Level of measurement

Level of measurement refers to the different ways in which variables or numbers can be classified and used in statistical analysis. The concept was introduced by psychologist Stanley Smith Stevens in 1946. Stevens proposed that measurements can be classified into four scales: nominal, ordinal, interval, and ratio, each with increasing levels of complexity and mathematical precision.

Nominal Scale

The nominal scale classifies data into distinct categories within which no order or ranking can be inferred. It is the simplest level of measurement, where data can only be categorized and counted. Examples include gender, nationality, or the presence of a condition in medical diagnosis. In this scale, mathematical operations are limited to counting and mode determination.

Ordinal Scale

The ordinal scale provides a ranking or ordering of values, but the intervals between these values are not necessarily equal or known. It is often used in surveys and questionnaires, where responses range from "very satisfied" to "very unsatisfied". While it allows for greater mathematical manipulation than the nominal scale, operations such as addition or subtraction are not meaningful because the distances between ranks are not uniform.

Interval Scale

The interval scale offers not only rankings but also equally spaced intervals between values. This scale does not have a true zero point; thus, ratios of numbers are not meaningful. Temperature measurements in Celsius or Fahrenheit are common examples. The interval scale allows for a wide range of mathematical operations, including addition, subtraction, and the calculation of means and variances.

Ratio Scale

The ratio scale possesses all the properties of the interval scale, with the addition of a true zero point, making ratios of numbers meaningful. Examples include weight, height, and age. This scale allows for the full range of mathematical operations, including meaningful calculations of ratios and geometric means.

Importance in Research and Statistics

The level of measurement determines the statistical tests that can be used on the data and the conclusions that can be drawn from it. For example, nominal and ordinal data are often analyzed using non-parametric tests, while interval and ratio data are suitable for parametric tests. Understanding the level of measurement is crucial for selecting the appropriate statistical technique and for the accurate interpretation of results.

See Also

• Statistics
• Data Analysis
• Stanley Smith Stevens
• Measurement

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