standardized test scores

Many of the terms used in describing scores on standardized tests, such as stanine and percentile, are used in two senses. Statisticians use them to refer to points dividing the scores into groups, but counsellors often often use the words to describe the group rather than its boundaries, e.g., “Johnny is in the fifth stanine.”

Because scores on standardized tests depend on comparing an individual's score with the scores of a large group of test-takers, it is important to know what group is being used for the comparison.  For example, if Johnny scored in the fifth stanine, is that in relation to everyone who took the test in his school, in the community, in the state, or nationally? He might be in the ninth stanine locally and the fifth nationally.

In grading many standardized tests, the raw scores are normalized: points are added to or subtracted from the raw scores, according to the size of the score, until their distribution fits a symmetrical, bell-shaped curve.  For scores expressed in stanines, normalizing will put 4% of the testees in the first stanine, 7% in the second, and so on through 12%, 17%, 20%, 17%, 12%, 7%, and 4%. Having the scores fit a normal curve is very convenient for statistical purposes, but it assumes that whatever ability the test measures is evenly distributed around a central peak, which is questionable.

Interpreting Scores
Median The median score divides the group in half, with as many scores below the median as above it.  The median is probably not the arithmetic average (the mean) of all the scores.  For example, the average of the set of scores 2,4,4,9 and 9 is 5.6, but the median score is 4.
Quartile The three points that divide the scores into four groups, each with the same number of test takers. Interpreted as a group, the first quartile contains the lowest 25% of the scores.
Stanine The raw scores are normalized and placed on a scale with 9 intervals.  The median falls in stanine 5. It is thought that the difference in ability between the students in any two adjacent stanines will be about the same, that is, a student in stanine 7 differs from a student in stanine 8 about as much as a student in stanine 3 differs from a student in stanine 4.
Scores are normalized as for stanines but instead of being sorted into 9 groups they are sorted into 99, which gives a more precise picture of the test-taker's relative standing than a stanine would. The raw scores are processed so that the median score falls in the 50th percentile rank. If a raw score of 88 puts the testee in the 65th percentile, 65% of the raw scores were below 88.
When a third-grader gets a grade equivalent score of 5.3 on a third-grade math test, it does not mean the student has mastered any fifth-grade math; it means that the student's score is what the average 5th grader would score on this test for third-graders.
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