The Dempster-Shafer theory of evidence is one of the most widely used frameworks for uncertainty inference. According to Shafer [11], there are two methods for assessing statistical evidence. The first method is to construct belief functions based on physically independent observations and then calculate the orthogonal sum by using Dempster's rule of combination. The second method is that the observations may be treated as a compound observation and a belief function can then be directly constructed by using product chance density. It is well known that the calculation of the Dempster's rule of combination is exponential in nature whilst using the product probability density function could simplify the calculation. It would therefore be of great interest to investigate consistence between the two methods, which is indeed the theme of this paper. Both sufficient and necessary conditions for such consistence will be developed in this paper. In addition, we will investigate the grouping consistence of observations that do not satisfy the consistence conditions, and also discuss the geometric meanings of the consistence and grouping consistence.