An extended set of statistical tests, aimed at assessing the quality of the magnetic reconstructions in JET, obtained with the code EFIT using the external magnetic measurements, is described and the results reported in detail. In addition to the traditional analysis of the global distributions of the residuals (the difference between the actual measurements and their reconstructions from the equilibrium), to determine to what extent they approximate a Gaussian, more sophisticated correlation tests have been performed. Since EFIT solves a highly non-linear equation, tests adequate for multi-input multi-output, non-linear systems have been implemented. Not only the reconstruction of the pickup coil signals but also the accuracy of the plasma boundary has been investigated. The results indicate quite clearly that the errors in the reconstruction of the pickup coils are not negligible. The coils, whose residuals present skewed monomodal distributions (distributions asymmetric with respect to their maximum value), are affected by average errors of the order of more than one millitesla and multimodal distributions of the residuals (distributions presenting more than one local maximum) are quite common. Also the correlation of the residuals is typically outside the 95% limits for a good model in typically more than 70% of the cases. With regard to the plasma boundary, the situation is better since the errors in the distances of the plasma from the wall are typically of the order of 1 cm. On the other hand, in this case the autocorrelations of the residuals are also well outside the 95% confidence interval for random residuals. A detailed analysis of the correlations indicates that the main reasons for the imperfections in the magnetic reconstructions do not reside in the measurements, since there is no evidence of systematic errors or problems with the calibrations. Therefore, the main improvements are to be expected by refinements in the used equilibrium code EFIT, whose constraints and boundary conditions are probably not the most appropriate to model H mode plasmas.