 Percentiles

Percentiles have been mentioned in passing in other articles on this site, but since numerical information is often presented in percentile form they deserve an article of their own. So here it is.

Percentiles are simply statements of the percentage of scores lower than a specific score. For example, if you score 60 on a test, and are told that that score puts you at the fiftieth percentile, that means that 50% of the people taking the test scored lower than 60. In standardized testing, the percentile score is the percentage of a norm group who scored lower than your score. If you score at the fiftieth percentile on a standardized test, that means that 50% of the sample used to set norms for the test scored lower than you.

The article on testing notes that usually differences in percentile scores mean less the closer you get to the average score. For example, in a normal (or bell curve) distribution of scores the difference between the 80th and the 85th percentiles is about half again as large as the difference between the 50th and 55th percentiles. The reason for the disparity is that in a normal distribution scores cluster towards the centre.

While this disparity can be a drawback, it has an advantage as well. It can clarify the importance of other types of score. For example, if information is presented both as standard scores and as percentiles, you get information from the standard scores about the size of differences between scores, and from the percentiles about their probability. Since the assessment of probability is what analysis is all about, this characteristic can be very helpful. For example, the article on effect size shows how it can be used to evaluate effect sizes.