•Alternative method to detect errors in EIS spectra.•Overcome of some practical issues for assessment of simple spectra.•Elucidation of analytical correlations between magnitude and phase. New analytical correlations between impedance magnitude and phase are developed and presented. These correlations are used for the assessment of impedance spectroscopy data. As correlations are obtained, they can be calculated point to point at each frequency of the spectra with no need to establish explicit premises related to stability, linearity or finite limits for their derivation. Their use is simpler than that based on the direct evaluation of the Kramers-Kroning transforms or alternative methods. An example of their derivation from basic equations involving complex numbers is described. They were obtained by looking for an explanation of the empirical fact that the slope of the Bode-Magnitude diagram vs frequency resembles the shape of the corresponding Bode-Phase diagram. Unlike the Kramers-Kronig transform, these new correlations can also be directly applied to test spectra with highly predominant capacitive or inductive responses or even incomplete loops. Their analytical expressions are exact for simple ideal elements and circuits, including the Warburg diffusion element. These correlations were tested with simulated spectra altered with known random error distributions, and they were able to detect the random distribution and the error level for simple spectra when the errors were > 0.5%. For more sophisticated spectra, the minimum error that can be detected without interference of the deviations due to the proper algorithm are around 2.5%. No exact correlation was found for a constant phase element (CPE), but a close empirical approximation was obtained for a single CPE. It is necessary to improve this approximation when a CPE is combined with some other elements because of detected deviations. In addition, it was found that in a first approach the algorithm does not detect non-linear behavior on a simple experimental circuit, but the test gave insights of how to detect it. On the contrary, it is well suited for detection of system stability issues. Examples of their application to actual experimental spectra, high capacitive or with several loops, are presented and the limitations discussed. More work and exhaustive tests are necessary to improve the method and stablish its real limitations, but its use for assessment of simple spectra at certain error level can already be done. Given that the derivation of the new correlations is only based on its complex number nature, this study concludes that the magnitude and phase of any complex number or 2D vector are not independent, and it is expected that similar correlations can be applied to any frequency-dependent complex variable, vector or transfer function, such as those used in optics or rheology.