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6ANALYSIS OF COMPETITIVE SELECTION OF ENTRANTS FOR ECONOMIC SPECIALTIES OF HIGHER EDUCATION: 2018 EIE VALIDITY SAMPLE
Shevchuk O.
Candidate of Physical and Mathematical Sciences, Associate Professor of the Department of Mathematics, Physics and Computer Technologies Vinnytsia National Agrarian University
(Vinnytsia) Shevchuk O.
Candidate of Economic Sciences, Associate Professor of the Audit and State Control Department, Vinnytsia National Agrarian University (Vinnytsia)
ABSTRACT
The article conducts an analytical study of statistical connections between the components of the competitive selection in 2018 and the average performance of first-year students in the branch of knowledge 07 "Management and Administration" of a particular institution of higher education (HEI). It is noted that in 2018, test EIE, within one field of knowledge, for the first time applied two different, according to the list of subjects of external independent evaluation (EIE), methods of calculating the competitive score of applicants (Cs). The use of such a two-model system had a positive effect on increasing the number of students in 2018 and 2019.
The calculation of correlation coefficients showed that the two-model system of competitive selection of entrants has a fairly high level of prognostic validity (R = 0.662). However, the competitive score calculated by the second method correlates much worse with the average learning outcomes of first-year students, compared to the first model (Rii = 0.564 vs. Ri = 0.718). With the help of variation of weight coefficients of EIE disciplines, a more optimal alternative model of calculating the competitive score of the entrant for the II method is determined and proposed, the correlation coefficient of which R*n = 0.621.
The analysis of the components of the competitive selection of students in this field of knowledge showed that the results of external examinations in the Ukrainian language and literature are a strong predictor of the success of freshmen in economics (R = 0.619). Instead, the EIE in the History of Ukraine correlates worst with their assessments, compared to other subjects (R = 0.364).
Keywords: prognostic validity, correlation coefficient, competitive selection, competitive score, external independent evaluation (EIE), higher education institution (HIE).
Formulation of the problem. The national system of external independent evaluation (EIE) began to take shape in Ukraine in 2004 with the support of international and public organizations, and since 2006 it has been put into operation at the official level. In such a relatively short period of time in Ukraine there has been a radical change in approaches to the final certification of graduates of secondary schools and a fundamental transformation of the rules of admission of entrants to higher educational institutions (HEI).
The set of organizational procedures for EIE at the state level is constantly being improved. After all, the purpose of high-quality, independent measurement of knowledge in selected disciplines and calculation on their basis of a single unbiased competitive score is quality ranking and selection of entrants with the best preparation for higher education.
The objective model of such competitive selection is realized by definition of the corresponding profile subject and introduction of weight coefficients of disciplines of EIE for each professional direction. In this regard, one of the urgent tasks facing higher education institutions is to build and implement the most optimal model of competitive selection of entrants. Based on the results of external independent evaluation and the average score of the certificate, the higher education institution, varying the weight, tries to make a ranking list, in which the first places will be those entrants who can better study in the specialty.
The evaluation of the applied model of competitive selection is investigated according to the indicator of prognostic validity of competitive score.
Prognostic validity is the correlation coefficient between the indicator in according to which the competitive selection is carried out and the results of the student's success during the first year of study. Thus, assessing the value of prognostic validity, it is possible to investigate the statistical relationships of the results of external evaluation in individual subjects or their corresponding weights with student performance and build on them based on optimal models of competitive selection. In this case, the efficiency of the system of admission to the HEI on the basis of the EIE is considered high if the correlation coefficient (R) is greater than 0.5; sufficient if the correlation coefficient is in the range [0.3, 0.5] and low if the correlation coefficient is less than 0.3 [1].
Formulation of the goals of the article. The purpose of this work is an analytical study of the statistical relationships between the components of the competitive selection conducted in 2018, and performance indicators of first-year students branch of knowledge 07 "Management and Administration" of a separate institution of higher education.
Analysis of recent research and publications. The study of the prognostic validity of competitive selection in the HEI due attention in many foreign coun-
tries is given [2 - 5]. Based on the results of such research, the effectiveness of existing models of selection for universities is studied and possible directions for their further improvement are identified.
