TESTING MEMO 11: ABSOLUTE VERSUS RELATIVE GRADING STANDARDS: WHAT DOES A PERCENTAGE MEAN? by Lawrence H. Cross Virginia Polytechnic Institute and State University In an interesting historical account of grading practices, Cureton (1971) reported that by the turn of the century "marking systems based on 100 points or 100 percent were pretty well entrenched in many quarters, schools and colleges, as well as civil service programs" (p. 4). However, she noted that during the first two decades of the century, percentage marking procedures were the target of a great deal of criticism and that most measurement specialists agreed that "grades were really just ranks" (p.6). Nonetheless, the practice of using a fixed percentage scale (e.g. 60%-70%=D, 70%-80%=C, etc.) for assigning letter grades is alive and well today. A recent survey of public school teachers in Virginia found that 73% of the respondents reported using fixed percentage scales for assigning letter grade to tests. A 1992 survey of Virginia Tech faculty members found that 48% of the respondents assigned letter grades using more or less fixed percentage ranges. The purpose of this memo is to challenge the use of fixed percentage ranges for assigning letter grades to tests of academic knowledge and to argue that letter grades can be assigned to test scores more reliably and equitably if fixed percentage ranges are abandoned in favor of flexible percentage ranges. At issue is whether percent-correct scores should be viewed as absolute or relative indicators of achievement. Given the enduring and pervasive use of fixed percentage scales, one might suspect that percent-correct scores can be interpreted in an absolute sense, as is the case for percentage of blood-alcohol or relative humidity. However, percent-correct scores have no external physical referent, and reflect the difficulty of the tests, or test questions, as much as they reflect the level of knowledge a student possesses. Only in relatively rare instances would it be reasonable to in- terpret percent-correct scores as indicating the absolute levels of knowledge, ability, or skill acquired by examinees. Such an inference is most defensible for tests designed to measure lower-level cognitive skills within well-defined domains, such as a test of the facts contained within the periodic table or a vocabulary test of legal terms. For such tests it would be reason- able to assume that a percent-correct score is an approximation of the percentage of the relevant knowledge held by the examinee. Moreover, because the knowledge required for such tests is not at a very high cognitive level, it is reasonable to expect a large proportion of the examinees to answer 70% or more of the questions correctly. This kind of testing leads to establishing standards such as 60% for the lowest passing grade. However, higher education is heavily committed to enhancing higher-level cognitive skills, and there is no limit to the understanding that a student may acquire in a given area. When assessing higher-level cognitive skills, individual achievement levels can be expected to differ widely among students, even among students who should all get satisfactory grades. Therefore, tests should be constructed to measure these differences and not force nearly all scores to fall within a 60%-100% range. If test scores are interpreted in a relative sense as indicating only the rank ordering among examinees, there is no reason to limit the percent-correct score range. Indeed, the wider the score range, the more reliable the rankings will be. Recommendations: 1. Do not prescribe percent-correct score ranges for letter grades in your course syllabus. Instead, indicate that you will exercise your professional judgment as to what constitutes A, B, C, etc., only after reviewing the test scores. You may wish to indicate only tentative letter grades for any given test and base final test grades on the average of standardized scores from several tests. This point is discussed in detail in Testing Memo 6. 2. When testing higher level cognitive skills, vary the difficulty of the questions so as to discriminate among all skill levels. Include items sufficiently difficult to challenge even the most talented students and a few items sufficiently easy that most will answer correctly. The latter may include a disproportionate number of lower level cognitive skills. The average percent- correct score should be somewhere in the range between 50% and 70% in order to maximize discrimination among achievement levels. See Testing Memo 2 for further discussion of this point. 3. Alert students to the fact that the test may be more difficult than what they are accustomed to, but that the percent-correct scores will be interpreted in a relative, rather than an absolute sense. 4. Determine the minimum passing score on each test by identifying items that you (and/or your colleagues) judge to represent essential knowledge, or that you (or they) believe should be correctly answered by any student deserving of a passing grade. Base the passing score on the percentage of the total points these questions contribute. You may wish to compute a separate score for items so identified, but it is probably sufficient to use this percentage regardless of which items are answered correctly. 5. Use your professional judgment to determine cut points between grades. You might consider the test performance of students about whom you have independent knowledge of achievement via other assignments or previous courses. Naturally occurring breaks in the score distribution can suggest cut points between letter grades that might minimize the number of students clamoring at your door for the extra point or two needed for the next higher grade. Ultimately, judgements in this area are subjective and should be acknowledged as such when implemented. 6. Do not feel obliged to "grade on the curve" whereby a specified percentage of students will receive each letter grade. To do so can be as arbitrary and capricious as to adopt prescribed percentage ranges for assigning scores, especially in smaller classes. (However, Testing Memo 7 points out that "grading on the curve" may be justified in large classes, when course content and student quality are stable from year to year.) Reference: Cureton, L. W. "A History of Grading Practices." _Measurement in Education_ 2 (Summer 1971): 1-8. For more information, contact Bob Frary at Robert B. Frary, Director of Measurement and Research Services Office of Measurement and Research Services 2096 Derring Hall Virginia Polytechnic Institute and State University Blacksburg, VA 24060 703/231-5413 (voice) frary#064;vtvm1.cc.vt.edu ###