We systematically investigate the Ni-Fe layer thickness (t) dependence of the anomalous Hall effect (AHE) and anomalous Nernst effect (ANE). The AHE and ANE show different behavior in the t dependence; the sign of the anomalous Hall resistivity changes around t = 9 nm, whereas the anomalous Nernst coefficient (S-ANE) keeps almost constant regardless of t, namely, no sign change of S-ANE with t. We analyze S-ANE and separate it into the contribution coming from the transverse thermoelectric conductivity (alpha(xy)) and the AHE contribution coming from the Seebeck effect. The detailed analysis for S-ANE concludes that the AHE contribution is negligibly small and alpha(xy), which is related to the anomalous Hall conductivity (sigma(xy)) via the Mott relation, is also independent of t. To gain insight into the difference in the t dependence of sigma(xy) and alpha(xy), we clarify the origin of sign reversal in the AHE. The sign reversal in the AHE is attributed to the competing contribution of the different sources of the AHE: the extrinsic and intrinsic mechanisms. The present experimental finding of the difference between the t dependence on sigma(xy) and alpha(xy) suggests that the relative degree between the extrinsic and intrinsic processes for the AHE is quite different from that for the ANE in the case of Ni-Fe.