Norm-Referenced Interpretation

Raw Scores

[Page 1161]Raw scores (i.e., the number of items answered correctly) are the main method of reporting results of criterion-referenced tests and are also provided on norm-referenced test reports. However, these scores are not very useful when interpreting test results for purposes of norm-referenced comparisons. Often, educators need to know how a particular student’s raw score compares to the specific norm group. In order to make these comparisons, raw scores must be converted to another scale. These new scales are referred to as transformed or derived scores and include percentile ranks, Z scores, T scores, stanines, normal curve equivalent (NCE) scores, and deviation IQ scores.

Percentile Ranks

A percentile rank is a single number that indicates the percentage of the norm group that scored below a given raw score. Percentile ranks range from 1 to 99. However, because percentile ranks indicate percentages of individuals above and below scores that are normally distributed, they do not represent equal units. Percentile ranks are more compactly arranged in the middle of the normal distribution because that is where the majority of individuals fall.

Consider a hypothetical test report for a student, Emma. Let us assume that Emma correctly answered 34 out of a possible 45 items on a reading subtest. When converted, this raw score converts to a percentile rank of 86. This means that Emma scored higher than 86% of the other students (in the norm group) who took the test. In other words, 86% of those students answered fewer than 34 items correctly.

Developmental/Growth Scores

Developmental scales indicate a student’s development across various levels (e.g., grade or age) of growth. Their purpose is to compare a student’s performance to a series of reference groups that vary with respect to developmental growth.

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