# MGHT: Statistical Methodology for Missing-Data Imputation in Food Composition Databases
## 3 Results
Since we are working with data from different national databases, and we made sure to only include values measured analytically, the datasets in our example are independent. 2. Normality is checked using the Shapiro-Wilk test from the \"stats\" package [36]. The test is applied to each column of experimental data, i.e., for each dataset separately, resulting in not meeting the requirement for normality for all columns. After this, there is already one condition that is not satisfied, which means a non-parametric test must be used. 3. Checking for homoscedasticity at this point does not bring any contribution to the result, but since this is not the only experiment conducted for evaluation it must be mentioned. The homoscedasticity is checked by applying the [PERSON]'s test from the \"lawstat\" package [52]. The result from the test indicates that the condition for homoscedasticity is not satisfied. Since our data do not satisfy the required conditions for the safe use of a parametric test, it is better to use an analogous non-parametric test. Because the set has more than two columns, we apply the [PERSON] test [53]. A requirement for the [PERSON] test is that the number of problems (in our case foods) must be greater than 10, so, for our methodology, \(r>10\)[43] and \(n=16\), which means that \(n\geq r\). Further, we have 16 instances, which means the following is repeated 16 times:  
1. One instance is removed for testing. 2. For each of the remaining 15 instances, repeat the following steps 15 times (i.e., perform leave one out validation): 1. One instance is removed. 2. Check conditions for the remaining 14 instances. 3. Apply [PERSON] test and obtain \(p\)-value. 4. The \(p\)-value is compared with the significance level, which in our case is chosen to be \(\alpha=0.05\)[54]. In all of the runs, we obtained a smaller \(p\)-value, \(p<\alpha\). As mentioned above, this indicates that the null hypothesis is rejected, meaning that there is a statistical significance between the datasets, i.e., between the FCD from the different countries. Further, to see where this differences come from, we use two different post-hoc procedures, which makes our methodology branch out into two different versions: * MIGHTv1: when All vs. all type of post-hoc procedure is applied. * MIGHTv2: when One vs. all type of post-hoc procedure is applied. (e) Friedman test post-hoc procedure: * Nemenyi test [55] is applied as an All vs. all post-hoc procedure for the previously used Friedman test. The Nemenyi test provides a matrix with \(p\)-values for each pairwise comparison. * Holm procedure [47] of \(p\)-value adjustment is applied nine times, where each time a different country is selected as a control (One vs. all). The end result is a matrix with \(p\)-values, where each row corresponds to the results obtained from the Holm procedure (i.e., the country that represents the row is selected as control country). (f) Using the \(p\)-values obtained in these matrices, for each pairwise comparison we can check if the null hypothesis is rejected (1), or not rejected (0). If the null hypothesis is rejected, it means that there is a statistical significance between the FCD, while, if it is not rejected, it means that there is no statistical significance between the FCD. Table 5 gives an example of a matrix with rules for one model generated from MIGHTv1. In these tables, we can see that, for example, for a missing Potassium (K) value in a food from the food group \"Fruits\" for the Italian FCDB following the rules of MIGHTv1 we cannot borrow from the FCDBs Canadian FCDB and following the rules of MIGHTv2 we cannot borrow from the FCDBs from Sweden, USA and Canada. (g) The two final matrices with rules are generated by sum the matrices obtained from each comparison using both versions, respectively.