=Paper=
{{Paper
|id=Vol-2732/20200948
|storemode=property
|title=Education Statistics: Looking for Case-Study for Modeling
|pdfUrl=https://ceur-ws.org/Vol-2732/20200948.pdf
|volume=Vol-2732
|authors=Liubov Panchenko,Andrii Khomiak
|dblpUrl=https://dblp.org/rec/conf/icteri/PanchenkoK20
}}
==Education Statistics: Looking for Case-Study for Modeling==
https://ceur-ws.org/Vol-2732/20200948.pdf
Education Statistics:
Looking for а Case-study for Modelling
Liubov Panchenko[0000-0002-9979-0625] and Andrii Khomiak[0000-0002-6661-4510]
National Technical University of Ukraine “Igor Sikorsky Kyiv Polytechnic Institute”,
37 Peremohy Ave., Kyiv, 03056, Ukraine
lubov.felixovna@gmail.com, andrii.khomiak@gmail.com
Abstract. The article deals with the problem of using modeling in social statistics
courses. It allows the student-researcher to build one-dimensional and
multidimensional models of the phenomena and processes that are being studied.
Social Statistics course programs from foreign universities (University of
Arkansas; Athabasca University; HSE University, Russia; McMaster University,
Canada) are analyzed. The article provides an example using the education data
set – Guardian UK universities ranking in Social Statistics course. Examples of
research questions are given, data analysis for these questions is performed
(correlation, hypothesis testing, discriminant analysis). During the research the
discriminant model with group variable – modified Guardian score – and 9
predictors: course satisfaction, teaching quality, feedback, staff-student ratio,
money spent on each student and other) was built. Lower student’s satisfaction
with feedback was found to be significantly different from the satisfaction with
teaching. The article notes the modeling and statistical analysis should be
accompanied by a meaningful interpretation of the results. In this example, we
discussed the essence of university ratings, the purpose of Guardian rating, the
operationalization and measurement of such concepts as satisfaction with
teaching, feedback; ways to use statistics in education, data sources etc. with
students. Ways of using this education data in group and individual work of
students are suggested.
Keywords: education statistics, Social Statistics courses, Guardian
methodology, university score, Excel, SPSS, correlation, hypothesis testing,
discriminant analysis
1 Introduction
1.1 Setting of a problem
The modern world is characterized by the diversity of data circulating in society and
waiting to be researched [1-3]. The European Digital Competence Framework for
Citizens defines information and data literacy as important component of digital
competence [2]. The Program for the Development of National Statistics by 2023 [3],
adopted by the Cabinet of Ministers of Ukraine (Resolution No. 222 of February 27,
2019), states, in particular, that the level of statistical literacy of the society needs to be
Copyright © 2020 for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
improved. Therefore, training of the specialists who can make data-based decisions is
an important task of both national and international education. One of the important
aspects of such training is the formation of student’s competences in building statistics
models for studying social phenomena.
The aim of the article, based on the data sets from Guardian UK university ranking
show steps for building one-dimensional and multidimensional models in education
statistics.
1.2 Analysis of recent research and publications
Researchers who have studied various aspects of statistical (data) literacy are: Iddo Gal,
Ellen Mandinach, Chantel Ridsdale, Siu-Ming Tam, Nigel Cross, W. Pat Taylor,
Anthony M. Townsend, Jane M. Watson, Rosemary A. Callingham, Robert Gould,
Ruth Krumhansl, Catherine D’Ignazio, Rahul Bhargava, William Finzer [4].
Many scholars are interested in the problems that arise in teaching statistics and data
analysis. The study of Svetlana Tishkovskaya and Gillian Lancaster [5] summarizes the
list of such problems. The main problems are the following:
─ Focus on mathematical and mechanical aspects of knowledge.
─ “Math-phobia”, “statistical anxiety” and lack of interest.
─ Shortage of students with basic statistical knowledge.
─ Statistics courses are conducted without reference to the subject area.
─ Lack of statistical literacy and inability of students to use statistics in daily life.
─ Lack of tools for assessing statistical thinking and statistical literacy of the
population in social settings.
To overcome these problems, the following strategies are proposed based on the
analysis of [5]:
─ Integration of statistical thinking and statistical literacy into curricula of different
disciplines;
─ Use of media and newspaper articles to evaluate students ‘and students’ ability to
interpret statistical thinking.
─ Shifting the focus of statistics into curricula from mathematical calculations to tasks
of a practical nature.
─ Problem solving skills development: students are offered open problems and the
teacher takes on the role of a “facilitator” in the learning process.
─ Using real life examples in project work.
