Guided by the non-relativistic effective field theory of interactions between Weakly Interacting Massive Particles (WIMPs) of spin 1/2 and nuclei we study direct detection exclusion plots for an example of non-standard spin-dependent interaction and compare it to the standard one. We analyze an extensive list of 15 existing experiments including the effects of momentum dependence and isospin violation. In our analysis, we fixed the dark matter velocity distribution to a Maxwellian.