Methodological approaches to the assessment of public opinion during the overhaul of apartment buildings

. In the article, using the example of a survey of residents of apartment houses (AH) on the quality of capital repairs, methodological approaches to assessing public opinion are considered. Processing the results of the survey showed that the definition of the coefficient of concordance is insufficient. It is shown that in order to assess the reliability of surveys conducted by the Delphi method, one should focus on achieving a greater confidence probability, and not on the value of the concordance coefficient. The survey showed that the priority factor for residents of apartment buildings of all ages and genders when assessing major repairs is the use of quality materials. For women of all ages, the issue of the cost of repairs was very important. Its importance for this group of respondents turned out to be almost at the level of the importance of the quality of materials. For the practical application of the results obtained, the weight coefficients of each studied factor were calculated for the total sample of respondents, which made it possible to create a methodology for express assessment of the quality of ongoing overhauls based on Harrington's verbal-numerical scales.


INTRODUCTION
An important part of the life of a modern metropolis is the construction of new buildings and structures, and the maintenance of the existing housing stock -the scope of major repairs of apartment houses.The relevance of the study is confirmed by the growth in the volume of capital repairs, for example, in the 1-st quarter of 2023, 286.44 million m 2 of space were repaired in Moscow [1].
One of the most effective ways to assess the quality of repairs is a public opinion poll.Studies conducted earlier consider issues of a general nature (awareness, participation in meetings on capital repairs, fundraising) [2].It is noted that homeowners practically cannot (or do not want to) influence the progress of repairs [3,4], or their complaints are often ignored by performers [5].At the same time, the federal law regulates the procedure for compensation for damage caused to the life or health of individuals during major repairs.[6] A review of foreign sources on the issue of capital repairs of apartment buildings as the main direction of research revealed the topic of energy efficiency of the activities carried out [7].There are works devoted to multi-criteria evaluation of contractors [8], as well as the development of models for estimating the time of building repairs based on machine learning [9].
In the presented work, the goal is to look at the problem of directly carrying out major repairs of AH from the point of view of the end consumer -residents of the AH during the period of major repairs without eviction and after repair.

MATERIALS AND METHODS
To achieve this goal, a survey was conducted using the Delphi method, the basic principle of which is that independent respondents or experts assess the situation more accurately than a structured group of specialists.In this study, not an expert survey was conducted, but a so-called mass survey, which differs from the expert survey by the principles of the selection of respondents.For an expert survey, a targeted selection is used according to pre-selected criteria, more often according to the level of competence.Mass selection is characterized by random sampling, nevertheless, the selection of respondents in the study under consideration was made from the target group (residents of the AH).For this type of survey, in order to avoid mistakes, the representativeness of not only the survey results, but also the actual sample of respondents is important.

Rationale for choosing the number of respondents
The survey involved 160 residents of Moscow and the nearest Moscow region (in the terminology of statistics and sociology -respondents) aged 18 to 75 years, 47 of them women, 113 men.To solve the question of the sufficiency of the number of respondents to solve the task, the apparatus of mathematical statistics was involved.Since there is no single methodology for assigning the number of respondents (experts), several options for solving this problem based on different approaches were considered.The literature (for example, in [10,11]) provides a rule for calculating the minimum number of respondents (experts) min depending on the allowable error value, according to which the expression is valid: (1) where α is the error of the result of the analysis, which takes values from 0 to 1. α=0.05 is taken based on a confidence level of 0.95.In accordance with the data [11], expression (1) is most applicable when conducting a survey using the Delphi method.
To determine the required number of respondents, when conducting a random non-repetitive selection, the required number in work [12] suggests the following relationship: (2) where is a confidence indicator for a confidence probability of 0.95 ( 1,96),  0,95  0,95 = ε1-is the maximum permissible error set before the start of the survey, expressed in fractions of the standard deviation σ, that is: where ε is the absolute error, ε1 is assumed to be equal to 0.5.
When conducting random non-repeat selection, the minimum number of respondents is also proposed to be determined by dependence [13]: where p is the proportion of respondents with characteristics inherent in the general population; q is not having characteristics inherent in the general population (refers to representativeness errors); is the marginal error of sampling observation.In the absence ∆  2 of information about the values of p and q, their values are assumed to be equal to 0.5.The marginal error of selective observation is 0.05.The calculation data according to formulas (1)-( 3) are included in the table 1.So, the analysis of the data in Table 1 showed that the number of experts who participated in the survey is sufficient (m> m min ).

Selection of assessed factors
For the initial survey, the following factors were selected, which needed to be ranked by respondents: • Compliance with repair work deadlines; • Cost of work performed; • Quality of finishing works; • Convenient organization of temporary storage of materials for residents; • Use of environmentally friendly, non-toxic materials; • Quality of elevator equipment replacement.The factors were chosen for reasons of time and money costs, as well as ensuring safety during major repairs [14].

