A factorial-moment analysis with real (integer and non-integer) phase space partition is applied to pi(+)p and K(+)p collisions at 250 GeV/c. Clear evidence is shown for self-affine rather than self-similar power-law scaling in multiparticle production. The three-dimensional self-affine second-order scaling exponent is determined to be 0.061 +/- 0.010. (...