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\begin{document}

\title{\vspace{-3mm}The Effect of the Choice of Hydration Strategy on
    Average Academic
Performance}

\author{Some concerned fellow students%
    \thanks{The authors would like to thank their hard-working peers as
        well as the staff of the KIT library for their unknowing - but vital
- participation.}}

\markboth{Journal of the Association of KIT Bibliophiles}{The Effect
of the Choice of Hydration Strategy on Average Academic Performance}

\maketitle

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\begin{abstract}
    We evaluate the relationship between hydration strategy and
    academic performance and project that by using the right button
    of the water dispenser to fill up their water bottles, students
    can potentially gain up to \SI{4.14}{\second} of study time per
    refill, which amounts to raising their grades by up to
    $0.0003$ points.
\end{abstract}

\begin{IEEEkeywords}
    KIT Library, Academic Performance, Hydration
\end{IEEEkeywords}

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\vspace*{-5mm}

%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Introduction}

% TODO: "The right strategy" pun?

\IEEEPARstart{T}{he} concepts of hydration and study have always been
tightly interwoven. As an example, an investigation was once
conducted by Bell Labs into the productivity of their employees that
found that ``workers with the most patents often shared lunch or
breakfast with a Bell Labs electrical engineer named Harry Nyquist''
\cite{gertner_idea_2012}, and we presume that they also paired their
food with something to drink. We can see that intellectual
achievement and fluid consumption are related even for the most
prestigious research institutions.

In this work, we quantify this relationship in the context of
studying at the KIT library and subsequently develop a novel and
broadly applicable strategy to leverage it to improve the academic
performance of KIT students.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Experimental Setup}

Over a period of one week, we monitored the use of the water
dispenser on the ground floor of the KIT library at random times
during the day. The experiment comprised two parts, a system
measurement to determine the flowrate of the water dispenser, and a
behavioural measurement, i.e., a record of participants' chosen
hydration strategies: $S_\text{L}$ denotes pressing the left
button of the water dispenser, $S_\text{R}$ the right one, and
$S_\text{B}$ pressing both buttons.

For the system measurement $10$ datapoints were recorded for each
strategy, for the behavioural measurement $113$ in total.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Experimental Results}

\begin{figure}[H]
    \centering

    \vspace*{-4mm}
    \begin{tikzpicture}
        \begin{axis}[
                width=0.8\columnwidth,
                height=0.35\columnwidth,
                boxplot/draw direction = x,
                grid,
                ytick = {1, 2, 3},
                yticklabels = {$S_\text{B}$ (Both buttons),
                $S_\text{R}$ (Right button), $S_\text{L}$ (Left button)},
                xlabel = {Flowrate (\si{\milli\litre\per\second})},
            ]
            \addplot[boxplot, fill, scol1, draw=black]
            table[col sep=comma, x=flowrate]
            {res/flowrate_both.csv};

            \addplot[boxplot, fill, scol2, draw=black]
            table[col sep=comma, x=flowrate]
            {res/flowrate_right.csv};

            \addplot[boxplot, fill, scol3, draw=black]
            table[col sep=comma, x=flowrate]
            {res/flowrate_left.csv};
        \end{axis}
    \end{tikzpicture}

    \vspace*{-3mm}

    \caption{Flow rate of the water dispenser depending on the
    hydration strategy.}
    \label{fig:System}
    \vspace*{-2mm}
\end{figure}

Fig. \ref{fig:System} shows the results of the system measurement. We
observe that $S_\text{L}$ is the slowest strategy, while $S_\text{R}$
and $S_\text{B}$ are similar. Due to the small sample size and the
unknown distribution, the test we chose to verify this observation is
a Mann Whitney U test. We found that $S _\text{L}$ was slower than
$S_\text{R}$ with a significance of $p < 0.0001$, while no
statistically significant difference was found between $S_\text{R}$ and
$S_\text{B}$. The results of the behavioural measurement can be seen in
Fig. \ref{fig:Behavior}.

\begin{figure}[H]
    \centering

    \vspace*{-2mm}
    \begin{tikzpicture}
        \begin{axis}[
                ybar,
                bar width=15mm,
                width=\columnwidth,
                height=0.35\columnwidth,
                area style,
                xtick = {0, 1, 2},
                grid,
                ymin = 0,
                enlarge x limits=0.3,
                xticklabels = {\footnotesize{$S_\text{L}$ (Left
                    button)}, \footnotesize{$S_\text{R}$  (Right
                button)}, \footnotesize{$S_\text{B}$}  (Both buttons)},
                ylabel = {No. chosen},
            ]
            \addplot+[ybar,mark=no,fill=scol1] table[skip first n=1,
            col sep=comma, x=button, y=count]
            {res/left_right_distribution.csv};
        \end{axis}
    \end{tikzpicture}

    \vspace*{-3mm}

    \caption{Distribution of the choice of hydration strategy.}
    \label{fig:Behavior}
\end{figure}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Modelling the grade improvement}

We can consider the water dispenser and students as comprising a
queueing system, specifically an M/G/1 queue
\cite{stewart_probability_2009}. The expected response time, i.e.,
the time spent waiting as well as the time dispensing water, is
\cite[Section 14.3]{stewart_probability_2009}%
%
\begin{align*}
    W = E\mleft\{ S \mright\} + \frac{\lambda E\mleft\{ S^2
    \mright\}}{2\mleft( 1-\rho \mright)}
    ,%
\end{align*}%
%
where $S$ denotes the service time (i.e., the time spent refilling a
bottle), $\lambda$ the mean arrival rate, and $\rho = \lambda \cdot
E\mleft\{ S \mright\}$ the system utilisation. Using our experimental
data we can approximate all parameters and obtain $W \approx
\SI{23.3}{\second}$. The difference to always using the fastest
strategy amounts to $\SI{4.14}{\second}$.

Strangely, it is the consensus of current research that there is only
a weak relationship between academic performance and hours studied
\cite{plant_why_2005}. Observing Figure 1 in
\cite[p. 950]{schuman_effort_1985} and performing a linear regression,
we quantified the grade gain per additional hour studied as
$\SI{0.054}{points/hour}$. Using an estimate of 5 refills per day, we
thus predict a possible gain of up to $0.0003$ points.

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\section{Discussion and Conclusion}

Further research is needed, particularly on the modelling of the
arrival process and the relationship between the response time and
the grade gain. Nevertheless, we believe this work serves as a solid
first step on the path towards achieving optimal study behaviour.

In this study, we investigated how the choice of hydration strategy
affects average academic performance. We found that always choosing
to press the right button leads to an average time gain of
\SI{4.14}{\second} per refill, which translates into a grade
improvement of up to $0.0003$ points. We thus propose a novel and
broadly applicable strategy to boost the average academic performance
of KIT students: always using the right button.

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