STATISTICAL BRIEFING: MEASUREMENT SCALES

Measurements are made to describe observations and to enable statistical analysis of results. The measurements that we make exist in scales that reflect the variable being studied. Scales can be classified as categorical or continuous (Table 1).

Variables that are measured by putting them into categories include those that have no order, only a name, such as gender, blood type, or imaging modality. Nominal variables such as these can be described by their number (count) or the proportion of patients in each category. Some nominal variables are dichotomous (binary), which means they have only two possible values, such as present or absent.

Ordinal variables are those that can be put into logically ordered categories according to their magnitude, such as grade of intensity of a heart murmur. In an ordinal scale, marked is more than moderate, but the difference between minimal and moderate is not necessarily the same as the difference between moderate and marked, nor can it be described numerically. Ordinal scales often rely on subjective judgments and are susceptible to bias. Ordinal variables with multiple categories can be summarized by their median value and range, and may be compared using the Chi-square-test or nonparametric tests, such as the Wilcoxon signed rank test.

Continuous measurement scales also have a logical order, but the differences between consecutive points on the scale (intervals) are equal in magnitude. Continuous measurement scales include temperature in degrees Celsius or weight in grams. Interval data have a zero point that is determined arbitrarily. Ratio data are similar to interval data because they exist on a continuous measurement scale but their scale has a true zero starting point. Examples of ratio data include heart rate (min⁻¹) and glomerular filtration rate (ml/kg/min). The intervals used for continuous variables can be subdivided, for example, a time interval of minutes can be subdivided into seconds or milliseconds. This contrasts with discrete variables, such as litter size, that cannot be subdivided. Continuous data may be summarized by their median value and range or—if distributed normally—their mean and standard deviation. Normally distributed continuous data may be analyzed using parametric tests, including Student's t-test and analysis of variance. For many statistical analyses, it does not matter if the data are interval or ratio or discrete.

With all measurements, it is necessary to know what quantity is measured, and how well.¹ Most measurements on continuous scales are defined according to a fundamental unit, such as weight or length. Such quantities have criterion validity, which means that we can check the validity of our measurements by comparison with a known standard. Other quantities are more difficult to define, for example, glomerular filtration rate can only be measured indirectly. In such instances, the reference standard is another indirect measurement that might not be very accurate. Some variables—such as pain—can only be defined subjectively, and it then becomes difficult to know if the scale used is valid. If the scale appears to be correct, it is said to have face validity. If it covers all the relevant aspects that we want to measure, it is said to have content validity. If use of the scale leads to meaningful results—such as a scale for assessing pain that detects changes in analgesic dose—it is said to have construct validity. Finally, a scale must give similar results each time it is used, i.e. it must be consistent. Cronbach's α is an example of a statistical method for assessing the consistency of a scale of measurement.²