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Introduction
Statistical and data analysis require that data be collected, classified, and interpreted using the correct scale of measurement. Whether data is nominal, ordinal, interval, or ratio, using the appropriate scale is key for valid analysis and for extracting insightful conclusions. Each scale carries specific assumptions about the data’s nature and dictates which statistical methods are most suitable. This article provides a decision-tree-style guide to help you choose the scale of measurement that best fits your data’s characteristics, research questions, and analysis needs.
Decision Tree to Choose the Right Measurement Scale
The diagram below depicts a visual guide to help you choose the right scale of measurement for your data analysis project.
Choosing the right scale of measurement in data analysis (click to enlarge)
The first and perhaps most obvious question to ask is whether the target variable in your data carries a sense of order. If there is no inherent ordering, then the choice of measurement scale is quite easy: nominal. For instance, categorical variables like gender — for example, male, female, non-binary — fall under the nominal scale, since there is no meaningful order between categories.
So, what happens if the values within the variable can be ordered? Does it imply that the data are numerical and continuous? Not necessarily, as there are still a few nuances to consider. First, it may be that the separation between ordered or ranked values is not uniform or quantifiable. In that case, an ordinal scale must be adopted, as is the case with quality bands for wine or olive oil, class ranks, etc. Notice that these are not necessarily numerical data, but their values can be ordered or ranked meaningfully.
If the separation between values is uniform and quantifiable, we can use more strictly numerical scales of measurement. The next question to ask is whether there is a true zero point, that is, whether a value of zero in your variable means a complete absence of the quantity or magnitude being measured, e.g., “income equal to zero means no income”, or “children count equal to zero means no children”. If that’s not the case — for instance, a temperature of 0 degrees Celsius doesn’t mean “no temperature” — the right measurement scale to use is interval, not ordinal.
Suppose, on the contrary, that there is a true zero point in your data. In that case, consider whether the variable has to be measured continuously or not. If it is measured continuously, like the height or weight of individuals, a ratio scale is the right approach because any arithmetic operations, including meaningful ratios, can be applied. Meanwhile, if there is no need or obligation to measure the data values continuously, as occurs with any counts of citizens, pieces of fruit, and so on, you may be dealing with an absolute scale, in which values represent whole units and zero indicates none.
Two special cases are worth considering besides the above set of nested rules:
- Some variables are circular or periodic, in the sense that they wrap around a fixed point and have a cyclic behavior, such as hours on a clock or compass directions expressed in degrees. In that case, a cyclic scale is the most appropriate approach to consider.
- Some real-world magnitudes move across such vast ranges, like sound intensity, earthquake magnitude, or pH levels in a substance, that a logarithmic scale is more suitable for analysis due to their exponential nature of variation.
Wrapping Up
Scales of measurement like nominal, ordinal, interval, and ratio are foundational in statistical and data analysis. However, it’s not always obvious if we are using the right scale or if we should consider others like logarithmic or cyclic scales. This article has provided a guide for choosing the most suitable scale of measurement based on your data and research needs.
