Frontiers in Applied Mathematics and Statistics (Oct 2024)
Empirical validation of the use of projective techniques in psychological testing using Galois fields
Abstract
It is shown that the problem of the adequacy of psychological testing methods, which are varieties of “projective techniques”, is far from being universally recognized. To solve this problem, we used an empirical method based on collecting of statistics of respondents’ answers, as well as a method of analyzing this statistics by means of representing permutations through functions taking values in Galois fields. Based on experimental data, it is shown that the distribution of respondents’ answers to a test in which they are asked to rank pictures in accordance with their own preferences is not homogeneous. Experimental data show that there are answer options that are statistically most common. An interpretation of testing is proposed in which passing the test is considered as “connecting” an external additional layer to the neural network formed by the respondent’s brain. In accordance with this interpretation, the most frequently occurring answer options can be considered as the basis for the formation of classification characteristics. It is shown that during using tests of this type it is advisable to take into account the code distances between the answer of a particular respondent and the codes corresponding to the most frequently occurring sequences. The possibilities of generating psychological tests directly based on experimental data and images generated by neural networks are discussed.
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