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191

Stojanović, S. et al. (2025). Application of statistical models for the analysis of data obtained from continuous assessment of

students in higher education, International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE),

13(3), xxx-xxx.

Original scientific paper

Received: October 01, 2025.

Revised: December 03, 2025.

Accepted: December 10, 2025.

UDC:

xxx

10.23947/2334-8496xxx

Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

Corresponding author:

jelena@pravni-fakultet.info

Abstract: This paper presents the findings of a study aimed at exploring students activities during lectures and exercises.

The research was conducted through basic population of students at the University “St. Kliment Ohridski” – Bitola, in academic

years from 2015 to 2023. The data obtained from the continuous checking of the students’ knowledge, which refer to: attendance

and activity in lectures and exercises, preparation of seminar papers, independent (home) work, completed or realized projects /

programs, as well as from the colloquium grades, are the basis for the application of linear statistical models that will be realized

through descriptive, correlation and regression analysis, factor analysis and statistical inference. In this way, information is obtained

from a series of indicators that will serve the professors to take appropriate corrective actions, in order to improve and better create

their teaching and educational process. As a result, it is expected to obtain better results that are of interest to students and higher

education institutions, in terms of increasing the quality and efficiency of the teaching and learning process in higher education.

Keywords: Statistical Models, Statistical Inference, Database of Statistical Data, Continuous Assessment (ECTS),

Higher Education.

Sanja Stojanović

, Radovan Dragić

, Gabrijela Dimić

,Čedomir Vasić

, Zoran Gordić

Educons University, PM College, Belgrade, Serbia, email:

sanjast@proton.me

University Business Academy in Novi Sad, Faculty of Economics and Engineering Management, Serbia,

email:

radovan.dragic@fimek.edu.rs

Academy of Technical and Art Applied Studies, Belgrade, Serbia, e‑mail:

gabrijela.dimic@viser.edu.rs

MB University Belgrade, Faculty of Business and Law, Serbia, email:

cvasic@mbuniverzitet.edu.rs

AsyTech Limited Honk Kong, Honk Kong, China, email:

zoran@asytech.net

Application of Statistical Models for the Analysis of Data Obtained from

Continuous Assessment of Students in Higher Education

Introduction

The problem of research in this paper consists in finding a way to improve the results in the educa‑

tional process in higher education institutions by applying statistical models, with appropriate software sup‑

port. Namely, the problem of the research can be expressed by the question: “Does the application of sta‑

tistical models in the analysis of the statistical data obtained from the continuous assessment of students

enable the improvement of the teaching and learning process in higher education institutions?” Solving this

problem will be possible only if a comprehensive statistical analysis (descriptive, correlational, regression,

factorial) and statistical inference (statistical hypothesis testing) is made of the available data related to the

continuous examination of students’ knowledge in higher education (Williamson, Bayne and Shay, 2020).

The main goal of the research should enable the identification, discovery and statistical conclusion of

the interaction that exists between the results of the different modalities of continuous assessment and the

final results achieved in the continuous assessment of students in higher education (Yang and Ge, 2022).

Specific research objectives should enable: obtaining insights from the review and identification of

the state of the results of continuous assessment through the methods of descriptive statistics; gaining

insights into the interaction between the different modalities and the final results of continuous assess‑

ment, through correlation and regression analysis; statistical inference for the results of the continuous

assessment through the parametric testing of statistical hypotheses and determination of the components

of the factors that are significant for the achieved results in the continuous assessment through factor

analysis (Wong and Li, 2020).

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192

Stojanović, S. et al. (2025). Application of statistical models for the analysis of data obtained from continuous assessment of

students in higher education, International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE),

13(3), xxx-xxx.

Many authors emphasise the importance of continuous assessment (CA) of students. M. Com‑

brinck and M. Hatch (

Combrinck and Hatch, 2012) emphasises that students perceived that their learning

is improved and that is evident that many students’ experiences of CA were positive.

D. Playfoot, L.L. Wilkinson, and J. Mead (Playfoot, Wilkinson, and Mead, 2023) in their work reports

a series of studies that assessed the performance of students on continuous assessment components

from two courses in an undergraduate psychology programme. The studies described in this paper set

out to examine whether students with additional learning needs might be disadvantaged when continuous

assessment tests are incorporated into courses and as result of this research there appears to be no such

disadvantage (Teeroovengadum, Nunkoo, Gronroos, Kamalanabhan and Seebaluck, 2019).

Y. R. Rincón, A. Munárriz, A. M. Ruiz (Rincón, Munárriz, and Ruiz, 2024) proposes a new approach of

continuous assessment of a formative nature, aimed at achieving meaningful learning with lower stress levels.

Author H.A. Bencsik (Bencsik, 2017) communicates the results of the research concerning the

maintenance of young students’ attention during higher education classes and their motivation for cooper‑

ation. At the same time. The results confirmed that the teaching methods do not affect the students’ open‑

ness. Their willingness to cooperate and their attitudes towards teamwork (Spitzig and Renner, 2022).

