I have $n$ clustering algorithms which are trained and evaluated on the same dataset, and I want to test whether the differences in their performances are significant or not.
The dataset is PAN17-Clustering, in which there are multiple clustering problem sets (60 for training, 120 for testing) and the clustering is operated on each problem set, which means the different runs and sub-scores are independent from each other.
The final score of an algorithm is averaged over the 120 test problem sets. Inasmuch as the ground truth is given, the evaluation criteria are extrinsic, and are $B^3 F$ score and the adjusted rand index $ARI$. Here are the results:
As you see, the differences aren't that remarkable. I would like to test for the significance of the differences I see in the performances of the clustering algorithms, so would you please advise in that regard?