In Ukraine, too few scientific papers to this question are devoted [1, 6 - 13]. In particular, it is worth noting the scientific and practical publication [1], which conducted a thorough study of the quality of competitive selection of students of higher education institutions based on the results of external evaluation during 2008-2015. The basis of scientific work is the study of three dimensions of the quality of the admission system: the prognostic validity of the competitive score, the fairness of evaluation and their public perception. The main directions and problems of further research of the quality of the system of admission to the HEI, ways of development of the system of EIE as a tool for ensuring the quality of the education system in terms of autonomy of educational institutions are also discussed.
This paper emphasizes the high prognostic validity of EIE, although it is shown that for the Branch of knowledge 07 "Management and Administration" its value is only in the range of 0.41 - 0.54. The authors also emphasize that the rules of the game, in the sense of using the EIE tests for admission to the HEI and final school certification, are constantly changing, and therefore the study of their statistical patterns remains relevant for researchers.
A radically opposite and critical view on the implementation of the external evaluation competition score and its low prognostic validity is given in [6]. The author believes that the system of scaling the results of external evaluation is not transparent, masks the true level of preparation of applicants and needs improvement. His observations show that the results of higher education mathematics students are weakly related to the scores of the relevant EIE certificates, and the correlation coefficient of examination grades with the EIE scores is only 0.45.
Therefore, in order to ensure the training of elite engineering personnel, the author proposes to higher education institutions to set a minimum score of at least 170 for entrants in mathematics and physics. Which, in our opinion, is significantly inflated and not statistically substantiated.
In [7], in order to determine the optimal formula for calculating the competitive score, the influence of the values of the weights of external evaluation disciplines on the prognostic validity of the competitive selection of entrants to the branch of knowledge "Health care" is investigated.
The study of correlations between the results of external evaluation and grades in higher mathematics of first-year students is devoted to [8-10].
A comparative analysis of the value of the indicator of prognostic validity of competitive selection in 2015-2018 for the specialty 151 "Automation and com-
puter-integrated technologies" is given in [13]. The author of the article also mathematically substantiates the expediency of changing the weights used in calculating the competitive score of entrants.
Presentation of the main material of the study. This statistical study will analyze the performance of first-year students in the branch of knowledge 07 "Management and Administration" of a separate institution of higher education, which will be called a test HEI. The volume of the observation group is 60 people.
The average rating score of students (Rs) on the results of first-year education, as well as assessments in certain disciplines, was obtained on the basis of electronic data on the success of the automated control system of test HEI further in a single 100-point scale are expressed.
Competitive score (Cs) and the results of the EIE in 2018, for this sample of students, were obtained using the information system "Competition" Public Association "Center for Educational Policy" of the Ministry of Education and Science of Ukraine [15].
It should be noted that higher education institutions, independently choosing the subjects of external evaluation and their weights, influence the formation of the model of competitive selection of entrants. Therefore, it is advisable to analyze the methodology used by the test EIE when calculating the competitive score for this branch of knowledge.
In 2018, the formula for calculating Cs when entering the bachelor's degree on the basis of complete general secondary education had a unified form:
Cs = Ci-Ei + C2E2 + C3E3 + C4-4+ C5-Os) ■Rc-Bc-Vc-Pc, (1)
where E1, E2, E3 - points of external independent evaluation; A - the average score of the document on education; C1, C2, C3, C4, C5 - non-negative weights, which are set by the university; O s - a score for the successful completion of preparatory courses for admission to the specialty (specialization), which is given special support;
Ra, Ba, Va, Pa - adjustment factors (regional, branch, rural and priority).
For our sample of students in the branch of knowledge 07 "Management and Administration" did not take into account the branch and priority coefficients as well as additional points for preparatory courses and therefore formula (1) takes a simplified form:
Cs = (0,45- E1 + 0,25- E2 + 0,2- E3 + 0,1-4) ■ Rc ■ Vc, (2)
In (2) the weight coefficients of the EIE disciplines, which were selected by the test HEI for this branch of knowledge, are also given. The largest value of the coefficient (0.45) corresponds to the profile subject. In fig. 1 presents the distribution of the competition score calculated by formula (2) for students of test HEI according to the results of admission in 2018 and 2019.
