This is about Stevens’ typology of scales and it’s probably the only bit of his hierarchy that matters for us.
Categorical or nominal scaling includes first names, eye or hair colour and, arguably, diagnostic labels. They carry no ordering implications: that Chris is Chris and Jo-anne is Jo-anne doesn’t imply ordering. Of course, if you want to sort first names alphabetically then first name move to ordinal scaling as Chris comes before Jo-anne in ascending alphabetical order (but after in descending order). (Oh make sure you choose your alphabetic ordering in case you hit some very unusual first names like “_nGreat” or “***happy”, oh, and watch conventions for sorting Mc and Mac for surnames.)
Stevens was right that you simply can’t do some mathematical things with nominal/categorical scale values and expect them to make sense as they might with ordinal, interval and ratio scales. However, beyond that there is almost nothing really useful in the distinctions.
When we have this sort of variable we can only count the numbers in each category and we can only use it against other variables to see if differences across these categories on the other variable seem random or interesting: does this counsellor seem to see clients whose baseline scores are higher than other counsellors? Does this counsellor see a higher proportion of male clients than other counsellors?
Further details! #
In 1953 Lord wrote the gloriously titled paper “On the statistical treatment of football numbers” which may be a bit of a baffling title outside North America as football numbers in the UK tend to be goal counts, attendance numbers or the eye watering transfer fees whereas numbers worn by players in American football are theoretically arbitrary: not relating to position, order of joining the team or anything. However, Lord takes the situation in which different year groups at a university argue that the coach is allocating higher numbers to more senior teams (or perhaps it was the other way around, I forget). Lord shows that immediately you can do statistical significance testing to see if the coach’s protestations of allocating the number randomly, with no thought of year group looks implausible. A bit like my rather daft example of alphabetic ordering of first names. Perhaps sadly, Lord didn’t open up the more general if philsophically complicated issue of “psychological scaling”: how things may not necessarily have the scaling it appears they have, see age.
Try also … #
Chapters 2, 4 and 10?
Lord, F. M. (1953). On the statistical treatment of football numbers. The American Psychologist, 8, 750–751.
Stevens, S. S. (1946). On the theory of scales of measurement. Science, 103, 677–680.