Stevens’ measurement scales in marketing research – A continuation of discussion on whether researchers can ignore the Likert scale’s limitations as an ordinal scale

Z = f(x), where f(x) is a mutually unique function.

Relations x_a = x_b, x_a ≠ x_b.

Counting events (number of relations of equality and difference)

A variable is on a nominal scale when it takes on values (labels) for which there is no inherent order resulting from the nature of the phenomenon.

Even if the values of a nominal variable are expressed numerically, these numbers are only conventional identifiers, so arithmetic operations cannot be performed on them and they cannot be compared. Examples: city names, eye color, gender, marital status, a series of “yes/no” answers.

Z = f(x), where f(x) is any monotonically increasing function.

Relations x_a = x_b, x_a ≠ x_b and relations x_a > x_b, x_a < x_b.

Counting events (number of relations of equality and difference, majority and minority)

As above, plus quantiles (in particular the median (Me), as well as quartiles (Q1, Q3), deciles (D1, D2, …), percentiles (P1, P2, …)).

As above, plus the Mann-Whitney test, Kruskal-Wallis test, Spearman’s rho, Kendall’s tau.

A variable is on an ordinal scale when it takes values for which an order is given, but the difference or ratio between two values cannot be meaningfully determined.

Examples: military ranks, boxing weight classes, the Beaufort scale of wind speed, education levels, customer attitudes.

Z = bx + a (b > 0), z ∈ R for all x contained in R, zero on the scale is arbitrary.

The relations from nominal and ordinal scales, plus equality of differences and intervals (x_a - x_b = x_c - x_d).

The above operations plus addition and subtraction.

As above plus the arithmetic mean (¯x ∙ X¯X or M), standard deviation (S or STD), variance (S²), coefficient of variation (VS), coefficient of skewness (WS), and kurtosis (K).

As above plus Student’s t-test, ANOVA, Pearson’s correlation coefficient (r)

A variable is on an interval scale when the differences between two of its values can be calculated and have an interpretation in the real world, but it does not make sense to divide two values of a variable by each other.

In other words, the unit of measurement is specified, but the zero point is chosen conventionally.

Examples: temperature in degrees Celsius, date of birth, financial gains/losses.

Z = bx + a (b > 0), z ∈ R for all x contained in R, zero on the scale is absolute, it limits the scale range on the left side.

The relations from the above scales, plus equalities of quotients x_a / x_b = x_c / x_d. The above operations plus multiplication and division.

A variable is on a ratio scale when the relations between its two values have an interpretation in the real world. There is a “natural”, absolute zero. The ratio scale, unlike the weaker scales, does not impose restrictions on the use of mathematical operations and statistical methods. However, unlike an absolute scale, the nature of the phenomenon does not result in a natural unit of measurement.

Examples: temperature in degrees Kelvin, age, weight, income, production value.