###### Abstract
Since it is already established that QoS parameters can be measured actively and are subject to sampling errors, these errors propagate to QoE when evaluating QoE for different QoS parameters. There is currently no literature that report the propagation of the errors in independent QoS variable through to dependent variable QoE. This paper addresses that fundamental limitation in the literature associated with QoE evaluation in networks. We build on earlier work (mapping QoE to different QoS parameters) to show how sampling errors in the measured QoS metrics propagate through to the estimated QoE. The importance of this is that networks/service providers are provided with a technique through which they can bound errors in the estimated QoE when the QoE is derived from a pre-existing mathematical relationship between QoS and QoE. This is in contrast to the current situation in which QoS metrics are measured, and then QoE predicted from them, without any way to understand or bound the precision of these QoE predications. In this paper, to ensure we are focusing on realistic values we use data acquired (using active packet sampling) by our industrial collaborator, Teragence. Teragence has collected all the QoS data measurements used in this research. Their data was composed of measurements of QoS parameters (packet loss and delay jitter) for cellular networks in the UK. We have used Teragence's data in the following ways:  
* We evaluated Goodness of Fit (GoF) tests to determine that the measured latency (delay) distributions are lognormal in shape--this information fed into programming our use of NetEm. * We determined the correlation between PLR and jitter measurements. Our overall concern in studying correlation between QoS metrics is to determine how that correlation affects the error propagation to the dependent variable (QoE), so we consider the correlation between the independent variables of loss and jitter. Within the field of packet networking research remarkably little has been published on the correlation between QoS metrics [16], and this paper also makes a contribution in this area by using the real network data provided by Teragence to evaluate actual correlation levels between QoS metrics. We then propose a novel technique to quantify the statistical error in the evaluated QoE functions. The technique we use is in line with earlier work on how a dependent variable is affected by errors in the measurement of the independent variable(s)--the propagation of uncertainty. The sampling error (uncertainty) in QoE is expressed as 95% Confidence Intervals (CIs) because investigation into all scientific research reveals that 95% CIs are the default values for showing uncertainty in scientific results [17; 18]. As we used NetEm in subjective testing, we have also evaluated the uncertainties caused by the sub-optimal performance of NetEm itself. We evaluated the effect of these errors on the QoE and again (for consistency) reported results as 95% confidence interval width. Moreover, we have also reported variations in the QoE due to perception of the users at different PLR levels using distributions and Standard deviation of Opinion Score (SOS). The remaining paper is organised as follows: In Section 2, we present related literature elaborating the dependence of QoE of VoD on QoS parameters and highlight the possible causes of sampling errors in QoS measurements. Section 2 also presents the literature related to the need for uncertainty analysis. Section 3 describes the methodology followed in this research, while results and discussion of the outcomes of this research was presented in Section 4. Finally, Section 5 concludes this paper and discusses the scope of future work.