  The spectra of empirical correlation matrices, constructed from multivariate
data, are widely used in many areas of sciences, engineering and social
sciences as a tool to understand the information contained in typically large
datasets. In the last two decades, random matrix theory-based tools such as the
nearest neighbour eigenvalue spacing and eigenvector distributions have been
employed to extract the significant modes of variability present in such
empirical correlations. In this work, we present an alternative analysis in
terms of the recently introduced spacing ratios, which does not require the
cumbersome unfolding process. It is shown that the higher order spacing ratio
distributions for the Wishart ensemble of random matrices, characterized by the
Dyson index $\beta$, is related to the first order spacing ratio distribution
with a modified value of co-dimension $\beta'$. This scaling is demonstrated
for Wishart ensemble and also for the spectra of empirical correlation matrices
drawn from the observed stock market and atmospheric pressure data. Using a
combination of analytical and numerics, such scalings in spacing distributions
are also discussed.
