Fix stray asterisk and punctuation

README.md

@@ -1,6 +1,6 @@
 # KIT Library Hydration Study
 
-Latex sources for a paper on the behavior of students at the KIT library with
+Latex sources for a paper on the behaviour of students at the KIT library with
 regard to their water bottle refilling habits.
 
 ## Build
@@ -17,7 +17,7 @@ $ make
    ```bash
    $ docker build -f Dockerfile . -t bib-paper
    ```
-2. Build examples
+2. Build document
    ```bash
    $ docker run --rm -v $PWD:$PWD -w $PWD -u `id -u`:`id -g` bib-paper make
    ```

paper.bib

@@ -214,7 +214,7 @@ TLDR: Investigation of the efficacy of two cognitive behavior modification proce
 }
 
 @article{schuman_effort_1985,
-	title = {Effort and {Reward}: {The} {Assumption} that {College} {Grades} {Are} {Affected} by {Quantity} of {Study}*},
+	title = {Effort and {Reward}: {The} {Assumption} that {College} {Grades} {Are} {Affected} by {Quantity} of {Study}},
 	volume = {63},
 	shorttitle = {Effort and {Reward}},
 	abstract = {The relation between college grades and self-reported amount of effort was examined in four major and several minor investigations of undergraduates in a large state university. Grades were operationalized mainly by using grade point average (GPA), though in one investigation grades in a particular course were the focus. Effort was measured in several different ways, ranging from student estimates of typical study over the term to reports of study on specific days. Despite evidence that these self-reports provide meaningful estimates of actual studying, there is at best only a very small relation between amount of studying and grades, as compared to the considerably stronger and more monotonic relations between grades and both aptitude measures and self-reported class attendance. The plausible assumption that college grades reflect student effort to an important extent does not receive much support from these investigations. This raises a larger question about the extent to which rewards are linked to effort in other areas of life—a connection often assumed but seldom investigated.},

paper.tex

@@ -1,43 +1,27 @@
 \documentclass[journal]{IEEEtran}
 
 \usepackage{amsmath,amsfonts}
+\usepackage{siunitx}
+\usepackage{mleftright}
 \usepackage{float}
 \usepackage{titlesec}
-\usepackage{algorithmic}
-\usepackage{algorithm}
-\usepackage{siunitx}
-\usepackage[normalem]{ulem}
-\usepackage{dsfont}
-\usepackage{mleftright}
-\usepackage{bbm}
 \usepackage[
     backend=biber,
     style=ieee,
     sorting=nty,
 ]{biblatex}
 
-\usepackage{tikz}
-\usetikzlibrary{spy, arrows.meta,arrows}
-
 \usepackage{pgfplots}
 \pgfplotsset{compat=newest}
 \usepgfplotslibrary{statistics}
 
-\usepackage{pgfplotstable}
-\usepackage{filecontents}
-
-\hyphenation{op-tical net-works semi-conduc-tor IEEE-Xplore}
-
 %
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 % Template modifications
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %
 
-% TODO: "The right strategy" pun
+\titlespacing*{\section}{0mm}{3mm}{1mm}
-
-\titlespacing*{\section}
-{0mm}{3mm}{1mm}
 
 \makeatletter
 \def\@maketitle{%
@@ -46,11 +30,11 @@
     \vspace*{-4mm}
     \begin{center}%
         {\Huge \linespread{0.9}\selectfont \@title \par}%
-        {\large
+        {\large \lineskip .5em%
-            \lineskip .5em%
             \begin{tabular}[t]{c}%
                 \@author
-        \end{tabular}\par}%
+            \end{tabular}
+        \par}%
     \end{center}%
     \vspace*{-8mm}
 }
@@ -111,12 +95,12 @@
 Performance}
 
