Why are the number on a ball in a lotto draw categorical nominal instead of categorical ordinal?
Don't the numbers have a natural ascending order and would thus be ordinal? Or am I making an incorrect assumption about numbers having a natural order?
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2$\begingroup$ They do have an order and they are ordinal. This really depends on how you choose to interpret the numbers, if you see the numbers as just symbols that could just as well be represented by A, B, C, ... then they would be nominal. $\endgroup$– user2974951Commented Feb 3, 2020 at 11:07
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$\begingroup$ @user2974951 Agree with your overall statement, but I think letters are a poor example of nominal data - since they have an inherent logical ordering, they're still just ordinal data. $\endgroup$– Nuclear HoagieCommented Feb 3, 2020 at 19:28
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$\begingroup$ @NuclearWang Agreed, presents the same kind of misunderstanding I had with numbers balls. But still I understand the point being made so thank you user2974951 $\endgroup$– LammaCommented Feb 4, 2020 at 8:00
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$\begingroup$ Lottery numbers don't have an order (the order is meaningless and the numbers are just labels). $\endgroup$– Sextus EmpiricusCommented Feb 6, 2020 at 15:41
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2 Answers
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You could color-code the balls without fundamentally changing the game. Instead of 6-12-11, we get red-blue-pink.
You could go with letters without fundamentally changing the game. Instead of 6-12-11, we get Y-Q-X.
You could use animal drawings without fundamentally changing the game. Instead of 6-12-11, we get dog-fish-horse.
The 6-ball isn’t worth half as much as the 12-ball. It doesn’t even represent a lesser value. The number is just on the ball as a link to lottery tickets.
It could be different if the number represented some kind of quantity, like rolling dice and advancing a game piece that many spots, but there’s nothing quantitative going on. The numbers on lottery balls just serve as links back to the tickets.
You probably can accept this for something like towns having zip codes or people having phone numbers. It’s the same idea.
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3$\begingroup$ Ah okay ths makes sense. It seems to come down to how you view the object of the lotto ball. Thank you for your response! $\endgroup$– LammaCommented Feb 3, 2020 at 11:45
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4$\begingroup$ @Dave , this is an excellent Answer, I up voted it. I just want to note that generally speaking zipcodes should be considered categorical nominal because zipcode 90210 isn't "twice as much as" 45105 or larger in any way, but there are limited cases in which it makes sense to think of zipcodes as categorical ordinal simply because they are, to a certain extent, assigned to areas in order north to south and east to west, and so considering them ordinally in a model can provide further information on approximately how far two zipcodes are, or how "west" they are, which can benefit some models. $\endgroup$ Commented Feb 4, 2020 at 20:35
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$\begingroup$ Except - colour coding the balls produces the question of colour blindness... imagine the court case where someone argues that the green ball is blue; to them. $\endgroup$– UKMonkeyCommented Feb 5, 2020 at 10:03
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1$\begingroup$ @UKMonkey your argument lies in the same "degree" as being blind - the lotto balls are for all matters and purposes "equal" - except for the printed number(s) .. if you can't see numbers .. you are likewise "out" $\endgroup$– eagle275Commented Feb 5, 2020 at 11:30
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The lines between the different types of variables are not as clear cut as we often define them. In many cases, the classification of a variables depends on how we use that variable instead of on the fundamental properties of the variable itself. Age in years and time measured in any fixed unit (days, hours, seconds) are good examples. These variables are fundamentally discrete (age in years falls in a countable set) but we often treat them as continuous in practice (e.g., regressing the probability of some disease on age as a continuous variable).
I'd argue in this case that the numbers on the balls are an ordinal variable but if the order is not important in the lottery then we treat them as nominal. This makes the difference between numbered balls and coloured balls clearer. You could run the lottery differently so that the order of the balls matters (maybe you win if you match the highest number out of, say, four balls drawn at random). You can't do this with coloured balls (unless you impose an ordering like the wavelength of light).
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$\begingroup$ I'd have said [integer] age in years is rounded or truncated, but not fundamentally discrete. After all, there are 3.5 (three-and-a-half) year olds. $\endgroup$ Commented Feb 4, 2020 at 21:49