A tricky question. Here is the famous graph of the running of the three coupling constants in the standard model: http://www-ekp.physik.uni-karlsruhe.de/~deboer/html/Forschung/unification_eng.eps .
The graph shows, in its top curve, the running of the coupling constant alpha_1. This is the coupling of the weak hypercharge coupling constant for the weak hypercharge group U(1)_Y, which is one of the three gauge groups of the standard model of particle physics.
But there is a tricky detail. In that curve, alpha_1 is multiplied with 5/3. This factor 5/3 comes from the assumption that GUTs are valid. The factor ensures that the various group traces of U(1)_Y, SU(2) and SU(3) are normalized in the correct way when they form the SU(5), SO(10) or any other grand unification gauge group.
In the case that grand unification is wrong, the factor 5/3 cannot be deduced. Which factor would be natural in this case?
Clarification added, after remarks by Lubos Motl: it is assumed in the question that the usual definition of the weak hypercharge is used, Y_W=2(Q-T_3), in which left-handed quarks have hypercharge 1/3.