Fig. 1. Histogram of the distribution of the competitive score of students in the branch of knowledge 07 "Management and Administration " of the test HEI on the results of the accession of 2018 and 2019 Source: generated and calculated by the author based on the data given in [15]
2018 _2019
21 18
■M
5 15 ■c
3
tt 12 MO
c 9
3
0
1 6
3
0
I
I I
190-180 180-170 170-160 160-150 150-140
Competitive score
140-130 130-120 120-110
For further analysis, it is important that in 2018, test HEI, within one specialty, was first applied two different, according to the list of subjects of external evaluation, models of calculation of CS. In the first model, the profile subject E1 with the highest weighting factor (C = 0.45) was Mathematics, C2 - Ukrainian language and literature and C3 - at the choice of the entrant or Geography or Foreign language.
In the second model, the profile subject E1 was the History of Ukraine, E2 - respectively, remained the Ukrainian language and literature, a E3 - at the choice of the entrant or Geography or Mathematics. Thus, according to this scheme, even those entrants who did not pass or did not pass the threshold of "passing / not passing" the external examination in mathematics had the opportunity to enter the university. It should be noted that enrollment in the HEI in this case took place only on a contractual basis.
Table 1 shows the quantitative distribution of students of test HEI between different methods of
calculating the competitive score. This table, for comparison, also presents the results of the introductory campaign in 2019, because then used a similar approach to determine the CS of this branch of knowledge. As can be seen from table 1 the number of students who chose the second method of calculating the Cs in 2019 has increased significantly. If in 2018 their share was 36.7%, then in the next year - almost half of the students enrolled in the test HEI.
It is worth noting that in 2019 the number of enrolled students who did not have an EIE Mathematics certificate also doubled. In general, the use of a two-model method of calculating the CS, allowed the test HEI to significantly increase the contingent of students in 2019. This approach proved to be attractive especially for those entrants who did not have an external examination in mathematics, or it was too small to successfully participate in the general competition.
Table 1.
Quantitative distribution of students in the branch of knowledge 07 "Management and Administration" between _different methods of calculating the competitive score, used by test HEI in 2018 and 2019_
Total number of students Used the I-st model calculation of Cs Used the II-nd model calculation of Cs Did not pass the external examination in mathematics
number of people % number of people % number of people %
According to the results of the 2018 accession 60 38 63,3 22 36,7 14 23,3
According to the results of the 2019 accession 85 43 50,6 42 49,4 28 32,9
Source: generated and calculated by the author based on the data given in [15]
Table 2 presents descriptive statistics of indicators HEI with different methods of calculating Cs. In the of competitive selection of students in the branch of given characteristics it is possible to pay attention that knowledge 07 "Management and Administration" test in 2018 the average competitive score calculated by the
I method is much higher than the corresponding indica- can conclude that students with potentially higher EIE tor of the II method and the total sample size. Thus, we scores chose the first method for calculating the Cs.
Table 2.
Descriptive statistics of indicators of competitive selection of students in the branch of knowledge 07 "Management and Administration" of test HEI
Indicator Year of entry Sample size Arithmetic mean The standard deviation Asymmetry Kurtosis
General competitive score 2018 60 143,4 16,26 0,596 0,167
2019 85 145,8 17,64 0,315 -0,704
Competitive score, which is calculated for the I method 2018 38 144,2 17,24 0,781 0,062
2019 43 149,97 17,28 0,084 0,669
Competitive score, which is calculated for the II method 2018 22 140,7 15,03 -0,071 -0,392
2019 42 141,5 17,16 0,62 0,284
EIE, Mathematics 2018 46 127,02 22,45 0,747 0,235
2019 57 131,25 22,30 0,372 0,969
EIE, Ukrainian language and literature 2018 60 150,55 20,82 -0,261 -0,435
2019 85 146,02 22,3 -0,093 -0,945
EIE, History of Ukraine 2018 22 129,1 17,6 0,24 0,258
2019 42 135,3 19,1 0,302 0,167
Source: generated and calculated by the author based on the data given in [15]
This correspondence is also observed for the indicators of 2019, but their values have significantly increased compared to last year. This is especially true for the average Cs, determined by the first method (149.97 in 2019 vs. 144.2 in 2018).
