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Three of the fundamental purposes for testing are (1) to identify students' areas of relative strength and weakness in subject areas, (2) to monitor year-to-year growth in the basic skills, and (3) to describe each student's developmental level within a test area. To accomplish any one of these purposes, it is important to select the type of score from among those reported that will permit the proper interpretation. Scores such as percentile ranks, grade equivalents, and standard scores differ from one another in the purposes they can serve, the precision with which they describe achievement, and the kind of information they provide. A closer look at these types of scores will help differentiate the functions they can serve and the meanings they can convey.
Raw Score (RS)
The first unadjusted score obtained in scoring a test. A Raw Score is
usually determined by tallying the number of questions answered
correctly or by the sum or combination of the item scores (i.e.,
points). However, a raw score could also refer to any number directly
obtained by the test administration (e.g., raw score derived by
formula-scoring, amount of time required to perform a task, the number
of errors, etc.). In individually administered tests, raw scores could
also include points credited for items below the basal. Raw Scores
typically have little meaning by themselves. Interpretation of Raw
Scores requires additional information such as the number of items on
the test, the difficulty of the test items, norm-referenced information
(e.g., Percentile Ranks, Grade Equivalents, Stanines, etc.), and/or
criterion-referenced information (e.g., cut-scores).
Percent Correct (PC)
The percentage of the total number of points that a student received on
a test. The percent correct score is obtained by dividing the student's
raw score by the total number of points possible and multiplying the
result by 100. For multiple-choice tests, this is the same as dividing
the student's raw score by the number of questions (i.e., each item is
worth one point) and multiplying by 100. Percent Correct scores are
typically used in criterion-referenced interpretations and are only
helpful if the overall difficulty of the test is known.
Grade Equivalent (GE)
A grade equivalent score represents the typical performance of students
tested in a given month of the school year at a particular grade. For
example, a grade equivalent of 5.3 represents the score achieved by the
median student in fifth grade after three months of instruction.
Developmental Standard Score (SS)
Standard scores are continuous across all levels and forms of a
specific test. Because they are built on equal-interval scales, the
magnitude of a given difference between two scores represents the same
amount of difference in performance wherever it occurs on the scale.
For example, the difference between standard scores of 15 and 20 is the
same as the difference between standard scores of 45 and 50.
Percentile Rank (PR)
The percentage of scores in a specified distribution that fall at or
below the point of a given score. Percentile Ranks range in value from
1 to 99, and indicate the status or relative standing of an individual
within a specified group (e.g., norms group), by indicating the percent
of individuals in that group who obtained lower scores. For example, if
a student earned a 72nd Percentile Rank in Language, this would mean he
or she scored better than 72 percent of the students in a particular
norm group who were administered that same test of Language. This also
implies that only 28 percent (100 - 72) of the norm group scored the
same or higher than this student. Note however, an individual's
percentile rank can vary depending on which group is used to determine
the ranking. A student is simultaneously a member of many groups:
classroom, grade, building, school district, state, and nation. Test
developers typically publish different sets of percentile ranks to
permit schools to make the most relevant comparisons possible.
An achievement test is built to help determine how much skill or knowledge students have in a certain area. We use such tests to find out whether students know as much as we expect they should, or whether they know particular things we regard as important. By itself, the raw score from an achievement test does not indicate how much a student knows or how much skill she or he has. More information is needed to decide "how much." The test score must be compared or referenced to something in order to bring meaning to it. That "something" typically is (a) the scores other students have obtained on the test or (b) a series of detailed descriptions that tell what students at each score point know or which skills they have successfully demonstrated. These two ways of referencing a score to obtain meaning are commonly called norm-referenced and criterion-referenced score interpretations.
Norm-Referenced Interpretation
Standardized achievement batteries like the ITBS and ITED
are designed mainly to provide for norm-referenced interpretations of
the scores obtained from them. For this reason they are commonly called
norm-referenced tests. However, the scores also permit
criterion-referenced interpretations, as do the scores from most other
tests. Thus, norm-referenced tests are devised to enhance
norm-referenced interpretations, but they also permit
criterion-referenced interpretation.
A norm-referenced interpretation involves comparing a student's score with the scores other students obtained on the same test. How much a student knows is determined by the student's standing or rank within the reference group. High standing is interpreted to mean the student knows a lot or is highly skilled, and low standing means the opposite. Obviously, the overall competence of the norm group affects the interpretation significantly. Ranking high in an unskilled group could represent lower absolute achievement than ranking low in an exceptional group.
Most of the scores on ITBS and ITED score reports are based on norm-referencing, i.e., comparing with a norm group. In the case of percentile ranks, stanines, and normal curve equivalents, the comparison is with a single group of students in a certain grade who tested at a certain time of year. These are called status scores because they show a student's position or rank within a specified group. However, in the case of grade equivalents and developmental standard scores, the comparison is with a series of reference groups. For example, the performances of students from third grade, fourth grade, fifth grade, and sixth grade are linked together to form a developmental continuum. (In reality, the scale is formed with grade groups from kindergarten up through the end of high school.) These are called developmental scores because they show the students' positions on a developmental scale. Thus, status scores depend on a single group for making comparisons and developmental scores depend on multiple groups that can be linked to form a growth scale.
