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wk7/week7.tex
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@ -23,9 +23,19 @@
\section{Introduction} \label{sec:introduction}
In this report we have documented a series of hypothesis tests regarding provided data in high-ranking
Tennis players. The focus of these hypotheses concerns a player's handedness with regards to overall
ranking. We first provide an overview of how we address these notions, with visualisations and
descriptions of our overall methodology. Following this, we then provide a brief discussion of what we
can infer given our statistical analysis techniques.
\section{Method} \label{sec:method}
We are testing two hypotheses. The first hypothesis that we test is that tall players have an advantage over smaller players. The second hypothesis that we test is that left-handed players have an advantage over right-handed players. To build an intuition of how the data behaves with respect to the hypotheses we are testing, we created visual representations using tools from the Matplotlib, and Seaborn libraries and then we perform statistical tests to measure these effects.
We are testing two hypotheses. The first hypothesis that we test is that tall players have an advantage
over smaller players. The second hypothesis that we test is that left-handed players have an advantage
over right-handed players. To build an intuition of how the data behaves with respect to the hypotheses
we are testing, we created visual representations using tools from the Matplotlib, and Seaborn libraries
and then we perform statistical tests to measure these effects.
\subsection{Visualisation} \label{subsec:visualisation}
@ -89,11 +99,25 @@
\section{Results} \label{sec:results}
We investigate both the advantage of height and the advantage of being
left-handed using a $\chi^2$ test and a T-test. For every test we will state
the exact hypothesis and the null-hypothesis.
\subsection{The advantage of height}
\textbf{$\chi^2$-test:} To test if there is an advantage of being tall we ran
a $\chi^2$ with the following hypotheses:\\
$H$: Players that are taller have a higher rank \\
$H_0$: The rank of a player is independent of their height \\
\\
To perform the test the players are groups into groups dependant on their
rank and if they are taller than the mean height for their gender. The
expected data is computed using the chances of being taller than the mean, and
the chance of being in the group of rankings. The data used is found in table
1.
\begin{table}[ht]
\centering
\label{tab:chi-height}
\begin{tabular}{|l|r|r|r|r|}
\hline
& \textbf{M: 168 - 188} & \textbf{M: 189 - 210} & \textbf{F: 155 - 171} & \textbf{F: 172 - 189} \\ \hline
@ -105,32 +129,39 @@
& 7 / 8 \\
\hline
\end{tabular}
\label{tab:chiheight}
\caption{Observed / Expected values used for the $\chi^2$-test. The groups are divided by their rank (vertical) and, per gender, their height (horizontal).}
\end{table}
$$
\chi^2 \approx 7.697606186049128
$$
The $\chi^2$ value found is approximately $7.697606186049128$. With 12 degrees
of freedom our $p$-value will be $0.8082925814979871$
$$
df = (5-1)(4-1) = 12
$$
$$
\chi^2(7.69\dots,12) \approx 0.8082925814979871
$$
\textbf {t-test men:} T score: 1.711723, P score: 0.043815
\textbf {t-test women:} T score: 1.860241, P score: 0.032030
\textbf{T-test:} A slightly different hypothesis can be tested using a T-Test:
\\
$H$: Players that are taller have significantly more point \\
$H_0$: The points a player has is independent of their height \\
We ran this T-test twice, once for the women and once for the men, by
splitting the groups of players into two: one being taller than the mean
height, one being shorter than the mean height. Our T-test for the men
revealed a T-value of 1.711723, this has a p-value of 0.043815. For the women
the T-value found was 1.860241, which has a p-value of 0.032030.
\subsection{The advantage of left-handedness}
\textbf{$\chi^2$-test:} To test if there is an advantage of being left-handed
we ran a $\chi^2$ with the following hypotheses:\\
$H$: Players that are left-handed have a higher rank \\
$H_0$: The rank of a player is independent their preferred hand \\
\\
To perform the test the players are groups into groups dependant on their rank
and if they play with their left hand. The expected data is computed using the
chances of being left-handed. The data used is found in table
2.
\begin{table}[ht]
\centering
\label{tab:chi-hand}
\label{tab:chihand}
\begin{tabular}{|l|l|l|l|l|l|}
\hline
& \textbf{1 - 99} & \textbf{100 - 199} & \textbf{200 - 299} & \textbf{300 - 399} & \textbf{400 - 499} \\
@ -143,22 +174,32 @@
\caption{Observed / Expected values used for the $\chi^2$-test. The groups are divided by which hand they use (vertical) and their rank (horizontal).}
\end{table}
The $\chi^2$ value found is approximately $6.467312944404331$. With 4 degrees
of freedom our $p$-value will be $0.1668616190847413$
$$
\chi^2 \approx 6.467312944404331
$$
\textbf{T-test:} A slightly different hypothesis can be tested using a T-Test:
\\
$H$: Players that are left-handed have significantly more point \\
$H_0$: The points a player has is independent of their preferred hand \\
$$
df = (2-1)(5-1) = 4
$$
$$
\chi^2(6.46\dots,4) \approx 0.1668616190847413
$$
\textbf {t-test:} T score: 0.451694, P score: 0.325815
We ran this T-test by splitting the groups of players into two depending on
their preferred hand. Our T-test revealed a T-value of 0.451694,
this has a p-value of 0.325815.
\section{Discussion} \label{sec:discussion}
In our investigation we did not find any strong correlation between the
ranking of a player (or their number of points) and with which hand they
played or how tall they are. Most tests failed to pass the required p value of
$<0.05$. The only tests that did give us positive results are the T-test that
were conducted on the correlation between height and the number of points.
However, without the $\chi^2$-test confirming the correlation, the existence
of the correlation is questionable.
These results might not be so surprising when the visual exploration is taken
into account. Only slight deviations are visible in our graphs, so the test
mainly confirmed our suspicion that no definitive correlation exists between
the different attributes.
\end{document}

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wk8/week8.tex
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The re-analysis is conducted on the data provided in the
paper\cite{dong2018methods}, using Python in conjunction with packages such as
pandas, matplotlib, numpy and seaborn, to process and visualise the data. As
aformentioned, only spatial data and the variables mentioned above are
aforementioned, only spatial data and the variables mentioned above are
considered, for the reference days and the change occuring Day 62 (day of
first socially disruptive event). The distribution of the difference between
the reference period and Day 62 is visualised by plotting a histogram for each