We have performed photometric optical observations of a sample of 17 core-dominated radio-loud quasars (CRLQs) and 17 radio-quiet quasars (RQQs). The aims were to confirm the existence of microvariations in strictly radio-quiet objects and to compare the properties of the variations in both types of quasars. Great care was taken to avoid selection effects and spurious biases in the samples. We present a new observational and statistical procedure for searching for microvariability, based on the analysis of variance. The results show that microvariations in RQQs may be as frequent as in CRLQs. The implications for the physical models for microvariations are briefly discussed.