Computer Administering of the Psychological Investigations: Set-Relational Representation

doi:10.4236/ojapps.2012.22015

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Open Journal of Applied Sciences, 2012, 2, 110-114

doi:10.4236/ojapps.2012.22015 Published Online June 2012 (http://www.SciRP.org/journal/ojapps)

Computer Administering of the Psychological

Investigations: Set-Relational Representation

Krasimir Yordzhev1, Ivelina Peneva2

1Faculty of Mathematics and Natural Sciences, South-West University, Blagoevgrad, Bulgaria

2Department of Psychology, Faculty of Philosophy, South-West University, Blagoevgrad, Bulgaria

Email: {yordzhev, ivelina_peneva}@swu.bg

Received March 23, 2012; revised April 25, 2012; accepted May 5, 2012

ABSTRACT

Computer administering of a psychological investigation is the computer representation of the entire procedure of psy-

chological assessments—test construction, test implementation, results evaluation, storage and maintenance of the de-

veloped database, its statistical processing, analysis and interpretation. A mathematical description of psychological

assessment with the aid of personality tests is discussed in this article. The set theory and the relational algebra are used

in this description. A relational model of data, needed to design a computer system for automation of certain psycho-

logical assessments is given. Some finite sets and relation on them, which are necessary for creating a personality psy-

chological test, are described. The described model could be used to develop real software for computer administering

of any psychological test and there is full automation of the whole process: test construction, test implementation, result

evaluation, storage of the developed database, statistical implementation, analysis and interpretation. A software project

for computer administering personality psychological tests is suggested.

Keywords: Computer Administering; Computer Testing; Computer Psycho Diagnostic; Mathematical Modeling; Set

Theory; Relational Algebra; Databases

1. Introduction

Psychological assessment will be called any psychology-

cal testing made with the help of a preliminary prepared

test—a list of questions or statements, that the assessed

person or group of people has to answer or to give their

opinion for. The separate parts of the test are called

items.

We will call computerized psychological assessment

any psychological testing, where one or several phases of

the testing are made with the use of a computer.

Computer administering of psychological tests is the

computer representation of the entire procedure of psy-

chological assessments—test construction, test implemen-

tation, results evaluation, storage and maintenance of the

developed database, its statistical processing, analysis

and interpretation.

Personality questionnaires are those psychological

tests, which are purposed for description and evaluation

of the characteristics of cognitive (behavioral), emotional

and motivation sphere, the interpersonal relations and

attitudes of an individual [1]. It’s typical for the Person-

ality questionnaires (in contrast to Achievement tests or

Intelligence tests) that the items are questions or state-

ments, for which answers the respondent has to report

certain information concerning himself, his experience

and relations. The format of the answers to items is also

specific—most often they are described with the help of

а finite set of preliminary known answers or statements,

which we will mark by

ns . In our examinations we

will accentuate mainly on finite sets of possible responds

to each item of the test. For example

ns = {“Yes”,

“No”},

ns = {“True”, “False”},

ns = {“I like it”,

“I don’t like it”},

ns = {“Often”, “Sometimes”,

“Never”},

ns = {“True”, “I don’t know”, “False”},

ns = {“Agree”, “I’m not sure”, “Disagree”}. Items

with rating scales are also used in practice, but we will

examine just rating scales that represent definite and

consequently discrete set of real numbers.

For more details about basic terms in personality psy-

chological testing see for example in [2,3].

There are different ways to structure, process and store

data in a software product. Data and data links are ab-

straction of facts and relations from the real world [4].

Very often this abstraction is rather complex and requires

a special mathematical model for its description – a data

model. The use of one or other model means that in cer-

tain information system are chosen different principles

for data structuring or data operation. The most wide-

spread data model nowadays is the relational model,

suggested for the first time by E. F. Codd at the begin-

K. YORDZHEV, I. PENEVA 111

ning of the 1970s of the last century and described in a

set of articles, one of the earliest is [5]. For this article E.

F. Codd won a prestigious A. Turing award of the Ameri-

can Association for Computing Machinery in 1980.

Let the family of sets





,,,

DDD D, which we

will call domains, be given. Let’s examine the Cartesian

product:



,,,,,1,2,,

ii i

nki i

WDDD



xxxDDDk n









(It is possible for some s and t,

DDi

.) Each subset





is called n-аrу relation on D. From a practical point of

view the finite relations are of interest, i.e. all possible

finite subsets of W and therefore in the present piece of

writing “relation” will mean „finite relation” (besides the

opposite is explicitly emphasized), no matter it is sup-

posed that the sets i, could possibly be

infinite (for example infinite sets of real numbers).

