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\begin{document}
\title{The Effect of Range on Paintball Shooting Accuracy and Shooting Speed
(Paintball is awesome you should all do it!)}
\author{Rein D. Otsason}
\affil{Affiliation not available}
\author{Natalie C. Landon-Brace}
\affil{Affiliation not available}
\author{Sgt. Samuel H. Buckstein}
\affil{Affiliation not available}
\date{\today}
\maketitle
Rein Otsason --- 999838396
Natalie Landon-Brace --- 999802254
Samuel Buckstein --- 998924598
\section{Introduction}
Paintball has beeng gaining significant ground in popularity in Canada, the US and around the world. In 2010, it was estimated that over 15 million people play paintball every year in the United States \cite{EmpirePaintball}. It is a sport in which players attempt to eliminate their opponents by tagging them with paintballs. The capsules filled with dye are fired through paintball markers powered by compressed air. In light of the popularity of the sport, this paper seeks to examine the relationship between shooting distance and shooting speed, and shooting distance and shooting accuracy.
In this experiment, participants were asked to fire five paintballs at a target at 10 m, 20 m and 30 m, and accuracy and shooting time was recorded. Accuracy was determined by measuring the distance from the centre of the paintball mark to the centre of the target. Speed was measured as the time between the first and last shot being fired.
It is hypothesized that accuracy and shooting time will be comparable at 10 m, 20 m and 30 m, i.e. irrespective of distance. The contrary null hypothesis is that the greatest accuracy and fastest shooting time will be at 10 m from the target.
The largest covariate that affects results is the experience of the participants. It is expected that the category of experienced participants will have a faster mean shooting time, and also have a greater mean accuracy. Experience is defined here as having used a paintball marker before. As such, the effect of experience on accuracy and shooting time shall be discussed later in this report.
\section{Background}
Modern military practice in regards to riflemanship hinges on repetitive drill in a few standard firing distances, until the rank and file learns an intuitive feel for projectile behavior, i.e. deviation from path, altitude loss over distance etc.
Repetitive drilling attempts to make recruits more or less equally effective at all distances up to the maximum effective distance of the weapon, although response time is expected to suffer if accuracy is to be maintained.
Experience is achieved when the activity becomes muscle memory. It is hoped that soldiers who need to return fire do so instinctively, in response to the external world, in a way no different than expecting an oncoming car's behavior in an intersection.
\subsection{Paintball Markers}
A paintball marker derives its name from its original use by forestry departments and cattle ranchers to respectively mark trees and cattle with paint from a range.
The operation of a semi-automatic blowback marker like the one used in this experiment involves a metal bolt on a strong spring, cocked in a back position and held in place by a spring-loaded trigger mechanism.
When the trigger is pulled, the bolt is no longer restrained and it travels forwards as a result of the compressive force stored in the spring. The movement of the bolt unblocks a valve, through which runs compressed air stored in a tank.
The rush of air drives a paintball out of the barrel, and the 'blowback' air pressure resets the bolt back into its starting position \cite{BlastzonePaintball:2012}.
Paintball is a very popular recreational sport played indoors and outdoors, in various senarios, and on different fields. The maximum muzzle velocity of most paintballs is 90 m/s, at which point paintballs begin to shatter in the barrel from the explosive force of the air, and also higher muzzle velocity becomes a safety concern.
In any case, proper protective clothing must be worn, including a face mask that protects the head and throat.
Paintball barrels lack rifling, and as a result markers are generally imprecise. Maximum effective distance is approximately 30 m \cite{Tippmann:2006}.
\subsection{Tippmann 98 Custom}
Tippmann paintball products are widely regarded by hobbyists as one of the most reliable maker of paintball markers, with a dedication to high quality and durability on both ends of the price spectrum.
The Tipmmann 98 used in this experiment is over ten years old and functions perfectly with little servicing. It is an inexpensive marker, costing less than \$100, but it is reknown for its longetivity \cite{Tippmann:2014}.
\section{Experimental Design}
\subsection{Participants}
11 participants were randomly selected such that 9 were male, and 2 female. The number of subjects was chosen so that each subject would generate three sets of data, resulting in a total of 33 sets of data, where each set contains 5 datapoints. With over 30 data sets, it is intended that a normal distribution can be validly assumed. The participants were all university students between the ages of 18 and 22. A Shapiro-Wilk test was conducted on the data from each range to verify a normal distribution of the data. This can be seen in the output of the R code in \ref{app:Output}.
