Outlier and Normality Testing of the Residuals for the Morgan-Mercer-Flodin (MMF) Model Used for Modelling the Total Number of COVID-19 Cases for Brazil

Abstract

Traditionally, testing for outliers is performed by first creating a null hypothesis, H0, indicating that the suspected results do not differ significantly from those of other members of the data set, and then rejecting it if the likelihood of getting the experimental results is extremely low (e.g., p=0.05). Similarly, if H0 can be rejected, the questionable findings may be discarded as outliers as well. If H0 is retained in the data set, it is important to keep the dubious findings in the data set. In general, in nonlinear regression, the residuals of the curve must be normally distributed before any test for the existence of outliers is performed. This is often accomplished through the use of normalcy tests such as the Kolmogorov-Smirnov, Wilks-Shapiro, D'Agostino-Pearson, and Grubb's tests, the latter of which checks for the presence of an outlier and is the subject of this study. Normality tests for residues used in general nonlinear regression revealed that the usage of the Morgan-Mercer-Flodin (MMF) Model used for Modelling the Total Number of COVID-19 Cases for Brazil was adequate due to lack of an outlier. The critical value of Z from statistical table for Grubbs’ test for a single outlier using mean and SD was 0.114 (n=50). The Grubbs (Alpha = 0.05) g value was 3.597. Individual Z value indicates that the residual with a value of -3 (row 3) was far from the rest and is deemed a significant outlier (p < 0.05). This outlier was removed, and subsequent Grubb’s test show the absence of other outliers. As the Grubbs’ test require for the normality of the residuals, several normality tests (Kolmogorov-Smirnov, Wilks-Shapiro, Anderson-Darling and the D'Agostino-Pearson omnibus K2 test) were carried out and the results were found to conform to normality. In addition, a visual inspection of the model’s normal probability or Q-Q plot shows a nearly straight and appeared to exhibit no underlying pattern. The resulting histogram overlaid with the ensuing normal distribution curve also reveals that the residuals were truly random and that the model used was adequately fitted.