Question

What are the different types of Scales? Please explain each and highlight when each can be used and in which case? What are the criteria for good measurement? Explain each.

Answer 1

Statisticians call an attribute on which observations differ a variable. The type of unit on which a variable is measured is called a scale.

There are four types of measurement scales:

(1) nominal scale

(2) ordinal scale

(3) interval scale

(4) ratio scale

1) Nominal Scales:

The word nominal is derived from nomen, the Latin word for name.

Nominal scales merely name differences and are used most often for qualitative variables in which observations are classified into discrete groups. The key attribute for a nominal scale is that there is no inherent quantitative difference among the categories. Sex, religion, and race are three classic nominal scales used in the behavioral sciences. Taxonomic categories (rodent, primate, canine) are nominal scales in biology. Variables on a nominal scale are often called categorical variables.

2) Ordinal Scales :

Ordinal scales rank-order observations. Class rank and horse race results are examples.

There are two salient attributes of an ordinal scale.

First, there is an underlying quantitative measure on which the observations differ. For class rank, this underlying quantitative attribute might be composite grade point average, and for horse race results it would be time to the finish line.

The second attribute is that individual differences individual on the underlying quantitative measure are either unavailable or ignored.

As a result, ranking the horses in a race as 1st, 2nd, 3rd, etc. hides the information about whether the first-place horse won by several lengths or by a nose.

There are a few occasions in which ordinal scales may be preferred to using a quantitative index of the underlying scale. College admission officers, for example, favor Class rank to overcome the problem of the different criteria used by school districts in calculating GPA.

In general, however, measurement of the underlying quantitative dimension is preferred to rank-ordering observations because the resulting scale has greater statistical power than the ordinal scale.

3) Interval Scales :

In ordinal scales, the interval between adjacent values is not constant.

For example, the difference in finishing time between the 1st place horse and the 2nd horse need not the same as that between the 2nd and 3rd place horses. An interval scale has a constant interval but lacks a true 0 point.

As a result, one can add and subtract values on an interval scale, but one cannot multiply or divide units.

Temperature used in day-to-day weather reports is the classic example of an interval scale. The assignment of the number 0 to a particular height in a column of mercury is an arbitrary convenience apparent to everyone anyone familiar with the difference between the Celsius and Fahrenheit scales. As a result, one cannot say that 30^o C is twice as warm as

15⁰C because that statement involved implied multiplication. To convince yourself, translate these two into Fahrenheit and ask whether 86^o F is twice as warm as 50^oF.

4)  Ratio Scales :

A ratio scale has the property of equal intervals but also has a true 0 point.

As a result, one can multiply and divide as well as add and subtract using ratio scales.

Units of time (msec, hours)

distance and length (cm, kilometers)

weight (mg, kilos)

volume (cc) are all ratio scales.

Scales involving division of two ratio scales are also themselves ratio scales.

Hence, rates (miler per hour) and adjusted volumetric measures (mg/dL) are ratio scales. Note that even though a ratio scale has a true 0 point, it is possible that the nature of the variable is such that a value of 0 will never be observed. Human height is measured on a ratio scale but every human has a height greater than 0. Because of the multiplicative property of ratio scales, it is possible to make statements that 60 mg of fluoexetine is three times as great as 20 mg.