Hypothesis Testing of Inclusion of the Tolerance Interval for the Assessment of Food Safety

In the testing of food quality and safety, we contrast the contents of the newly proposed food (genetically modified food) against those of conventional foods. Because the contents vary largely between crop varieties and production environments, we propose a two-sample test of substantial equivalence that examines the inclusion of the tolerance intervals of the two populations, the population of the contents of the proposed food, which we call the target population, and the population of the contents of the conventional food, which we call the reference population. Rejection of the test hypothesis guarantees that the contents of the proposed foods essentially do not include outliers in the population of the contents of the conventional food. The existing tolerance interval (TI(0)) is constructed to have at least a pre-specified level of the coverage probability. Here, we newly introduce the complementary tolerance interval (TI(1)) that is guaranteed to have at most a pre-specified level of the coverage probability. By applying TI(0) and TI(1) to the samples from the target population and the reference population respectively, we construct a test statistic for testing inclusion of the two tolerance intervals. To examine the performance of the testing procedure, we conducted a simulation that reflects the effects of gene and environment, and residual from a crop experiment. As a case study, we applied the hypothesis testing to test if the distribution of the protein content of rice in Kyushu area is included in the distribution of the protein content in the other areas in Japan.