The focus of this research is to describe and analyze the results of a pedagogical experiment which sought to introduce online Englishlanguage courses into the educational process of Sevastopol State University (SevSU). In doing so, we evaluated the e cacy of these online English-language courses using the Principal Component Analysis (PCA) in the GRETL Statistical Software Package. That is, we created two random samples of 30 third-year undergraduate students in each. The rst sample, the control group, consisted of students who study English using traditional methods without the use of distance learning technologies. The second sample is an experimental group, which included students whose English-language professional training from the fourth semester is provided using the Moodle online course in English. Then we created a set of initial data in GRETL for the experimental group, which consisted of the nal grades of students in English for ve semesters. Since the Moodle course was introduced for the experimental group in the fourth semester, we used the method of Principal Components Analysis to create two integral evaluation indicators calculated as the rst principal components: before the introduction of Moodle and after that. Then we analyzed the dynamics of the di erence between these values for the worst student of the experimental group. After the introduction of Moodle, the worst student improved his integrated result to 7.57. From the results of the calculations obtained, it can be concluded that with other permanent factors the reason for the improvement of learning achievement in the experimental group is the
use of the e-learning environment. 1
Signi cant in uence on the formation of the theory of pedagogical experiment was made by such authors as C. Hicks[Hic67], E.V. Yakovlev [Yak10], I.A. Stepankin[Step17], V.A. Sto [Sto78] ,G.I. Batischev[Bat90], etc. Summarizing their de nitions of this concept, we can agree with the following interpretation: a scienti c experiment of transforming the pedagogical process under precisely measured conditions[Sol02]. However, despite signi cant developments in theoretical statements, the contemporary pedagogical science and practice are lacking a widely recognized unambiguous understanding of methodological foundations of a pedagogical experiment, as well as ways to e ciently implement it[Kle15] [Pol00]. 2
In this regard, the purpose of this article is, rst, to test the hypothesis of the experiment conducted to estimate e cacy of online English courses, second, to expand the set of methods used to analyze pedagogical experiment data. 3 3.1
Experiment Purpose The purpose of the experiment is to assess the impact of the digitalization of the educational process at Sevastopol State University. In particular, of the introduction of e-learning English courses[Gal04], on the e ectiveness of the English-language professional education of students at the bachelor's level, thus creating conditions for the further development of the e-learning environment at the university[Kor02] [Schr08]. 3.2
Tasks And Location Of The Experiment { Create two random samples of 30 third-year undergraduate students in each, so that di erent areas of study and di erent Institutes of the University are represented. The rst sample, the control group, would consist of students who study English using traditional methods without the use of distance learning technologies. The second sample is an experimental group, which would include students whose English-language professional training from the fourth semester is provided using the Moodle online course in English. { To generate a set of initial statistical data for both the control and experimental groups derived from recorded nal grades in English for each student for each of the ve semesters of study. { Process the basic data in the GRETL statistical package using the Primary Component Analysis (PCA) tools to determine if the English language teaching inLMS Moodle is providing students with better performance in English. { Analyze the results and make conclusions. The location of the experiment is Sevastopol State University. 3.3
Experiment Sample Bachelor's degree students studying English are randomly selected from a variety of backgrounds. All students at the time of the experiment (January 10th, 2019) were studying in the third year (beginning of the sixth semester). Their total number is 60 people, 30 of whom are members of the control group, which used traditional methods of learning English (did not work in the system of Moodle), and 30 in the experimental group, who began using online English courses in Moodle at beginning of the fourth semester. 3.4
Hypothesis The use of online English courses in LMS Moodlefor all full-time students, regardless of their specialty, increases their achievement in this discipline. The integral grade indicator can be obtained using Principal Component Analysis (PCA) [Kou07]in the Open Source Software { GRETL { by calculating the rst principal component based on the aggregate valueofeach student's grades in time[Kal5]. That is, the PCA is applied in order to provide a generalization of initial grade metrics of students before and after online English courses were introduced in LMS Moodle[Dud08]. The principal component analysis, developed in 1901, is usually applied to compress excessive volumes of information for its easier interpretation[Rak99] . As far as initial indicators x1; ; xp are correlated with each other, it is possible to de ne new aggregated variables y1; ; yp0 (yj {principal component), p0 < p. The new indicators y1; ; yp0 are linear combinations of initial indicators x1; ; xp, formula (1).
