Levels and Scales of Measurement in Statistics

Levels and Scales of Measurement in Statistics Level of measurement refers to the particular way that a variable is measured within scientific research, and  scale of measurement refers to the particular tool that a researcher uses to sort the data in an organized way, depending on the level of measurement that they have selected. Choosing the level and scale of measurement are  important parts of the research design process  because they are necessary for systematized measuring and categorizing of data, and thus for analyzing it and drawing conclusions from it as well that are considered valid. Within science, there are four commonly used levels and scales of measurement: nominal, ordinal, interval, and ratio. These were developed by  psychologist Stanley Smith Stevens, who wrote about them in a 1946 article in  Science, titled On the Theory of Scales of Measurement. Each level of measurement and its corresponding scale is able to measure one or more of the four properties of measurement, which include identity, magnitude, equal intervals, and a minimum value of zero. There is a hierarchy of these different levels of measurement. With the lower levels of measurement (nominal, ordinal), assumptions are typically less restrictive and data analyses are less sensitive. At each level of the hierarchy, the current level includes all the qualities of the one below it in addition to something new. In general, it is desirable to have higher levels of measurement (interval or ratio) rather than a lower one. Let’s examine each level of measurement and its corresponding scale in order from lowest to highest in the hierarchy. The Nominal Level and Scale A nominal scale is used to name the categories within the variables you use in your research. This kind of scale provides no ranking or ordering of values; it simply provides a name for each category within a variable so that you can track them among your data. Which is to say, it satisfies the measurement of identity, and identity alone. Common examples within sociology include the nominal tracking of  sex (male or female),  race  (white, Black, Hispanic, Asian, American Indian, etc.),  and class  (poor, working class, middle class, upper class). Of course, there are many other variables one can measure on a nominal scale. The nominal level of measurement is also known as a categorical measure  and is considered qualitative in nature. When doing statistical research and using this level of measurement, one would use the mode, or the most commonly occurring value, as a  measure of central tendency. The Ordinal Level and Scale Ordinal scales are used when a researcher wants to measure something that is not easily quantified, like feelings or opinions. Within such a scale the different values for a variable are progressively ordered, which is what makes the scale useful and informative. It satisfies both the properties of identity and of magnitude. However, it is important to note that as such a scale is not quantifiable- the precise differences between the variable categories are unknowable. Within sociology, ordinal scales are commonly used to measure peoples views and opinions on social issues,  like racism  and sexism, or how important certain issues are to them in the context of a political election. For example, if a researcher wants to measure the extent to which a population believes that racism is a problem, they could ask a question like How big a problem is racism in our society today? and provide the following response options: its a big problem, it is somewhat a problem, it is a small problem, and racism is not a problem. When using this level and scale of measurement, it is the median which denotes central tendency. The Interval Level and Scale Unlike nominal and ordinal scales, an interval scale is a numeric one that allows for ordering of variables  and provides a precise, quantifiable understanding of the differences between them (the intervals between them). This means that it satisfies the three properties of identity, magnitude,  and  equal intervals. Age is a common variable that sociologists track using an interval scale, like 1, 2, 3, 4, etc. One can also turn non-interval, ordered variable categories into an interval scale to aid  statistical analysis. For example,  it is common to measure income as a range, like $0-$9,999; $10,000-$19,999; $20,000-$29,000, and so on. These ranges can be turned into intervals that reflect the increasing level of income, by using 1 to signal the lowest category, 2 the next, then 3, etc. Interval scales are especially useful because they not only allow for measuring the frequency and percentage of variable categories within our data, they also allow us to calculate the  mean, in addition to the median, mode. Importantly, with the interval level of measurement, one can also calculate  the standard deviation. The Ratio Level and Scale The ratio scale of measurement is nearly the same as the interval scale, however, it differs in that it has an absolute value of zero, and so it is the only scale that satisfies all four properties of measurement. A sociologist would use a ratio scale to measure actual earned income in a given year, not divided into categorical ranges, but ranging from $0 upward. Anything that can be measured from absolute zero can be measured with a ratio scale, like for example the number of children a person has, the  number of elections a person has voted in, or the  number of friends who are of a race different from the respondent. One can run all the statistical operations as can be done with the interval scale, and even more with the ratio scale. In fact, it is so called because one can create ratios and fractions from the data when one uses a ratio level of measurement and scale. Updated  by Nicki Lisa Cole, Ph.D.