One of the process of continuous assessment of students is also evaluating lecturers by students.

In this regard, D. D. Trung, B. Dudić, D. V. Duc, N. H. Son and A. Mittelman (Trung, Dudić, Duc, Son,

and Mittelman, 2024) emphisises that the current landscape of higher education, the quality of teaching

plays a crucial role in supporting the comprehensive development of students. Authors also focuses on

constructing a lecturer ranking system, particularly in the context of a specific course through the evalua‑

tion process from students.

For this research very important is the use of linear models which M. Kutner, C Nachtsheim, J.

Neter, and W. Li (Kutner, Nachtsheim, Neter, and Li, 2004) present in detail (the most important linear

statistical models and their application possibilities).

According to (Bowman, 2012) quantitative meta‑analysis is very useful, yet an underutilized tech‑

nique for synthesizing research findings in higher education. He emphasizes that meta‑analysis scientists

have concluded that standardized regression coefficients applied to higher education represent an ap‑

propriate metric for effect size and that linear modeling provides an efficient method for conducting meta‑

analytic research (Morales, Salmerón, Maldonado, Masegosa and Rumí, 2022).

Also, according to (Tüzüntürk, 2015) the importance of using parametric and nonparametric statisti‑

cal methods is inevitable for many scientific branches in the scientific world, especially for the quality of

services in education. At the same time, it has great significance for personal development and perfor‑

mance, for the success of an institution, as well as for the development of the country.

The authors R. Januškevičius and D. Pumputis (Romanas and Dalius, 2011) consider the most

common inaccuracies and errors when using statistical methods that are applied in educational research,

especially related to the definition of the population or sample. In doing so they propose recommendations

on how to avoid the mentioned inaccuracies and errors аs well as an example of real statistical research

in the real research of education (Abbas, 2020).

Materials and Methods

Materials and methods are the second section of an IMRAD paper. Its purpose is to describe the

experiment in such retail that a competent colleague could repeat the experiment and obtain the some or

equivalent results. Provide sufficient detail to allow the work to be reproduced. Methods already published

should be indicated by a reference: only relevant modifications should be described.

For solving the defined research problem, the research strategy case study (correlation study, sur‑

vey research) is suitable. Namely, in the research from the basic population of students at the University

“St. Kliment Ohridski” ‑ Bitola, using a case study as a sample, students from the second year of the Fac‑

ulty of Economics in Prilep, from all study programs, in the subject of statistics for economists in academic

years 2014/2015, 2015/2016, 2016/2017, 2017/2018, 2018/2019, 2019/2020, 2020/2021, 2021/2022 and

2022/2023, that is, from 2015 to 2023 .

This should enable obtaining a series of answers to the following questions: Is there a difference

in the results of continuous assessment in the first and second colloquium? Is there a difference in the

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Stojanović, S. et al. (2025). Application of statistical models for the analysis of data obtained from continuous assessment of

students in higher education, International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE),

13(3), xxx-xxx.

results of continuous assessment in the first (second colloquium) achieved by students from different

study programs? Does the presence of students at classes and exercises affect the results of colloquia?

Does the activity of students in teaching and exercises affect the results of colloquiums? Does the activity

(attendance) of students in teaching and exercises affect the results of seminars?

Of course, a series of indicators for the average grades from the colloquiums (for example, by

study programs), the average final grade, the average variability of the grades, the laws of probability, the

distribution functions and the symmetry or asymmetry of the distribution of the continuous assessment

results are also obtained here (Smeds, 2022). All this after academic years with appropriate comparative

analysis and understanding of development tendencies. Also, with the survey research, answers should

be obtained for questions related to the quality of teaching, the relationship with the students, as well as

the evaluation of the students.

The application of survey statistics is observed using a representative sample (students of the

second year of study in the subject of statistics for economists) for sufficiently significant time periods of

recorded valid data (Castillo-Manzano, Castro-Nuño, López-Valpuesta, Sanz-Díaz and Yñiguez, 2024).

Based on these data, statistical processing was performed using statistical methods: descriptive

statistics (average values, standard deviations, coefficients of variation), correlation and regression analy‑

sis (linear, simple and multiplicative), factor analysis (based on a survey of students), statistical inference,

that is, testing of statistical hypotheses using the parametric ANOVA test (Luan and Tsai, 2021).

The data on the results of the continuous assessment of students in higher education are recorded

in mandatory databases that should be operated by the subject teacher according to the rules for continu‑

ous checking and recording of the results achieved from the first cycle of studies at the University “St.

Kliment ‑ Ohridsk” ‑ Bitola. That data is continuously recorded with all changes up to the final results of

the continuous assessment, and then archived.

The research is carried out in the final part of the semester through a previously constructed survey

questionnaire that is filled out by students who are regular at classes and exercises. Also, important data

from the continuous assessment (attendance, activity, seminar/project assignments and colloquiums) are

collected at the end of the semester for all registered students from the second year of study (Clemons

and Jance, 2024). The overall procedure of creating and applying a statistical model for the analysis of

data obtained from the continuous assessment of students in higher education is presented in Figure 1.