y1(x) = w11( x1 1 x1 ) + + w51( x5 5 x5 ); (1) where xj and j { the average and standard deviation of xj ; wj1 { coe cients of the most signi cant principal component (P6 j=1 wj21 = 1); y1 { the most signi cant principal component that can be interpreted as the integral grade indicator. The value 1 is the maximum eigenvalue for the rst principal component y1. 4
Below we will describe results of the experiment by stages. Stage 1.At the rst stage, we created a set of initial data in GRETL software[Pol05] for the experimental group, which consists of the nal grades of students in English for ve semesters, Fig. 1. and 2. "Student" is a variable indicating the student's number, and the variables Semester1...Semester5 indicate the nal grade for the corresponding semesters according to the 100point system. Stage 2: Since the Moodle course was introduced for the experimental group in the fourth semester, we use the method of principal components to create two integral evaluation indicators[Dyak09] [Mukh04] (calculated as the rst principal components): before the introduction of Moodle (Y1 1) and after that (Y2 1). Y1 1 builds on the space of the initial indicators: Semester 1, Semester 2 and Semester 3, taking into account the estimates for the rst three semesters of English language teaching. The implementation of this stage in the GRETL software environment is shown in Fig. 3 On Fig.3,the rst principal component Y1 1 has the designation PC1, it has the highest signi cance and is considered as an integral (generalized) evaluation indicator, formula (2) :
Y1 1 = 0; 689 Semester1 + 0; 608 Semester2 + 0; 394 Semester3 (2) The formula (2) shows the dependency of the integral index Y1 1 on the initial indicators of Semester1...Semester3. Equation coe cients (2) show the contribution of each individual index to the integral indicator Y1..1.
The columns of the P Ci in the modeling results window (Fig. 3) contain values of the coe cients of the principal components wj = (w1j ; ; wpj)0, and according to the column PC1 the rst principal component Y was developed.
The contribution of P C1 (Y1 1) to the total variance of individual indices of the estimations is maximal and in absolute terms is equal to 1 = 130, and in percentage - 81,71%. Therefore, the rst principal component Y1 1 (PC1) can be considered the integral grade indicator. The other principal components of PC2 and PC3 with insigni cant contributions to the overall variance can be ignored. For each of the thirty students in the experimental group, we will calculate the values of Y1 1 by formula (2). The result of the calculations is shown in Fig. 4. Integral index Y2 1 is built on the basis of the initial indicators Semester 4, Semester 5, taking into account the estimates for the last two semesters of English language teaching in Moodle. The realization of this stage in the GRETL software environment is shown in Fig. 5. Based on the results of modeling of Fig.5, we will construct an integral index of Y2 1 evaluation as the rst principal component, formula (3): Y2 1 = 0; 865
Semester4 + 0; 502
Semester5 (3) This is possible because the PC1 (Y2 1) contribution to the total variance is enough and amounts to 80.1%. The values of this principal component are shown in Fig.(6)
Figure 6: The value of the principal component Y2 1
We analyzed the dynamics of the integral grade indicator in English language as a di erence of values Y1 1 and Y2 1 for the worst student of the experimental group. In the rst three semesters the best results were shown by students 15 and 23, showing the integral result Y1 1= 20.4 (Fig. (5). The worst result on this indicator (-22.74) was shown by student 20. After the introduction of Moodle, the worst student improved his integrated result (two semesters) to 7.57, which may be the result of using an online Englishcourse[Sal09][Kle15]. This statement is supported by the visual analysis of the experimental grouppresented by the box diagram in Fig. (7)
In the rst three semesters, the means, as well as medians decrease, and after the introduction of e-learning tend to increase. In the control group, such dynamics were not indicated. 6
From the results of the calculations obtained, it can be concluded that with other permanent factors the reason for the improvement of learning achievement in the experimental group is the use of the e-learning environment. In other words, the use of online courses is a factor in improving English learning achievement. This research was supported by the grant 19-010-00377 of the RFBR (Russian Foundation for Basic Research), Developing a strategic management system for the digital education enhancement in the Russian Federation. [Hic67] C. Hicks Basic principals of experiment planning. M.,Mir, 1967.
Pedagogical research:content and presentation of results
[Step17] I. A. Stepankin Features of the organization of pedagogical experiment. Modern scientist, 6 2010.
[Sto78] V. A. Sto Problems of the methodology of scienti c knowledge. M.:Higher School, 1978.
[Kou07] T. Koufel Econometrics. Problem solving with the use of GRETL. Moscow: Hot line - Telecom, 2007.
[Dud08] G. Dudeney, N. Hockly How to Teach English with Technology. Pearson Longman, 2008.
[Sol02]
[Pol00] E. S. Polat Project method for foreign language lessons. Foreign languages at school, 2{3, 2000.
[Dyak09] V. P. Dyakonov New information technologies: textbook. MOSCOW: SO