I have a table where each column represents a variable and each row represents a measurement. And I have a list of "hypothesis" about the relationship of the variables. For example, one "hypothesis" is that "the value of column A is greater than the value of column B". I can easily count how many times this is true given this dataset. In this case, in 96% of the measurements, "the value of column A is greater than the value of column B". I don't have a priori information about the expected distribution of these variables.
My question is this: how can I formulate this problem as a statistical hypothesis testing (what test statistic could be used)? What other information I might need?
Remember that the hypotesis you want to prove cannot be the null hypothesis (see, e.g., https://www.statlect.com/glossary/null-hypothesis for a discussion of this point). For example, if you want to prove that A is greater than B on average, your null hypothesis should be that A is equal to B on average. "A greater than B" is going to be your alternative hypothesis. For example, you could use a t test to test the null that the mean of A-B=0. Given your alternative hypothesis, your t test should be one-tailed (you are excluding a priori that the mean of A-B is negative).