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The concept of levels of measurement, proposed by S. S. Stevens, categorizes the assignment of scores to individuals based on the type of quantitative information conveyed about a variable. There are four distinct levels: nominal, ordinal, interval, and ratio. These levels are significant for two main reasons. First, they emphasize the broad generality of measurement itself, illustrating that even categorizing or ranking individuals qualifies as measurement provided it represents a specific characteristic of the individuals. Second, they serve as a practical guide for determining which statistical procedures are appropriate to use with the collected data and what conclusions can be drawn.

Levels of Measurement

S. S. Stevens was a psychologist who introduced the widely used framework of the four levels of measurement: nominal, ordinal, interval, and ratio. In 1946, he proposed that scores assigned to individuals can communicate varying amounts of quantitative information about a given variable. His conceptualization emphasizes the generality of measurement and serves as a fundamental guide for determining which statistical procedures are appropriate for different types of data.

S. S. Stevens

The nominal level of measurement is the lowest level of measurement, used for categorical variables. It involves assigning scores that function simply as category labels, communicating only whether any two individuals are the same or different regarding the measured variable. Responses are merely categorized without implying any inherent order or ranking among them, such as classifying individuals by their marital status or favorite color. For this level of measurement, the only available measure of central tendency is the mode.

Nominal Level of Measurement

The ordinal level of measurement involves assigning scores that represent the rank order of individuals on a given variable. This level communicates not only whether individuals differ, but also whether one is higher or lower than another, such as ranking runners in a race or rating satisfaction from least to most. However, ordinal scales do not assume that the differences between adjacent scale values are equal; they only provide the sequence or order of responses. For ordinal-level measurement, the median or mode can be used as indicators of central tendency.

Ordinal Level of Measurement

The interval level of measurement involves assigning scores on a numerical scale where the intervals between values have the same consistent interpretation throughout. For instance, the difference between $$30$$ and $$40$$ degrees Fahrenheit represents the same amount of temperature change as between $$80$$ and $$90$$ degrees. In psychology, the intelligence quotient (IQ) is measured at the interval level; the difference between IQ scores of $$80$$ and $$100$$ is the same as between $$120$$ and $$140$$. However, interval scales lack a true zero point that indicates the complete absence of the measured quantity, meaning it is not meaningful to compute ratios of these scores. Furthermore, interval-level measurement permits any indicators of central tendency to be computed, including the mean, median, or mode.

Interval Level of Measurement

The ratio level of measurement is the highest level of measurement, encompassing all properties of nominal, ordinal, and interval scales, with the addition of a true zero point. This true zero represents the complete absence of the measured quantity, such as zero Kelvin indicating no kinetic energy, or zero money indicating no money. Because of the true zero, it allows for meaningful statements about the ratios of scores. For example, while one cannot say someone with an IQ of $$140$$ is twice as intelligent as someone with an IQ of $$70$$ because IQ is an interval scale, one can say that someone with $$6$$ siblings has twice as many as someone with $$3$$ because the number of siblings is measured at the ratio level. Additionally, ratio-level measurement permits any indicators of central tendency to be computed, including the mean, median, or mode.

Ratio Level of Measurement

Based on S. S. Stevens's concept of levels of measurement, what is one of the main practical reasons for categorizing variables into nominal, ordinal, interval, or ratio levels?

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