Figure 1. Statistical models for the analysis of data obtained from continuous assessment.

Data on colloquiums, attendance, activity, the creation of seminar works or research tasks, as

well as data from survey research, are created in a special database for continuous assessment and are

subject to statistical processing and analysis through the use of: descriptive statistics, correlational and

regression analysis, factor analysis and statistical inference. Data analysis tools in Microsoft Excel, SPSS

or other statistical software and applications are used in the processing. The goal is to obtain information

and knowledge about the success of the education process, as a basis for taking corrective actions to

continuously improve that success.

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194

Stojanović, S. et al. (2025). Application of statistical models for the analysis of data obtained from continuous assessment of

students in higher education, International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE),

13(3), xxx-xxx.

The multiple regression model for this research can be represented by the following formulation:

= b

+ b

where:

General assessment;

‑ Average points from colloquiums;

‑ Attendance at classes and exercises;

‑ Teaching activity and exercises;

‑ Preparation of a seminar paper (projects, programs, etc.).

Based on the above‑defined model, simple regression models can be defined and a regression

analysis can be performed on them, whereby relevant indicators for the quantitative interaction of the

variables of interest will be obtained.

Hypothetical research framework

Based on the subject and objectives of the research, the following basic hypothesis can be defined,

as well as the auxiliary hypotheses derived from it:

Basic hypothesis: The results of the additional activities in the continuous knowledge test do not

affect the final grade in the continuous assessment.

Auxiliary hypotheses:

• The results of the colloquia do not affect the final grade in the continuous assessment.

• Students’ attendance at classes and exercises does not affect the final grade in continuous assessment.

• Activity in teaching and exercises does not affect the final grade in continuous assessment.

• Completion of project assignments or term papers does not affect the final grade in continuous as‑

sessment.

The processing and analysis of the data, the subject of this research, is quite convenient to real‑

ize, considering that the entire record of the continuous evaluation is created in a database in Microsoft

Excel. Namely, Data Analysis is used as a tool for statistical data processing and Microsoft Excel with all

available statistical procedures, in order to solve the problem of decision‑making: descriptive statistics,

correlation and regression analysis, parametric ANOVA testing, etc. The convenience of importing data

from Microsoft Excel into the data editor in the statistical package SPSS is also used, where there is an

opportunity for additional processing and analysis with other statistical methods, non‑parametric tests,

factor analysis, etc.

Results

By applying descriptive statistics to the recorded data for continuous evaluation, a series of in‑

formation is obtained regarding the average grades, the average variability of the grades (Table 1), the

asymmetry of the distribution of the grades, as well as the possibility of generalization through interval

evaluation with an appropriate confidence threshold. All this is made possible by using Data Analysis in

Microsoft Edge, (See Table 2).

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Stojanović, S. et al. (2025). Application of statistical models for the analysis of data obtained from continuous assessment of

students in higher education, International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE),

13(3), xxx-xxx.

Table 1. Statistics from processed data for continuous assessment of students in the subject statistics for econo-

mists according to school years

Academic year Average grade Standard deviation Coefficient of variation

2014/2015 7,52 1,33 17,67

2015/2016 8,04 1,44 17,92

2016/2017 7,59 1,16 15,26

2017/2018 8,27 1,47 17,72

2018/2019 6,83 0,98 14,39

2019/2020 7,94 1,30 16,42

2020/2021 8,5 0,972 11,43

2021/2022 8 1,73 21,65

2022/2023 8 1,225 15,31

The average grade from the continuous assessment in 5 out of 9 school years is 8 or above 8. Only

in the 2018/2019 academic year we have the lowest average grade, i.e. an average grade below 7. (Table 1

and Figure 2). The greatest variability in grades, expressed by the coefficient of variation, was observed in

the school year 2021/2022, and the lowest in the academic year 2020/2021. (Table 1 and Figure 3).

Coefficient of variation

Average grade

Figure 2. Average final grades across academic years. Figure 3. Coefficient of variation.

There is also the possibility to calculate and compare the average grades and their variability be‑

tween the different study programs, the first and second colloquium and so on.

This provides information on success and corrective actions to be taken to improve that success.

Based on the processed data related to the subject of research in this paper, the following informa‑

tion presented in Table 1 is obtained.

Table 2. Descriptive statistics on the additional activities of students in the subject statistics for economists in the

respective academic years

Academic

year

Total students

Insufficient

attendance (%)

Insufficient

activity (%)

Not interested in

seminary (%)

Passed through

colloquiums (%)

2014/2015 181 16,02 60,22 75,14 45,86

2015/2016 149 12,08 36,91 77,85 35,57

2016/2017 95 17,89 53,68 86,32 35,78

2017/2018 90 4,44 51,11 78,89 41,11

2018/2019 72 19,44 81,94 84,72 8,33

2019/2020 95 25,26 73,68 92,61 18,95

2020/2021 60 13,33 58,33 90,00 16,67

2021/2022 46 30,43 84,78 80,43 23,91

2022/2023 18 5,55 72,22 72,22 27,78

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Stojanović, S. et al. (2025). Application of statistical models for the analysis of data obtained from continuous assessment of

students in higher education, International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE),

13(3), xxx-xxx.

