On what basis can only ratio and interval measurements have units of measure?

Ratio and interval measurements are both types of quantitative data that possess inherent numerical properties, allowing for meaningful arithmetic operations. This means that both types of measurement can be manipulated mathematically to yield useful results. For instance, with interval measurements—like temperature in Celsius or Fahrenheit—you can add and subtract values, but they lack a true zero point, meaning ratios may not be meaningful. In contrast, ratio measurements, such as height or weight, allow for a complete range of mathematical functions including multiplication and division, as they include a true zero point that represents the absence of the quantity being measured.

This numerical rigor and structure associated with ratio and interval scales enable them to have units of measure, making them suitable for calculations and comparative analysis. Other types of measurements, such as qualitative assessments or categorical data, do not support arithmetic operations in the same way, as they do not represent quantities and thus lack units that would make calculations meaningful. Visual training purposes may involve these measurements, but the focus on arithmetic operations highlights the fundamental relation between numerical data types and their functions.