\subsection{Apparatus}
The construction of this experiment involves a Tippmann 98 paintball marker, 1000 paintballs, 3 pressurized air tanks, a target constructed from wood and spray-paint, a stopwatch, a tape measure, some chalk and an unobstructed range 30 m in length.
\subsection{Procedure}
A range was constructed by placing the target on one side, and measuring 10 m, 20 m, 30 m from the target with a meter stick. Each distance was marked with a chalk line.
Participants were asked to stand on a 'ready line' with a loaded paintball marker awaiting permission to start. The subject was to remain on the marked position on the line, opposite the target at 10 m.
An experimenter then started a stopwatch and indicated to the subject to begin firing. The experimenter counted the shots fired, and stopped the timer when the fifth and final shot had been fired.
The experimenter then checked that the marker was 'safed', after which another experimenter would approach the target and measure the distance from each round to the centre of the target. The accuracy for each range is an average of the five distances from the center. The experimenter then documented the results, as well as the time required to complete the task, and the distance from the target.
The target was then wiped clean and moved to 20 m, and the procedure was repeated. Finally, procedure was repeated for 30 m.
\subsubsection{Notes on Safety}
When a trial was not being conducted the paintball marker was in the hands of an experienced experimenter.
At all times during a trial, both experimenter and subject wore proper paintball safety equipment.
The marker was only loaded with rounds immediately prior to firing.
\subsection{Biases and Limitations}
There were several biases and limitations which can be identified in the selection of participants and execution of the experiment.
The first is that the sample participants were drawn from engineering students at the University of Toronto. As such there is a significantly lower percentage of girls to draw from in the student pool. The population tested in this experiment therefore represents the standard engineering male:female ratio of 3:1.
Furthermore, due to the busy time of year it was difficult to attract students to participate in the study as it involved more time than a simple online form. This led to a smaller sample size than desired.
Another limitation is that due to the long range of distances required, the experiment had to be conducted outside. This lead to differences in weather conditions such as wind and cloud cover between participants. Most significantly, the 20 m target was not shaded as well as the 10 m and 30 m targets, which may have decreased accuracy at this distance.
It is also significant to note that the paintball is powered by pressurized air tanks. With use or extended storage, the pressure in the tanks decreases, leading to a decrease in muzzle velocity and apparent accuracy. As such, those shooting later ``in'' a tank would be shooting with a lower velocity and it might be more difficult to shoot accurately. Tanks were changed several times throughout the experiment in an effort to compensate for this as best as possible, though the effect may still have been noticeable.
Additionally, not all of the sample population fired paintballs from all three distances, requiring different t-tests to be used depending on the case.
Finally, the target size is limited and thus some individuals miss the target entirely. As such, a spread value can not be measured entirely accurately for this shot and instead a penalty spread value of 150 cm was applied for each shot which missed the target.
\section{Results and Discussion}
\subsection{Descriptive Statistics}
Table \ref{tab:stats} gives the size, means and the standard deviations of the main groups in the analysis.\selectlanguage{english}
\begin{table}
\caption{{Key descriptive statistics for experimental data.
Units for accuracy are in cm (lower is better), units for time are in seconds (faster is better)}}
\label{tab:stats}
\begin{tabular}{l | c c}
Group & Mean & Variance \\ \hline
Accuracy, 10 m & 23.76 cm & 125.36 cm^2 \\
Accuracy, 20 m & 59.44 cm & 785.80 cm^2 \\
Accuracy, 30 m & 91.53 cm & 1077.7 cm^2 \\
Time, 10 m & 4.013 s & 5.342 s^2 \\
Time, 20 m & 5.165 s & 8.990 s^2 \\
Time, 30 m & 6.506 s & 6.815 s^2 \\
\end{tabular}
\end{table}
\subsection{Shooting Time vs. Distance}
\subsubsection{Comparing Shooting Time at 10 m vs. 20 m}
A F-test was conducted and it was found that the p-value was greater than the alpha-significance level of 0.05, correlating with equal variances.
