# Percentile rank

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The percentile rank of a score is the percentage of scores in its frequency distribution which are lower. For example, a test score which is greater than 90% of the scores of people taking the test is said to be at the 90th percentile.

Percentile ranks are commonly used to clarify the interpretation of scores on standardized tests. For the test theory, the percentile rank of a raw score is interpreted as the percentages of examinees in the norm group who scored below the score of interest (Crocker & Algina, 1986). The mathematical formula is

$\frac{cf_l +.5(f_i)}{N} \times {100\%}$

where ${cf_l}$ is the cumulative frequency for all scores lower than the score of interest, ${f_i}$ is the frequency of the score of interest, and N is the number of examinees in the sample. If the distribution is normally distributed, the percentile rank can be inferred from the standard score.

Unlike a normal distribution of scores, which are bell shaped, the distribution of percentile ranks is uniform and is rectangular in shape. Percentile rank is not an equal-interval scale; that is, the difference between any two scores is not the same between any other two scores. For example, 50 - 25 = 25 is not the same distance as 60 - 35 = 25 because of the bell-curve shape of the distribution. Some percentile ranks are closer to some than others. Percentile rank 30 is closer on the bell curve to 40 than it is to 20 (see [1] and [2] for examples).

## ReferencesEdit

Crocker, L., & Algina, J. (1986). Introduction to classical and modern test theory. New York: Harcourt Brace Jovanovich College Publishers.

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