The following can be seen from table 2 and figure 4:

• The number of students registered in the subject statistics for economists continuously and signifi‑

cantly decreases in the observed time period, almost by 4 times, as of the academic year 2021/2022.

From the academic year 2022/2023, the subject statistics for economists is optional for the accounting

and auditing, banking and finance and international business study programs. (Table 2 and Figure 5).

• Not all registered students attend classes and exercises on the subject of statistics for economists.

30.43% of the registered students in the academic year 2021/2022 do not have or have received 1 point

for attending classes and exercises. Also, a significant percentage, more than a quarter, or 25.26% of

the registered students, are doing so in the 2019/2020 academic year. Of course, there are various rea‑

sons for this that are not the subject of discussion in this paper. There is a greater attendance at classes

and exercises in the academic years 2017/2028 and 2022/2023. (Table 2 and Figure 6).

• The data concerning the inactivity of students in all observed academic years are worrying and an

increase in the development tendency is observed. Except for the academic year 2015/2016, in all the

others it can be seen that more than half of the students do not show activity in teaching and exercises.

That percentage is even over 80. (Table 2 and Figure 7).

• The interest in producing seminar papers on the subject of statistics for economists is a concern. Namely,

more than ¾ of the students in all academic years are not interested in making a seminar paper. At most

or less than 10% of students are interested in making a seminar paper in the academic years 2019/2020

and 2021/2022. From the graphic display in Figure 8, one can see the consistency in that lack of interest.

• The pass rate, i.e. the percentage of passed students through colloquiums, decreases until the aca‑

demic year 2018/2019, so that percentage starts to grow again continuously. (Table 2 and Figure 9).

Figure 4. Percentage participation/non-participation of students for the additional activities of students in the

subject statistics for economists by academic years

100

150

200

Total students

Figure 5. The number of students Figure 6. Classes attendance

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Stojanović, S. et al. (2025). Application of statistical models for the analysis of data obtained from continuous assessment of

students in higher education, International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE),

13(3), xxx-xxx.

Figure 7. Classes activity Figure 8. The interest in producing seminar papers

Passed through colloquiums

(%)

Figure 9. Colloquiums pass rate

Based on the data from table 2 that refer to the additional activities: attendance at classes and

exercises, activity at classes and exercises, and preparation of seminar papers, the following hypotheses

can be defined:

H1: There is no difference in the percentage participation in the additional activities of the students

according to the different academic years

H2: There is no difference in the percentage of students’ participation in extracurricular activities

compared to the different modalities of extracurricular activities.

To test the above-defined hypotheses, we apply the parametric ANOVA test with two factors and

multiple modalities. We get the following results (Table 3).

Since the calculated value of the F variable (2.493614) is lower than the theoretical value of the F

variable which is 2.591096, we accept H1 and statistically conclude that there is no difference in the per‑

centage participation in the additional activities of the students according to the different academic years.

We come to the same conclusion by comparing the measured value of p, which is 0.057022, which

is greater than the theoretical value p=0.05.

Since the calculated value of the F variable (128.6174) is greater than the theoretical value of the

F variable which is 3.633723, we reject H2 and statistically conclude that there is a significant difference

in the percentage participation in the additional activities of the students according to the different modali‑

ties of extracurricular activities. We come to the same conclusion by comparing the measured value of p,

which is approximately equal to 0, which is lower than the theoretical value p=0.05.

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Stojanović, S. et al. (2025). Application of statistical models for the analysis of data obtained from continuous assessment of

students in higher education, International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE),

13(3), xxx-xxx.

Table 3. Anova: Two-Factor without Replication

SUMMARY

Count

Sum

Average

Variance

2014/2015

151.38

50.46

945.2368

2015/2016

126.84

42.28

1103.051

2016/2017

157.89

52.63

1171.493

2017/2018

134.44

44.81333

1415.437

2018/2019

186.1

62.03333

1362.576

2019/2020

191.55

63.85

1206.477

2020/2021

161.66

53.88667

1484.38

2021/2022

195.64

65.21333

912.1408

2022/2023

149.99

49.99667

1481.63

Insufficient attendance (%)

144.44

16.04889

71.83606

Insufficient activity (%)

572.87

63.65222

245.8493

Not interested in seminary (%)

738.18

82.02

46.8371

ANOVA

Source of Variation

P-value

F crit

Rows

1618.258

202.2822

2.493614

0.057022

2.591096

Columns

20866.92

10433.46

128.6174

1.38E‑10

3.633723

Error

1297.922

81.1201

Total

23783.1

If the basic multiple regression model is implemented for all academic years, the following indica‑

tors are obtained for the quantitative interactions of the variables of interest (Table 4).

Table 4. shows a very strong relationship between the final grade and the points obtained from the

colloquiums, the presence of classes and exercises, the activity of classes and exercises and preparation of

seminar papers. This relationship is also confirmed by the high values of the coefficients of determination.

