Finish content of paper

paper.tex

@@ -115,7 +115,8 @@ of the Choice of Hydration Strategy on Average Academic Performance}
     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 is amounts to 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}
@@ -153,12 +154,12 @@ performance of KIT students.
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%
 \section{Experimental Setup}
 
-Over a period of one week, we monitored the usage of the water
+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 recording of the choice of hydration
-strategy of the participants: $S_\text{L}$ denotes pressing the left
+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.
 
@@ -209,11 +210,11 @@ 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 $S _\text{L}$ is faster than
+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
-significant statement could be made about $S_\text{R}$ and
-$S_\text{B}$. Fig. \ref{fig:Behavior} shows the results of the
-behavioural measurement.
+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
@@ -264,24 +265,24 @@ the time spent waiting as well as the time dispensing water, is
 %
 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 utilization. Using our experimental
+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}. The largest investigation into the matter
-found a correlation of $\rho = 0.18$ \cite{schuman_effort_1985}
-between GPA and average time spend studying per day. Using a rather
-high estimate of 5 refills per day, we predict a possible grade gain
-of up to $0.00103$ points.
+\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 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.
 
@@ -289,7 +290,7 @@ 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 $0.00103$ 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.
 
@@ -302,3 +303,4 @@ of KIT students: always using the right button.
 \printbibliography
 
 \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