─ Development of student motivation strategies.
─ Development of statistical literacy and critical thinking skills, use of examples of
incorrect analysis.
─ Focus on daily arguments that use statistics as evidence.
In [4] new forms of student’s activity related to data analysis introduced by academics
and practitioners are discussed: building art objects and storytelling based on data;
shared data collection by citizens through mobile devices, “play with data” using
modern data visualization services.
The different problem of computer modeling in education are summarized by
Ukrainian scientists in framework of CoSinE-2019 workshop. Serhiy O. Semerikov and
other studied computer simulation of neural networks using spreadsheets [6]; Oleksandr
H. Kolgatin and other discussed about computer simulation as a method of learning
research in computational mathematics [7]; Vladimir N. Soloviev and other presented
report of modeling of cognitive process using complexity theory methods [8].
The issues of preparing sociology students and future PhDs to use statistics models
during analysis social statistics data are debated in papers [9-12].
2 Results of the study
During our research we analyzed several Social Statistics course programs from foreign
universities [13-17].
In the research University of Arkansas at Little Rock the SOCI-3381 course is taught
to Sociology majors [13]. The course deals with basic statistical techniques and their
theoretical premises, which are often used in statistical reasoning in sociology:
qualitative variables, characteristics of attributes, variation, correlation, tests of
significance. Course consists of three credit hours.
The course Sociology 301: Social Statistics by the Athabasca University provides an
overview of the uses of statistical analyses for the social sciences. The textbook for this
course is [18]. Course consists of 11 units [14]:
─ Introduction to Statistics and Displaying Information in Tables and Graphs
─ Measures of Central Tendency and Variability
─ Correlation and Prediction
─ Some Key Ingredients for Inferential Statistics: The Normal Curve, Sample versus
Population, and Probability
─ Introduction to Hypothesis Testing
─ Hypothesis Tests with Means of Samples
─ Making Sense of Statistical Significance
─ Introduction to the t Test
─ The t Test for Independent Means
─ Introduction to the Analysis of Variance
─ Chi-Square Tests
The learning goals of the Economic and Social Statistics Course of HSE University
(Russia) [15] is understanding basic principles of collecting and using data from various
statistical sources; familiarization with main statistical indicators used in different fields
of social science; introduction to basic programming tools in STATA programming
package. The course covers the following topics: a short introduction into principles of
collecting and using data from various data sources; data sources on six topics which
include: labor market, household welfare, poverty and inequality, health, education and
economic development.
Sociology 6Z03 is an introductory Social Statistics course by the McMaster
University, Canada [16]. The principal goal of this course is to introduce students to the
fundamentals of statistical reasoning and to the role of statistical methods in social
research. At the end of the course students should be able to read sociological research
that uses basic statistical methods; to undertake elementary data analysis; and to take
more advanced courses in Social Statistics. The textbook for the course is [19]. Course
objectives are:
─ Conduct univariate, bivariate, and introductory multivariate analyses and choose an
appropriate analytical technique depending on the levels of measurement of
variables of student’s interest.
─ Design a quantitative research project and write a research paper that can be
presented in an academic sociology conference (e.g. Canadian Sociological
Association annual meetings).
─ Operationalize concepts and social phenomena of student’s interest and to derive
hypotheses that can be tested using survey data.
─ Write syntax for managing data and conducting analysis using statistical software
(SPSS or PSPP).
─ Download public use microdata and read the dataset on SPSS (or PSPP).
─ Analyze public use microdata (e.g. GSS, ISPP, Censuses) using relevant documents
(e.g. codebooks, data dictionaries, questionnaires).
─ Effectively present findings from data analysis using PSPP (or SPSS), Excel, and
PowerPoint.
─ Read and critique academic sociology journal articles that are using basic social
statistics.
Sociology 740 is a second (more advanced) Social Statistics course from McMaster
University, Canada. This course focuses on regression analysis, linear models, and
generalized linear models, such as logistic regression and Poisson regression. One of
the goals of the course is to introduce students to modern statistical computing [17].
The textbooks for the course are [20-21].
Analysis of the courses programs allows making such conclusions. Most Western
courses in Social Statistics are introductory statistics courses for sociology majors [13,
14, 16]. We see a slightly different approach in the domestic tradition, where Social
Statistics courses are taught to students after taking the introductory course of
mathematical and statistical methods. At National Technical University of Ukraine
“Igor Sikorsky Kyiv Polytechnic Institute” Social statistics course is a second-year
course for sociology majors. This course is preceded by a mathematical methods course
(3 semesters), so there is every reason to use these methods when analyzing social
statistics data in different areas of social life: education, health, labor, population and
other.
