There are many ways of reporting test performance. A variety of scores can be used when interpreting students' test performance.

### Raw Scores

The **raw score** is the number of items a student answers correctly without adjustment for guessing. For example, if there are 15 problems on an arithmetic test, and a student answers 11 correctly, then the raw score is 11. Raw scores, however, do not provide us with enough information to describe student performance.

### Percentage Scores

A **percentage score** is the percent of test items answered correctly. These scores can be useful when describing a student's performance on a teacher-made test or on a criterion-referenced test. However, percentage scores have a major disadvantage: We have no way of comparing the percentage correct on one test with the percentage correct on another test. Suppose a child earned a score of 85 percent correct on one test and 55 percent correct on another test. The interpretation of the score is related to the difficulty level of the test items on each test. Because each test has a different or unique level of difficulty, we have no common way to interpret these scores; there is no frame of reference.

To interpret raw scores and percentage-correct scores, it is necessary to change the raw or percentage score to a different type of score in order to make comparisons. Evaluators rarely use raw scores and percentage-correct scores when interpreting performance because it is difficult to compare one student's scores on several tests or the performance of several students on several tests.

### Derived Scores

**Derived scores** are a family of scores that allow us to make comparisons between test scores. Raw scores are transformed to derived scores. Developmental scores and scores of relative standing are two types of derived scores. Scores of relative standing include percentiles, standard scores, and stanines.

#### Developmental Scores

Sometimes called age and grade equivalents, **developmental scores** are scores that have been transformed from raw scores and reflect the average performance at age and grade levels. Thus, the student's raw score (number of items correct) is the same as the average raw score for students of a specific age or grade. Age equivalents are written with a hyphen between years and months (e.g., 12–4 means that the age equivalent is 12 years, 4 months old). A decimal point is used between the grade and month in grade equivalents (e.g., 1.2 is the first grade, second month).

Developmental scores can be useful (McLean, Bailey, & Wolery, 1996; Sattler, 2001). Parents and professionals easily interpret them and place the performance of students within a context. Because of the ease of misinterpretation of these scores, parents and professionals should approach them with extreme caution. There are a number of reasons for criticizing these scores.

For a student who is 6 years old and in the first grade, grade and age equivalents presume that for each month of first grade an equal amount of learning occurs. But, from our knowledge of child growth and development and theories about learning, we know that neither growth nor learning occurs in equal monthly intervals. Age and grade equivalents do not take into consideration the variation in individual growth and learning.

Teachers should not expect that students will gain a grade equivalent or age equivalent of one year for each year that they are in school. For example, suppose a child earned a grade equivalent of 1.5, first grade, fifth month, at the end of first grade. To assume that at the end of second grade the child should obtain a grade equivalent of 2.5, second grade, fifth month, is not good practice. This assumption is incorrect for two reasons: (1) The grade and age equivalent norms should not be confused with performance standards, and (2) a gain of 1.0 grade equivalent is representative only of students who are in the average range for their grade. Students who are above average will gain more than 1.0 grade equivalent a year, and students who are below average will progress less than 1.0 grade equivalent a year (Gronlund & Linn, 1990).

A second criticism of developmental scores is the underlying idea that because two students obtain the same score on a test they are comparable and will display the same thinking, behavior, and skill patterns. For example, a student who is in second grade earned a grade equivalent score of 4.6 on a test of reading achievement. This does not mean that the second grader understands the reading process as it is taught in the fourth grade. Rather, this student just performed at a superior level for a student who is in second grade. It is incorrect to compare the second grader to a child who is in fourth grade; the comparison should be made to other students who are in second grade (Sattler, 2001).

A third criticism of developmental scores is that age and grade equivalents encourage the use of false standards. A second-grade teacher should not expect all students in the class to perform at the second-grade level on a reading test. Differences between students within a grade mean that the range of achievement actually spans several grades. In addition, developmental scores are calculated so that half of the scores fall below the median and half fall above the median. Age and grade equivalents are not standards of performance.

A fourth criticism of age and grade equivalents is that they promote typological thinking. The use of age and grade equivalents causes us to think in terms of a typical kindergartener or a typical 10-year-old. In reality, students vary in their abilities and levels of performance. Developmental scores do not take these variations into account.

A fifth criticism is that most developmental scores are interpolated and extrapolated. A normed test includes students of specific ages and grades—not all ages and grades—in the norming sample. Interpolation is the process of estimating the scores of students within the ages and grades of the norming sample. **Extrapolation** is the process of estimating the performance of students outside the ages and grades of the normative sample.

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