D1, 2,,im

Let’s mark with R the set of all n-ary relations formed

by n, (not definitely different) sets (domains)

from the family D.

1, 2,n

Let R



 and let 12

,, ,

iii i

rrr r be the i-th

element of



. is called the i-th record of the rela-

tion



. In this case i is an element index, not an expo-

nent. The component i

r of is called value of the

j-th attribute in the i-th record of



. The values of the

j-th attributes of all records of



make the j-th field of



. From the definition of the term field follows that the

elements of j-th field can receive values from one sole

domain .

In the set R of all relations in D in certain circum-

stances it is possible to define various operations– union,

intersection, subtraction, complement, projection, com-

position, indexing, sorting, etc. Relationships responding

to certain conditions are possible between the separate

attributes. Thus R together with the introduced operations

and relationships between attributes turns into algebra,

called relational algebra. Relational algebra is in the

base of relational data model. The database management

systems, which have the relational model in their bases,

are also called relational databases. Basic knowledge in

the field of the theory of relational algebras can be ob-

tained in [6].

DD

Each relation R



 could be visually presented like

a rectangular table in which the i-th row is the i-th record,

and the j-th column is the j-th field of



. This corre-

spondence is one-to-one, i.e. the so built table completely

determines the relation presented by it. Due to that rea-

son and to help each user easily understand the main no-

tions of relational algebra, in the most of software manu-

als for relational database they talk about and operate

mostly with the notion table as a synonym of the notion

relation in the family of domains [4], never mind that

from a practical point of view there could be a greater

number of table types and not every table could present

concrete relation, i.e. not every type of table could be

used in a software for relational database. For example

the calendar is a rectangular table, which cannot be iden-

tified with the above defined term relation.

2. Sets of Values and Relation on Them,

Which Are Necessary for Creating a

Personality Psychological Test

To create a Personality psychological test, using the help

of a computer, it is necessary to define and specify the

following sets:

1) The set is compound of questions or state-

ments, presented for answer or opinion to the tested indi-

vidual or group of people from the research psychologist.

The elements of are the items of the test.

Qst

The presenting order of the items has a significant

meaning for the psychologist, as the sequence of the dis-

cussed items has influence to answers and therefore is

important for drawing the final conclusion and test re-

sults interpretation. In this relation arises the need of next

set:

2) Set





1, 2,,

m

where mQst is the cardinal number of the elements

of set . Each element of the set

Qst m

is a unique

number of item in the set .

Qst

3) There is a bijective mapping m

Qst Z



 be-

tween the sets m

and , and the author of the psy-

chological test for each has to define very

carefully the image

Qst

qQst







q of the element q in the

mapping



. In this case k is a number of the item q and

determines the order of items presentation to the tested

individual. As it was above emphasized, determining the

number of each item is important for the final conclusion

and all that is in the competence of the psychologist –

author of the test. In addition the number must be in the

interval





1, m of natural numbers. In this sense in a

database management system, needed for computer

Personality psychological test (Tests generator) devel-

opment when deleting an item or inserting a new one

between two existing items, an automatic items renum-

bering has to be provided. In this sense the field m

quite different from the auto increment field envisaged in

a number of database management systems, which serves

a primary key. For fields of that type the above men-

tioned operations division and item insertion are not fol-

lowed by renumbering, even more it’s not allowed to

make changes in the primary key value.

4) A finite set

ns of possible answers to the items

(see section 1).

K. YORDZHEV, I. PENEVA

112

5) A set of psychological categories (Personal-

ity characteristics), which are subject of analysis and

evaluation concerning the assessed individual or group of

people with the aid of the items from the set and

the concrete answer that is chosen. It is not obligatory for

each item to be related to given psychological category.