Table 4. Quantitative indicators of the interaction of variables in the general linear multivariate regression model.

Academic year Multiple R Adjusted R Square Standard Error F‑variable p‑ value

2014/2015 0.9997 0.9995 0.3109 38906.95 0,0000

2015/2016 0.9999 0.9997 0.2008 63449.68 0,0000

2016/2017 0.9994 0.9986 0.4572 6163.435 0,0000

2017/2018 0.9999 0.9998 0.2352 37945.25 0,0000

2018/2019 0.9999 0.9999 0,0001 95829,15 0,0000

2019/2020 0.9834 0.9582 2.6511 109.82 0,0091

2020/2021 0.9684 0.9024 2.8074 26.43 0,0003

2021/2022 0,9999 0,9997 0.0001 97546.32 0,0000

2022/2023 0,9999 0,9998 0,0001 98238.49 0,0000

Also, for all academic years, it can be seen that the calculated values of the F‑variable are greater

than the corresponding theoretical values, that is, all the calculated p‑values are lower than the theoreti‑

cal value p=0.05. In all cases, that is, for all academic years, the hypothesis that there is no difference

in the influence of grades from colloquiums, attendance, activity, the preparation of seminar papers, and

the final grade is rejected. So there is a statistically significant difference in the influence of all modalities

of additional activities and colloquium grades on the final grade. Or rather they have a different impact.

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Stojanović, S. et al. (2025). Application of statistical models for the analysis of data obtained from continuous assessment of

students in higher education, International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE),

13(3), xxx-xxx.

If we realize the simple regression models, that is, the separate impacts of the success of the col‑

loquia and each modality of additional activities separately on the final grade, we will get the following

results:

Table 5. Quantitative indicators of the interaction of colloquium grades and the final grade

Academic year Multiple R Adjusted R Square Standard Error F‑variable p‑ value

2014/2015 0.9326 0.8681 4.9208 540.61 0,0000

2015/2016 0.9452 0.8913 4.6255 427.18 0,0000

2016/2017 0.9349 0.8701 4.5063 222.11 0,0000

2017/2018 0.9387 0.8779 5.2644 266.95 0,0000

2018/2019 0.9297 0.8609 5.5079 254.79 0,0000

2019/2020 0.9552 0.9075 3.9426 187.38 0,0000

2020/2021 0.8018 0.6071 5.6326 17.997 0,0017

2021/2022 0.9574 0.9090 5.5590 120.87 0,0000

2022/2023 0.9235 0.8160 5.3159 23.18 0,0086

In Table 5, through the values of the correlation coefficients, a very strong relationship between

the colloquium grades and the final grade can be seen. That strong interaction is also represented by the

high values of the coefficients of determination. Also, for all school years it can be seen that the calculated

values of the F‑variable are greater than the corresponding theoretical values, that is, all the calculated p‑

values are lower than the theoretical value p=0.05. This means that, for all cases, that is, for all academic

years, the hypothesis that colloquium grades do not affect the final grade is rejected. So, the grades from

the colloquiums have a significant impact on the final grade.

Table 6. Quantitative indicators of the interaction of the attendance of classes and exercises and the final grade

Academic year Multiple R Adjusted R Square Standard Error F‑variable p‑ value

2014/2015 0.3826 0.1358 12.5945 13.89 0,0004

2015/2016 0.5732 0.3154 11.6060 24.95 0,0000

2016/2017 0.1021 0.0104 12.6324 0.34 0,5657

2017/2018 0.5628 0.2978 12.6237 16.69 0,0002

2018/2019 0.4892 0.2203 13.0408 12.59 0,0010

2019/2020 0.1168 0.0136 13.2267 0.25 0,6239

2020/2021 0.2003 0.0401 9.2337 0.42 0,5325

2021/2022 0.5757 0.2706 15.7386 5.45 0,0395

2022/2023 0.1511 0.0228 13.6972 0.09 0,7750

In table 6, through the values of the correlation coefficients, it can be seen that in certain academic

years (2014/2015, 2015/2016, 2017/2018, 2018/2019 and 2021/2022) there is a significant relationship

between the attendance of classes and exercises and the final grade , and while in some academic

years (2016/2017, 2019/2020, 2020/2021 and 2022/2023) the presence of classes and exercises has a

weak influence on the final grade ‑ this is also seen from the insignificant value of the coefficients of de‑

termination. Also, for the corresponding academic years, it can be seen that the calculated values of the

F‑variable are greater than the corresponding theoretical values, i.e. calculated p‑values are lower than

the theoretical value p=0.05, and for the others they are higher than the theoretical value of p=0.05. This

means that in some academic years, the hypothesis that the attendance of classes and exercises does

not affect the final grade is rejected (that is, attendance has a significant impact on the final grade), and

in other academic years, the hypothesis that the attendance of classes and exercises does not affect the

final grade is accepted. on the final grade (meaning attendance does not affect the final grade).

