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Consider a measurement scale with which you are familiar that you know to be a ratio scale, say, distance. If two roads are five kilometres and three kilometres long respectively then they differ in length by two kilometres. If two other roads are nine kilometres and 7 kilometres long then they also differ in length by the same amount. Furthermore, that two kilometre distance is the same in both cases; it would take the same effort to travel that two kilometre distance on either road. This implies that distance is a ratio scale.
However, suppose persons A and B score 110 and 125 respectively on some test, a difference of 15 test points; meanwhile C and D score 75 and 90 on the test, again a difference of 15 test points. In general it would be impossible to know whether the difficulty in going from a score of 75 to 90 would be the same as going from 110 to 125. But of course the scores are ordered by difficulty. Therefore, the test scores make ordinal data.
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What type of data is random test scores ordinal or nominal?
ratio
What statistical test do you use for nominal by ordinal data?
Kruskal-Wallis H test.
Are multiple choice tests measured at ordinal scale or interval scale?
Ordinal. Tests responses are usually correct or incorrect. This would be assigned a value and the number of correct answers is the score of the test. There is a logical order, a correct answer is better than an incorrect answer, so it is not nominal data. Even though we calculate averages, test responses are not interval data, as there is no meaning to the interval. See related link.
What test assess two ordinal variables?
spearman rhos
Which conditions must be met to conduct a test for the difference in two sample means?
The two samples must be independent and the data must be at least ordinal. Under those conditions the Mann-Whitney U test can be used.
