# Prediction and Surveillance Sampling Assessment in Plant Nurseries and Fields
## 3 Results
### Application of the Sampling Methods  
Table 2 shows the summary of the measurements obtained using random sampling. This method is conceptually simple and involves taking the individuals at random from a list. In our case, the list is made up of 10,920 saplings. In order to propose the best sampling design, we tested various percentages and sample sizes under different sampling strategies. Table 2 presents both the estimated parameters and the different measures of error for random samples of 10%, 15%, 20% and 25%. Under this method, smaller errors occur in those random samples of 25%. With 25% of representation, smaller discrepancies are obtained under the mean square error and the coefficient of variation. However, no significant improvements in the absolute error are found. Table 3 presents the summary of the measurements obtained using a systematic sampling. In this case, the first subject is chosen randomly, and the rest are conditioned by this choice. This method is simple to apply in practice and has the advantage of not needing a framework survey. It can be applied in most situations, and the only precaution that should be considered is to check that the characteristic studied does not have a periodicity coincident with the sample. Figure 4: Configuration of nursery for the calibration process; values for x (**left**) and percentage of diseased saplings (**right**). In the samples that represent 50%, we defined a systematic jump equal to two, i.e., we consider one in every 2 plants. In samples that represent 25%, we consider one in every four plants, while for the remaining percentages, one in every five and one in every eleven, respectively, was chosen. Clearly, with a systematic 50% sample, we have smaller errors due to the large size of the sample. However, when analysing the rest of the systematic samples, we observe that the 25% samples have smaller errors. The discrepancy measure of these samples compared with the 20% samples is similar. However, the mean square error (MSE) for the latter is greater. The measure that recognizes greater discrepancy remains the mean square error. Finally, according to the results in Table 3 and due to the need to study both smaller samples as the most representative, we may conclude that under this scheme, it is advisable to select a 25% sample of all saplings in the nursery. The third method used is a mixed sampling method, where stratified sampling is combined with the random sampling method. In this case, we build blocks or layers considering the value of \(x\) coordinate of each tree \(i\) with \(i=1,\ldots,10,920\). We form three blocks or subsets of data, the first block being made up of those subjects located in band 1, the second by the saplings located in bands 2, 3, 4, 5, 6, 7 and 8, and the third block by saplings located in band 9. Once the blocks are formed, we take random samples of different sizes in each of them (see Table 4). Table 5 presents a summary of the measures obtained using a mixed sampling and shows that as \(n\) increases, it progressively decreases the error measure considered. However, the differences between the errors of the last samples is not significant. Therefore, in such situations, a mixed sampling method can be used with sample sizes of 30% in block 1, 30% in block 2 and 20% in block 3, or samples in each block of 35%, 35% and 25%, respectively. With both sampling schemes, we have approximately 23% and 31% of all the nursery. As in the other sampling methods, the mean square error (MSE) is the statistic which recognizes major differences. \begin{table}
\begin{tabular}{c c c c c} \hline
**Measure** & **Sample 10\%** & **Sample 15\%** & **Sample 20\%** & **Sample 25\%** \\ \hline \(\kappa\) & 0.0058 & 0.0084 & 0.0044 & 0.0029 \\ \(\phi\) (cm) & 6.26 & 3.83 & 8.39 & 12.44 \\ \(\tau\) (cm) & 19.44 & 11.81 & 6.76 & 4.82 \\ \hline MSE & 3.1419 & 2.8638 & 2.8448 & 2.4847 \\ ABSE & 0.0134 & 0.0116 & 0.0118 & 0.0106 \\ CV & 0.2025 & 0.2183 & 0.2075 & 0.1689 \\ \hline \end{tabular}
\end{table}