Various measured size distributions obtained from aircraft measurements at different regions and seasons are used in the retrieval algorithms for ice cloud properties by several major satellite instruments such as MODIS, CERES and VIIRS. These measured size distributions are characterized by one parameter: effective size (diameter or radius). This study shows that the adoption of such measured size distributions leads to inconsistent results in retrieved cloud properties because neglecting the effect of effective variances causes non-monotonic relations between crystal size and single scattering properties. We also show that single scattering properties of most observed size distributions of hexagonal columns can be adequately characterized by effective radius and effective variance. Therefore, in remote sensing of ice cloud properties, theoretical size distributions with explicitly assumed effective variances should be used, similar to the practice adopted for water clouds.