An important problem in data analysis teaching is the formation of student’s
motivation. One example of the formation of positive educational motivation, in our
view, is the use of interesting data sets relevant to learner area. One of the most
important sections of social statistics is education statistics. One of the main objectives
of the statistical study of education is the study of the state and development of
educational institutions.
University rankings are a useful example of measurement in education statistics.
There are many different methodology of universities rankings [13]. In looking for data
for our case-study, we settled on the UK experience. Each year, three national
university rankings are published there. They are: The Complete University Guide [14-
15], The Guardian [16] and the guide jointly published by The Times and The Sunday
Times. The primary aim of these rankings is to inform potential undergraduate
applicants about UK universities based on a range of criteria.
Consider how you can use the Guardian ranking in teaching the analysis of
educational statistics. First, you can show students, by way of example, how to retrieve
raw data from web pages and then prepare them for analysis.
So, first, we recommend that students go to the following page:
https://www.theguardian.com/education/ng-interactive/2019/jun/07/university-league-
tables-2020.
The variables that students see in the table have the following explanation:
1. Guardian ranking for this year
2. Guardian ranking for last year
3. Name of university
4. The Guardian score, out of 100, is a rating of excellence based on a combination of
all the other factors
5. Course satisfaction: the rating for the overall quality of the course, given by the
final-year students in the latest National Student Survey (NSS)
6. Teaching quality: the rating for the quality of teaching on the course, given by the
final-year students in the NSS
7. Feedback: the rating for the quality of feedback and assessment, given by the final-
year students in the NSS
8. Staff-student ratio: the number of students per member of teaching staff
9. Spend per student: money spent on each student, excluding academic staff costs,
given as a rating out of 10
10. Average entry tariff: typical Ucas scores of young entrants (under 21) to the
department
11. Value-added score: this compares students’ degree results with their entry
qualifications, to show how effectively they are taught. It is given as a rating out of
10.
12. Career after six months: percentage of graduates who find graduate-level jobs, or
are in further study at professional or HE level, within six months of graduation. It
reflects how good the university is at employability.
13. Continuation rate: the percentage of first-year students continuing to second year
[16].
The next step is to read the data and transfer it to Excel. The following steps can be
followed:
First step: open Excel.
Second step: select Data > From Web. Enter the url of the web-page in the address
box of the From Web window, select “Table 0” object, click Transform Data and edit
data types in Power Query Editor. Then click Close & Load (Fig. 1).
Fig. 1. Retrieve web page data
This is what the raw data sheet looks like (Fig. 2).
Fig. 2. Raw data
The next, third step is to remove everything from this data sheet, to leave only the data
for 121 universities; it is advisable to use sorting by column 2020.
Fig. 3. Data sorting
The fourth step is to change the semicolon in all columns that contain non-integers. As
a result (Fig. 4), we get the following table (showing a fragment for 20 universities).
The students then save the file, create a similar file in SPSS, and analyze the data.
In the experiment we conducted, the students worked in pairs, they had to put
forward three statistical hypotheses regarding the data and test them. An analysis of
students’ work showed that they used correlation confidently and be able to construct
a scatterplot; two groups of students conducted cluster analysis, all group used
descriptive statistics. There were difficulties with exporting this data as a .csv file in
SPSS. Therefore, during the lecture we showed a visual presentation “How to export a
.csv file to SPSS”.
Fig. 4. Fragment of the cleared data
For teachers working with students of different majors, note that you can get a
workbook with different majors on different sheets
(https://uploads.guim.co.uk/2019/06/04/Guardian_University_Guide_2020.xlsx.
Fig. 5. Fragment of workbook for different majors of the UK universities
We apply correlation analysis, hypothesis testing, and discriminant analysis to these
data by raising relevant research questions.
Question 1. Is there a correlation between university ranks in 2020 and 2019?
We obtained a significant correlation at the level of 0,001; Spearman correlation
coefficient is 0,940 and Kendall’s coefficient is 0,803. That is, university rankings are
consistent. Universities that have improved and worsened their ranks should be
considered separately.
Fig. 6. Scatter diagram. Correlation between university ranks in 2020 and 2019
We also found a positive correlation between course satisfaction and satisfaction with
teaching: Pearson correlation coefficient is 0,871 and it is significant at the level of
0,001. Similarly, we also found a positive correlation between learning satisfaction and
feedback satisfaction; Pearson’s correlation coefficient is 0,544 and is significant at
0,001.
