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

\section{Introduction: Aims and Hypotheses}
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\section{Methods}

\subsection{Participants}
\subsection{Apparatus}

Experimental setting was completely adopted from experiment II (see chapter \ref{ApparatusEWAT2}).

\subsection{Task and procedure}

Like the first two experiments, experiment III started with an introduction phase, where all participants were informed about the procedure of the experiment. They were told that two types of trial existed in this experiment. On one hand there would be trials with change in transformation so that from a given point of time length of a drawn line on the writing pad would appear ten percent longer on the monitor. They would be informed about the change of transformation by the change of cursor colour from blue to red. On the other hand they would deal with trial without any change in transformation. Again, their task was to draw circles of constant sizes on the computer screen. Further procedure was exactly as described for experiment II. Figure \ref{AblaufTrialEWAT3} summarizes the procedure in each trial. Altogether, three types of trial existed in this third experiment. They are also displayed in figure \ref{AblaufTrialEWAT3} and will be described in the next section (see chapter \ref{TypesEWAT3}).

\begin{figure}[htbp]
\begin{center}
\includegraphics[width=14.6cm]{kapitel/graphiken/AblaufTrialEWAT3.pdf}
\caption{Procedure of each trial of the third experiment. After starting the trial by
moving the cursor to the starting position, synchronisation 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. Trials with change in transformation are highlighted in blue (increasing gain factor) and light blue (decreasing gain factor). Trials without change in transformation are highlighted in red}.
\label{AblaufTrialEWAT3}
\end{center}
\end{figure}


\subsection{Types of trials}
\label{TypesEWAT3}

Altogether, there were three types of trial. Two of them were consistent with the information given to the participants during the instruction phase. On one hand these were trials where change in transformation was applied and marked by colour change of the cursor and gain factor was increased from 1 to 1.1. Trials of this type will be called Increasing gain trials. On the other hand, there were trials without change in transformation and no change in cursor colour. These trials will be referred to as No change trials\\
In the third type of trial change in transformation also occured and was marked by a colour change of the cursor from blue to red. The only difference between these trials and the other trials with change in transformation was that the gain factor was decreased from 1 to 0.9. This condition asked for an adaptation that was inverse to information given in the instruction. Here, participants had to enlarge the radius by ten percent during change in transformation. These trials will be called Decreasing gain trials.

\subsection{Application of change in transformation}

\subsubsection{Trials with change in transformation}

\textbf {Trials with increasing gain factor}

Position of the dot on the screen was computed by multiplying the cartesian coordinates of the position of the pen on the writing pad with the gain factor, as it was already done for the first two experiment (see section \ref{ChangeTrialsEWAT1}). The only difference for change trials with increasing gain factor in this third experiment is that the maximum gain factor was only 1.1 instead of 1.2. The gain factor g(t) was again calculated with the help of the formulas summarized in table \ref{GainComputationEWAT1}. Only two parameters had different values than those described in experiment I. The gain factor $g_{0}$, representing the value of gain at the point of time when half of the gain change was reached, was now 1.05 and a, standing for the amplitude of gain change, was only 0.05 instead of 0.1 in these trials. Figure \ref{gainFormelplusEWAT3} displays the gain factors in the course of one trial with increased gain factor.

\begin{figure}[htbp]
\begin{center}
\includegraphics[width=14.6cm]{kapitel/graphiken/gainFormelplusEWAT3.pdf}
\caption{Gain values in trials with increasing gain factor. Gain values for each point of time are represented by the
red curve. The parameters used to compute gain at each point of
time are displayed. Trials were again divided into five phases. }
\label{gainFormelplusEWAT3}
\end{center}
\end{figure}

During maximum change in transformation gain factor was 1.1. Therefor participants had to adapt the radius of drawn circles by ten percent of the radius before change in transformation. Hence, again a circle of 4.72 cm was presented during each synchronisation phase. An adaptation of radius by ten percent means, that radius has to be diminished by 0.47 cm to a radius of 4.25 cm during change in transformation.\\
Once more onset of change was varied between 2.5 and 3.3 standard circles (in 0.2-steps). Number of standard circles were the same as in experiment II, with the exception that all participants completed nine circles after change in transformation.

\textbf{Trials with decreasing gain factor} 

As described for trials with increasing gain factor, position of the cursor on the screen were computed by multiplying coordinates of the pen on the writing pad with the gain factor. Only in these trials, gain did not increase, but decrease by an negative amplitude of a=-0.05 to a minimum gain factor of $g(t)=0.9$. Figure \ref{gainFormelminusEWAT3} shows resulting gain factors at each point of time in the course of a Decreasing gain trial.

\begin{figure}[htbp]
\begin{center}
\includegraphics[width=14.6cm]{kapitel/graphiken/gainFormelminusEWAT3.pdf}
\caption{Gain values in trials with decreasing gain factor. Gain values for each point of time are represented by the
red curve.The parameters used to compute gain at each point of
time are displayed. Trials were divided into five phases.}
\label{gainFormelminusEWAT3}
\end{center}
\end{figure}


\subsubsection{Trials without change in transformation}


\subsection{Design}

\subsection{Analysis of data}
\subsubsection{Determination of the dependent variable ``Radius''}
\subsubsection{Determination of invalid segments, trials and participants}
\subsubsection{Analysis of radius}
\subsubsection{Interview}


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\section{Results}
\subsection{Data Analysis and excluded data}
\subsection{Movement time}
\subsection{Awareness of change}

\subsection{Radius}
\subsubsection{Analyses of radius including all participants}
\subsubsection{Analyses of radius including only participants without awareness of false introduction}

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\section{Discussion}

\subsection{Summary of Results}

\subsection{Interpretation of Results}

\subsection{Suggestions for future studies}

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