First hyperpolarizabilities (beta) of two tricyanovinylthiophene nonlinear optical chromophores were determined using second harmonic, hyper-Rayleigh, scattering. The use of an external standard in the determinations is compared with the previous use of an internal standard. The first hyperpolarizability of the well-known chromophore 4 dimethylamino 4’ nitrostilbene (DANS) was also determined using the external standard method and its value is compared to those in the literature. A new method of analyzing the hyper-Rayleigh scattering signal by recording a histogram of the scattered energy is reported. This method is shown to give more reliable results in a shorter period of time than the usual static gate method. The histogram function provides additional information in the form of the histogram width which is shown to be an indication of the mean-square concentration fluctuations of the chromophores in solution. The effects of molecular interactions on the concentration dependence of the hyper-Rayleigh scattering signal is discussed. It is shown that depending on the concentration range, the beta value of para-nitroaniline, used as the external standard, can agree with two different values reported in the literature. Results on the depolarization ratio of the hyper-Rayleigh scattered light from one of the tricyanovinylthiophene chromophores are presented. At low concentration the depolarization ratio agrees with the theoretically predicted value based on C-2v symmetry. However, at higher concentration the measured depolarization ratio increases indicating molecular interactions.