Visual tests using several safe confidence intervals

We propose a new statistical hypothesis testing framework which decides visually, using confidence intervals, whether the means of two samples are equal or if one is larger than the other. With our method, the user can at the same time visualize the confidence region of the means and do a test to decide if the means of the two populations are significantly different or not by looking whether the two confidence intervals overlap. To design this test we use confidence intervals constructed using e-variables, which provide a measure of evidence in hypothesis testing. We propose both a sequential test and a non-sequential test based on the overlap of confidence intervals and for each of these tests we give finite-time error bounds on the probabilities of error. We also illustrate the practicality of our method by applying it to the comparison of sequential learning algorithms.