Question 2. The next research question is whether the average satisfaction with
teaching and the average satisfaction with feedback differ. To answer this question,
students can use a Paired Student Test to compare the mean of the two groups
Fig. 7. Paired Samples Test
We can observe that these differences will be significant at the level of 0,001; the
Student’s Test value is 36.
Question 3. The next question is whether certain variables will be distributed
normally. We use the Kolmogorov-Smirnov Test and construct a histogram with a
curve of normal distribution.
Fig. 8. Kolmogorov-Smirnov test
We see that the Kolmogorov-Smirnov criterion indicates a significant difference in
distribution from normal for these variables.
Fig. 9. The histogram with a curve of normal distribution for “satisfied with course”
We show how multidimensional methods can be applied to this data, including
discriminant analysis. To do this, we introduce new variable with gradations: 1) a low-
ranking university, 2) a high-ranking university. These include the first group –
universities whose Guardianscore100, below the median; the second group –
universities whose Guardianscore100, higher the median.
The median for the Guardianscore100 variable is 53,3. We then transcoded the
Guardianscore100 into a new Guardiangroup variable, and received a frequency
distribution. The first group included 61 universities, the second 60 (50,4% and 49,6%
respectively).
Fig. 10. Frequency distribution by Guardiangroup
We then constructed a discriminant model using the Guardiangroup variable as a group
variable and the other variables as the predictors. A linear discriminant analysis was
conducted using 9 predictors – independent variables: who defined the affiliation of the
university to one of two groups: low-ranking, high-ranking. To determine the
coefficients of the discriminant function, a direct method was used in which the
discriminant function was calculated with all predictors simultaneously entered. In this
case, each independent variable is taken into account.
The Fig. 12 shows group statistics and Fig. 11 – the results of the test about
significantly different variables in each group. For this purpose, Wilks-Lambda test
value are given and a simple ANOVA is applied. One-way ANOVA showed that
groups differ significantly by all variables, except “satisfied with feedback” (at 0,001
level).
Fig. 11. Tests of Equality of Group Means
Fig. 12. Group Statistics
From Fig. 13 we see that the Wilks criterion = 0,40 is significant (p <0,001); the model
will explain 100 – 40 = 60% of data variability.
Fig. 13. Eigenvalues and Wilks’ Lambda
The following Fig. 14 lists the unstandardized coefficients of discriminant function (b0,
b1-b9).
The Fig. 15 summarizes the classification results. The redistribution of cases based
on new canonical variables was quite successful: 81,9% of cases were correctly
reclassified into their initial categories. An analysis of Fig. 15 shows that 93,4% of low-
level observations were correctly classified and 6,6% were assigned to high-ranking
universities. 84,5% of high-level observations were attributed to their group while
15,5% were attributed to the low-rated group.
Fig. 14. The unstandardized coefficients of discriminant function
Fig. 15. Classification results
Note that the statistical analysis should be accompanied by a meaningful interpretation
of the results. In this example, we discussed the essence of university ratings, the
purpose of these ratings being a guide for the future applicants and their parents, the
operationalization and measurement of such concepts as satisfaction with teaching and
feedback; ways to use statistics in education, data sources, etc.
The ability to visualize and interpret visual representations is one of the important
parts of modeling training. In our course students were using the Education at a Glance
infographic [26] for analysis and interpretation, as well as samples for visualizing data
in student’s course papers.
3 Conclusions and perspectives of further research
Measurements that are used in modern education statistics are becoming more and more
complex. Modeling methodology helps determine the effectiveness of educational
innovations in different educational contexts, and study phenomena in their
interrelations; understand the influence of latent factors, develop systemic thinking.
The education statistics section in Social Statistics course provides extensive
material for training data literate students. The datasets of Universities rankings can be
used in the educational process both for constructing one-dimensional models, and for
constructing multidimensional models: cluster, discriminant. A Guardian ranking is
accessible, open and contains criteria that are easily understood by students. Also, it is
possible to conduct comparative studies with the different university majors.
As our experience shows, such data can be used in various ways. The teacher can
formulate various research questions for groups of students and organize the group
work; the teacher can conduct module tests on this data set, offering everyone different
questions; but the best (while more difficult) way is to ask students to formulate their
own questions and get answers to them. Moreover, Guardian ranking methodology can
be studied in detail [25].
During this research the discriminant model of Guardian score was built. We were
using the Guardiangroup variable as a group variable and the other variables as the
predictors. A linear discriminant analysis was conducted using 9 predictors –
independent variables that defined the affiliation of the university to one of two groups:
low-ranking, high-ranking.
Further development of work in this direction is the creation and study structural
equations model [27-28] with data set of migration statistics.
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