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Levels of Measurement

Nominal, Ordinal, Interval, and Ratio Variables

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Level of measurement refers to the way that a variable is measured. There are four main levels of measurement that variables can have: nominal, ordinal, interval, and ratio. Being familiar with the level of measurement of the variables in your data set is crucial because they will help determine what statistical procedure you use. Not every statistical operation can be used with every variable. The type of procedure used depends on the variables’ level of measurement.

There is a hierarchy implied in the levels of measurement such that that at lower levels of measurement (nominal, ordinal), assumptions are typically less restrictive and data analyses are less sensitive. At each level up 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 in order from lowest to highest on the hierarchy:

Nominal Level Of Measurement

At the nominal level of measurement, variables simply name the attribute it is measuring and no ranking is present. For example, gender is a nominal variable because we classify the observations into the categories "male" and "female." Because the different categories (for instance, males and females) vary in quality but not quantity, nominal variables are often called qualitative variables. An important feature of nominal variables is that there is no hierarchy or ranking to the categories. For instance, males are not ranked higher than females or vice versa – there is no order or rank, just different names assigned to each.

Other examples of nominal variables include political party, religion, marital status, and race. Nominal variables are also commonly referred to as categorical variables.

Ordinal Level Of Measurement

Variables that have an ordinal level of measurement can be rank-ordered. For example, social class is an ordinal variable because we can say that a person in the category "upper class" has a higher class position than a person in a “middle class” category, which again is higher than "lower class."

In ordinal variables, the distance between categories does not have any meaning. For example, we don’t know how much higher "upper class" is to "middle class" or "lower class." All we know is the order of the categories, but the interval between values is not interpretable.

Other examples of ordinal variables include education level (less than high school, high school degree, some college, etc.) and letter grades (A, B, C, D, F).

Interval Level Of Measurement

In interval measurement, the distance between the attributes, or categories, does have meaning. For example, temperature is an interval variable because the distance between 30 and 40 degrees Fahrenheit is the same as the distance between 70 and 80 degrees Fahrenheit. The interval between the values is interpretable. For this reason, it makes sense to compute averages, or means, of interval variables, where it doesn’t make sense to do so for ordinal variables. With interval variables, however, ratios do not make sense. That is, 80 degrees Fahrenheit is not twice as hot as 40 degrees Fahrenheit, even though the attribute value is twice as large.

Ratio Level Of Measurement

Variables that are measured at the ratio level are similar to interval variables, however they have an absolute zero that is meaningful (i.e. no numbers exist below zero). That is, you can construct a meaningful ratio, or fraction, with a ratio variable.

Height and weight are both examples of ratio variables. If you are measuring a person’s height in inches, there is quantity, equal units, and the measurement cannot go below zero inches. A negative height is not possible.

References

Frankfort-Nachmias, C. & Leon-Guerrero, A. (2006). Social Statistics for a Diverse Society. Thousand Oaks, CA: Pine Forge Press.

Trochim, W. M. K. (2006). Levels of Measurement. Research Methods Knowledge Base. http://www.socialresearchmethods.net/kb/measlevl.php

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