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@@ -376,9 +376,13 @@ This shortcoming was addressed by \citeauthor{hutto2014vader} who introducted a
% ursprüngliches paper ITS, wie hat man das früher (davor) gemacht
\subsection{Trend analysis}
When introducing a change to a system (experiment), one often wants to know whether the intervention achieves its intended purpose. This leads to 3 possible outcomes: a) the intervention shows effect and the system changes in the desired way, b) the intervention shows effect and the system changes in an undesired way, or c) the system did not react at all to the change. There are multiple ways to determine which of these outcomes occur. To analyze the behavior of the system data from before and after the intervention as well as the nature of the intervation has be aquired. The are multiple ways to run such an experiment and one has to choose which type of experiment fits best. There are 2 categories of approaches: actively creating an experiment where one design the experiment before it is executed (for example randomized control trials in medical fields), or using existing data of an experiment which was not designed beforehand or where setting up a designed experiment is not possible (quasi-experiment).
When introducing a change to a system (experiment), one often wants to know whether the intervention achieves its intended purpose. This leads to 3 possible outcomes: a) the intervention shows effect and the system changes in the desired way, b) the intervention shows effect and the system changes in an undesired way, or c) the system did not react at all to the change. There are multiple ways to determine which of these outcomes occur. To analyze the behavior of the system, data from before and after the intervention as well as the nature of the intervation has be aquired. The are multiple ways to run such an experiment and one has to choose which type of experiment fits best. There are 2 categories of approaches: actively creating an experiment where one design the experiment before it is executed (for example randomized control trials in medical fields), or using existing data of an experiment which was not designed beforehand or where setting up a designed experiment is not possible (quasi-experiment).
As this thesis investigates a change which has already been implemented by another party, this thesis covers quasi-experiments. A tool that is often used for this purpose is an \emph{Interrupted Time Series} (ITS) analysis. The ITS analysis is a form of segmented regression analysis, where data from before, after and during the intervention is regressed with seperate line segements\cite{mcdowall2019interrupted, bernal2017interrupted}. ITS requires data at (regular) intervals from before and after the intervention (time series). The interrupt signifies the intervention and the time of when it occured must be known. The intervention can be at a single point in time of it can be streched out over a certain time span. This property must also be known to take it into account when designing the regression. Also, as the data is aquired from an quasi-experiment, it may be baised, for example seasonality, ....%TODO
As this thesis investigates a change which has already been implemented by another party, this thesis covers quasi-experiments. A tool that is often used for this purpose is an \emph{Interrupted Time Series} (ITS) analysis. The ITS analysis is a form of segmented regression analysis, where data from before, after and during the intervention is regressed with seperate line segements\cite{mcdowall2019interrupted}. ITS requires data at (regular) intervals from before and after the intervention (time series). The interrupt signifies the intervention and the time of when it occured must be known. The intervention can be at a single point in time or it can be streched out over a certain time span. This property must also be known to take it into account when designing the regression. Also, as the data is aquired from an quasi-experiment, it may be baised\cite{bernal2017interrupted}, for example seasonality, time-varying confunders (for example a change in measuring data), variance in the number of single observations grouped together in an interval measurement, etc.. These biases need to be addressed if present. Seasonality can be accounted for by subtracting the average value of each of the months in succesive years (i.e. subtract the average value of all Januaries in the data set from the the values in Januaries).
%\begin{lstlisting}
% deseasonalized = datasample - average(dataSamplesInMonth(month(datasample)))
%\end{lstlisting}
This removes the differences between different months of the same year thereby filtering out the effect of seasonality. The variance in data density per interval (data samples in an interval) can be addressed by using the each single data point in the regression instead of an average.