Ctg

Qst

6) We are examining the finite family of subsets of

Qst



TTQstcCtg 



(2)

with the element which belongs to the subset

, if and only if the item q has a relation to the category

in the correspondent psychological assessment.

qQst

cCtg

Obviously and if and

, then the item q will not effect the entire test

and will drop out.

cCtg

TQs







qQst

cCtg





7) Let



,,,

nsa aa. For every i we

put together the set of numbers i, i.e. we examine the

following family of sets of numbers

aAns



,1,2,,

Sa Ansik



We are building the Cartesian product of the sets ,

1, 2,,ik



,,,,1,2,,,

aAns

ki i

Scl S



sssSikkAns













Each element ii

S, aAns



from a practical

point of view represents an assessment numerical value

of the psychological categories from the set Ctg on

condition that the assessed person could possibly respond

to a random item with an answer or a statement aAns



Quite often these assessment values are 1 or 0. For ex-

ample, if 2Ans  and we assume that the assessment

value for each positive answer is equal to 1 and for each

negative answer is 0, then we can easily calculate the

total number of positive answers.

8) Let’s remind that a binary relation

AB is

called function, if for each



there is no more than

one

B, so that ,

yf. The fact that

AB

is a function is presented also like that

AB and

instead of ,

yf, we write



f



For each psychological category is defined

one function

Qst Scl

cCtg

cC

with the aid of which the

psychologist evaluates the assessed person regarding the

category . Such function is called a scale for the

psychological category . It’s a common practice

the name of the scale to be exactly the same as the name

of the psychological category. The set of functions





What is the assessment of the different items, regard-

ing the correspondent answers, i.e. how the functions are

defined :

Qst Scl, and what is the in-

fluence of this to the summary assessment of the test

implementation can be estimated after wide psychology-

cal and statistical investigations [1-3,7].

cCtg

9) Relation







,,,

Bndc qfqcCtgqQstCtgQstScl

where , and are sets, which are defined

correspondingly in subsections 5), 1) and 7), and the

relation c

Ctg Qst Scl

, cCtg



is a function defined in 8) (scale

of psychological category c). Every record in DBName_

Bnd contains the number of the scores we can take when

the person does the corresponding answer

aAns



ac-

cording the scale





q for category and item cCtg

qQst



10) Let cCtg



and let





min

qQst











(5)

where







12 12

,,,min,,,

xx xxx





In other words c is the minimum assessment value

(minimum score), which could possibly be obtained in a

random testing, related to the category cC



and

depending on the correspondent scale :

Qst Scl .

Analogously we specify the maximum assessment value





max

qQst







 (6)

where







12 12

,,,max ,,,

xxxxx





Obviously c



. We examine the finite sequence

of numbers

 

01 1.

lc lc

mbbbb M





 

As we denote





lc we emphasize the fact that the

number of the members in the row depends on the cate-

gory .cCtg



We are separating the interval





to the subintervals





,bb





,bb,





,bb , ···,

 



1,bb





lclc. Let’s mark with the set of all intervals

of that type





,bb

and 





iii



 ,





l2, 3,,ic, corresponding to the category cCtg



The number





lc and each of the intervalsi







1, 2,,ilc

should be a result of profound psycho-

logical investigations.

Let denote by

cCtg





cCtg

, composed by all scales for the examined

psychological categories is called a scale of the Person-

ality psychological test.

the set of all intervals of numbers, which could be useful

for certain personality psychological test.

K. YORDZHEV, I. PENEVA 113

11) For each of the intervals , de-

fined in 10), we create text i

t, , corre-

sponding to the text given by a professional psychologist

about the psychological condition of the assessed person

regarding the psychological category cC, in case

that the total summary (the sum of all concrete evaluation

for the corresponding item for the implementing test ac-

cording to the scale c

D

1, 2,i



cCtg



,lc

) belongs to the interval i



Thus for each we obtain the sets of texts

cCtg





1, 2,,

Tti lc

12) Let . By the things we have mentioned

above it follows that there exists function

cCtg

cc c

DT

Let





,,1,2,

ciicii

Gtgti l 



,c (7)

is the corresponding binary relation of this function. The

function c

DT is called interpretation of the test,

concerning the psychological category .

cCtg

We denote by

cCtg





the set of all interpretations, which can be given of the

psychological examiner after the implementation of a

given personality psychological test.

13) Then we define the relation





,, ,

ic iic

NtpcgcCtgDCtgD T 

(8)

where c and D are the sets of number intervals, we

have already looked at 10), and c

, and T are

correspondingly the functions and the set of interpreta-

tions, defined in 12).

cCtg

The sense of each record in is as follows: For

each psychological category cC when the test is

implemented if the assessed person obtain r number of

points (obtained assessment value for the category), then

we check in which interval of numbers

r is situated and we give the expert interpretation of the

test accordingly with the category and the

function

Ntp

tg

Dc Ctg 

cCtg

cc c

DT defined in 12).

