Grade-Equivalent Scores

Grade-equivalent scores are scores reported on norm-referenced assessments indicating the level at which an individual student performed compared with the average performance of students at other grade levels. The score is on a continuous developmental scale used for describing developmental level and measuring growth. Grade-equivalent scores are reported as a decimal number indicating the performance of a student in terms of grade level and month. For example, a score of 6.4 indicates performance at the sixth-grade level, the fourth month of school. Educational psychologists are interested in grade-equivalent scores for students to help provide a frame of reference for their developmental growth. It is important to understand the method for the development of the score and how the score should be interpreted.

Test publishers generally conduct norming studies twice a year: in the fall and in the spring. Tests are administered to students in various grades. The norms are computed by finding the mean raw scores of students in each grade. The score is based on typical performances of students across grade levels. Therefore, the information is aggregated without regard to individual differences within the group. For example, a test publisher may develop an achievement test for third-grade mathematics. To assign norms, the test is administered to large groups of students in successive grade levels. The raw scores are computed for each student in each grade level. The mean raw score is then assigned as the norm for that grade level at that specific time of year. For instance, if the mean number of questions answered correctly is 27 for a group of students in the fifth month of third grade, then any student who also answers 27 questions correctly will receive a grade-equivalent score of 3.5 (third grade, fifth month).

As test publishers typically only do norming studies twice a year, the conversions for months in between the studies are found through interpolation. Interpolation involves plotting the scores on a bivariate axis. The baseline is divided into 10 parts. For third grade, the units would be 3.0, 3.1, 3.2, and so on, until 3.9. The scores are then plotted on the y axis. Once the computed scores are graphed, the points are connected, or interpolated, with a straight line and then extended, or extrapolated, with a line going beyond the specific grades tested to indicate how students in other grades may also perform. Interpolation and extrapolation are necessary to compute norms because the specific test was not given to all grades, nor was it given at all the different points on the continuum within a grade.

Grade-equivalent scores, while intuitively appealing, are the most misinterpreted scores provided by testing companies. The scores are frequently misused to assess student learning. For instance, if a third-grade student earns a grade-equivalent score of 5.7 on a math assessment, this is not an indication that the student is capable of doing fifth-grade math. Instead, it means that this student performed the same as a fifth-grade student did when taking the third-grade math test. Or, the third-grade student can do third-grade math as well as a fifth-grade student in the seventh month of school can do third-grade math. Additionally, does this mean the student should be promoted to fifth-grade math class? No. It is unlikely that the student has been exposed to, or mastered, fifth-grade math material. In fact, if a third-grade student were given a test designed to assess fifth-grade math, it is unlikely that the student would attain the grade-equivalent score of 5.7.

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