The aim of the paper is to test the accuracy of classical spectroscopic methods in the visible domain dedicated to measurements of temperature and electron density in order to conclude about the validity of thermal disequilibrium. The influence of various factors is studied: accuracy of the intensity calibration, Abel inversion of the experimental spectra, excitation temperature deduced from the relative method, absolute excitation temperature, influence of the transition probability accuracy, influence of the Biberman factor value, electron temperature from the line-to-continuum intensity ratio, electron density deduced from Stark broadening, and electron density deduced from the continuum intensity. This spectroscopic investigation is carried out for argon plasma and argon copper plasma both produced by means of an ICP torch operating at atmospheric pressure. Results are given with uncertainties for each evaluated parameter. We show that, first, the electron temperature deduced from the line-to-continuum intensity ratio has to be considered with great care; second, for argon plasma no evidence of thermal disequilibrium can be discerned, whereas for argon copper plasma a small disequilibrium of 1.2 to 1.4 at most is experimentally observed.