 \author{Some concerned fellow students%
-    \thanks{The authors would like to thank their hard-working peers as well as
+    \thanks{The authors would like to thank their hard-working peers as
-        the staff of the KIT library for their unknowing - but vital -
+        well as the staff of the KIT library for their unknowing - but vital
-participation.}}
+- participation.}}
 
-\markboth{Journal of the Association of KIT Bibliophiles}{The
+\markboth{Journal of the Association of KIT Bibliophiles}{The Effect
-Effect of the Choice of Hydration Strategy on Average Academic Performance}
+of the Choice of Hydration Strategy on Average Academic Performance}
 
 \maketitle
 
@@ -126,14 +110,13 @@ Effect of the Choice of Hydration Strategy on Average Academic Performance}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 %
 
-% \vspace*{-10mm}
-
 \begin{abstract}
     We evaluate the relationship between hydration strategy and
-    academic performance and project that by using the right button of
+    academic performance and project that by using the right button
-    the water dispenser to fill up their water bottles, students can potentially
+    of the water dispenser to fill up their water bottles, students
-    gain up to \SI{4.14}{\second} of study time per refill, which is amounts to
+    can potentially gain up to \SI{4.14}{\second} of study time per
-    raising their grades by up to 0.00103 points.
+    refill, which amounts to raising their grades by up to
+    $0.0003$ points.
 \end{abstract}
 
 \begin{IEEEkeywords}
@@ -151,41 +134,37 @@ Effect of the Choice of Hydration Strategy on Average Academic Performance}
 %%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{Introduction}
 
-\IEEEPARstart{T}{he} concepts of hydration and study have always been tightly
+% TODO: "The right strategy" pun?
-interwoven. As an example, an investigation was once conducted by Bell Labs
+
-into the productivity of their employees that found that ``workers with the
+\IEEEPARstart{T}{he} concepts of hydration and study have always been
-most patents often shared lunch or breakfast with a Bell Labs electrical
+tightly interwoven. As an example, an investigation was once
-engineer named Harry Nyquist'' \cite{gertner_idea_2012}, and we presume that
+conducted by Bell Labs into the productivity of their employees, that
-they also paired their food with something to drink. We can see that
+found that ``workers with the most patents often shared lunch or
-intellectual achievement and fluid consumption are related even for the most
+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
+In this work, we quantify this relationship in the context of
-KIT library and subsequently develop a novel and broadly applicable strategy
+studying at the KIT library and subsequently develop a novel and
-to leverage it to improve the academic performance of KIT students.
+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 usage of the water dispenser
+Over a period of one week, we monitored the use of the water
-on the ground floor of the KIT library at random times during the day.
+dispenser on the ground floor of the KIT library at random times
-The experiment comprised two parts, a system measurement to determine the
+during the day. The experiment comprised two parts: a system
-flowrate of the water dispenser, and a behavioural measurement, i.e.,
+measurement to determine the flowrate of the water dispenser, and a
-a recording
+behavioural measurement, i.e., a record of participants' chosen
-of the choice of hydration strategy of the participants: $S_\text{L}$ denotes
+hydration strategies: $S_\text{L}$ denotes pressing the left
-pressing the left button of the water dispenser, $S_\text{R}$ the right one,
+button of the water dispenser, $S_\text{R}$ the right one, and
-and $S_\text{B}$ pressing both buttons.
+$S_\text{B}$ pressing both buttons.
 
-For the system measurement $10$ datapoints were recorded for each strategy,
+For the system measurement $10$ datapoints were recorded for each
-for the behavioural measurement $113$ in total.
+strategy, for the behavioural measurement $113$ in total.
-
-% As is always the case with measurements, care must be taken not to alter
-% quantities by measuring them. To this end, we made sure only to take system
-% measurements in the absence of participants and to only record data on the
-% behaviour of participants discreetly.
-
-% TODO: Describe the actual measurement setup? (e.g., filling up a 0.7l bottle
-% and timing with a standard smartphone timer)
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{Experimental Results}
@@ -228,16 +207,13 @@ for the behavioural measurement $113$ in total.
 \end{figure}
 
