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\usepackage[utf8]{inputenc} %support umlauts in the input
% Easier compilation
\usepackage{bookmark}
\usepackage{natbib}
\usepackage{graphicx}
\begin{document}
\title{Week 8 - Quantitative data analysis}
@ -25,8 +27,161 @@
\section{Method} \label{sec:method}
The purpose of this report is to re-analyse the data presented in the paper by
\cite{dong2018methods}, which investigates the effect that protests (as an
example of disruptive social behaviours in general) have on consumer
behaviours. \cite{dong2018methods} hypothesise that protests decrease
consumer behaviour in the surrounding area of the event, and suggest that
consumer spending could be used as an additional non-traditional economic
indicator and as a gauge of consumer sentiment. Consumer spending was analysed
using credit card transaction data from a metropolitan area within a country
that is part of The Organisation for Economic Co-operation and Development
(OECD). Although \cite{dong2018methods} investigate temporal and spatial
effects on consumer spending, for the purposes of this analysis, only the
spatial effect of variables (with relation to the geographical distance from
the event) is considered. The dataset consists of variables measured as a
function of the distance from the event (in km), including: the number of
customers, the median spending amount, the number of transactions, and the
total sales amount.
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
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
variable. Since the decrease of each the variables from the reference period
to Day 62 is provided, the mean and the median of these distributions can be
used to perform a one-sample (as we have are given the difference) hypothesis
test to assess whether the protests on Day 62 had a discernable effect.
Assuming the mean of each variable over the reference period is the midpoint
between their respective maximum and minimum values, we can reconstruct
approximate actual values for Day 62 (given the decrease in value on Day 62
from the reference period). By comparing these value to the range over the
reference period, another assessment can be made to determine whether the data
presents a discernible effect on consumer spending as a result of social
discuption, scaling with distance.
Although time series data was not explicitely provided, by extrapolating
information from a graph in \cite{dong2018methods} we can quantify the decrease
in number of customers and median spending on Day 62 using information about the
reference days (from 43 to 61). After collecting the values for each of the
reference days (43-61), the mean and standard deviation of this sample can be
calculated. Assuming a normal distribution of the data, we can calculate a
z-score for each observation on Day 62, and use this to assess the original
hypothesis.
By performing each of the above test, a re-analysis will be conducted on
\cite{dong2018methods}'s paper hypothesising that consumer spending decreases
as a result of social events such as protests. In the Results section, we will
perform the statistical analyses described above. The results of these tests
will then be explored in the Discussion section, along with assumptions and
limitations of the tests and what can be conclused from them.
\section{Results} \label{sec:results}
For each of the variables in the given data (number of customers, median
spending amount, number of transactions, and sales totals) we construct a
histogram of the decrease of each (on Day 62). We then compute the mean and
median of the data so we can proceed to perform a one-sample hypothesis test.
\begin{figure}[ht]
\centering
\label{fig:distr}
\includegraphics[width=\textwidth]{distr.png}
\caption{Distribution of each of the variables recorded in the data, as a function of the distance from an event}
\end{figure}
Using a mean/median of the reference period, obtained by taking the midpoint of the minimum and maximum values over for each distance measure, a value can be reconstructed for the measurement on Day 62 (for each location) using:
\begin{equation}
\textrm{value} = \frac{\textrm{min} + \text{max}}{2} - \textrm{decrease.}
\tag{1}
\end{equation}
\\
We can then plot the maximum and minimum values for the reference period, as well as the reconstructed Day 62 variables to observe the behaviour of consumer spending after the event.
\begin{figure}[ht]
\centering
\label{fig:effect}
\includegraphics[width=\textwidth]{effect.png}
\caption{The reconstructed values for Day 62 of each variable plotted against their respective minimums and maximums over the reference period}
\end{figure}
Using the data recorded, for each of the three distance recorded, the mean and standard deviation of the reference period can be calculated. The z-score for each observed value on Day 62 can be computed using:
\begin{equation}
\textrm{Z} = \frac{\textrm{X} - \mu}{\sigma},
\tag{2}
\end{equation}
\\
where X is the observed value, $\mu$ and $\sigma$ are the mean and standard deviation (respectively) of the reference period.
\begin{table}[ht]
\centering
\label{my-label}
\begin{tabular}{|l|l|r|r|}
\hline
\textbf{Variable} & \textbf{Distance} & \textbf{X} & \textbf{Z} \\
\hline
\textbf{Customers} & \textless 2km & -0.600 & 6.87798 \\
\textbf{Customers} & 2km - 4km & -0.200 & -3.33253 \\
\textbf{Customers} & \textgreater 4km & -0.100 & -3.70740 \\
\textbf{Median Spending} & \textless 2km & -0.200 & -3.05849 \\
\textbf{Median Spending} & 2km - 4km & -0.100 & -1.46508 \\
\textbf{Median Spending} & \textgreater 4km & -0.035 & -1.99199 \\
\hline
\end{tabular}
\caption{The $Z$ score computed using equation 2 and the temporal data}
\end{table}
\section{Discussion} \label{sec:discussion}
As shown in each of the subplots of Figure 1, the mean and median values of
the decrease in each of the distributions are greater than zero (note: higher
values of the decrease variable indicate a larger decrease/negative change).
These mean and median values can be used to perform a one-sample hypothesis
tests, which finds that since each of the mean/median values is greater than
zero, we can infer that the event had a net decreasing affect on the number of
customers, median spending amount, number of transactions, and total sales
amount.
In Figure \ref{fig:effect} values were approximated for each variable on Day
62, using Equation 1, and plotted against the minimum and maximum values of
the respective variables. This allows us to visually assess whether the
reconstructed value for Day 62 lies outside the range of recorded values for
the reference period, and presents uncharacteristic behaviour. A decrease is
evident in each of the variables after the event has occurred (on Day 62)
within a distance of approximately 2 km, and appears to stabilise thereafter.
This provides support to \cite{dong2018methods}'s hypothesis that consumer
spending is affected by socially disruptive events, and also provides evidence
to the notion of spatial scaling of this effect (based on the event location).
It is important to note that the approximation used in this technique is
subject to a level of error due to the ideal calculation of the mean/median of
the reference data as the midpoint between the minimum and maximum values
provided.
Extrapolating data from a graph in \cite{dong2018methods} provided time series
data (divided into three radius') to analyse. This data was collected by
visually estimating the values from the graph which will inherently introduce
a source of error. However, by computing the z-score as described in Equation
2, the table provided in Figure 3 was constructed. Each of the z-score values
in the table are negative, indicating a decrease in both the number of
customers and median spending on Day 62. The much larger magnitude of z-scores
for the <2km distance ring for both variables is in agreement with earlier
discussion, strengthening the hypothesis of the spatial correlation of
consumer spending.
Each of the above tests have agreed on the spatial and temporal correlation of
consumer spending and socially disruptive events. With the limited data
available, we can therefore concur with the hypothesis of Dong et al. that
consumer spending decreases in the area around disruptive social behaviour,
after finding the temporal correlation on Day 62, as well as the spatially
decreasing effect further from the event.
\bibliographystyle{humannat}
\bibliography{references}
\end{document}