper velocity was
achieved. After completing 5 circles, the white circle disappeared
and participants continued drawing for another 10 circles. Drawing
velocity from this training phase was used to compute an
appropriate velocity for the test phase. For this purpose the mean
of durance for drawing the sixth to fifteenth circle was
calculated and saved.

\begin{figure}[htbp]
\begin{center}
\includegraphics[width=8cm]{kapitel/graphiken/uebungEWAT1}
\caption{Screenshot from training session. Participants moved the
white dot around the white circle.} \label{uebungEWAT1}
\end{center}
\end{figure}

After finishing the training, the test phase of the experiment
started. Participants started each trial by moving the cursor
(visualized by a white arrow) to a yellow rectangle. This
rectangle was positioned above the 12 o'clock position of the
circle participants had to draw. When they had reached this
starting position and had pushed the tip of the pen onto the
drawing pad, the trial started. The cursor symbol changed from
arrow to a white dot with a radius of 0.21 cm. Furthermore, a
turquoise coloured dot became visible and began to move on a
circular path with a radius of 4.72 cm with the velocity
calculated from the training session of the participant.
Participants were told to follow the turquoise dot with the white
dot by drawing circles on the writing pad. It was emphasized that
the turquoise dot was only there to help participants drawing
circles of the same size with the same velocity. This part of each
trial will be referred to as synchronization phase. See figure
\ref {synchroEWAT1} for an example of this phase.

\begin{figure}[htbp]
\begin{center}
\includegraphics[width=14cm]{kapitel/graphiken/ablaufEWAT1}
\caption{Four screenshots from synchronisation phase. Participants
followed the turquoise dot with the white dot. Pictures show
scenes from the completion of one circle (from left to right
picture).} \label{synchroEWAT1}
\end{center}
\end{figure}


After five full circles, the turquoise dot disappeared when it had
reached the 12 o'clock position. Participants had to continue
drawing circles in the same size and with the same velocity
without any additional orientation on the screen. In each trial
seven full standard circles had to be accomplished after the
synchronization phase. Drawing one standard circles means that one
circle with the radius of 4.72 cm and the velocity computed in the
training session is completed. Due to changes in velocity and size
individuals varied
in the number of completed circles in the continuation phase.\\
This part of each trial is called continuation phase. Only in this
part of the trial, transformation changes were applied. Figure
\ref {AblaufTrialEWAT1} summarizes the procedure of each trial.

\begin{figure}[htbp]
\begin{center}
\includegraphics[width=14cm]{kapitel/graphiken/AblaufTrialEWAT1}
\caption{Procedure of each trial. After starting the trial by
moving the cursor to the starting position, synchronization phase
is started. After following the turquoise dot for five circles,
continuation phase starts. In this phase changes in transformation
are applied in trials with transformation changes. }
\label{AblaufTrialEWAT1}
\end{center}
\end{figure}


\subsection{Application of change in transformation}

In trials with change of transformation, participants completed at
least one standard circle and at most 1.9 standard circles in the
continuation phase, before change of transformation was applied.

 The position of the dot on the
screen ($P_{S}$) representing the position of the pen on the
writing pad (PT) was computed by multiplying the current position
on the writing pad with a gain factor.
\\
\\
(1) PS(x,y)= gain factor x PT(x,y)
\\
\\
This gain factor was 1 in trials without changes in transformation
and before onset of change in transformation in trials with change
in transformation. When transformation change started, the gain
factor was changed with the help of the following function.
\\
\\
(2)


Figure \ref{onsetEWAT1} shows the variation in onset of change in
transformation during continuation phase and the number of trials
before, during and after change in transformation

\begin{figure}[htbp]
\begin{center}
\includegraphics[width=12cm]{kapitel/graphiken/onsetEWAT1}
\caption{Variation in onset of change in transformation.}
\label{onsetEWAT1}
\end{center}
\end{figure}




\subsection{Design}

Altogether, three blocks had to be accomplished. Each block
consisted of 20 trials. In ten of these trials a change in
visuomotor coupling occurred, while there was no change in the
other ten trials. The occurrence of change-trials and
no-change-trials was permuted for every participant in each block.
In change-trials the onset of change was varied in 0.1 steps
between 1 and 1.9 standard circles after the beginning of the
continuation phase, so that ten different onsets of changes
resulted (see figure \ref{onsetEWAT1}). The onset of change was
also permuted for each block and every participant.


\subsection{Analysis of data}

\subsubsection{Determination of the dependent variable ``Radius''}

\subsubsection{Determination of invalid trials}

\subsubsection{Analysis of radius}

\subsubsection{Questionnaire}

\newpage
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\section{Results}

\subsection{Data Analysis}

\subsection{Radius}

\subsection{Explicit knowledge}
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\section{Discussion}

\subsection{Summary of Results}

\subsection{Interpretation of Results}

\subsection{Suggestions for future studies}

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