Hi, Eddie,
If you used any ordinar probgramms like excell, you can use ordinar numerals like 11, 12 , 25 etc. And, of couse, you can multiply or add or do any other ariphemitc operation. In such pragramm you can not use ordinal numerals.
Dear @Eddie, it makes sense, in general, to do mathematical operations on ordinal numerals. For example, if you have a group of numbers ordered in ascending order and you did select the best 5 then to reorder the rest of the elements of the group you can subtract 5.
If you are conducting a quantitative research then ordinal and interval data are much better than nominal data In that case it is best using a Likert-type scale (for many questions about attitudes and beliefs). Hence, ordinal numbers can be manipulated to provide descriptive data, but comparing them to other numbers is difficult because they are not on a consistent scale.
To go back to your comment about nominal data. Nominal or categorical data can be analyzed using chi-squared tests. While chi-squared tests are not high on the statistical sophistication list, they can be used to determine whether an association (or relationship) between 2 categorical variables is real or due to chance.
I agree that when possible set up your data in a interval system. For example, Instead of asking a person's age, give age ranges in which subjects would fall.
Thank you Madelaine. In chi-square analysis, nominal (and for that matter categorical) data are simply counted (as frequency). It' is because if for gender 1 represents male and 2 female, we cannot add 1 and 2 or divide 1 by 2 or get the square root of 2 because that would mean male + female, male divided by female, and square root of female.
It does not make sense to multiply, divide, add, subtract, square or get the square root of nominal numerals. But it is correct to multiply, divide, add, subtract, square or get the square root of ordinal, interval, and ratio numerals.
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