I am working with a collaborator who is interested in showing that two states that people in the field might expect to differ in fact do not differ. I am writing to ask what are the most convincing ways to do this both visually and statistically.
Here are my thoughts:
Visually, I think if we took the gene signature that would be expected to differ most strongly, then we showed that those genes in fact do not differ using a heatmap and a distance matrix, that could be a good way to make the argument visually in a context that is relevant in the field.
Statistically, we might think about using permutation-based testing to show that the p-value distribution of the conditions does not significantly differ from random permutations of the labels. This option seems more rigorous numerically but I think it is also less likely to be immediately grasped by a larger audience.
What other approaches could be fruitful to take?