  We consider the problem of independence testing for two univariate random
variables in a sequential setting. By leveraging recent developments on safe,
anytime-valid inference, we propose a test with time-uniform type I error
control and derive explicit bounds on the finite sample performance of the
test. We demonstrate the empirical performance of the procedure in comparison
to existing sequential and non-sequential independence tests. Furthermore,
since the proposed test is distribution free under the null hypothesis, we
empirically simulate the gap due to Ville's inequality, the supermartingale
analogue of Markov's inequality, that is commonly applied to control type I
error in anytime-valid inference, and apply this to construct a truncated
sequential test.
