One reason that it's important to recognize levels of measurement is that different measurement scales are amenable to different analytical operations (Chrisman 2002). Some of the most common operations include:
- Group: Categories of nominal and ordinal data can be grouped into fewer categories. For instance, grouping can be used to reduce the number of land use/land cover classes from, say, four (residential, commercial, industrial, parks) to one (urban).
- Isolate: One or more categories of nominal, ordinal, interval, or ratio data can be selected, and others set aside. As a hypothetical example, consider a range of georeferenced soil moisture readings taken over a farm field. A subrange of readings that are amenable to a particular fertilizer or pesticide might be isolated so that application is limited to the appropriate areas of the field.
- Cross tab: Two or more sets of nominal or ordinal categories can be associated one to another in pairs, triplets, etc. Chrisman (2002) points to the multicharacter codes used in the National Wetland Inventory as an example of a cross tab. Each position in the NWI code represents a particular attribute. Each unique code, therefore, represents a cross tabulation of the possible combinations of attributes.
- Difference: The difference of two interval level observations (such as two calendar years) results in one ratio level observation (such as one age).
- Other arithmetic operations: Two or more compatible sets of ratio or interval level data can be added, subtracted, multiplied, or divided. For example, the per capita (average) income of a census tract can be calculated by dividing the sum of the income of every individual in a census tract (a ratio level variable) by the sum of persons residing in the tract (a second ratio level variable).
- Classification: Interval and ratio data are frequently sorted into ordinal level categories for thematic mapping.
Registered Penn State students should return now to the Chapter 3 section of the Modules page in Canvas to take a self-assessment quiz about Levels and Operations. You may take practice quizzes as many times as you wish. They are not scored and do not affect your grade in any way.