An achievement battery like the ITBS or ITED is a collection of tests in several subject areas, all of which have been standardized with the same group of students. That is, the norms for all tests have been obtained from a single group of students at each grade level. This unique aspect of the achievement battery makes it possible to use the scores to determine skill areas of relative strength and weakness for individual students or class groups, and to estimate year-to-year growth. The use of a battery of tests having a common norm group enables educators to make statements such as "Suzette is better in mathematics than in reading" or "Danan has shown less growth in language skills than the typical student in his grade." If norms were not available, there would be no basis for statements like these.
Norms also allow students to be compared with other students and schools to be compared with other schools. If making these comparisons were the sole reason for using a standardized achievement battery, then the time, effort, and cost associated with testing would have to be questioned. However, such comparisons do give educators the opportunity to look at the achievement levels of students in relation to a nationally representative student group. Thus, teachers and administrators get an "external" look at the performance of their students, one that is independent of the school's own assessments of student learning. As long as our population continues to be highly mobile and students compete nationally rather than locally for educational and economic opportunities, student and school comparisons with a national norm group should be of interest to students, parents, and educators.
A common misunderstanding about the use of norms has to do with the effect of testing at different times of the year. For example, it is widely believed that students who are tested in the spring of fourth grade will score higher than those who are tested in the fall of fourth grade with the same test. In terms of grade-equivalent scores, this is true because students should have moved higher on the developmental continuum from fall to spring. But in terms of percentile ranks, this belief is false. If students have made typical progress from fall to spring of grade 4, their standing among fourth-grade students should be the same at both times of the year. (The student whose percentile rank in reading is 60 in the fall is likely to have the same percentile rank when given the same test in the spring.) The reason for this, of course, is that separate norms for fourth grade are available for the fall and the spring. Obviously, the percentile ranks would be as different as the grade equivalents if the norms for fourth grade were for the entire year, regardless of the time of testing. Those who believe students should be tested only in the spring because their scores will "look better" are misinformed about the nature of norms and their role in score interpretation.
Scores from a norm-referenced test do not tell what students know and what they do not know. They tell only how a given student's knowledge or skill compares with that of others in the norm group. Only after reviewing a detailed content outline of the test or inspecting the actual items is it possible to make interpretations about what a student knows. This caveat is not unique to norm-referenced interpretations, however. In order to use a test score to determine what a student knows, we must examine the test tasks presented to the student and then infer or generalize about what he or she knows.
Criterion-Referenced Interpretation
A criterion-referenced interpretation involves comparing a student's
score with a subjective standard of performance rather than with the
performance of a norm group. Deciding whether a student has mastered a
skill or demonstrated minimum acceptable performance involves a
criterion-referenced interpretation. Usually percent-correct scores are
used and the teacher determines the score needed for mastery or for
passing.
The user must establish some performance standards (criterion levels) against which comparisons can be made. For example, how many math estimation questions does a student need to answer correctly before we regard his/her performance as acceptable or "proficient?" This can be decided by examining the test questions on estimation and making a judgment about how many the minimally prepared student should be able to get right. The percent of estimation questions identified in this way becomes the criterion score to which each student's percent-correct score should be compared.
When making a criterion-referenced interpretation, it is critical that the content area covered by the test – the domain – be described in detail. It is also important that the test questions for that domain cover the important areas of the domain. In addition, there should be enough questions on the topic to provide the students ample opportunity to show what they know and to minimize the influence of errors in their scores.
The percent-correct score is the type used most widely for making criterion-referenced interpretations. Criterion scores that define various levels of performance on the tests are generally percent-correct scores arrived at through teacher analysis and judgment. Several score reports available thru the Riverside Scoring Service include percent-correct skill scores that can be used to make criterion-referenced interpretations: Group Skills Analysis, Group Item Analysis, Individual Performance Profile, and Group Performance Profile.
Interpreting Scores from Special Test Administrations
When students have been tested with accommodations or modifications,
should their answer documents be scored separately, or should they be
included with those of other students? Should the scores of such
students be included with the scores of all other students in group
averages? Can the norms for the test be used? Should scores be
interpreted differently? These are some of the many important
questions that arise when testing accommodations/modifications have
been used. Of course, school policy or state requirements may determine
how each of these questions is answered in any given locale, but in the
absence of such regulations, the rest of this section provides some
ideas about how to resolve these issues.
To the extent that the accommodations used with a student were chosen carefully and judged to be necessary, the anticipated effect is to reduce the impact of that student's disability on the assessment process. That is, the student responses are like those we would expect the student to make if that student had no disability. Consequently, it seems reasonable to use that student's scores in the same ways we would use the scores of all other students. The student's answer document should be placed among the others for scoring, the student's scores should be included with all others in group averages, and the various derived scores (e.g., grade equivalents and percentile ranks) should be interpreted as though the student had been tested without any accommodations.
To learn more about Total and Composite Scores that can be obtained
with each test level please click on the following link.
Total and Composite Scores