In western industrialized countries men are on average more than twice as active in entrepreneurship as women. Based on data from a recent representative survey of the adult population in Germany this paper uses an empirical model for the decision to become self-employed to test for differences between women and men in the ceteris paribus impact of several characteristics and attitudes, taking the rare events nature of becoming an entrepreneur into account. Furthermore, a non-parametric approach using Mahalanobis- distance matching of man and woman which are as similar as possible in all characteristics and attitudes but the ``small difference'' is used to investigate the difference in the propensity to become self-employed by sex. A core finding is that the difference between men and women in both the extent and the effect of considering fear of failure to be a reason not to start one's own business is important for the explanation of the gap in entrepreneurship by sex.