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Stojanović, S. et al. (2025). Application of statistical models for the analysis of data obtained from continuous assessment of

students in higher education, International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE),

13(3), xxx-xxx.

Table 7. Quantitative indicators of the interaction of class activity and exercises and the final grade

Academic year Multiple R Adjusted R Square Standard Error F‑variable p‑ value

2014/2015 0.5658 0.3117 11.2402 38.13 0,0000

2015/2016 0.6267 0.3809 11.0370 32.99 0,0000

2016/2017 0.2693 0.0435 12.2297 2.50 0,1236

2017/2018 0.6832 0.4520 11.1517 31.52 0,0000

2018/2019 0.6964 0.4721 10.7304 37.67 0,0000

2019/2020 0.3068 0.0438 12.6756 1.87 0,1883

2020/2021 0.6756 0.4020 6.9487 8.40 0,0159

2021/2022 0.8489 0.6950 10.1776 28.34 0,0002

2022/2023 0.7660 0.4835 8.9069 5.680672 0,0757

In table 7, through the values of the correlation coefficients, it can be seen that in certain academic

years (2014/2015, 2015/2016, 2017/2018, 2018/2019, 2020/2021 and 2021/2022) there is a significant

relationship between the activity of teaching and exercises and the final grade, and while in some aca‑

demic years (2016/2017, 2019/2020 and 2022/2023) the activity of classes and exercises has a weak in‑

fluence on the final grade ‑ this can be seen by the insignificant value of the coefficients of determination.

Also, for the corresponding academic years, it can be seen that the calculated values of the F‑variable are

greater than the corresponding theoretical values, that is, the calculated p‑values are less than the theo‑

retical value p=0.05, and for the rest they are greater than the theoretical value p =0.05. This means that

in some academic years the hypothesis that the activity in classes and exercises does not affect the final

grade is rejected (that is, the activity has a significant impact on the final grade), and in other academic

years the hypothesis that the activity in classes and exercises does not affect the final grade is accepted.

grade (meaning the activity does not affect the final grade grade).

Table 8. Quantitative indicators for the interaction of preparation of the seminar and the final grade

Academic year Multiple R Adjusted R Square Standard Error F‑variable p‑ value

2014/2015 0.7569 0.5676 8.9095 108.62 0,0000

2015/2016 0.7860 0.6103 8.7560 82.44 0,0000

2016/2017 0.6868 0.4552 9.2299 28.57 0,0000

2017/2018 0.7514 0.5525 10.0775 46.68 0,0000

2018/2019 0.6782 0.4464 10.9889 34.06 0,0000

2019/2020 0.5890 0.3118 10.7531 9.61 0,0062

2020/2021 0.6111 0.3108 7.4603 5.96 0,0348

2021/2022 0.8956 0.7842 8.5609 44.60 0,0000

2022/2023 0.9615 0.9056 3.8067 49.00 0,0022

In Table 8, through the values of the correlation coefficients, it can be seen that in all academic

years there is a significant relationship between the preparation of a seminar paper and the final grade. It

can also be seen from the values of the coefficients of determination. Also, for all academic years it can

be seen that the calculated values of the F‑variable are greater than the corresponding theoretical values,

that is, the calculated p‑values are less than the theoretical value p=0.05. This means that for all academic

years, the hypothesis that the preparation of seminar papers does not affect the final grade is rejected,

that is, it is statistically concluded that the preparation of the seminar paper has a significant impact on

the final grade. If we include in the regression model the independent variables expressed through all

modalities of additional activities, that is, attendance at classes and exercises, activity at classes and

exercises and preparation of seminar papers, then we get the following results from the interaction with

the final grade.

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students in higher education, International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE),

13(3), xxx-xxx.

Table 9. Quantitative indicators of the interaction of additional activities and the final grade

Academic year Multiple R Adjusted R Square Standard Error F‑variable p‑ value

2014/2015 0.7906 0.6107 8.4529 43.88 0,0000

2015/2016 0.8263 0.6634 8.1385 35.15 0,0000

2016/2017 0.6988 0.4371 9.3819 9.54 0,0001

2017/2018 0.8208 0.6450 8.9756 23.41 0,0000

2018/2019 0.7856 0.5870 9.4915 20.42 0,0000

2019/2020 0.7102 0.4115 9.9443 5.43 0,0091

2020/2021 0.7799 0.4613 6.5952 4.14 0,0480

2021/2022 0.9021 0.7518 9.1813 13.11 0,0012

2022/2023 0.9720 0.8618 4.6077 11.39 0,0000

In Table 9, through the values of the correlation coefficients, it can be seen that in all academic

years there is a significant or very strong relationship between the additional activities and the final grade.

It can also be seen from the values of the coefficients of determination. Also, for all academic years it can

be seen that the calculated values of the F‑variable are greater than the corresponding theoretical values,

that is, the calculated p‑values are less than the theoretical value p=0.05. This means that for all academic

years, the hypothesis that the additional activities do not affect the final grade is rejected, that is, it is sta‑

tistically concluded that the additional activities have a significant impact on the final grade.

