This paper explores dimensions of similarity in analogy-based design through a user study. Analogy is used in design to help designers use knowledge that exists between and across domains in order to solve design problems at hand. The five dimensions of similarity that were explored in this paper are: function, form, energy flow, material flow, and motion. Fifty student volunteers, majoring in Mechanical Engineering, were given electro-mechanical products that are to be designed, and were asked to select, from a set of options, other products that they considered could be useful references for their task, if those options were offered by a hypothetical design-by-analogy web-service. In their response, they were also asked to identify the dimensions along which they found their preferred reference products to be similar to the design product. It was observed that participants selected products based on similarity along multiple dimensions of analogy. Function-based similarity was the most dominant trait, followed by energy, motion, material, and form. The results from this study will help to design more elaborate studies that will inform the design of computational support algorithms that will aid designers by recommending analogous solutions to help with solution search and ideation.