Ways to cope with the problem of psychological measurements through combining results of theoretical and practical research are presented. The example of attitude scale building with regard to psychological measurements is considered in the context of soundness of mathematical models application to psychological measurements when building interval scales. Using the results of direct methods of psychological measurement of stimuli having no physical metric it is possible to build metric scales of intervals and attitudes. The structure of the scale makes it possible not to use particular unit of measure as permissible transformations enable using conditional units. Mathematical model of any process will be valid if there is a preconceived idea of the process nature. When using probability, the problem is not solved but its contentious issues are skirted.