It should also be noted that the average score of the EIE in Mathematics in 2018 (127.02) was significantly lower than the corresponding indicator of the EIE in Ukrainian language and literature (150.55). This situation is typical, mostly, for students of economic specialties and corresponds to the general trend of decreasing the level of physical and mathematical education of school graduates, which has been observed recently in Ukraine. In 2019, the difference between the average EIE scores for these subjects becomes less significant. The average score of the EIE in mathematics increased slightly (131.25), and the average score of the EIE in the Ukrainian language and literature decreased (146.02).
Also noteworthy is the low average indicator of external evaluation in history of Ukraine (129.1 in 2018), which was used as a profile subject for the second method of calculating the Cs. Taking into account also the lower average competitive score for this group of students, it is expedient to further evaluate their results of success in the HEI.
The use of two different models of competitive selection of entrants for one branch of knowledge, is of interest in assessing their indicators of prognostic validity, even with small sample sizes. Table 3 shows the Spearman correlation coefficients between the grades obtained by students during their studies in the test HEI, and the indicators that were used as criteria for selecting students for admission. A higher correlation coefficient means a greater prognostic validity of the criterion.
As can be seen from Table 3, use by the test HEI two-model system of competitive selection of entrants, for one branch of knowledge, has a fairly high level of prognostic validity (R > 0.5). In fig. 2 also shows the correlation field of dependence between the average score of students of test HEI and their competitive score.
It is significant that the values of Cs are better correlated with the average student performance, calculated from the results of the second session. And this is typical for all, without exception, the indicators listed in table 3. One of the main reasons for this pattern may be the problem of psychological adaptation of freshmen in the autumn (first) semester to new, unfamiliar to them methods of teaching and assessment.
c -o
4-J
(A
<u
o
ai ^
o
u
(A
ai tu
ra >
ra ai
100 90 80 70 60 50 40 30 20 10
y = 0,3503x + 25,259 R2 = 0,43832 R = 0,662
110 120 130 140 150 160
Competitive student score
170
180
190
Fig. 2. Correlation field of dependence of the average score of the success offreshmen in the branch of knowledge 07 "Management and Administration" on their competitive score, obtained according to the EIE
2018. The sample size is 60 people Source: generated and calculated by the author based on the data given in [15]
0
Analysis of the data shown in table 3 shows that the highest prognostic validity is the I method of calculating the competitive score. We will remind that in this method Mathematics is a profile subject with the highest weighting factor. But, as it turned out, the results of the EIE only in this discipline are less correlated with the average scores of students of the test
HEI (R = 0.421 for the first semester and R = 0.541 for the second). Therefore, the improvement of the forecast function of competitive selection is achieved through the use of an integrated model of calculation of the Cs with a successful combination of EIE subjects with their corresponding weights (1).
Table 2
Prognostic validity of components of competitive selection of students in the branch of know-ledge 07 "Manage_ment and Administration" of test HEI according to the results of EIE 2018_
Indicator Sample size Average score of the first ses- Average score of the second Average score of first-year
sion session students
Correlation of the competitive score with
the assessments of first-year students of the 60 0,573 0,674 0,662
total sample size
Correlation of the competitive score calcu-
lated according to the first method with the 38 0,643 0,728 0,718
assessments of first-year students
Correlation of the competitive score calculated according to the II method with the 22 0,417 0,581 0,564
estimations of first-year students
Correlation of the competition score with
the grades of first-year students who passed 46 0,597 0,699 0,682
the external examination in mathematics
Correlation of external evaluation results in
mathematics and grades of first-year 46 0,421 0,541 0,509
students
Correlation of external evaluation results in
Ukrainian language and literature with the 60 0,577 0,600 0,619
assessments of first-year students
Correlation of external evaluation results in
history of Ukraine and assessments of first- 22 0,324 0,329 0,364
year students
Source: generated and calculated by the author based on the data given in [15]
To assess the impact of the results of the external examination in mathematics on the prognostic validity of the two-model system of competitive selection of students, from the general sample were excluded persons who did not have a certificate in this subject and redefined correlation coefficients (Table 3). The result of the calculation was slightly better than the corresponding indicator of the total sample size. Thus,
Table 3
Average success rates of first-year students in the branch of knowledge 07 "Management and Administration"
despite the fact that the external examination in mathematics is not a strong predictor of the success of freshmen, its mandatory inclusion in the two-model calculation formula CS leads to an increase in the prognostic validity of competitive selection of students in the branch of knowledge 07 "Management and Administration" test HEI.
