How are percentile norms computed?
Even though the norm sample has been carefully selected so that the demographics of each subgroup (e.g., age or grade) match the U.S. population, sampling error still introduces irregularities into the raw-score distribution of each subgroup, and also causes unevenness in the year-to-year progression of scores. A primary objective of norm development is to smooth out the irregularities while preserving the true shapes of the within-year distributions and the age trends. In the most common norming method, the overall sample is first divided into subgroups with enough cases to produce fairly accurate estimates of percentile points. For example, groups for grade norms might correspond to the spring and fall of each grade, while those for age norms might be formed from 3-month, 6-month, or 12-month ranges. Within each subgroup, the raw scores corresponding to selected percentile points are identified. Then, for each percentile point, the across-age or across-grade progression is smoothed t
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