Types of Data › Data Type Hierarchy and Subcategories
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Nominal vs. Ordinal Data
Within qualitative data, we can distinguish between nominal and ordinal data. The distinction changes which summaries and encodings preserve the available information.
Nominal Data
Nominal data consists of categories without an inherent order or ranking. The displayed order or numeric codes assigned to these categories are arbitrary. Examples include a documented set of gender categories, product colors, or sales regions. Whether a variable is nominal depends on its operational definition and the analysis context, not on how its values happen to be sorted.
Frederic Lord made this point memorable in a 1953 satire about football jersey numbers:
“Since the numbers don’t remember where they came from, they always behave just the same way, regardless.”
The joke is not permission to calculate anything with any numeric code. It warns that the stored values alone do not tell you what the numbers mean; you also need the question and the process that produced them.
Ordinal Data
Ordinal data consists of categories with an inherent order, but the distances between adjacent categories are not established as equal. We can rank the categories, but assigning codes 1, 2, and 3 does not by itself justify treating the gaps as equal. Education levels, satisfaction ratings, and letter grades are common examples when their ordering is defined for the task (Australian Bureau of Statistics, 2023a).
Interval vs. Ratio Data
Within quantitative data, we can distinguish between interval and ratio data based on the presence of a true zero point and the types of mathematical operations that are meaningful.
Interval Data
Interval data has equal units but an arbitrary zero point. Differences and comparisons of differences are meaningful, while ratios of raw values are not. Celsius temperature is a standard example: the difference from 20°C to 30°C equals the difference from 30°C to 40°C, but 20°C is not twice as hot as 10°C. Calendar years are also commonly treated as interval values. Some standardized scores, including certain IQ scores, are treated approximately as interval data only when their construction supports that interpretation (Stevens, 1946).
Ratio Data
Ratio data has equal units and a meaningful zero, so differences and ratios of measurements of the same attribute are interpretable. Height illustrates this property: 180 cm is twice 90 cm, and that ratio is unchanged after conversion to meters (Stevens, 1946). Weight and nonnegative elapsed time are also ratio variables. Income can be treated as ratio data only when observations share a compatible currency, period, and accounting definition; quantities such as net income may also be negative. Sums and products still require attention to units and domain meaning.