## 6 Precision
### CNM Precision Validity Score  
With the help of the previous definitions, a comparable score is now defined to indicate whether sufficient measurements are available for a given criterion to meet a certain precision. On the one hand, this helps to compare data sets of different sizes, whether the accuracy is statistically different or not. On the other hand, the score can be used to quantitatively indicate for a CNM what percentage of the required measurements were already made to achieve a specified precision. The measure is defined as follows. Given a target precision \(t^{*}\), e.g., \(t^{*}=\delta^{*}=100\) kbit/s or \(t^{*}=\gamma^{*}=0.01\) (i.e., for the latter, the deviation of \(\overline{y}_{S}\) from \(\overline{y}_{U}\) corresponds to maximum 1% of the mean value \(\overline{y}_{U}\)), the _CNM Precision Validity Score_ is defined as \[Val. Score_{prec.}(t^{*})=\min\left\{\frac{m}{n_{q}^{min}(t^{*})},1\right\} \tag{10}\]  
with \(m=|S|\), \(S\subseteq U\), as the number of measurements done within the CNM \(S\) with measurement plan \(p\), target precision \(t^{*}\) (\(\delta^{*}\), resp. \(\gamma^{*}\)), required number of measurements \(n_{q}^{min}\) to meet precision of type \(q\) as \(q=\)'_abs. '_ for absolute precision, resp. \(q=\)'_rel. '_ for relative precision, as defined in Section 6.1. It corresponds to the percentage number of measurements in CNM \(S\) compared to the number required to achieve the desired precision. The minimum condition within the formula with 1 (\(\geq\) 100%) ensures that the score results in \(0<Val. Score_{prec. }(t^{*})\leq 1\). In case enough measurements are contained in the CNM (\(\geq\)100%), the score thus reflects the same value with 1 (=100%). If there are too few measurements for the target precision, it shows what percentage of the measurements are already included until the desired precision is achieved. The validity score is intended to be mentioned additionally in connection with a CNM result to prove the given precision and error margin, for example, in the case of throughput calculations for a region, which are customary in practice. With a target precision given by the maximum absolute difference, the calculated CNM Precision Validity Score depends largely on the estimated standard deviation of the underlying population by sample \(S\). This means that if the sample size is small, a poor estimate of the actual standard deviation has a significant influence on the score. In case of a calculation of the validity score with relative target precision, the estimate of the mean value of the underlying population also plays a role. In the case of small samples, the estimator for the standard deviation and the mean value can therefore be poor and both can falsify the result. Based on our experience in applying the score with our CNM data, a sample size of at least 100 is recommended in practice to avoid falsified results. A practical example of the influence of a small sample size and its estimators on the validity score can be found in Section 7. We differentiate between five different types of the CNM Precision Validity Score as listed in Table 2. They differ in the method to estimate the distribution of the statistics for the confidence interval, i.e., when calculating the quantile \(z_{\frac{\delta}{2}}\). This means that they stand out in terms of their requirements, such as their computational effort, the minimum number of measurements required, and whether the data set has to be approximately normally distributed or not. Depending on the assumed underlying distribution for the measured parameter, \(z_{\frac{\delta}{2}}\) can be derived according to (1) the Standard Normal Interval, (2) the Studentized \(t\) Interval, (3) the Basic Bootstrap Confidence Interval, (4) the Percentile Confidence Interval, or (5) the Bias Corrected and Accelerated (BCa) Confidence Interval.