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Levels of Measurement refers to the numerical qualities associated with the attributes of our variables.

A variable is any characteristic that varies among the sample members. For example, age, sex, race, religion, education, ethnicity are common variables in sociological analyses.
An attribute is a specific characteristic of a sub-set of the same. For example "under 20" is an attribute of age, "male" is an attribute of sex, "African-American" is an attribute of race, "Jewish" is an attribute of religion, "BA/BS" is an attribute of education, "Polish" is an attribute of ethnicity.

The attributes of variables measured at the NOMINAL level are different from each other, but have no other numerical relationship. The attributes merely "name" characteristics. Common examples are race and religion.

The attributes of variables measured at the ORDINAL level are different from each other and can be arrayed along a continuum. The attributes name and order characteristics. Common examples are confidence and satisfaction.

The attributes of variables measured at the INTERVAL level are different from each other and are arrayed along a continuum where the extent of difference between any two attributes is known. Common examples are education and income. The difference between $100 and $200 is the same as the difference between $800 and $900.

The attributes of variables measured at the RATIO level of measurement are different and are arrayed along a continuum which has a true zero point. A true zero point is the point where there is an absence of the quality measured by the variable. An example could be age. There is a point at which an individual did not exist--there can be an absence of age.

For most statistical work in the social sciences, whether the level of measurement is interval or ratio is not important. The tests and techniques we can use with interval data and with ratio data are the same. For the most part, data at the nominal level are analyzed differently from data at the interval/ratio level and interval/ratio statistics are the most powerful and useful. The sticky issue is data measured at the ordinal level--should those data be treated as if they were nominal measures or as if they were interval measures?^*Treating them as nominal measures fails to utilize all the information contained in the measure. Treating them as interval claims a more precise measurement than exists. An example may help illuminate this conundrum:

Age might be measured by the following response possibilities on a survey:
Option 1        Option 2         Option 3
Young           Under 20         How old were you on your
Middle-Age    20-29              last birthday?_____
Old                30-39
                     40-49             Option 4
                     50-59             What is your birth date?____
                     60-69
                     70-79
                     80 or above

Option 1 is definitely an ordinally measured variable. "Old" is more age than "Middle-Age" which is more age than "Young," but it is impossible to specify the interval between the three attributes. Options 2 and 3 are much more precise. At first glance they appear to be interval measures. However, they might also be thought of as ordinal measures because they clump together dissimilar respondents. Two people who checked the "20-29" category might be 21 and 29. Both are definitely older than someone who checked the "under 20" category, but it would be a mistake to assume they were the same extent older. The appearance of an equal interval is due to the crudeness of the option 2 measurement strategy. The same problem exists with option 3--someone whose birthday was yesterday and someone whose birthday is tomorrow might both report they were 26; treating them as if they are equally different from respondents who say they are 29 is a mistake, but this is a small mistake in comparison to that made in the option 2 example. Option 4 is the most precise measure of age, but it requires the researcher to calculate the respondent's age and thus adds to the researcher's workload. (Birth dates may also compromise the anonymity of a respondent unless the sample is quite large and age diverse.)

Option 1 should be treated as a nominally measured variable. Option 4 is an intervally measured variable. Option 3 can easily be treated as an interval measure. Most researchers would probably treat option 2 as an interval measure because interval level statistics are much more powerful than are nominal level statistics.

As is evident from this example, determining the level of measurement is a judgment, not a straight forward decision.
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*There are a large number of tests designed specifically for ordinal measures. For the most part, these are not included in statistical software packages, and they are rarely used in the research literature. For a discussion of these techniques see Sidney Siegel, Non-Parametic Statistics for the Behavioral Sciences (McGraw Hill, 1956).

OVERVIEW OF STATISTICAL THINKING Levels of Measurement

OVERVIEW OF STATISTICAL THINKING
Levels of Measurement