Information about Percentile Rank
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 85% of the scores of people taking the test is said to be at the 85th 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).
Percentile ranks (PRs or "percentiles") compared to Normal curve equivalents (NCEs)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). References Crocker, L., & Algina, J. (1986). Introduction to classical and modern test theory. New York: Harcourt Brace Jovanovich College Publishers.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
where
is the cumulative frequency for all scores lower than the score of interest, 
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.
Percentile ranks (PRs or "percentiles") compared to Normal curve equivalents (NCEs)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). References Crocker, L., & Algina, J. (1986). Introduction to classical and modern test theory. New York: Harcourt Brace Jovanovich College Publishers.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
where
is the cumulative frequency for all scores lower than the score of interest, 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.
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Percentile ranks (PRs or "percentiles") compared to Normal curve equivalents (NCEs)
References
Crocker, L., & Algina, J. (1986). Introduction to classical and modern test theory. New York: Harcourt Brace Jovanovich College Publishers. In statistics, a frequency distribution is a list of the values that a variable takes in a sample. It is usually a list, ordered by quantity, showing the number of times each value appears.
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A standardized test is a test administered and scored in a standard manner. The tests are designed in such a way that the "questions, conditions for administering, scoring procedures, and interpretations are consistent" [1]
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normal distribution, also called the Gaussian distribution, is an important family of continuous probability distributions, applicable in many fields. Each member of the family may be defined by two parameters, location and scale: the mean ("average",
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standard score, also called the z-score or normal score, is a dimensionless quantity derived by subtracting the population mean from an individual raw score and then dividing the difference by the population standard deviation.
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