Indicator Sample size Average score of the first session Average score of the second session Average score of first-year students
The average score of first-year students in the total sample 60 77,5 73,4 75,5
The average score of freshmen, for whom the index of Cs was calculated by the I method 38 77,4 73,2 75,3
The average score of freshmen, for whom the index of Cs was calculated by the II method 22 77,9 73,8 75,9
The average score of freshmen who had a certificate of external examination in mathematics 46 78,2 73,9 76,1
The average score of freshmen who did not have a certificate of external examination in mathematics 14 75,2 71,7 73,5
In the II method of calculating the Cs as a profile subject used the results of external evaluation of the History of Ukraine. Thus, this discipline had the highest weighting factor (0.45) and the greatest influence in determining the competitive score by formula (2). But, as can be seen from Table 3, the external evaluation of the History of Ukraine is the worst correlated with the success of first-year students in economics, compared to other subjects (R = 0.324 in the first semester, R = 0.329 in the 2nd semester and R = 0.364 for the academic year) .
The consequence of this is also a much lower prognostic validity of the second model of competitive selection relative to the first model (Rn = 0.564 against Ri = 0.718 on the average performance of students during the first year of study).
Instead, EIE of the Ukrainian language and literature, as shown by the calculations given in table. 3, is a strong predictor of success of first-year students in economics.
The above analysis of the prognostic validity of the components of competitive selection, which is used in the II method of calculating the CS, allows, varying the weights of the disciplines of external evaluation, to obtain a more optimal model for calculating the competitive score. Since the highest indicators of the forecast were the assessments of the External Evaluation of Ukrainian Language and Literature, their weighting in the structure of the competition score should be the highest. Therefore, it is advisable to use this subject as a profile with a weighting factor Ci = 0.45 instead of
the external evaluation of the History of Ukraine. Thus, the formula for calculating CS (2) in this case remains unchanged, and only subjects change places: Ei - History of Ukraine and E2 - Ukrainian language and literature.
Another, alternative option for calculating the Cs by the II method, you can consider a model for which all subjects of external evaluation have the same weighting factor Ci = C2 = C3 = 0.3. Then the formula for its calculation takes the following form: Cs = (0.3- Ei + 0.3- E2 + 0.3- E3 + 0.1 v4) • Rc • Vc, (3) where Ei - EIE History of Ukraine, E2 - EIE Ukrainian language and literature, E3 - at the choice of the entrant or Geography or Mathematics.
To evaluate and compare the proposed methods of calculating the Cs, the competitive score of entrants in this sample was listed according to the chosen method, and the correlation indicators were determined (Fig. 3).
As expected, the best result of the forecast of the average success of first-year students (R = 0.62i) is the model in which the EIE Ukrainian language and literature has the highest weighting factor Ci = 0.45, and the worst (R = 0.564) - used by the test HEI in 20i8. In other words, this means that the change of places of objects EIE Ei and E2 in the II model of calculation of Cs, leads to a significant increase in its prognostic validity, and as a result there is an increase of the correlation coefficients in the total sample size (Table 4).
«
ti o
u ifl
a o
J_I_
Calculated by
the formula: Ke = <°>3 ' n> + °'3 ' "2 + 0,3 'n* + 0J 'A) ' Pk Ck
Calculated bv
the formula: Ke = (0,45' "2 + 0,25 ' + 0,2 '™ + 0,1 'A) 'Ph" Ck
Used in HEI: ke = (0,45 ■ /7, + 0,25■ tl2 + 0,2■ ü3 + 0,1 • a) ■ pk-ck
Prognostic validity of the II model of competitive selection of first-year students of economic direction
Fig. 3. Prognostic validity of the II model of competitive selection offirst-year students of economic direction
with different calculation methods of CS
Note also that the use of formula (3) for the calculation of Cs has little effect on the change in the value of the correlation coefficient.
