Arguably one of the most important skills you must have in order to get started with using statistical methods is knowing the scale or level of measurement of your data. The appropriate method of analysis for your data is dependent on the scale it was measured in.
Here’s a quick rundown of the four levels of measurement starting from the simplest.
Can meaningfully compute for: counts, proportions
Measurements in the nominal level are just names or categories. A nominal level measurement would be the biological sex — male or female.
One thing you can do with these types of measurements is to sort the data points by category. You can also count how many data points fall into each one.
Attribute: categorisation, order
Can meaningfully compute for: counts, proportions, ranks
Measurements in the ordinal scale retain the attribute of those in the nominal scale. However, it adds in a level of complexity. In an ordinal level of measurement, there is an inherent order in the categories.
An example will be t-shirt size measurements. There are three typical categories: small, medium, and large. Aside from knowing these categories, we also know that there is an order in these categories given by how large they are relative to one another.
Given that there is order, you can also rank your data aside from being able to sort and count them.
Attribute: categorisation, order, evenly-spaced intervals
Can meaningfully compute for: counts, proportions, ranks, sums and differences
Moving up another level, the interval level of measurement builds on the attributes of both the nominal and ordinal scales. This level of measurement now has evenly-spaced intervals.
An example of a measurement in interval scale is the Fahrenheit scale. The difference of 214 °F and 212 °F is exactly two degrees. You couldn’t say the same thing for t-shirt sizes across all brands.
School rankings though, are not interval data. For instance, the difference in grade averages of the Top 1 and Top 2 of University A may not be the same with that of University B. With this, school rankings are another example of ordinal data.
Since we have even intervals, sums and differences are meaningful. This is because we know exactly how far the distances of the measurements are.
Attribute: categorisation, order, evenly-spaced intervals, absolute zero
Can meaningfully compute for: counts, proportions, ranks, sums and differences, ratios
The highest level of measurement if the ratio scale. What sets it apart from the interval scale of measurement is the presence of an absolute zero. When measurement scale has an absolute zero, then the zero stands for the absence of the measurement being measured.
Take the Fahrenheit scale for example, 0 °F is definitely cold, but it doesn’t mean the lack of temperature in the physical sense.
An absolute level of measurement will be height measurements. For instance, 0 feet is the absence of height itself.
With an absolute zero present, ratio comparisons are meaningful in the ratio level. We know that 40 feet is twice as long as 20 feet. However, we couldn’t say that 40°F is twice as hot as 20°F.
Know your level
Before beginning your analysis, make sure you know what level of measurement your data is in. This way, you wouldn’t run the risk of getting falsely significant — or even worse — falsely insignificant results.