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Scales of Measurement with Examples

A basic understanding of scales of measurement is essential in order to know something about presenting, interpreting and analyzing data. What a scale actually means depends on what its numbers represent Numbers can be grouped into 4 types or levels nominal, ordinal, interval, and ratio The scales are distinguished on the relationships assumed to exist between objects having different scale values. The four scale types are ordered in that all later scales have all the properties of earlier scales plus additional properties.

Categorical or qualitative variables tend to be reported in nominal and ordinal scales and Quantitative variables are reported in interval or ratio scales

Nominal Scales-

Not really a ‘scale’ because it does not scale objects along any dimension, It simply labels objects. Categorical data are measured on nominal scales which merely assign labels to distinguish categories.

Nominal is hardly measurement. It refers to quality more than quantity A nominal level of measurement is simply a matter of distinguishing by name, E.g., 1= male, 2 = female. Even though we are using the numbers 1 and 2, they do not denote quantity. The binary category of 0 and 1 used for computers is a nominal level of measurement. They are categories or classifications. Nominal measurement is like using categorical levels of variables,

Nominal basically refers to categorically discrete data such as name of your school, type of car one drive or name of a book. This one is easy to remember because nominal sounds like name.

In nominal measurement the numerical values just “name” the attribute uniquely. A nominal scale tells you to which group a unit/individual belongs. A nominal scale can be used to categorize. For example, gender can be categorized as male or female and religion can be categorized as Jewish, Muslim, Christian, Buddhist, and ‘other’. Sometimes a numerical code is assigned to nominal variables (e.g. 1 = female, 2 = male) but the code does not imply order.

Ordinal Scales-

Ordinal refers to order in measurement. In ordinal measurement the attributes can be rank-ordered. Here, distances between attributes do not have any meaning Ordinal refers to quantities that have a natural ordering. For example, we often use rating scales (Likert questions).

This is also an easy one to remember, ordinal sounds like order. An ordinal scale indicates direction, in addition to providing nominal information. Low/Medium/High; or Faster/Slower are examples of ordinal levels of measurement.” Many psychological scales or inventories are at the ordinal level of measurement.

An ordinal scale extends the information of a nominal scale to show order, i.e. that one unit has more of a certain characteristic than another unit. For example, an ordinal scale can be used-(i) to rank job applicants from the best to the worst, (ii) to categorize people according to their level of education, or (iii) to measure people’s feelings about some matter using a measure like ‘strongly agree’, ‘agree’, ‘neutral’, ‘disagree’, ‘strongly disagree

Interval Scales-

An interval scale is a scale on which equal intervals between objects, represent equal differences.

Interval scales provide information about order, and also possess equal intervals. Equal-interval scales of measurement can be devised for opinions and attitudes. Constructing them involves an understanding of mathematical and statistical principles. But it is important to understand the different levels of measurement when using and interpreting scales.

Interval data is like ordinal except we can say the intervals between each value are equally split. The most common example is temperature in degrees Fahrenheit. The difference between 29 and 30 degrees is the same magnitude as the difference between 78 and 79. With attitudinal scales and the Likert questions, are rarely interval, although many points on the scale likely are of equal intervals.

Interval scales are not simply ordinal. They give a deeper meaning to order. An interval scale is a scale of measurement in which the magnitude of difference between measurements of any two units is meaningful. If weights are measured in kilograms (kg), then the difference in weights between two people whose weights are respectively 82 kg and 69 kg is the same as that between people whose respective weights are 64 kg and 51 kg. That is, the ‘intervals’ are the same (13 kg) and have the same meaning. Further, someone who weighs 100 kilograms is twice as heavy as someone who weighs 50 kilograms. Consequently, most interval scales are also meaningful on a ratio scale.

Ratio Scales-

A ratio scale is a special form of interval scale that has a true zero. For some interval scales, measurement ratios are not meaningful. For example, 40° C does not represent a temperature which has twice the heat of 20° C because the zero on the Celsius scale is arbitrary, and does not represent an absence of heat. However, when we consider the metric system for temperature (known as ‘degrees Kelvin’), then there is a true zero (called “absolute zero’). Therefore, a measure of 40K (i.e. 40 degrees Kelvin) is twice as hot as 20K.

Finally, in ratio measurement there is always an absolute zero that is meaningful. This means that you can construct a meaningful fraction (or ratio) with a ratio variable. Weight is a ratio variable. In addition to possessing the qualities of nominal, ordinal, and interval scales, a ratio scale has an absolute zero (a point where none of the quality being measured exists) Ratio data is interval data with a natural zero point. Using a ratio scale permits comparisons such as being twice as high, or one-half as much. Reaction time (how long it takes to respond to a signal of some sort) uses a ratio scale of measurement time. Although an individual’s reaction time is always greater than zero, we conceptualize a zero point in time, and can state that a response of 24 milliseconds is twice as fast as a response time of 48 milliseconds.

Scales of Measurement with Examples

Nominal Scales-

Ordinal Scales-

Interval Scales-

Ratio Scales-

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