# Data and Measurement

By Levi Clancy for Student Reader on *updated *

###### Qualitative (aka *nominal*) data is not numerical.

This includes eye color, voting preference or if a vaccinated patient still gets infected. In fact, counting is the only way that qualitative data can be represented numerically (ie, 60 aye votes and 40 nay votes), but this has no physical meaning. Quantitative data is numerical, such as body weight, age or how long an infected patient survives when treated.

###### Data can also be categorized as either continuous or discrete.

Continuous data can take on any possible value or category. When recording body weight or survival time, there is an infinite number of outcomes. Conversely, discrete data has a limited number of values or categories. Examples include 1-to-10 performance rankings, or study participants' gender. Discrete data has only so many possible outcomes.

###### So far as discrete data is concerned, it can be ordinal (aka *count*) or categorical.

Ordinal data can be said to have an order. For instance, pain on a very-somewhat-none scale has an order. However, voting preference or gender are not ordered, and thus illustrate categorical data. Both ordinal and categorical data have a limited number of possibilities, yet the former has an innate order, and the latter does not.

###### For quantitative data, there are interval scales and ratio scales.

An interval scale has an arbitrary zero value. Consider centigrade measurements, which set the melting point of water as zero. Is 40° C actually 2x as much warmth as 20° C? No. Imagine if the melting point of ethanol (-114° C) were set as zero. In that case, 40° C and 20° C would be 154° and 134°. The exact same temperatures, measured with a different zero value, are suddenly 1.15x instead of 2x apart.

###### Ratio scales have physically significant zero values.

Consider Kelvin measurements. 0° K is absolute zero, the absence of temperature, heat or motion. Converting 40 and 20° C to Kelvin (313.15 and 293.15), one finds that 40° C is actually just 1.07x as much warmth as 20° C. However, 40° K is genuinely 2x as much warmth as 20° K. A single unit of warmth is arbitrary in both centigrade and Kelvin, but having a physically significant zero value makes for genuine ratios.