I have the following question: Are there any statistical methods (e.g. hypothesis tests) that allow you to compare the order of two different lists?
Suppose there are two students : John and Sarah. These two students make a list of the foods they ate in the last week and how often they ate them:
food frequency name ice cream 15 john french fries 13 john cake 12 john oranges 11 john pineapple 11 john pizza 11 john sushi 11 john apples 10 john celery 10 john mango 10 john tacos 10 john grapes 8 john food frequency name sushi 14 sarah cake 14 sarah pizza 12 sarah tacos 12 sarah grapes 11 sarah pineapple 11 sarah french fries 11 sarah apples 10 sarah oranges 10 sarah celery 10 sarah mango 10 sarah ice cream 10 sarah
Question: Do any statistical methods exist that allow you to determine how similar are the food preferences between both of these students?
For example - looking at this list, I can see that both students ate a lot of cake in the last week (3rd most popular choice for John and 2nd most popular choice of Sarah), and both students did not eat a lot of mango (3rd least popular choice for John and 2nd least popular choice for Sarah).
But apart from these manual comparisons, are there any statistical methods which allow you to compare the similarity between the food preferences between both students? For instance, could some statistical method conclude that the overall preferences of both students are "approximately the same"?
I came across a few methods such as the Wilcox Rank Test (https://en.wikipedia.org/wiki/Wilcoxon_signed-rank_test), but I am not sure if this statistical test can be directly applied to this type of question.
Does anyone have any ideas?