Statistical Inference: A Short Course

1.4 Measurement Scales

We previously referred to data² as “information,” that is, as a collection of facts, values, or observations. Suppose then that our data set consists of observations that can be “measured” (e.g., classified, ordered, or quantified). At what level does the measurement take place? In particular, what are the “forms” in which data are found or the “scales” on which data are measured? These scales, offered in terms of increasing information content, are classified as nominal, ordinal, interval, and ratio.

1. Nominal Scale: Nominal should be associated with the word “name” since this scale identifies categories. Observations on a nominal scale possess neither numerical value nor order. A variable whose values appear on a nominal scale is termed qualitative or categorical. For example, a variable X depicting the sex of an individual (male or female) is nominal in nature as are variables depicting religion, political affiliation, occupation, marital status, color, and so on. Clearly, nominal values cannot be ranked or ordered—all items are treated equally. The only valid operations for variables treated on a nominal scale are the determination of “=” or “≠.” For nominal data, any statistical analysis is limited and usually relegated to the calculation of percentages.

2. Ordinal Scale: (think of the word “order”) Includes all properties of the nominal scale with the additional property that the observations can be ranked from the “least important” to the “most ...