To address your question about the social assumptions of different kinds of assessments, it's important to first clarify what "kinds of assessment" you're interested in. Assessments can be categorized in various ways, such as by purpose (e.g., formative, summative), by type (e.g., standardized tests, performance assessments), or by subject area (e.g., math, literacy).
I will outline the social assumptions underlying several common types of assessments.

Standardized Tests

Assumption of Fairness and Equity: Standardized tests assume that all test-takers have had equal opportunities to learn the material being tested.
Assumption of Validity: These tests assume that they accurately measure the knowledge or skills they are intended to measure.
Assumption of Reliability: There's an assumption that the test will produce consistent results across different administrations and scoring.
Cultural Neutrality: Standardized tests often assume that the content is culturally neutral and does not unfairly advantage or disadvantage any particular group.
Objectivity in Scoring: These assessments assume that scoring is objective and free from bias.

Performance Assessments

Contextual Relevance: Performance assessments assume that the tasks are relevant to real-world situations and that students have had opportunities to develop the skills needed to perform these tasks.
Subjectivity in Scoring: These assessments acknowledge that there may be some subjectivity in scoring.
Assumption of Clear Criteria: Performance assessments assume that the criteria for evaluating student performance are clear, transparent, and consistently applied.
Authenticity: There's an assumption that the tasks are authentic and reflect meaningful applications of knowledge and skills.

Formative Assessments

Teacher Knowledge of Students: Formative assessment assumes that teachers have a good understanding of their students' individual needs and learning styles.
Open Communication: These assessments assume that there is open communication between teachers and students.
Value of Feedback: Formative assessment assumes that feedback is valuable and that students will use it to improve their learning.
Safe Learning Environment: There's an assumption that the classroom environment is safe and supportive.

Summative Assessments

Comprehensive Coverage: Summative assessments assume that they comprehensively cover the material taught over a period of time.
Accurate Reflection of Learning: These assessments assume that the results accurately reflect what students have learned.
Usefulness for Decision-Making: Summative assessments assume that the results will be used to make informed decisions.

General Considerations

Access to Resources: Many assessments assume that all students have access to necessary resources.
Motivation and Engagement: Assessments often assume that students are motivated and engaged in the assessment process.
Test-Taking Skills: There's an assumption that students have adequate test-taking skills.

Keep in mind that these assumptions are not always valid in practice. Factors such as socioeconomic status, cultural background, and access to resources can significantly impact student performance on assessments. It's important to be aware of these social assumptions and to use assessments in a way that is fair, equitable, and supportive of all students' learning.