Normalizing Data

Abstract

We often want to compare scores or sets of scores obtained on different scales. For example, how do we compare a score of 85 in a cooking contest with a score of 100 on an I.Q. test? In order to do so, we need to “eliminate” the unit of measurement, this operation is called to normalize the data. There are two main types of normalization. The first first type of normalization originates from linear algebra and treats the data as a vector in a multidimensional space. In this context, to normalize the data is to transform the data vector into a new vector whose norm (i.e., length) is equal to one. The second type of normalization originates from statistics, and eliminates the unit of measurement by transforming the data into new scores with a mean of 0 and a standard deviation of 1. These transformed scores are known as Z-scores.