In this study we present a compressible test-field method (CTFM) for computing $\alpha$ effect and turbulent magnetic diffusivity tensors, as well as those relevant for mean ponderomotive force and mass source, applied to the full MHD equations. We describe the theoretical background of the method, and compare its properties to the quasi-kinematic test-field method (QKTFM), and the previously studied variant working in simplified MHD (SMHD). We present several test cases using velocity and magnetic fields of the Roberts geometry, and also compare with the imposed-field method. We show that in all cases investigated, the CTFM gives results in agreement with the imposed field method. Some deviations in between CFTM and SMHD variant exist. As a relevant physical application, we study non-helically forced shear flows, which exhibit large-scale dynamo (LSD) action of variable strength, and present a re-analysis of low Reynolds number, moderate shear systems, where we previously neglected the pressure gradient in the momentum equation, and found no coherent shear-current effect. Another key difference is that in the earlier study we used magnetic forcing to mimic small-scale dynamo (SSD) action, while here it is self-consistently driven by purely kinetic forcing. We still find no coherent shear-current effect, but do recover strong large-scale dynamo (LSD) action, that, according to our analysis, is driven through the incoherent effects.