A paired t-test was conducted because the same set of people participated at 10 m and 20 m, and the p-value was found to be less than the significance level. The means are therefore unequal, with a shooting time that was an average 1.152 seconds faster at 10m. The alternate hypothesis was therefore accepted over the null hypothesis.
\subsubsection{Comparing Shooting Time at 20 m vs. 30 m}
Using a F-test it was found that the p-value was greater than the significance level, therefore the variances are assumed to be equal between the two sets of data.
Participants did not all fire at 20 m and 30 m, therefore a two-sample t-test was used instead of a paired t-test.
It was found that the p-value was greater than the significance level, corresponding with equal means. This means that shooting time was the same at both distances. The result is fail to reject the null hypothesis.
\subsubsection{Comparing Shooting Time at 10 m vs. 30 m}
A F-test was conducted and it was found that the p-value was greater than the significance level of 0.05, corresponding with equal variances.
Participants did not all fire at 10 m and 30 m, so a two-sample t-test was used instead of a paired t-test.
It was found that the p-value was lower than the significance level. The mean at 10 m was 2.943 seconds less than the mean at 30 m, meaning that shooting time was faster at 10 m. Therefore the null hypothesis was rejected in favor of the alternate hypothesis.
\subsection{Summary}
Two of the three comparisons made of shooting times at different distances resulted in a p-value less than the significance level, with the mean of the data from the closer range being less than the mean of the data at the further range.
The null hypothesis was therefore rejected, that shooting time does not change with distance, in favor of the alternate hypothesis, that shooting time is fastest the closer the shooter is to the target.
\subsection{Accuracy vs. Distance}
A Student's t-test with a 0.05 significance level was also conducted on the accuracy data at the three distances and established a difference in the mean of the distributions between the 10 m, 20 m and 30 m mark. The distribution mean was lowest for accuracy at 10 m.
The null hypothesis is therefore rejected in favor of the alternate hypothesis that shooting accuracy is best closest to the target.
\subsubsection{Comparing Accuracy at 10 m vs. 20 m}
By examining the results of the F-test and the paired t-test (as the same individuals shot in both trials), we can make several conclusions about the relationship between the variances and means for shooting accuracy at 10 m and 20 m. Using the F-test distribution, it was determined that the variances of the two samples are unequal, as p < 0.05 for this test. Furthermore, it was determined using the paired t-test that the mean accuracy of the two samples was not the same, as p < 0.05. The mean value of accuracy at 10 m and the mean value of accuracy at 20 m differed by 35.68 cm. From this information, we can initially reject the null hypothesis, as it is clear that accuracy decreases with distance.
\subsubsection{Comparing Accuracy at 20 m vs. 30 m}
The F-test revealed a p-value of greater than 0.05, indicating that the variances were equal. As not all individuals participated in both 20 m and 30 m shooting trials, a two-sample t-test was used to compare sample means. Using this test, a p-value less than the alpha significance value of 0.05 was obtained and it was concluded that there was a difference in the means. This difference was equal to 32.09 cm. This test allows us to reject the null hypothesis.
\subsubsection{Comparing Accuracy at 10 m vs. 30 m}
The F-Test revealed a p-value less than 0.05, indicating that the variances of the two samples were unequal. As not all individuals participated in both the 10 m and the 30 m test, a Welch's two sample t-test was used to compare sample means. This test revealed a p-value of less than 0.05, indicating a difference in th emeans. This difference was equal to 67.77 cm. This leads us to once again reject the null hypothesis.
\subsection{Summary}
By comparing shooting accuracy between all three target distances, it was clearly shown that the null hypothesis of accuracy being evenly distributed across the distances could be rejected. As such, accuracy is dependent on the distance from the target, with a shorter distance being associated with higher accuracy.
\subsection{Effect of the Covariate}
Figure \ref{fig:experience} shows the effect of the covariate.
As predicted, more experienced shooters were more accurate.
The difference between the groups did not affect the other results of this study.\selectlanguage{english}
\begin{figure}[h!]
\begin{center}
\includegraphics[width=0.70\columnwidth]{figures/experience-boxplot/experience-boxplot}
\caption{{\label{fig:experience}
This boxplot shows the effect of the covariate in the results.
