Effect of the Scattering of Measured Values of Sample on the Concentration Estimation

Standard curves are used to estimate the concentration of a target substance in food samples and the curves are generally made with the least square method. The least square method is allowed to apply only under the condition that the measurements follow the normal distribution with a constant variance. Actually, however, it is thought that as the measurements of samples are higher, the scattering of the measurements would be also larger. In this study, thus, the effect of the scattering of measured values of samples on the concentration estimation was studied with two normal distribution models with a constant variance and a variance changing to measured values. Measurement data analyzed here were random samples from the normal distributions with various variance. As a result, in the case that the concentrations of the target substance and the measurements were linear, the latter model with the changing variance was statistically more appropriate for the data whose scattering increased with it. However, no remarkable differences were observed between the two models in the standard curves and the estimates from those curves for the measurement sets studied. In the case that the concentrations and the measurements were nonlinear being concave downward and upward, the same results were also observed. These results showed that the model with the changing variance would be more appropriate than the one with the constant variance for various measurement data, while both models could also successfully estimate the concentration of unknown samples.