Based on my experiences, I found that different kinds of assessments carry embedded social assumptions that influence both design of assessment and impact on learners. Here are the implications:
1. Criterion referenced (in higher education, it can be IELTS, TOEFL, EnglishScore, ProLE that are commonly used as standardized assessment for measuring English language proficiency level)
The social assumptions:
The assessment tools measure students' language proficiency objectively. The students are assessed based on CEFR level as the common benchmark.
The consequences:
For better: I think the tools provide students with global recognition that is useful for their academic access. For worse: However, the tools merely promote teaching to the test. As a results, students, in EFL context, need extra time and spend more money for taking IELTS course.

2. Norm referenced
The social assumptions:
In a university level, it can be a kind of final exam (summative assessment). Lecturers must provide a well-designed assessment tool that is aligned to their course learning objectives as well as the way they teach (pedagogical/instructional design).
The consequences:
For better: I believe that the lecturers must be guided by the curriculum. For worse: It is difficult to some lectures in ensuring one of the aspects of curriculum alignment.

3. Self referenced
The social assumptions:
For this kind of assessment, learning is the focus. The students are provided with instructional activities for doing reflection, reviewing their peer's work, and so forth.
The consequences:
For better: I found that this assessment encourage students to be self-regulated learners. Moreover, their learning performance pressure is more reduced. For worse: It works best for active students. Therefore sometimes I provide group work or collaborative learning activity for this kind of assessment.