Significant information about the quality of the teaching process is also obtained from a continuous

survey of students, which refers to the teaching staff, using appropriate response modalities of the type:

5‑ yes, completely agree, 4‑ mostly agree, 3‑ I hesitate, 2‑ I mostly disagree, 1‑ no, I don’t agree at all.

Questions related to the teacher are defined as variables shown in Table 10.

Table 10. Questions related to the teacher defined as variables

Variable Meaning Variable Meaning

SPRN readiness to implement teaching DAFZ expands knowledge of the subject

PPI

commitment and the ability to provoke

interest among students

RPFC realizes a planned fund of lessons

KSMN using modern methods of teaching work OSODL

provides appropriate basic and additional

literature

knows how to motivate and involve students

in the teaching process

PST applies modern technologies

SDA stimulates additional activities ODK open and available for consultation

LKO has a personal culture and relationship OO allows objective assessment

exams / colloquiums are with questions

within the subject program

OIZ

the assessment is a reflection of the knowledge

and achievement of the students

At the beginning, it is tested whether the data in the model are suitable for the application of factor

analysis. We do that with Kaiser‑Meyer‑Olkin Measure of Sampling Adequacy.

Table 11. Kaiser-Meyer-Olkin Measure of Sampling Adequacy.

KMO and Bartlett's Test

,790

439,996

,000

Kaiser-Meyer-Olkin Measure of Sampling

Adequacy.

Approx. Chi-Square

Sig.

Bartlett's Test of

Sphericity

KMO (Kaiser‑Meyer‑Olkin Measure of Sampling Adequacy) for the analyzed model is 0.790, which

shows that the data in the model are suitable for factor analysis. It is also confirmed by the significance

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Stojanović, S. et al. (2025). Application of statistical models for the analysis of data obtained from continuous assessment of

students in higher education, International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE),

13(3), xxx-xxx.

of the Chi‑Sguare test for 91 degrees of freedom. Factor analysis is used to process the survey data. At

the same time, the basic information from the answers presented through descriptive statistics such as

average values of the answers and average variabilities of the answers are presented in Table 12.

Table 12. Average values and average variabilities of students’ answers

Descriptive Statistics

4,90

,325

114

4,63

,584

114

4,37

,744

114

4,56

,625

114

4,74

,625

114

3,71

,948

114

3,80

,979

114

4,46

,766

114

4,08

,970

114

4,77

,533

114

4,80

,551

114

4,63

,834

114

4,59

,577

114

4,71

,528

114

SPRN

PPI

KSMN

SDA

DAFZ

RPFC

OSODL

PST

LKO

ODK

OIZ

Mean

Std. Deviation

Analysis N

From Table 12, it can be seen that the students, through their answers, mostly agree that the teacher

contributes to the realization of a quality and correct teaching process. If each question is analyzed, then

the teacher should introduce additional activities that will serve to increase and expand the knowledge of

the subject. The students mostly differ in their answers regarding the realization of the planned fund of

classes, and they mostly agree that the teacher is adequately prepared for the realization of the teaching.

We apply principal components factor analysis. In doing so, we get them Communalities (Table 13):

Table 13. Communalities

Communalities

1,000

,731

1,000

,587

1,000

,430

1,000

,607

1,000

,576

1,000

,608

1,000

,656

1,000

,482

1,000

,662

1,000

,449

1,000

,556

1,000

,477

1,000

,701

1,000

,654

SPRN

PPI

KSMN

SDA

DAFZ

RPFC

OSODL

PST

LKO

ODK

OIZ

Initial

Extraction

Extraction Method: Principal Component Analysis.

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Stojanović, S. et al. (2025). Application of statistical models for the analysis of data obtained from continuous assessment of

students in higher education, International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE),

13(3), xxx-xxx.

Table 14. Extraction of the factors affecting the level of the teaching process

Total Variance Explained

4,412

31,512

4,412

31,512

1,609

11,493

43,005

1,609

11,493

43,005

1,105

7,892

50,897

1,105

7,892

50,897

1,050

7,502

58,399

1,050

7,502

58,399

,977

6,975

65,374

,852

6,088

71,462

,732

5,227

76,690

,701

5,007

81,697

,627

4,480

86,177

,511

3,650

89,828

,471

3,367

93,195

,362

2,588

95,783

,317

2,264

98,048

,273

1,952

100,000

Component

Total

% of Variance

Cumulative %

Total

% of Variance

Cumulative %

Initial Eigenvalues

Extraction Sums of Squared Loadings

Extraction Method: Principal Component Analysis.

Four factors explain 58.399% of the variability in the level of the teaching process.

Component Number

1413121110987654321

Eigenvalue

Scree Plot

Figure 10. Cattelli diagram for 14 variables

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Stojanović, S. et al. (2025). Application of statistical models for the analysis of data obtained from continuous assessment of

students in higher education, International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE),

13(3), xxx-xxx.