3. A Software Project for Computer

Administering Personality Psychological

Tests

Because of all that is written above, we consider that it is

appropriate a computer system for administering person-

ality psychological tests to contain three basic and sev-

eral contributive, relatively independent modules. How

do these separate modules work is shown on a diagram in

Figure 1.

1) Module “Generator”. This module will create files,

containing sets and relations described in section 2 for a

concrete personality psychological test. At the moment

we do not take an account of the data form, correspond-

ing to the concrete database management system (Oracle

Database, dBase, Paradox, FoxPro, MS Access, SQL,

etc.). Concrete realization of the module “generator” is

described in [8].

2) One or several contributive modules. They serve for

additional forming of a concrete computer test - creating

starting window, enter a preliminary instruction, descrip-

tion of “demographic field” (if it is necessary) and others.

The demographic field is a set of different data, charac-

terizing the examined person as what is his/her sex, age,

education, work, settlement, etc.

3) Module “Executor”. This is a computer program,

which reads the data from files and makes a concrete

computer testing. From psychological point of view it is

desirable the interface of this program to be as simple as

possible. It is enough in the main window to appear the

text of the serial item of the set . The order they

appear is according to the bijective mapping between the

elements of the set and the set

Qst



1, 2,,

m,

mQst in ascending order of the elements in m

described in subsection 3). By request just before the

program finishes working appears a window “interpreta-

tion”, in which are described the conclusions obtained

from analyzing the data of the concrete testing according

to the relation described in subsection 13). The

data will be recorded in a file, because we will need it for

the coming modules of the system for computer admin-

istering of psychological tests.

Ntp

4) Modules for statistic processing. They serve for

automated statistic processing of the data, which is ob-

tained when the module “executor” is used many times,

testing many persons. We can use universal programs for

statistic process, which are often used in practice, such as

SPSS, STATISTICA, MatLab, Maple, MS Excel and

others. Certainly as we have in mind the specific features

of the data, obtained in a result of a computer psycho-

logical testing, we consider that it is advisable to create

specific software for the concrete statistic processing,

which has to read and process the data, obtained when

the module “executor” works. This will lead to maximum

automation of the psychological examinations.

Contributive

Modules

Generator

Modules for

statistic

processing

Executor

Figure 1. A computer system for administering personality

psychological tests.

K. YORDZHEV, I. PENEVA

114

4. Conclusion

The described mathematical model is a useful task for

university studies in databases course. On the other hand,

discussed in the work notes will stimulate the psycholo-

gists to make wider use of computer methods in their

work. This model could be used to develop real software

for computer administering of any psychological test and

there is full automation of the whole process: test con-

struction, test implementation, result evaluation, storage

of the developed database, statistical implementation,

analysis and interpretation.

REFERENCES

[1] E. Sidorenko, “Methods for Mathematical Processing in

Psychology,” Rech, Sankt Petersburg, 2000.

[2] A. Anastasi and S. Urbina, “Psychological Testing,” Pren-

tice-Hall, Englewood Cliffs, 1997.

[3] S. A. Miller, “Developmental Research Methods,” 2nd

Edition, Prentice-Hall, Englewood Cliffs, 1998.

[4] M. J. Hernandez, “Database Design for Mere Mortals,”

2nd Edition, Addison Wesley, Boston, 2003.

[5] E. F. Codd, “A Relational Model of Data for Large Shared

Data Banks,” Communication of the Association for Com-

puting Machinery, Vol. 13, No. 6, 1970, pp. 377-387.

doi:10.1145/362384.362685

[6] D. Maier, “The Theory of Relational Databases,” Com-

puter Science Press, New York, 1983.

[7] A. Nasledov, “Mathematical Methods for Psychological

Assessments—Analysis and Data Interpretation,” Rech,

Sankt Petersburg, 2004.

[8] K. Yordzhev, I. Peneva and B. Kirilieva-Shivarova, “A

Relational Model of Personality Psychological Tests,” Pro-

ceedings of the 3rd International Conference of Faculty of

Mathematics & Natural Science (FMNS2009), Blagoev-

grad, 3-7 June 2009, pp. 69-77.