In this study, by obtaining some Korovkin type approximation results in statistical sense for certain positive linear operators constructed by means of the Chan-Chyan-Srivastava multivariable polynomials [W.-C.C. Chan, C.-J. Chyan, H.M. Srivastava, The Lagrange polynomials in several variables, Integral Transform. Spec. Funct. 12 (2001) 139-148], we show that our approximation method is stronger than the corresponding classical aspects in the approximation theory settings. Furthermore, we investigate their statistical rates by means of the modulus of continuity and the elements of the Lipschitz class. (c) 2006 Elsevier Inc. All rights reserved.