Lesson 1.4: Frame of Reference for Interpreting Scores—
Commonly Used Test Scores
- Lesson Objectives
- Common Types of Test Scores and Norms
- Standard Scores
- Percentile Ranks
- Grade Equivalents
- Scaled Scores
- Define different types of scores: standard scores, percentile rank, grade equivalents, and scaled scores.
- Interpret student performance and progress using different types of test scores.
Many of the measures you will be using for Screening, Diagnosis, Progress Monitoring, and Outcome will be standardized tests using normative data. Several different types of scores are reported with standardized tests. Normative data can help to answer the following types of questions:
- How does a student’s test performance compare with that of other students?
- How does a student’s performance on one test (or subtest) compare with performance on another test (or subtest)?
- How does a student’s performance on one form of a test compare with performance on another form of the test, administered at an earlier date?
Common Types of Test Norms (Linn & Gronlund, 2000, p. 480)
Type of Test Norm | Name of Derived Score | Meaning in Terms of Test Performance |
Standard score norms | Standard scores | Distance of student’s raw score above or below the mean of the reference group in terms of standard deviation units |
Percentile norm | Percentile ranks | Percentage of students in the reference group who fall below student’s raw scores |
Grade norms | Grade equivalents | Grade group in which student’s raw score is average |
Back to Top
Standard ScoresStandard scores are so named because they are based on standard deviation (SD) units, a numerical index that indicates how far a particular score is above or below the mean. They have a preset mean and standard deviation. Standard scores most commonly used in schools are T-scores, stanine scores, and normal curve equivalent (NCE) scores.
T-scores have a mean of 50 and standard deviation of 10. Thus, a student with a T-score of 60 is one standard deviation above the mean. T-scores are used to report results on the Preliminary SAT/National Merit Scholarship Qualifying Test (PSAT/NMSQT).
Stanine scores are derived from standard deviations and have nine levels. They have a mean of 5 and standard deviation of 2. There is a convenient way to relate stanine scores to other scores by using the “Rule of Four.” Starting with either end of the stanine scale, 1 or 9, 4% of the cases in a normal distribution fall into the end of the stanines. Remember, stanine 5 falls in the middle and has 20%, 6 has 16%, 7 has 12%, 8 has 8%, and 9 has 4%. To find the stanine corresponding to any percentile, start from stanine 1 and add up the percents included in consecutive stanines until you find the stanine that includes the percentile you are interested in.
Example: 45th percentile 5th stanine (4% + 8% + 12% + 16%). Stanine scores are range scores, not point scores. The percentiles corresponding to stanine 3 are the 12th percentile and the 24th percentile.
NCE (normal curve equivalent) scores have a preset mean of 50 and a standard deviation of 21.06. Scores of NCE’s and percentiles are identical at 1, 50, and 99. The interpretation of scores, however, is very different. Notice that the intervals on the NCE scale are equal. The table below summarizes commonly used standard scores.
Commonly Used Scales
Standard Scores | Mean | Standard Deviation |
T-score | 50 | 10 |
SAT / GRE | 500 | 100 |
Stanine | 5 | 2 |
NCE | 50 | 21.06 |
Commonly Used Standard Scores
Consider when interpreting standard scores
- Converting raw scores to standard scores does not change the meaning of the students’ performance on that test – the conversion simply changes the reporting from one scale to another.
- Interpretations of standard scores depend on the nature of the norm group and the skills measured.
- Precision of a test must be taken into account.
- When using SD’s, make interpretation easier by using descriptive words such as those shown below.
Percentile Rank and NCE Score Intervals, compared with Standard Deviation Units
Oosterhof, (2003) p. 234
Back to Top
Percentile RanksThe percentile rank is the percentage of students in the reference group scoring below a given raw score. If the student’s percentile rank is 80, you know that 80% of the students in the reference group received lower scores. A percentile rank indicates the percentage of scores falling below a certain score. Percentile scores range from 1 to 99. In Figure 4.2, notice that the intervals between scores are not equal. The distance between the 1st and 10th percentile is not the same as the distance between the 40th and the 50th percentile, although the difference in both instances is 10 percentile points. The inconsistent intervals occur because more students achieve middle scores than low or high scores.
Nitko (2003) cautions that percentile ranks should not be interpreted too precisely. To reflect that all scores contain measurement error, publishers will often report percentile bands instead of single scores, which are based on the standard error of measurement. To ensure that scores are interpreted appropriately, the norm referenced group must be clearly defined. Linn and Gronlund (2000, pp. 499-500) provide the following criteria to judge the adequacy of norms: Test norms should be relevant, representative, comparable, and adequately described.
Standard Deviations and PercentilesTo interpret percentiles, several points are worth noting:
- When divided in SD units, the number of cases in each unit is predictable:
34% of the cases fall between the mean and +1 SD
14% fall between +1 SD and +2 SD, and
2% fall between +2 SD and + 3 SD.
- The same percentages apply to the SD’s below the mean.
The following example (Linn & Gronlund, 2000, p. 488) illustrates the value of SD units for indicating relative position in a group (see Figure 4.3).
Figure 4.3 Value of Mean and Standard Deviation (Test A and Test B)
|
- Note that +1 SD equals 60 (56+4) on Test A and 78 (72+6) on Test B. A raw score of 64 on Test A would be + 2 SD from the mean, while a score of 78 on Test B would only be +1 SD from the mean. Therefore, compared to the norm group, the student did much better on Test A than on Test B, although the raw score was lower on Test A. The SD allows us to convert raw scores from different tests to a common scale that can be interpreted in terms of the normal curve.
- 68% of the cases fall within +1 and (–1) SD from the mean.
- The fixed percentages allow us to convert standard deviation units to percentiles. For example, (-2) SD equals to a percentile rank of 2; that is, two percent of the cases fall below this point. Each point on the base line of the figure can be equated to the following percentiles.
(-2) SD = 2%
(-1) SD = 16% (2 + 14)
0 SD = Mean = 50% (16 + 34)
+1 SD = 84% (50 + 34)
+2 SD = 98% (84 + 14)
Example of using NCE scores to calculate NCE Gains
Grade EquivalentsGrade equivalents represent the median test score for a particular grade level, and they represent growth. Scores are reported as a decimal fraction, i.e., (5.6) or (7.3). The whole number represents a grade level. The decimal portion refers to months within the school year and represents relative performance. Grade equivalent scores can be misleading so they should be interpreted with caution.
Scaled ScoresScaled scores are a set of numbers (usually three digits) used across levels of an achievement test and show growth in achievement across grades. Like grade equivalent scores, scaled scores cannot be used to compare performance across content areas. For example: the FCAT-SSS has developmental scaled scores to show growth across grade levels. See //www.firn.edu/doe/sas/fcat/fcat_score/dev_scores.htm.
Back to Top