Hi Guillaume,
I would discourage you from using active noise cancelling headphones for psychoacoustic experiments due to their unpredictable nature -- the noise attenuation typically involves some phase inversion of the surrounding background noise (your stimuli are not immune to that), they are really only efficient for lower frequencies, and their output will change with the change in the background noise. Ensuing is the loss of experimental control.
Instead, you could use insert earphones (as Neil suggested) and use earmuffs designed for hearing protection over the insert phones. You'll get greater combined attenuation than from any active noise attenuating headphones, and no unpredictability associated with the use of the latter.
marcin
We must not forget that when radium was discovered no one knew that it
would prove useful in hospitals. The work was one of pure science. And
this is a proof that scientific work must not be considered from the
point of view of the direct usefulness of it. It must be done for
itself, for the beauty of science, and then there is always the chance
that a scientific discovery may become like the radium a benefit for
mankind.
Maria Skłodowska-Curie