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In this paper, we address the issue of testing for stochastic independence and its application as a guide to selecting the standard independent component analysis (ICA) algorithms when solving blind source separation (BSS) problems. Our investigation focuses on the problem of establishing tests for the quality of separation among recovered sources obtained by ICA algorithms in an unsupervised environment. We review existing tests and propose two contingency table-based algorithms. The first procedure is based on the measure of goodness-of-fit of the observed signals to the model of independence provided by the power-divergence (PD) family of test statistics. We provide conditions that guarantee the validity of the independence test when the individual sources are nonstationary. When the sources exhibit significant time dependence, we show how to adopt Hotelling's T2 test statistic for zero mean to create an accurate test of independence. Experimental results obtained from a variety of synthetic and real-life benchmark data sets confirm the success of the PD-based test when the individual source samples preserve the so-called constant cell probability assumption as well as the validity of the T2-based test for sources with significant time dependence.