Question

Why are measures of relative standing (e.g.. percentiles, percentile ranks, and standard scores) important?

Answer 1

Measures of relative standing, which are numbers showing the location of data values relative to the other values within a data set, can be used to compare values from different data sets, or to compare values within the same data set.

A percentile indicates the relative standing of a data value when data are sorted into numerical order, from smallest to largest. p % of data values are less than or equal to the p ^thpercentile.Percentiles are measures of location. There are 99 percentiles denoted P1, P2, . . . P99, which divide a set of data into 100 groups with about 1% of the values in each group.

The percentile rank of a score is the percentage of scores in its frequency distribution that are equal to or lower than it. For example, a test score that is greater than 75% of the scores of people taking the test is said to be at the 75th percentile, where 75 is the percentile rank. In educational measurement, a range of percentile ranks, often appearing on a score report, shows the range within which the test taker’s “true” percentile rank probably occurs. The “true” value refers to the rank the test taker would obtain if there were no random errors involved in the testing process. ^[1]

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 at or below the score of interest

The major purpose of standard scores is to place scores for any individual on any variable having any mean and standard deviation on the same standard scale so that comparisons can be made. Without some standard scale, comparisons across individuals and/or across variables would be difficult to make. In other words, a standard score is another way to compare a student's performance to that of the standardization sample. A standard score (or scaled score) is calculated by taking the raw score and transforming it to a common scale. A standard score is based on a normal distribution with a mean and a standard deviation. The black line at the center of the distribution represents the mean. The turquoise lines represent standard deviations.