A norm-referenced test translates test scores of a specific subject into an estimate of the position of a student with that score in a specific testing group. The estimate is based upon analysis of the test scores and possibly other relevant data drawn from a group sample. In other words, a norm-referenced test identifies whether the student performed better or worse than the other students who took the test, and not whether the student knows more or less of the subject matter than is necessary for a given purpose. This is a test of relative rank. Norm-referenced assessments can be contrasted with criterion-referenced assessments.
If the criterion is "students should be able to construct electron dot formulas to illustrate ionic and covalent bonds," then a test question might look like "In the correct electron dot structure for the methane (CH4) molecule, how many unshared electron pairs surround the carbon atom?" A norm-referenced test would identify whether the student correctly answered the question compared to other students in the testing group. On the other hand, a criterion-referenced test would identify only whether this student correctly answered the question. Most tests and quizzes that are written by teachers are criterion-referenced tests. The objective is simply to see whether the student has learned the subject matter.
Unlike norm-referenced tests, most criterion-referenced tests involve a cutscore, where the student passes if the student's score exceeds the cutscore and fails if it does not. This is often called a mastery test. The criterion is not the cutscore, but the domain of subject matter that the test is designed to assess, e.g., the criterion may be "students should be able to construct electron dot formulas to illustrate ionic and covalent bonds," and the cutscore may be that students should correctly answer a minimum of 80% of the electron dot questions to pass.
In other words, the criterion-referenced test score identifies the student's relationship to the subject matter. In the case of a mastery test, this means identifying whether or not the student has mastered a subject to a specific level by comparing the student's score to the cutscore. However, not all criterion-referenced tests have a cutscore, and the student's score can simply refer to the student's knowledge of the subject domain. Because of this common misunderstanding, criterion-referenced tests have also been called standards-based assessments by some education agencies, as students are assessed on state standards that define what they should know.
Even when testing similar subject matter, a test designed to show relative ranking may use different questions than one designed to assess mastery. This is because some questions are better at differentiating between the best students and the worst students while some other test questions are better at identifying the actual achievement of the student, although many questions will do both. A norm-referenced test will use questions which were correctly answered by the best students but not correctly answered by the worst students. A criterion-referenced test will use questions which were correctly answered by students who know the specific subject.
Many college entrance exams use norm-referenced tests. The SAT and the Graduate Record Examination (GRE) compare student performance to the performance of a testing sample. Students cannot fail a norm-referenced test, as each student receives a score that compares the student to others that have taken the test. This is useful when there is a wide range of acceptable scores, and the goal is to find out who performs better.
In the case of the State of Texas Assessments of Academic Readiness (STAAR), it is a criterion-referenced standardized test that measures a student's performance in comparison to the domain of state curriculum standards, the Texas Essential Knowledge and Skills (TEKS), for a subject area and grade level.