Initial processing of survey results
When filling out the questionnaire, the following rules were used: the most significant factor was assigned rank 1, the least significant 6.If the respondent did not take into account one factor, then the maximum value of the rank was taken as an estimate, if the respondent did not take into account several characteristics, then they were assigned the same ranks equal to the arithmetic mean of the remaining unused estimates.To assess the consistency of respondents' opinions, an alternative consistency coefficient was used [15,16], which is a modification of the Kendall concordance coefficient as a multiple variant of rank correlation: where n is the number of factors.
On fig. 1 shows the distribution of the sums of ranks for all considered sample options.Obviously, in this survey, the minimum sum of ranks (the most significant factor) corresponds to the "Quality of finishing works" factor, the maximum to the factor "Convenient organization of places for temporary storage of materials for residents" (the least significant factor).Nevertheless, it would be incorrect to draw conclusions based on the results of this part of the study without assessing the significance of the calculated values of the concordance coefficients.The calculated values of the concordance coefficient for all samples of respondents are given in Table 2 (Column 4).It is obvious that from a formal point of view, only one of the concordance coefficients (the sample of "Women") corresponds to a satisfactory consistency of respondents' opinions (0.5).But for surveys with a large number of respondents, this approach is not complete (this question is discussed further).Therefore, the significance of the obtained values of the concordance coefficients is evaluated according to two criteria -Pearson's and Fisher's Z-criterion.χ 2 According to [17], the empirical value of the Pearson criterion is determined by the expression: For the Fisher Z-criterion, according to [18], the following value is used as a critical statistic: Degrees of freedom of statistics (6) according to [19] are calculated for the task of determining significance as: v1=n-1, v2=(m-1)•v1 (7) The calculated data are included in table 2 columns 7-9.Since, according to Table 2, the empirical value of for all samples is greater than the χ 2 criterion value even for the significance level of 0.01, the opinions of experts at this significance level can be considered consistent in all the samples considered.A similar result was shown by the analysis of the data according to the Fisher criterion.

Second round of research. Grouping factors
Further, according to the ideology of the survey method used, the factors were grouped (Table 3) into three groups -conditionally designated as "Organization of a major overhaul", "Cost of a major overhaul" and "Quality of finishing work and materials used", hereinafter referred to as "Organization", "Cost", "Quality".The results of statistical processing of the second round are shown in Tables 4 and Fig. 2.

Practical application of the results obtained to assess the quality of capital repairs in the AH
As a small example, let's consider a survey conducted in the Moscow AH after major repairs.Respondents are residents of the house of all ages and genders.The factors "Organization of major repairs (duration, timing, storage of materials)", "Quality of finishing works and materials used", "Cost of major repairs (including the cost of materials and elevator equipment)" were evaluated.The assessment was conducted on a 10-point scale, the highest score is 10, the lowest is 1.The average score of the survey conducted on the "Organization" factor is 3.2; according to the "Quality" factor -7.0; according to the "Cost" factor -9.5.It is necessary to give a comprehensive assessment of the major repairs carried out.

DISCUSSION
The survey does not cover all aspects of the overhaul [20,21], which was not the goal initially, however, the practical significance of the study lies in a detailed presentation of statistical processing methods.An analysis of the survey data obtained as a result of processing revealed a number of interesting things.Both stages showed (Fig. 1, 2) that the issue of the convenience of residents during the overhaul of apartment buildings is not a priority for the residents themselves.Residents of all ages and gender are willing to endure the inconvenience of the renovation.But the question of the use of high-quality, non-toxic materials and the quality of the finish is a priority.For women of all ages, the issue of the cost of the repair turned out to be very important.Its importance for this group of respondents turned out to be almost at the level of the importance of the quality of materials.This is due to the fact that it is women who control expenses in families and make sure that the funds allocated for major repairs are spent purposefully.
The survey made it possible to calculate the weighting coefficients of factors, which led to the creation of a methodology for express assessment of capital repairs in apartment buildings based on a statistical approach.Important for which is the formation of a sample of respondents.The processing of the survey results showed that the determination of the concordance coefficient is insufficient for the representativeness of the results obtained.A high concordance coefficient may have a low confidence level (i.e.low significance) and vice versa.For n=6 and n=3 (corresponding to the number of factors studied in the first and second stages of this study), in the course of this study, special tables were constructed using the Pearson method (Tables 6, 7), linking the confidence probability with the concordance coefficient W and number of respondents (experts) m.
The study of public opinion at a higher level will identify topical issues during the overhaul (justification and preparation of work plans, the choice of effective and acceptable technological solutions, etc.) [22,23], as well as supplement existing regulatory documents [24][25][26].
In addition, with the development of digitalization and data storage technologies, it becomes relevant to introduce the technology of "people's" construction control, based on the desire of owners to live in conditions corresponding to the funds spent in the form of monthly contributions for major repairs.

RESULTS AND CONCLUSION
1.The processing of the results of the survey showed that the determination of the concordance coefficient is insufficient for the representativeness of the results obtained.A high concordance coefficient may have a low confidence value and vice versa.It is shown that in order to assess the reliability of surveys conducted by the Delphi method, it is necessary to focus on achieving a higher confidence probability, and not on the value of the concordance coefficient.2. The survey showed that the use of high-quality, non-toxic materials and the quality of finishing is a priority factor for residents of the AH of all ages and genders when evaluating major repairs.For women of all ages, the issue of the cost of the repair turned out to be very important.Its importance for this group of respondents turned out to be almost at the level of the importance of the quality of materials.3.For the practical application of the results obtained, the weighting coefficients of each factor under study were calculated from a general sample of respondents: "Organization" -0.19; "Cost" -0.35; "Quality" -0.46, which allowed us to create a methodology for rapid assessment of the quality of major repairs carried out from the point of view of the end consumer -residents of the AH on the basis of verbal-Harrington numerical scales.

Fig. 1 .
Fig. 1.Distribution of the sum of ranks by factors , in this case, the average scores obtained as a result of the  н survey.

Table 1 .
The minimum number of respondents to conduct a survey, ensuring the representativeness of the results Number of degrees of freedom v=n-1.For all samples, the value of the degree of freedom is 5. Empirical values of in column 5 of Table2.χ

Table 2 .
On the calculation of the significance of the concordance coefficients

Table 4 .
Results of expert consensus in the second round

Table 5 .
Private desirability according to Harrington