  Advances in material growth methods have renewed the interest in localization
of one-dimensional systems in the presence of scale-free long-range correlated
disorder potentials. We analyze the validity of single parameter scaling for
the \beta-function away from the band center, in the presence of correlations.
A renormalized disorder strength emerges reducing the regime of validity of the
single parameter scaling hypothesis. Analysis of localization lengths and
participation ratios leads to correlation dependent critical and fractal
exponents, consistent with the extended Harris criterion.
