# MGHT: Statistical Methodology for Missing-Data Imputation in Food Composition Databases
## 2 Materials and Methods
### Might--Missing Nutrient Value Imputation Using Null Hypothesis Testing
The most common assessment for homogeneity of variance is the [PERSON]'s test, which uses an F-test to test the null hypothesis that the variance is equal across groups (i.e., datasets). With regard to obtained results for checking of assumptions, an appropriate statistical test must be selected. Each statistical test has its own required assumptions. Parametric tests have been commonly used in analyses, however, as a general rule, a non-parametric test is less restrictive than a parametric one, although it is less robust than a parametric when data are well conditioned. For example, if a violation of homogeneity of variance occurs, it is likely that conducting the non-parametric equivalent of the analysis is more appropriate. After selecting the appropriate statistical test, we then test the null hypothesis \(H_{0}\). In our case:  
* \(H_{0}\): There is no effect/difference between the separate datasets. * \(H_{1}\): There is an effect/difference between the separate datasets. Each statistical test has a test statistic, which is a mathematical formula used to obtain a value using the collected data samples. One way is that this value is then compared with a value from a table that contains information about the distribution of the test statistic. These tables contain extreme values (critical values) of the test statistic that are highly unlikely to occur if the null hypothesis is true (depending of the type I error rate of the test). Before obtaining a value from such a table, we first need to specify a level of significance (\(\alpha\)). This value is a probability threshold below which the null hypothesis will be rejected. In [41], the authors detailed the selection of the level of significance (\(\alpha\)), and the relation between \(\alpha\) and the sample size. From the work in [42], we can get more details on the choice of \(\alpha\) and its connection with sample size. Instead of using critical values, nowadays, in frequentist statistics, a \(p\)-value (i.e., probability value or asymptotic significance) can be used, which is the probability for a given statistical model that, when the null hypothesis is true, the statistical summary would be greater or equal to the actual observed results. A smaller \(p\)-value indicates that the null hypothesis is rejected, while a larger \(p\)-value indicates that the null hypothesis is not rejected. After applying the appropriate statistical test, we obtain the result of testing the null hypothesis, i.e., the \(p\)-value, which is then compared with the chosen significance level \(\alpha\) to see if the null hypothesis \(H_{0}\) is rejected (\(p<\alpha\)) or not rejected (\(p\geq\alpha\)). If \(H_{0}\) is rejected that means that the result is statistically significant, thus it is important from which country (or countries) the value is borrowed. Once the test rejects the null hypothesis, the detection of the specific differences among the countries can be made with the application of post-hoc statistical procedures, which are methods used for specifically comparing a country that is a subject of imputation with two or more countries. The post-hoc tests differ in the way they adjust the value in order to compensate for multiple comparisons [43]. The results obtained from the post-hoc test are again compared with the significance level, \(\alpha\), and based on that a matrix of ones and zeros is generated, which represents the rules for borrowing:  
* \"0\": \(H_{0}\) is not rejected, indicating that the datasets can borrow interchangeably. * \"1\": \(H_{0}\) is rejected, meaning that the datasets cannot borrow from each other. Figure 1 presents a flowchart of the methodology. If we have \(n\) instances (problems), we repeat the following steps \(n\) times:  
1. Leave one instance for testing. 2. On the \(n-1\) instances repeat \(n-1\) times:  
* Leave one instance out. * Check conditions for the \(n-2\) instances left. * Choose the appropriate omnibus test.