Experienced shooters clearly have better accuracy than inexperienced shooters.%
}}
\end{center}
\end{figure}
\section{Conclusions}
The results of this study allow us to reject the null hypothesis in favour of the alternate hypothesis for both shooting time and accuracy. The P-Value for the accuracy statistic was less than 0.05 indicating that there was a significant difference in the mean accuracy at different distances.The difference between accuracy at 10 m in comparison with 20 m was 35.68 cm and with 30 m was 67.77 cm. The P-Value for the speed statistic was also less than 0.05 indicating a difference in the mean shooting time at different distances. The difference between average shooting time at 10 m in comparison with 20 m was 1.152 seconds and with 30 m was 2.943 seconds. Thus, the null hypothesis was rejeccted in favor of the alternate hypothesis for both shooting time and accuracy as the mean shooting time was significantly faster at 10 m, and the mean accuracy was significantly greater at 10 m as well.
It was also found in this study that experienced shooters were more accurate than inexperienced shooters. This confirms that experience was well chosen as a covariate. This study could be extended in the future by examining the effect of age, gender and/or height and weight (or other physical characteristics) on accuracy and shooting time.
In conclusion, this study shows us that when attempting to hit your target quickly, it is certainly best done at close range. It also reveals to us that in this case, practice really does make perfect.
\appendix
\section{R Code}
\begin{verbatim}
# AUTHOR: Rein Otsason
# TEAM: Samuel Buckstein, Natalie Landon-Brace, Rein Otsason
sink("statsresults.txt", split=TRUE, append=FALSE)
# Import the raw data
data <- read.csv("statsdata.csv", header=TRUE, sep=",", na.strings = "x")
# Data with misses replaced with the penalty value
data.penalty <- data
data.penalty[is.na(data.penalty)] <- 150 # Penalty for missing; arbitrary
# Accuracy metric -- simple average of the 5 shots
accuracy <- (data.penalty$Shot1 + data.penalty$Shot2 + data.penalty$Shot3 + data.penalty$Shot4 + data.penalty$Shot5) / 5
data.accuracy <- data.frame(data, accuracy)
# Vectors of time data
times.10 <- data$Time[which(data$Distance == 10)]
times.20 <- data$Time[which(data$Distance == 20)]
times.30 <- data$Time[which(data$Distance == 30)]
# Vectors of accuracy data
accuracy.10 <- data.accuracy$accuracy[which(data.accuracy$Distance == 10)]
accuracy.20 <- data.accuracy$accuracy[which(data.accuracy$Distance == 20)]
accuracy.30 <- data.accuracy$accuracy[which(data.accuracy$Distance == 30)]
## Time data analysis
# Test for normality of time data
print("Shapiro-Wilks results for time data: ")
shapiro.test(times.10)
shapiro.test(times.20)
shapiro.test(times.30)
# Test homogeneity of variances
var.test(times.10, times.20) # Between 10 m and 20 m
var.test(times.10, times.30) # Between 10 m and 30 m
var.test(times.20, times.30) # Between 20 m and 30 m
# Two-sample Student's t-test, assuming equal variance and independence
t.test(times.10, times.20, var.equal=TRUE, paired=TRUE)
t.test(times.10, times.30, var.equal=TRUE, paired=FALSE)
t.test(times.20, times.30, var.equal=TRUE, paired=FALSE)
## Accuracy data analysis
# Test for normality of accuracy data
print("Shapiro-Wilks results for accuracy data:")
shapiro.test(accuracy.10)
shapiro.test(accuracy.20)
shapiro.test(accuracy.30)
