Far better an approximate answer to the right question, which is often vague, than an exact answer to the wrong question, which can always be made precise.
-- John W. Tukey
As Justin Matejka & George Fitzmaurice's nice illustrations show ("Same Stats, Different Graphs: Generating Datasets with Varied Appearance and Identical Statistics through Simulated Annealing", ACM SIGCHI 2017), statistical tests do not tell us everything. Know your data: always plot it first!