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We develop E-variables for testing whether two or more data streams come fromthe same source or not, and more generally, whether the difference between thesources is larger than some minimal effect size. These E-variables lead toexact, nonasymptotic tests that remain safe, i.e. keep their type-I errorguarantees, under flexible sampling scenarios such as optional stopping andcontinuation. In special cases our E-variables also have an optimal 'growth'property under the alternative. While the construction is generic, weillustrate it through the special case of k x 2 contingency tables, where wealso allow for the incorporation of different restrictions on a compositealternative. Comparison to p-value analysis in simulations and a real-worldexample show that E-variables, through their flexibility, often allow for earlystopping of data collection, thereby retaining similar power as classicalmethods, while also retaining the option of extending or combining dataafterwards.

Generic E-Variables for Exact Sequential k-Sample Tests that allow for Optional Stopping