# Test homogeneity of variances
print("F-test for homogeneity of variances:")
var.test(accuracy.10, accuracy.20)
var.test(accuracy.10, accuracy.30)
var.test(accuracy.20, accuracy.30)
# Two-sample Student's t-test
t.test(accuracy.10, accuracy.20, var.equal=FALSE, paired=TRUE)
t.test(accuracy.10, accuracy.30, var.equal=FALSE, paired=FALSE)
t.test(accuracy.20, accuracy.30, var.equal=TRUE, paired=FALSE)
## Summary statistics
print("Accuracy, 10 m:")
print(sprintf("Mean: %f", mean(accuracy.10)))
print(sprintf("variance: %f", var(accuracy.10)))
print("Accuracy, 20 m:")
print(sprintf("Mean: %f", mean(accuracy.20)))
print(sprintf("variance: %f", var(accuracy.20)))
print("Accuracy, 30 m:")
print(sprintf("Mean: %f", mean(accuracy.30)))
print(sprintf("variance: %f", var(accuracy.30)))
print("Time, 10 m:")
print(sprintf("Mean: %f", mean(times.10)))
print(sprintf("variance: %f", var(times.10)))
print("Time, 20 m:")
print(sprintf("Mean: %f", mean(times.20)))
print(sprintf("variance: %f", var(times.20)))
print("Time, 30 m:")
print(sprintf("Mean: %f", mean(times.30)))
print(sprintf("variance: %f", var(times.30)))
sink()
png(filename="experience_boxplot.png")
boxplot(accuracy~Experience, data=data.accuracy, main="Accuracy compared with experience", xlab="Experience", ylab="Accuracy (lower is better)")
dev.off()
\end{verbatim}
\section{Output of R Code}
\label{app:Output}
\begin{verbatim}
[1] "Shapiro-Wilks results for time data: "
Shapiro-Wilk normality test
data: times.10
W = 0.8473, p-value = 0.03938
Shapiro-Wilk normality test
data: times.20
W = 0.909, p-value = 0.2372
Shapiro-Wilk normality test
data: times.30
W = 0.9464, p-value = 0.6504
F test to compare two variances
data: times.10 and times.20
F = 0.5942, num df = 10, denom df = 10, p-value = 0.4247
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
0.1598802 2.2086721
sample estimates:
ratio of variances
0.5942415
F test to compare two variances
data: times.10 and times.30
F = 0.7839, num df = 10, denom df = 8, p-value = 0.7044
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
0.182503 3.021747
sample estimates:
ratio of variances
0.7838735
F test to compare two variances
data: times.20 and times.30
F = 1.3191, num df = 10, denom df = 8, p-value = 0.7086
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
0.3071192 5.0850482
sample estimates:
ratio of variances
1.319116
Paired t-test
data: times.10 and times.20
t = -3.6879, df = 10, p-value = 0.004191
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-1.8491707 -0.4562838
sample estimates:
mean of the differences
-1.152727
Two Sample t-test
data: times.10 and times.30
t = -2.2649, df = 18, p-value = 0.0361
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-4.8052187 -0.1804378
sample estimates:
mean of x mean of y
4.012727 6.505556
Two Sample t-test
data: times.20 and times.30
t = -1.0526, df = 18, p-value = 0.3064
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-4.014821 1.334619
sample estimates:
mean of x mean of y
5.165455 6.505556
[1] "Shapiro-Wilks results for accuracy data:"
Shapiro-Wilk normality test
data: accuracy.10
W = 0.8859, p-value = 0.1236
Shapiro-Wilk normality test
data: accuracy.20
W = 0.9201, p-value = 0.3195
Shapiro-Wilk normality test
data: accuracy.30
W = 0.925, p-value = 0.4352
[1] "F-test for homogeneity of variances:"
F test to compare two variances
data: accuracy.10 and accuracy.20
F = 0.1595, num df = 10, denom df = 10, p-value = 0.007655
