We examine the dependence of parton distribution functions (PDFs) on the value of the QCD coupling strengths(MZ). We explain a simple method that is rigorously valid in the quadratic approximation normally applied in PDF fitting, and fully reproduces the correlated dependence of theoretical cross sections ons and PDF parameters. This method is based on a statistical relation that allows one to add the uncertainty produced bys, computed with some special PDF sets, in quadrature with the PDF uncertainty obtained for the fixeds value (such as the CTEQ6.6 PDF set). A series of four CTEQ6.6AS PDFs realizing this approach, fors values in the interval 0.116 � �s(MZ) � 0.120, is presented. Using these PDFs, the combineds and PDF uncertainty is assessed for theoretical predictions at the Fermilab Tevatron and Large Hadron Collider.