# MGHT: Statistical Methodology for Missing-Data Imputation in Food Composition Databases
## 3 Results
When we use median instead of average, MIGHTv1 also gives better results (84.7%) versus calculating the nutrient value as a median from all nine countries, without considering the rules for borrowing. MIGHTv2 provides better results in 66.94% of the cases compared to calculating the nutrient value as an average without considering the rules, and in 76.0% of the cases compared to calculating the nutrient value as a median wihout considering the rules. In all cases better results are measured as smaller absolute error. The distributions of the absolute error for each version of our methodology and the common approach using average or median from all of the countries involved in borrowing are presented in Figures 2 and 3. In the figures, we can see that the distributions of the absolute errors for averages calculated with MIGHT and regular averages are different. The same is also true for the distributions of the absolute errors for medians calculated with MIGHT and regular medians. Comparing the distributions between averages calculated with MIGHT and regular averages (or medians calculated with MIGHT and regular medians), it becomes obvious that MIGHT provides smaller absolute errors. In addition, the interquartile range, which is a measure of variability (statistical dispersion), is smaller, indicating a small variability in the absolute error. This is not the case when using regular averages or medians. We selected absolute error for comparison in order to provide a general estimation for the magnitude of the error, without considering if the value is above or below the true analytical value. This is done because nutrients are substances used by an organism to survive, grow, and reproduce. All organisms, including humans, obtain nutrients from the surrounding environment and require some of the nutrients (i.e., macronutrients, such as fats, carbohydrates, proteins and water) in relatively large amounts (grams), while other nutrients (i.e., micronutrients, such as vitamins and minerals) are needed in smaller amounts (milligrams, micrograms or even nanograms). Table 7 shows the percentage of cases when MIGHTv1/MIGHTv2 gives a smaller absolute error than the common approach using either the average or the median from all of the countries. In this  
Table 6.0 Distribution of absolute error of: MIGHTv2 average, regular average, MIGHTv2 median and regular median calculated for the Potassium (K) content in foods from the food group “Fruits”. Table 6.1 Distribution of absolute error of: MIGHTv1 average, regular average, MIGHTv1 median and regular median calculated for the Potassium (K) content in foods from the food group “Fruits”. table, MIGHT with averages is compared to regular averages (measure: average), while MIGHT with medians is compared to regular medians (measure: median). From these results, it is clear that no matter the MIGHT version, if the median is used for the eligible countries, the percentage of cases when the proposed methodology gives a smaller absolute error is higher than the percentage when the average value from the eligible countries is used. This is expected because it is known that outliers affect averaging. Because the comparisons presented in Table 7 are made by reporting percentages, we further investigate if there is a statistical difference between the absolute errors obtained by MIGHTv1, MIGHTv2 and regular approach using average/median. To perform this, we compare the absolute errors obtained from the three approaches on the dataset for Potassium (K) in Fruits separately for three different countries (Italy, UK, and USA). For all comparisons, the assumptions for using the Friedman test are satisfied and the significance level is set at 0.05 [54]. The obtained \(p\)-values are reported in Table 8, where the comparisons are made between: MIGHTv1 with averages, MIGHTv2 with averages, and regular averages (measure: average); and MIGHTv1 with medians, MIGHTv2 with medians, and regular medians (measure: median).