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
0.04292146 0.59294030
sample estimates:
ratio of variances
0.1595301
F test to compare two variances
data: accuracy.10 and accuracy.30
F = 0.1163, num df = 10, denom df = 8, p-value = 0.002644
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
0.02708321 0.44842343
sample estimates:
ratio of variances
0.1163258
F test to compare two variances
data: accuracy.20 and accuracy.30
F = 0.7292, num df = 10, denom df = 8, p-value = 0.6278
alternative hypothesis: true ratio of variances is not equal to 1
95 percent confidence interval:
0.1697686 2.8109012
sample estimates:
ratio of variances
0.7291779
Paired t-test
data: accuracy.10 and accuracy.20
t = -4.4675, df = 10, p-value = 0.001202
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-53.46421 -17.88125
sample estimates:
mean of the differences
-35.67273
Welch Two Sample t-test
data: accuracy.10 and accuracy.30
t = -5.918, df = 9.526, p-value = 0.0001789
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-93.45811 -42.08128
sample estimates:
mean of x mean of y
23.76364 91.53333
Two Sample t-test
data: accuracy.20 and accuracy.30
t = -2.3601, df = 18, p-value = 0.02976
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-60.668859 -3.525081
sample estimates:
mean of x mean of y
59.43636 91.53333
[1] "Accuracy, 10 m:"
[1] "Mean: 23.763636"
[1] "variance: 125.358545"
[1] "Accuracy, 20 m:"
[1] "Mean: 59.436364"
[1] "variance: 785.798545"
[1] "Accuracy, 30 m:"
[1] "Mean: 91.533333"
[1] "variance: 1077.650000"
[1] "Time, 10 m:"
[1] "Mean: 4.012727"
[1] "variance: 5.342022"
[1] "Time, 20 m:"
[1] "Mean: 5.165455"
[1] "variance: 8.989647"
[1] "Time, 30 m:"
[1] "Mean: 6.505556"
[1] "variance: 6.814903"
\end{verbatim}
\section{Raw Data}
\begin{tabular}{ c c c c c c c c c }
Experience & Sex & Distance & Time & Shot1 & Shot2 & Shot3 & Shot4 & Shot5 \\ \hline
Y & M & 10 & 1.6 & 28 & 21 & 34 & 41 & 48 \\
Y & M & 20 & 1.81 & 60 & 52 & 64 & 75 & 79 \\
Y & M & 10 & 1.62 & 15 & 8 & 13 & 22 & 25 \\
Y & M & 20 & 1.7 & 15 & 22 & 31 & 30 & 22 \\
Y & M & 30 & 1.66 & 19 & 33 & 32 & 38 & 115 \\
N & F & 10 & 2.29 & 15 & 12 & 26 & 37 & 48 \\
N & F & 20 & 3.1 & 30 & 30 & 32 & 27 & 44 \\
N & F & 30 & 5.87 & 36 & 32 & x & x & x \\
Y & M & 10 & 2.43 & 22 & 20 & 19 & 10 & 13 \\
Y & M & 20 & 3.43 & 35 & 36 & 90 & 112 & x \\
Y & M & 30 & 3.48 & 50 & 110 & x & x & x \\
N & M & 10 & 3.74 & 10 & 33 & 12 & 36 & 42 \\
N & M & 20 & 4.44 & 40 & 54 & 76 & 61 & x \\
N & M & 30 & 7.49 & 84 & x & x & x \\
Y & M & 10 & 1.74 & 6 & 15 & 10 & 7 & 12 \\
Y & M & 20 & 3.43 & 14 & 36 & 33 & 40 & x \\
Y & M & 30 & 7.44 & 61 & 32 & 42 & x & 63 \\
N & M & 10 & 4.82 & 5 & 10 & 17 & 15 & 33 \\
N & M & 20 & 4.6 & 33 & 25 & x & x & x \\
N & M & 30 & 7.91 & 82 & 44 & 18 & 27 & x \\
N & M & 10 & 7.24 & 14 & 25 & 22 & 28 & x \\
N & M & 20 & 9.29 & 53 & 30 & 31 & x & x \\
N & M & 30 & 10.10 & 63 & 33 & 56 & x & x \\
Y & M & 10 & 7.12 & 16 & 26 & 6 & 16 & 20 \\
Y & M & 20 & 8.10 & 20 & 12 & 22 & 49 & 64 \\
Y & M & 30 & 5.98 & 33 & 22 & 51 & 49 & x \\
N & F & 10 & 4.31 & 10 & 12 & 28 & 51 & 63 \\
N & F & 20 & 6.44 & 26 & 44 & 20 & x & x \\
N & F & 30 & 8.62 & 80 & 114 & x & x & x \\
N & M & 10 & 7.23 & 14 & 16 & 5 & 10 & 35 \\
N & M & 20 & 10.48 & 22 & 28 & 15 & 21 & 14 \\
\end{tabular}
\selectlanguage{english}
\FloatBarrier
\bibliographystyle{plain}
\bibliography{bibliography/converted_to_latex.bib%
}
\end{document}