A ranked distribution is one using an ordinal scale of measurement, even if the distribution was not originally ranked. Thus, in such distribution, scores are ranked in order of importance, but any differences between successive scores is not relevant any longer.
A good example of a ranked distribution is when school children are asked to line up according to height. The resulting line will show in increase in relative height as we move from the shortest to the tallest child, but the height difference between children do not affect the overall length of the line (which is the number of children in the distribution).
1.10 1.11 1.12 1.15 1.19 1.20 1.30
- Ranked distributions are more robust than other distributions, meaning that they are less affected by extreme cases. This is so because the length of the distribution is not affected by the value of each score.
- Ranked distributions do not have kurtosis. Indeed, if represented graphically, they would look like a flat box, as each case in the distribution contribute the same amount of information: its relative standing between the immediately lower and higher score.
- The most appropriate statistics to use with these distributions are non-parametric statistics for ordinal variables, such as the median, interquartile range, Mann-Whitney-U-tests, etc. In any case, even if using parametric statistics, these would be giving non-parametric results, as the data is artificially constrained to an ordinal level of measurement.
Want to know more?
- Wikipedia - Level of measurement
- You can learn a bit more about levels of measurement in Wikipedia.