13.2 : Ranks

Unlike parametric methods, nonparametric statistics are ideal for nominal and ordinal data, requiring fewer assumptions about the population's nature or distribution. This makes nonparametric methods easier to apply and interpret, as they do not depend on parameters like mean or standard deviation. One common approach in nonparametric analysis is to sort data according to a specific criterion. For instance, we might arrange weather data from hottest to coldest days in a month or rank cities from smallest to largest in population.

Once the data is ordered, each item is assigned a rank based on its position. For example, we could rank actors by their number of Oscar wins, with the actor with the most wins given rank one, the next highest rank two, and so forth. If two actors have the same number of wins, the tie is resolved by averaging their ranks and assigning the mean rank to each tied actor. Rankings like these are commonly used in statistical tests, such as rank correlation and signed-rank tests, to assess relationships or differences without relying on interval or ratio-scale data.