The effective radius of droplets in water clouds is an important parameter for meteorology and for climate studies. Recent studies have shown that this parameter can be retrieved from simultaneous radar and lidar measurements. This article is directed to the study of the relation between the radar reflectivity to lidar extinction ratio and the effective radius of droplets. The different statistical models of drop size distributions for water clouds (like gamma, log-normal, and uniform probability density functions) were used for the analysis and interpretation of measured data. The analytical relationships between radar to lidar ratio and effective radius of droplets for such model drop size distributions as functions of distribution's parameters were derived. These relationships show a power dependence of 4th order, which does not completely describe the complicated character of observed data. For this study we used in-situ data that were measured by aircraft's probes during a few field campaigns in different geographical regions, for different cloud types and under different meteorological conditions. For every measured drop size distribution we calculated the ratio of the radar reflectivity (for Rayleigh scatterers) to the lidar extinction (for optical scatterers) and the effective radius of droplets (i.e. the ratio of the 3rd to the 2nd moment of the drop size distribution). These values represent a given drop size distribution as one point on the "radar to lidar ratio versus droplet's effective radius" plane. The position of this point on the plane can be used for the classification of the type of observed drop size distribution. The subregion that corresponds to the droplet distributions of the clouds without drizzle mode is limited by analytically derived relationships for the delta-function-like distribution and for the exponential distribution. The positions of the set of points for the clouds with drizzle do not satisfy the power relationship of 4th order. Nevertheless it was found that their behavior on the "radar to lidar ratio versus effective radius of droplets" plane agrees well with numerical calculations in the case of the mixture of simple probability functions. We analyzed two models of such mixtures - the mixture of gamma and exponential distributions and the mixture of gamma and Pareto distributions. For such representations of drop size distributions it is possible to give clear physical interpretation of their positions on the "radar to lidar ratio versus effective radius of droplets" plane. The results can be used for improving the retrieval of the effective radius of droplets in water clouds by use of simultaneous radar and lidar measurements.