## 8 Conclusions  
When using crowdsourced network measurements (CNMs), network operators, regulators, and big data companies are faced with the challenge of making valid statements out of measurements in uncontrolled environments of the crowd. There is always the question of validity of such measurements, as the temporal and spatial coverage as well as the total number of measurements can fluctuate strongly. Thus, this article defines concepts and guidelines for analyzing the validity of crowdsourced mobile network measurements with statistical measures.  
We consider CNMs to be a mathematical sampling process and, as a result, derive from this the need for high-precision and validity. Therefore, we define a measure called CNM Precision Validity Score to indicate whether a sufficient number of measurements is available for a sample statistic like the mean throughput to meet a certain precision. This score can be used to quantify what percentage of the required CNMs were already conducted to achieve a specified precision. To satisfy different types of measurements, e.g., small number of samples or skewed data distributions, we present different versions of the CNM Precision Validity Score, including different confidence interval methods, namely Standard Normal Interval, the Studentized \(t\) Interval, the Basic Bootstrap Confidence Interval, and the Percentile Confidence Interval. In addition to the theoretical background of the score, we illustrate its applicability by applying it to a large CNM dataset. Using the example of a data set from France, we showed for which regions the data are sufficient to  
Figure 3: Depiction of the average downlink throughput for regions (**left**) and departments (**right**). All areas with sufficient measurements are colored, as precision there corresponds to target value of at least \(\delta^{*}=100\) kbit/s, i.e., real average throughput lies actually within an interval of 100 kbit/s. Annotations include for selected areas the number of measurements and associated validity score in percent, which shows whether enough CNM samples were taken or whether more measurements need to be made to avoid throughput calculations with large error margins.  
achieve an accuracy of at least 100 kbit/s. We show that the measurements are sufficient for regions, but not at the departmental level. For the consideration of individual departments, more measurements need to be made to achieve the same precision.  
In future work, we would like to further explore the methodology of evaluating CNM data and define metrics for the representativeness, e.g., the spatial and temporal distribution of the data. This could later be used to write comprehensive guidelines on how to deal best with CNM data.  
Conceptualization, F.W. and A.S.; methodology, F.W., A.S. and T.H.; software, F.W.; validation, F.W., A.S., A.H., S.W. and T.H.; formal analysis, F.W., A.S. and T.H.; investigation, F.W. and A.S.; resources, A.H.; data curation, F.W., A.S. and A.H.; writing--original draft preparation, F.W. and A.S.; writing--review and editing, A.H., S.W. and T.H.; visualization, F.W. and A.S.; supervision, A.H., S.W. and T.H.; project administration, A.H. and S.W.; funding acquisition, A.H., S.W. and T.H. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Bavarian Ministry of Economic Affairs, Regional Development and Energy under grant number DIK-2010 5 GQMON within the framework \"5G\" of the BAYERN DIGITAL strategy of the Information and Communication Technology R&D program of the State of Bavaria.  
3 rd Party Data. Restrictions apply to the availability of these data. Data was obtained from Tutela Technologies, Ltd., Victoria, BC, Canada.  
The authors declare no conflict of interest.