A Practical Way for Computing Approximate Lower and Upper Correlation Bounds

Correlations among variables are typically not free to vary between -1 and 1, with bounds determined by the marginal distributions. Computing upper and lower limits of correlations given the marginal characteristics often raises theoretical and computational challenges. We propose a simple sorting technique that is predicated upon a little-known consequence of a well-established fact from statistical distribution theory to obtain approximate correlation bounds. This approach works regardless of the data type or distribution. We believe that it has practical value in appropriately specifying the correlation structure in simulation studies.