We consider univariate Gaussian mixtures theory and applications, and particularly the problem of testing the null hypothesis of homogeneity (one component) against two components. Several approaches have been proposed in the literature during the last decades. We focus on two different techniques, one based on the Likelihood-Ratio Test, and another one based on estimation of the parameters of the mixture grounded on some specific adaptation of the well-known EM algorithm often called the EM-test. We aim to provide useful comparisons between different techniques, together with guidelines for practitioners in order to enable them to use theoretical advances for analysing actual data of realistic sample sizes. We finally illustrate these methods in an application to real data corresponding to the number of days between two events concerning ovarian response and lambing for ewes.