Valid Statements by the Crowd: Statistical Measures for Precision in Crowdsourced Mobile Measurements  
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1 Chair of Communication Networks, University of Wurzburg, 97074 Wurzburg, Germany; [EMAIL_ADDRESS] (A.S.); [EMAIL_ADDRESS] (T.H.) [PERSON]  
2 Tutela Technologies, Ltd., Victoria, BC V8W 1H8, Canada; ahall@tutelaet technologies.com 2  
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2 Tutela Technologies, Ltd., Victoria, BC V8W 1H8, Canada; ahall@tutelaet technologies.com 2  
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3 Nokia Networks, 89081 Ulm, Germany; [EMAIL_ADDRESS] 3  
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1 Chair of Communication Networks, University of Wurzburg, 97074 Wurzburg, Germany; [EMAIL_ADDRESS] (A.S.); [EMAIL_ADDRESS] (T.H.) Footnote 1: [[https://www.mdpi.com/journal/network](https://www.mdpi.com/journal/network)]([https://www.mdpi.com/journal/network](https://www.mdpi.com/journal/network))  
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Footnote 6: https://www. a typical speed test application in the mobile network [1]. Similar mobile measurements are carried out within an app in the background without the active involvement of end-users, but also involve the mass of end users in a crowdsourced sense. Crowdsourced measurements take into account a special type of crowdsourcing: the collection and processing of data that are measured by the crowd [3]. Network operators and data provider companies (i.e., companies that collect CNM data and then resell it, e.g., to network operators) use this approach to take large-scale measurements of mobile networks. The measurement apps, tools, or mobile websites, usually provided by the measurement provider such as a network operator, regulatory agencies, or a big data company, typically measure one or more aspects of the network: signal strength, mobile app performance such as video streaming quality, QoE ratings on a numeric scale (e.g., 1-5), or QoS. As a result, however, a large amount of data is obtained from uncontrolled measurements through the crowd. The density, number, and accuracy of the measurements differs due to the uncontrolled measurement environment, which is especially true in case of crowdsourced mobile measurements. It is typical for crowdsourced measurements that a lot of data originate from large cities, that measurements are taken during the day, and that the measurements per device are at different intervals, which can be attributed to the concentration of mobile phone users in cities and the times when devices are commonly used. There is always the question of the validity [4] of such measurements, i.e., is it permissible to make this statement based on the available data? In the simplest case, an outcome is based on one measuring point that is one-year old. In the best case, there is high temporal and spatial coverage. This raises the question of the number of measurements required for a meaningful and generally applicable statement. The Super Bowl 2019 can serve as an example of such a challenge. After the match, different CNM companies, for example Ookla and Tutela, published statistics about the mobile network speed during the Super Bowl. Ookla quantified the throughput during the Super Bowl at about 100 Mbit/s, with T-Mobile as the fastest network [5]. In contrast, according to Tutela, Verizon delivered the fastest average download speeds in the stadium at around 40 Mbit/s. The evaluations of the two providers thus differ significantly.