 Fig. \ref{fig:System} shows the results of the system measurement.
-We observe that $S_\text{L}$ is the slowest strategy, while $S_\text{R}$
+To investigate the difference in flowrate between strategies, we used
-and $S_\text{B}$ are similar. Due to the small sample size and the
+a Mann Whitney U test, because of its nonparametric nature.
-unknown distribution, the test we chose to verify this observation is a Mann
+We found that $S _\text{L}$ was slower than
-Whitney U test. We found that $S _\text{L}$ is faster than $S_\text{R}$ with a
+$S_\text{R}$ with a significance of $p < 0.01$, while no
-significance of $p < 0.0001$, while no significant statement could be made
+statistically significant difference was found between $S_\text{R}$ and
-about $S_\text{R}$ and $S_\text{B}$.
+$S_\text{B}$. The results of the behavioural measurement are shown in
-Fig. \ref{fig:Behavior} shows the results of the behavioural measurement.
+Fig. \ref{fig:Behavior}.
-% During this part of the experiment, we also measured the time each participant
-% needed to fill up their bottle. Using the measured flowrates we calculated
-% the mean refill volume to be $\SI{673.92}{\milli\liter}$.
 
 \begin{figure}[H]
     \centering
@@ -272,108 +248,51 @@ Fig. \ref{fig:Behavior} shows the results of the behavioural measurement.
 \end{figure}
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-\section{Modelling}
+\section{Modelling the grade improvement}
 
-We can consider the water dispenser and students as comprising a queueing
+We can consider the water dispenser and students as comprising a
-system, specifically an M/G/1 queue \cite{stewart_probability_2009}.
+queueing system, specifically an M/G/1 queue
-The expected response time, i.e., the time spent waiting as well as
+\cite{stewart_probability_2009}. The expected response time, i.e.,
-the time dispensing water, is \cite[Section 14.3]{stewart_probability_2009}%
+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
+    W = E\mleft\{ S \mright\} + \frac{\lambda \cdot 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\{
+where $S$ denotes the service time (i.e., the time spent refilling a
-S \mright\}$ the system utilization. Using our
+bottle), $\lambda$ the mean arrival rate, and $\rho = \lambda \cdot
-experimental data we can approximate all parameters and obtain
+E\mleft\{ S \mright\}$ the system utilisation. Using our experimental
-$W \approx \SI{23.3}{\second}$. The difference to always using
+data we can approximate all parameters and obtain $W \approx
-the fastest strategy amounts to $\SI{4.14}{\second}$.
+\SI{23.3}{\second}$. The difference to always using the fastest
-% We examine the effects of the choice of hydration strategy. To
+strategy amounts to $\SI{4.14}{\second}$.
-% this end, we start by estimating the potential time savings possible by always
-% choosing the fastest strategy:%
-% %
-% % We can model the time needed for one person to refill their
-% bottle as a random
-% % variable (RV) $T_1 = V/R$ and the time saved by choosing the
-% fastest strategy
-% % as $\Delta T_1 = T_1 - V/\max r$, where $V$ and $R$ are RVs representing the
-% % bottle volume and flowrate. The potential time saving for the
-% last person in a
-% % queue of $N$ people is thus $\Delta T_N = N\cdot\Delta T_1$. We
-% can then model
-% % the total time savings as $\Delta T_\text{tot} = \sum_{n=1}^{N} \Delta T_n$,
-% % where N is an RV describing the queue length. Assuming the
-% independence of all
-% % RVs we can compute the mean total time savings as
-% %
-% \begin{gather*}
-%     T_1 = V/R, \hspace{3mm} \Delta T_1 = T_1 - V/\max R,
-% \hspace{3mm} \Delta T_n = n \cdot \Delta T_1 \\
-%     \Delta T_\text{tot} = \sum_{n=1}^{N} \Delta T_\text{n} =
-% \sum_{n=1}^{N} n \cdot \Delta T_1 = \Delta T_1 \frac{N\mleft( N+1
-% \mright)}{2} \\
-%     \Delta t := E\mleft\{ \Delta T_\text{tot} \mright\} = E\mleft\{
-% \Delta T_1 \mright\} \cdot \mleft[ E\mleft\{ N^2 \mright\} +
-% E\mleft\{ N \mright\} \mright]/2
-%     ,%
-% \end{gather*}
-% %
-% where $V$ and $R$ are random variables (RVs) representing the volume of a
-% bottle and the flowrate, $\Delta T_n$ describes the time the last of $n$
-% people saves, $\Delta T_\text{tot}$ the total time savings and $N$ the length
-% of the queue. It is plausible to assume independence of $R,V$ and $N$.
-% Using our experimental measurements we estimate $\todo{\Delta t =
-% \SI{20}{\second}}$
 