The values of the indicator of prognostic validity of the two-model competitive selection system for the above proposed alternative methods of calculating Cs are given in table 4.
As can be seen from the data in table. 4, for alternative methods, the mentioned above tendency to increase the correlation of the competitive score with the average scores of the second semester is stored, compared with the scores of the first semester. And the
use of EIE Ukrainian language and literature as a profile subject of the II model, contributes to the increase of its forecast indicators and the total sample size. The correlation equation, which allows with some error to predict the average performance of a freshman, in this case, is:
Y = 0.3489- Cs + 24.986 , (4)
where Y is the average score of the student in the branch of knowledge 07 "Management and Administration" according to the results of the first year.
Table 4
Predictive validity of alternative two-model systems of competitive selection of students branch of knowledge 07 _"Management and administration" test HEI according to the results of EIE 2018 _
Type of model Indicator Sample size Average score of the first session Average score of the second session Average score of first-year students
Two-model competitive selection system used in the HEI Predictive validity of the total sample size 60 0,573 0,674 0,662
Prognostic validity of the II method of calculation of Cs 22 0,417 0,581 0,564
An alternative two-model system, in which the objects of external evaluation E\ and E2 are changed in places when calculating the Cs of the II method Predictive validity of the total sample size 60 0,584 0,688 0,676
Prognostic validity of the II method of calculation of Cs 22 0,459 0,640 0,621
An alternative two-model system in which the Cs II method is calculated by formula (3) Predictive validity of the total sample size 60 0,564 0,681 0,662
Prognostic validity of the II method of calculation of Cs 22 0,378 0,608 0,567
Preliminary calculations (Table 2) also showed that the average competitive score calculated by the first method is much higher than the corresponding indicator of the second method and the total sample size. Therefore, it is advisable to compare the average performance of students in these groups during the first year of study in the HEI (Table 5).
Analysis of the data given in table 5 shows that the average student performance is almost the same for
each group, and therefore, they are independent of the method of calculating the competitive score. This is in favor of a two-model Cs calculation system, as its application does not lead to a general decrease in the level of average success of freshmen.
It should also be noted that students who have not submitted certificates of external examination in Mathematics have slightly lower learning rates compared to other persons.
Table 5
Average success rates of first-year students in the branch of knowledge 07 "Management and Administration"
Indicator Sample size Average score of the first session Average score of the second session Average score of first-year students
The average score of first-year students in the total sample 6Q 77,5 73,4 75,5
The average score of freshmen, for whom the index of Cs was calculated by the I method 3S 77,4 73,2 75,3
The average score of freshmen, for whom the index of Cs was calculated by the II method 22 77,9 73,S 75,9
The average score of freshmen who had a certificate of external examination in mathematics 46 7S,2 73,9 76,1
The average score of freshmen who did not have a certificate of external examination in mathematics 14 75,2 71,7 73,5
Conclusions. A statistical study of the correlations between the components of the competitive selection in 2018, and the average performance of first-year students in the branch of knowledge 07 "Management and Administration" indicates that:
1) the two-model system of calculating the competitive score used by the test HEI has a fairly high prognostic validity (R = 0.662) and has a positive effect on increasing the contingent of students in 2018 and 2019;
2) the highest prognostic validity (Ri = 0.718) has the first method of calculating the competitive score, in which Mathematics is a profile subject with the highest weighting factor;
3) EIE Ukrainian language and literature, in comparison with other disciplines, is a relatively strong predictor (R = 0.619) of the success of first-year students in economics, and for EIE assessments in the History of Ukraine this indicator is the lowest (R = 0.364);
4) the use of external evaluation Ukrainian language and literature, as a profile subject of the second method of calculating the competitive score, allows to increase its prognostic validity (Rii = 0.621) and improve the correlation indicators of the total sample size (R = 0.676).
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