We study the scaling behavior of the pressure structure function for isotropic turbulence. This function is given exactly by Hill and Wilczak [J. Fluid Mech.296, 247 (1995)] in terms of the three independent fourth order velocity structure functions,L(r)=⟨&Dgr;u4(r)⟩,T(r)=⟨&Dgr;v4(r)⟩,andM(r)=⟨&Dgr;u2(r)&Dgr;v2(r)⟩.We show from direct numerical simulation (DNS) that the cancellation between the positive terms proportional toL(r)andT(r)and the negative terms proportional toM(r)is almost complete. This suggests that the pressure structure function is extremely sensitive to recently observed small differences in scaling among the three quantitiesL(r),T(r), andM(r). We illustrate this sensitivity by calculating the pressure structure function in the atmospheric boundary layer using the recent data of B. Dhruva, Y. Tsuji, and K. R. Sreenivasan [Phys. Rev. E56, R4928 (1997)]. The cancellation among the three terms persists, and gives an effective scaling exponent for the pressure structure function,⟨(&Dgr;p(r))2⟩∝r1.17,which is smaller than the scaling exponent for any of the three velocity structure functions. ©1998 American Institute of Physics.