 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}.
+\cite{plant_why_2005}. Observing Figure 1 in
-The largest investigation into the matter found a correlation of
+\cite[p. 950]{schuman_effort_1985} and performing a linear regression,
-$\rho = 0.18$ \cite{schuman_effort_1985} between GPA and average time
+we quantified the grade gain per additional hour studied as
-spend studying per day. Using a rather high estimate of 5 refills per
+$\SI{0.054}{points/hour}$. Using an estimate of 5 refills per day, we
-day, we predict a possible grade gain of up to $0.00103$ points.
+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 gain
+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.
 
-% Many attempts have been made in the literature to relate
-% the time spent studying to academic achievement -  see, e.g.
-% \cite{schuman_effort_1985, zulauf_use_1999, michaels_academic_1989,
-% dickinson_effect_1990}.
-% The overwhelming consensus is that there is a significant relationship,
-% though it is a weak one.
-%
-%Many of the studies were only performed over
-% a period of one week or even day, so we believe care should be taken when
-% generlizing these results. Nevertheless, the overwhelming consensus in the
-% literature is that a significant relationship exists, though it is a weak one.
-
-% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% \section{Conclusion}
-
 In this study, we investigated how the choice of hydration strategy
-affects average academic performance. We found that always
+affects average academic performance. We found that always choosing
-choosing to press the right button leads to an average time gain of
+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 $0.00103$ levels. We thus propose a novel and
+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.
 
-% Further research is needed to develop a better model of how the choice of
-% hydration strategy is related to academic performance. We
-% suspect that there is a compounding effect that leads to $S_\text{L}$ being an
-% even worse choice of hydration strategy: When the queue is long, students are
-% less likely to refill their empty water bottles, leading to reduced mental
-% ability. Nevertheless, we believe that with this work we have laid a solid
-% foundation and hope that our results will find widespread acceptance among the
-% local student population.
-
 %
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 % Bibliography
@@ -382,75 +301,5 @@ of KIT students: always using the right button.
 