Table 15. Matrix of factor structure after VARIMAX rotation of factors

Component Matrix

,341

,132

,476

,609

,510

-,450

,275

-,222

,538

-,006

,345

-,145

,685

-,219

,292

-,071

,377

-,411

-,110

,503

,576

-,428

-,275

-,130

,785

-,099

,143

-,096

,443

-,478

-,221

,090

,721

,091

-,232

-,281

,388

,487

-,078

-,235

,492

,401

,326

-,217

,488

,410

,024

,265

,648

,350

-,330

,224

,649

,231

-,406

,124

SPRN

PPI

KSMN

SDA

DAFZ

RPFC

OSODL

PST

LKO

ODK

OIZ

Component

Extraction Method: Principal Component Analysis.

4 components extracted.

The component: during the lesson, the teacher is dedicated and arouses interest among the stu‑

dents; uses modern teaching methods; motivates and involves students in the teaching process, stimu‑

lates additional activities in order to increase and expand knowledge of the subject; realizes the planned

fund of classes; applies modern technology in the implementation of teaching (computers, software sup‑

port, information bases, etc.); open and available for consultation and cooperation with students; the

exam/ colloquium questions are within the scope of the subject program and the provided basic literature;

the content and structure of the exams/colloquium questions enable objective assessment; the grade is

a reflection of the students’ knowledge and achievement, they refer to the first factor of influence on the

teaching process. This factor refers to the quality of teaching and assessment.

The teacher component provides adequate basic and additional literature, the personal culture and

attitude of the teacher are at an appropriate level, refer to the second factor of influence on the teaching

process. This factor refers to the attitude towards students.The component, the teacher is adequately

prepared for teaching, refers to the third factor of influence on the teaching process. This factor refers to

the quality of the teacher. The component, the teacher stimulates additional activity for the students (mak‑

ing homework, projects, term papers) refers to the fourth factor of influence on the teaching process. This

factor refers to the improvement of the teaching process.

Discussions

The statistical model offered in this paper, which can be practiced very easily, enables continuous

monitoring and a basis for corrective actions in order to provide an opportunity on the way to a higher qual‑

ity teaching‑educational process and thus a higher quality higher education. The meaning of the offered

statistical model refers to the following:

• A clear picture of the course and realization of the continuous assessment in the academic years is

obtained, thereby identifying the weaknesses and realizing the possibilities for their removal by taking

corrective actions with the aim of increasing the quality of the teaching‑educational process.

• Consultations and communication with students becomes easier based on accurate information at

every moment.

• It represents the basis for planning the educational process, that is, the performance of lectures and

exercises.

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Stojanović, S. et al. (2025). Application of statistical models for the analysis of data obtained from continuous assessment of

students in higher education, International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE),

13(3), xxx-xxx.

In future research, we will consider Hierarchical Linear Models (HLM) as an advanced statistical

technique designed to analyze student achievement data that have internal nested structure, such as

students nested within classrooms, institutions of higher education, or districts.

Unlike traditional regression models, which assume independence of observations, HLM explicitly

takes this hierarchical arrangement of data into account, allowing for the simultaneous assessment of the

effects of individual‑level factors (e.g., prior achievement) and group‑level variables (e.g., teacher quality

or institutional resources) on student outcomes.

This methodological approach is essential to address violations of the independence assumption inher‑

ent in standard regression analysis because it models the non‑independence of observations within groups,

thereby providing more accurate and valid inferences regarding the determinants of student achievement.

Conclusions

The realization and improvement of the quality of higher education, and especially of the teaching‑

educational process, is a continuous need, obligation and task of every higher education institution and

every teacher actively involved in that process. In that sense, the continuous record, the creation of

databases that relate to the realization of that process, the processing and analysis of that data with the

application of statistical methods and techniques and with appropriate software support is not only a ne‑

cessity but an imperative.

The proposed statistical model is significant because it can serve as a basis for developing higher

education enrollment policies and is designed to be flexible, applicable, and efficient for use at both indi‑

vidual and institutional levels. Its benefits extend to students, faculty, and the entire educational institution.

Acknowledgements

The authors thank the Linguistics Department of PM College Belgrade for their support in the pro‑

cess of translation and proofreading of the manuscript.

Funding

This research did not receive any specific grant from funding agencies in the public, commercial,

or not‑for‑profit sectors.

Conflict of interests

The authors declare no conflict of interest.

Data availability statement

The original contributions presented in the study are included in the article/supplementary material,

further inquiries can be directed to the corresponding author/s.

Institutional Review Board Statement

Not applicable.

Author Contributions

Conceptualization: S.S., R.D. and G.D.; methodology: S.S. and Č.V.; software: Č.V. and Z.G.;

formal analysis: S.S. and R.D.; writing—original draft preparation: S.S, R.D. and G.D.; writing—review

and editing: Č.V. and Z.G. All authors have read and agreed to the published version of the manuscript.

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Stojanović, S. et al. (2025). Application of statistical models for the analysis of data obtained from continuous assessment of

students in higher education, International Journal of Cognitive Research in Science, Engineering and Education (IJCRSEE),

13(3), xxx-xxx.

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