## 2 Data and Methods
Using the layout and notation defined for the confusion matrix shown in Table 5, which is used throughout the article, overall accuracy, \(O\), was calculated using Equation (1):  
\[O=\frac{\sum n_{ii}}{n} \tag{1}\]  
In addition to the global estimate of classification quality conveyed by overall accuracy, the producer's, \(P\), and user's accuracy, \(U\), were calculated with reference to each class [1; 18]. These were obtained for class \(i\) from Equations (2) and (3) respectively:  
\[P_{i}=\frac{n_{ii}}{n_{,i}} \tag{2}\] \begin{table}
\begin{tabular}{c c} \hline
**Dataset** & **Size and Class Composition** \\ \hline Training & 110 cases of each class; total = 660 cases \\ \hline \multirow{6}{*}{Validation (random)} & 100 sugar beet \\  & 99 wheat \\  & 53 barley \\  & 34 carrot \\  & 26 potato \\  & 18 grass; total = 330 cases \\ \hline Validation (stratified) & 55 cases of each class; total = 330 cases \\ \hline \multirow{6}{*}{Testing} & 100 sugar beet \\  & 99 wheat \\  & 53 barley \\ \cline{1-1}  & 34 carrot \\ \cline{1-1}  & 26 potato \\ \cline{1-1}  & 18 grass; total = 330 cases \\ \hline \end{tabular}
\end{table} 
Table 4: Class composition of the datasets used for analyses of the remotely sensed data. \[U_{i}=\frac{n_{ii}}{n_{i}}. \tag{3}\]  
Note that, as is common, the calculations of these measures of accuracy are based on the raw counts of cases shown in the elements of the confusion matrix. These approaches to accuracy assessment were used to support all analyses, whether based on the training, validation, or testing datasets. Most focus is, however, on the accuracy values arising from analyses of the validation and testing datasets. To determine if the use of different validation samples impacted on the accuracy of the final thematic classification, the statistical significance of differences in the accuracy of the classifications of the testing set were assessed. Standard approaches for the comparison of accuracy values that are popular in remote sensing projects are unsuitable here as the same sample of testing cases was used throughout. To accommodate for this situation, the statistical significance of differences in accuracy was assessed using the McNemar test [45; 46]. The latter is a non-parametric test that is based on a binary confusion matrix which shows the cross-tabulation of the cases that have been labelled correctly and incorrectly by the two classifications being compared. The test focuses on the discordant cases, those which were classified correctly by one classifier, but incorrectly by the other. Without continuity correction, the test is based on the normal curve deviate, \(z\), as expressed as:  
\[z=\frac{n_{CI}-n_{IC}}{\sqrt{n_{CI}+n_{IC}}} \tag{4}\]  
where \(n_{CI}\) indicates the number of cases in the relevant element of the matrix with the subscript \(C\) indicating if the classification was correct in its labelling or \(I\) if it was incorrect and order of the subscripts indicates the specific classification from the pair under study. For a standard two-tailed test at the 95% level of confidence, the null hypothesis of no significant difference is rejected if the calculated \(z\) exceeds the critical value of \(\left|1.96\right|.\) Similarly, for a one-tailed test, if the hypothesis under test has a directional component, the direction (sign) needs consideration and the magnitude of the critical value of \(z\) to indicate that a significant difference exists at the 95% level of confidence is 1.645.