Abstract
The problem of the agreement in experts’ opinions is one of the main ones in making collective decisions. The quality of the collective decision (accuracy, reliability, reliability, number of experts, time and laboriousness of decision making) depends on the degree of consistency of expert decisions. The article discusses the issues of reliability of estimates given by a group of experts for dependent samples. The dependence of random variables in samples is manifested, first of all, in testing systems. The dependence can be between the test questions, as well as between the student’s answers to the test questions on different topics. A connection can also be found between the answers of different trainees with a similar assimilation of the educational material. In the article, to determine the consistency of expert assessments, the indicator is the sum of centered values of random variables corresponding to the assigned estimates. This indicator characterizes the total scatter of expert assessments relative to the arithmetic mean of the collective assessment. In case of complete agreement of opinions, the value of the indicator is zero. The characteristics of the scatter of estimates are derived from the Chebyshev theorem. The lower and upper bounds of the estimation error are obtained. The confidence interval for the correlation coefficient is built. A formula for finding the proportion of possible deviations in the score is derived. The behavior of the boundaries of the confidence interval was investigated for different values of the point estimate. The case is considered when all correlation coefficients are non-negative. A comparison is made of the behavior of the boundaries of the confidence intervals for non-negative correlation coefficients and the general case. The results obtained can be used, for example, in testing systems for personnel training, in product quality control systems, to select promising technologies, and medical diagnostics.
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