Previous research on the Hansel-Spittel constitutive model enhanced the constitutive model with extra terms accounting for unresolved deterministic trends missed by the original Hansel-Spittel constitutive model. To further examine the augmented Hansel-Spittel constitutive model, we applied statistical analysis to the constitutive parameters with the help of statistical hypothesis testing. As a result, a partial F-test on the augmented Hansel-Spittel model parameters showed that the augmented parameters are statistically significant. In addition, a t-test on the last augmented Hansel-Spittel model parameter revealed that the last parameter is statistically insignificant, thus can be removed.