Suppose I have the data of 300 patients containing their age and grade of tumor at the diagnosis. The grading has only 3 levels: Grade 1, Grade 2 and Grade 3.
Is it appropriate to use Spearman correlation to infer if the age was associated initial tumor grade?
Would it be better than one-way ANOVA with post-hoc tests? (treating grading as subgroups)
Spearman correlation is not really meant to be used with highly discrete variables. The usual distribution theory (as used for hypothesis tests) do assume no (or at least very few) ties. It could still have some, very limited, descriptive value, but for hypothesis testing combine it with a permutation test. But there must be better ways:
I would try ordinal regression see for instance How to understand output from R's polr function (ordered logistic regression)?. And for a start, some simple data visualization, in this case a simple stripchart, see plotting part of data using violin plot and the other part as stripchart (stripplot) for an example.