'Code numbers given to the religion of persons' is an example of data on which…

Concept: A level (scale) of measurement is decided by what the numerals actually stand for, never by the fact that they look like numbers. Stevens’ four levels form a ladder, and each rung adds one property to the rung below it: a nominal scale’s numerals only name mutually exclusive categories; an ordinal scale’s numerals also rank those categories; an interval scale’s numerals additionally place them equal distances apart, with a conventional zero; a ratio scale’s numerals add an absolute zero that means the attribute is wholly absent. So the level of any coded variable is found by asking, in order, whether the numerals rank, whether their gaps are equal, and whether their zero is absolute — and stopping at the first “no”.

Applying it here: the variable being coded is religion, and the coding replaces each category name with a digit.

1. Identify the variable. Religion is a qualitative attribute whose values are mutually exclusive named groups; the code merely substitutes a digit for a name, so the digit carries exactly the information the name carried — group membership.

2. Test for rank. Asking whether one religion is “more” than another has no defensible meaning, so the codes cannot be read as a ranking; a person coded 3 is not above a person coded 1.

3. Test for equal gaps. Because there is no rank, the difference 3 − 1 = 2 measures nothing: subtracting the codes of two religions returns a number with no interpretation.

4. Test for absolute zero. There is no “no religion at all” origin that the numbering counts up from, so a statement such as “twice as much” is undefined for these codes.

5. Confirm arbitrariness. The codes may be permuted freely — swap the digits used for any two religions — and not one item of information is lost, which is the defining signature of labels rather than magnitudes. The data therefore lie on the nominal scale.

Cross-check by contrast: each higher level demands a property these codes do not have.

The ladder therefore stops at the first rung: the code numbers given to the religion of persons are data on the nominal scale. A useful takeaway is that any numeral used purely as a name — a jersey number, a route number, a pin code — sits at this same level, however large the digits are.