1. Older forms of CTB's tests yielded less than the 99th percentile for a student who got all questions correct. Is that the case with TerraNova?"
This is not an issue with TerraNova; perfect scores will yield the 99th percentiles. This is an issue only for older tests, like the CTBS/4 and CAT/5, and tests from other publishers. Our newest achievement tests--TerraNova and TerraNova, The Second Edition--were developed and scaled using advanced statistical models that ensure that students with perfect scores receive national percentiles of 99.
As the following chart illustrates, perfect scores on TerraNova and TerraNova, The Second Edition would result in scale scores that are actually higher than the scale score required for a national percentile of 99. Because of this, our score reports for TerraNova and TerraNova, The Second Edition show the national percentiles for students with perfect scores as 99* (with the * referring to a footnote that the student has achieved a perfect score). This is because it is possible for students with less than perfect scores (e.g., answering one or two items incorrectly) to also achieve a national percentile of 99. (All data are from the TerraNova Spring Norms Book, for Complete Battery. Scale scores associated with perfect scores are the same for the Multiple Assessments and Survey editions.)
| ý | Reading | Language | Mathematics | Science | Social ýStudies |
| Grade 2 Perfect Number Correct Score | 32 | 28 | 47 | 25 | 25 |
| Grade 2 Scale Score for Perfect Number Correct Score | 722 | 706 | 720 | 743 | 720 |
| Grade 2 Scales Score required for National Percentile of 99 | 696 | 699 | 665 | 701 | 709 |
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| Grade 4 Perfect Number Correct Score | 50 | 30 | 57 | 40 | 40 |
| Grade 4 Scale Score for Perfect Number Correct Score | 780 | 757 | 770 | 799 | 763 |
| Grade 4 Scales Score required for National Percentile of 99 | 734 | 724 | 711 | 723 | 735 |
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| Grade 6 Perfect Number Correct Score | 42 | 38 | 56 | 40 | 40 |
| Grade 6 Scale Score for Perfect Number Correct Score | 800 | 808 | 820 | 833 | 786 |
| Grade 6 Scales Score required for National Percentile of 99 | 746 | 748 | 757 | 755 | 752 |
When considering this issue for our older tests and some of other publishers' tests, several things need to be considered when interpreting a perfect score on a standardized achievement test. First of all, a perfect score may not be an accurate measure of a student's true level of achievement. It is likely that a higher level of the test, one with a higher ceiling, would provide a better picture of the student's true achievement level. For this reason, CTB and other agencies such as the Chapter 1 Technical Assistance Centers, advocate use of testing with those students who fall outside the normal range of the test--that is, neither too easy nor too difficult for the examinee but within the achievement range at which the student is functioning.
Secondly, it must be understood that in virtually all standardized achievement test sections there is a relatively small number of items. Thus, it is impossible to have a Raw Score--or Number Correct Score--for each of the 99 points on the National Percentile Scale. On a test section with 25 items, for example, each Number Correct Score must represent an average of about 4 points on the Percentile Scale.
Thirdly, on such test sections--especially those measuring skills in the lower grades during which growth is generally quite rapid--it is not unusual for a substantial number of students in the standardization population, as well as in an average group of examinees, to obtain perfect scores. When this occurs, there are three possible approaches to assigning a National Percentile Rank or score to a perfect score. For example, if 20 students out of 100 make a perfect score, such a score could be assigned a Percentile Rank of anywhere between 80 and 99. One approach would be to assign the lowest score in the possible range of Percentiles (80); another would be to assign the highest possible Percentile (99); and still a third would be to assign the Percentile that is in the middle of the range (90). The last is the practice followed by CTB/McGraw-Hill: we believe that to assign the lowest or highest Percentile would tend to understate or overstate the student's true level of achievement. The middle score seems to be a better description of what a perfect score means in such an instance.
There is no one way to assign Percentile Ranks to perfect scores. CTB believes its practice is reasonable. In order to reduce the confusion that can arise from this situation, we flag such scores on our scoring reports with an asterisk and a footnote to the effect that the maximum possible score was obtained.
CTB's method follows the standard textbook procedure that is also the most common practice among test development specialists. Specifically, using this methodology the Percentile Rank for any given obtained score is calculated as the percent of the distribution with lower scores, plus one-half of the percent receiving that score. If, as noted in the example given above, 80 percent of the students in the group have scores that are less than perfect and 20 percent have perfect scores, a perfect score would be assigned a Percentile Rank of 90 (80+10).
Those wishing a detailed explanation of this method of calculating Percentile Ranks are referred to: Guliksen, Harold (1950), Theory of Mental Tests, (New York: Wiley and Sons). This standard text was reprinted most recently in 1961 and is still widely used.
