Lesson 1.2: Terminologies and Scales of Measurement

The scales of measurement in statistics

Refer to the methods used to classify variables based on how their values can be named, ordered, compared, or measured.

NOMINAL

is the simplest level of measurement. It groups observations into named categories that are mutually exclusive and exhaustive. There is no implied ranking, no sense in which one category is greater or lesser than another, and no arithmetic relationship between categories

NOMINAL

Key properties:

Categories are labels only; no order exists.

The only permitted measure of central tendency is the mode.

The only arithmetic operation is counting (frequency).

Percentages can be calculated across categories

ORDINAL

adds a meaningful order to the categories of the nominal scale. However, the distances between adjacent ranks are not guaranteed to be equal or even measurable. Knowing that one observation ranks higher than another tells you nothing about how much higher.

ORDINAL

Categories can be ranked from lowest to highest (or vice versa).

Intervals between ranks are not assumed to be equal. Permitted statistics include the median, mode, percentiles, and the interquartile range.

The mean is technically not valid, though it is widely used in practice (see Common Errors section).

INTERVAL

has all the properties of the ordinal scale, with the additional feature that the distances between consecutive points are equal and meaningful. A difference of 10 units means the same thing at any point on the scale. However, the interval scale lacks a true zero point: zero does not mean the absence of the measured attribute.

INTERVAL

Equal, measurable distances between all points.

No true zero; zero is an arbitrary reference point.

Addition and subtraction are meaningful; multiplication and division of the values themselves are not.

Permitted statistics include the mean, median, mode, standard deviation, variance, and Pearson correlation.

RATIO

is the highest level of measurement. It has all the properties of the interval scale and additionally has a true zero point, meaning that zero represents the complete absence of the quantity being measured. Because of this, ratio comparisons (twice as much, half as many) are valid and meaningful.

RATIO

Equal, measurable distances between all points.

A true zero that represents the absence of the measured attribute.

All arithmetic operations (addition, subtraction, multiplication, division) are valid.

All descriptive statistics are permitted, including ratios, proportions, geometric means, and the coefficient of variation.

Level of measurement

The classification system that describes the nature of data values and the mathematical operations that can legitimately be performed on them

Nominal Scale

A scale that groups data into named categories with no inherent order

Ordinal Scale

A scale that ranks categories in a meaningful order, but with unequal or unknown distances between ranks

Interval Scale

A scale with equal, measurable distances between values but no true zero point

Ratio Scale

A scale with equal distances between values and a true zero point, enabling ratio comparisons

True Zero

A zero value that indicates the complete absence of the measured attribute, not merely an arbitrary reference point.

Stevens’ Typology

The four-level classification of measurement scales proposed by psychologist Stanley Smith Stevens in 1946.