 \printbibliography
 
-% \appendix
-%
-% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
-% \section{Derivation of Service Time}
-% \label{sec:Derivation of Service Time}
-%
-%
-% We want to compute the response time of our queueing system, i.e.,
-% \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*}%
-% We start by modelling the service time and subsequently calculate $\lambda$
-% and $\rho$.
-%
-% Let $S, V$ and $R$ be random variables denoting the service time,
-% refill volume
-% and refill rate, respectively. Assuming that $V$ and $R$ are independent, we
-% have
-% \begin{gather*}
-%     S = \frac{V}{R} \hspace{5mm} \text{and} \hspace{5mm}
-%     P_R(r) = \left\{\begin{array}{rl}
-%         P(S_\text{L}), & r = r_{S_\text{L}} \\
-%         1-P(S_\text{L}), & r = r_{S_\text{R}}
-%     \end{array}\right.
-% \end{gather*}%
-% \begin{align*}
-%     E\mleft\{ S^2 \mright\} &= E\mleft\{ V^2 \mright\}E\mleft\{ 1 /
-% R^2  \mright\} \\
-%     & = E\mleft\{ V^2 \mright\} \mleft(
-% P(S_\text{L})\frac{1}{r^2_{S_\text{L}}} + \mleft( 1 - P(S_\text{L})
-% \mright)\frac{1}{r^2_{S_\text{R}}}  \mright)
-%     .%
-% \end{align*}
-% We now use our experimental data (having calculated $v_n, n\in [1:N]$ from the
-% measured fill times and flow rates) to compute
-% \begin{align*}
-%     \left.
-%     \begin{array}{r}
-%         E\mleft\{ V^2 \mright\} \approx \frac{1}{N+1}
-% \sum_{n=1}^{N} v_n^2 = \todo{15}\\
-%         P(S_\text{L}) \approx \frac{\text{\# times $S_\text{L}$ was
-% chosen}}{N} = \todo{123} \\
-%         r^2_{S_\text{L}} \approx \todo{125} \\
-%         r^2_{S_\text{R}} \approx \todo{250}
-%     \end{array}
-%     \right\} \Rightarrow
-%     \left\{
-%     \begin{array}{l}
-%         E\mleft\{ S \mright\} \approx \todo{678} \\
-%         E\mleft\{ S^2 \mright\} \approx \todo{123}
-%     \end{array}
-%     \right.
-%     .%
-% \end{align*}
-%
-% $\lambda$ is the mean arrival time.
-%
-% \todo{
-%     \textbf{TODOs:}
-%     \begin{itemize}
-%         \item Complete text describing / obtaining $\rho$ and $\lambda$
-%         \item Move model derivation to method section
-%         \item Move calculations with model to results section
-%         \item Add grade gain derivation
-%         \item Idea: Make the whole thing 2 pages and print on A3
-%     \end{itemize}
-% }
-
 \end{document}
+

scripts/find_grade_gain.py

@@ -0,0 +1,51 @@
+import matplotlib.pyplot as plt
+from scipy import stats
+import numpy as np
+import argparse
+
+
+def main():
+    """
+    [1] H. Schuman, E. Walsh, C. Olson, and B. Etheridge, “Effort and Reward:
+        The Assumption that College Grades Are Affected by Quantity of Study*,”
+        Social Forces, vol. 63, no. 4, pp. 945–966, June 1985.
+    """
+    # [1, p. 950]
+    hours_studied = np.array([1, 2.5, 3.5, 4.5, 5.5, 6.5])
+    gpa = np.array([2.94, 2.91, 2.97, 2.86, 3.25, 3.18])
+
+    # Parse command line arguments
+
+    parser = argparse.ArgumentParser()
+    parser.add_argument("--plot", action="store_true")
+
+    args = parser.parse_args()
+
+    # Compute Spearman rank order correlation
+
+    corr, p = stats.spearmanr(hours_studied, gpa)
+
+    print("======== Spearman rank order correlation ========")
+    print(f"Correlation: {corr}")
+    print(f"p-value: {p}")
+
+    # Perform linear regression
+
+    slope, intercept, r, p, std_err = stats.linregress(hours_studied, gpa)
+
+    print("======== Linear regression ========")
+    print(f"slope: {slope:.8f} points/hour = {slope / (60 * 60):.8f} points/second")
+    # Printing the p-value here doesn't make much sense, because we don't know
+    # whether the assumptions for the test are satisfied
+
+    if args.plot:
+        plt.plot(hours_studied, gpa, label="Plot from publication")
+        plt.plot(hours_studied, slope * hours_studied + intercept, label="Best fit")
+        plt.xlabel("Hours studied")
+        plt.ylabel("GPA")
+        plt.legend()
+        plt.show()
+
+
+if __name__ == "__main__":
+    main()

tex-fmt.toml

@@ -0,0 +1 @@
+tabsize = 4