A Framework for Selecting Sample Size in Educational Research

on e-business Application

Andreas Ahrens

and Jeļena Zaščerinska

Hochschule Wismar, University of Applied Sciences - Technology, Business and Design,

Philipp-Müller-Straße 14, 23966 Wismar, Germany

Keywords: e-business Application, Generalization, Population, Sample, Sample Size, Measurement Procedures,

Probability Sample, Information-Oriented Sample, Case, Factor.

Abstract: Sample size has a two-fold role in research: sample size is inter-connected with statistical analysis of the

data and generalization. Therefore, sample size has attracted a lot of research efforts in all the research fields

including educational research on E-Business application. However, little attention has been given to a

framework for selecting sample size in educational research on E-Business application. The research

question is as follows: what shapes sample size in educational research on E-Business application? The aim

of the research is to analyze theoretically sample size shaping underpinning elaboration of a framework for

selecting sample size in educational research on E-Business aplication. The present research involves a

process of analysing the meaning of the key concepts statistical analysis, generalisation, population,

sample, measurement procedures, probability sample, information-oriented sample, case and factors.

Moreover, the study demonstrates how the key concepts are related to the idea of “sample size”. Explorative

research was employed. Interpretive research paradigm was used. The empirical study involved four experts

from different countries in February - April 2013: The findings of the research allow drawing the

conclusions on the framework for selecting sample size in educational research on E-Business aplication.

Directions of further research are proposed.

1 INTRODUCTION

E-Business application has been widely spreading

since its emerging as e-Business application

provides businesses with such benefits as time

saving, cost reduction, service improvement,

management facilitation, etc.

For the increase of efficiency of e-Business

application in complex and constantly self-

regenerating environments (Kardoff, 2004), a

number of issues in e-Business application has to be

taken into consideration such as context analysis,

customer needs analysis, etc. Success in dealing with

the above-mentioned issues in e-Business

application is generated by a couple of strategies.

For the synergy between theory and practice in e-

Business application, one of the strategies is focused

on the sample analysis (Mayring, 2007).

Sampling focuses on obtaining a group of

subjects who will be representative of the larger

population or will provide specific information

needed (McMillan, 1996). The goal is to select a

sample that will adequately represent the population,

so that what is described in the sample will also be

true of the population (McMillan, 1996). In

educational research, the best procedure for selecting

such a sample is to use probability sampling as non-

probability sampling does not ensure the

construction of a parameter for a population. The

primary distinction between the two domains is that

the probability sampling study findings can be

generalized to the target population while the

nonprobability sampling study findings can only be

generalized to the institution where the sample was

studied (Summers, 1991).

The key characteristic of a

probability sample is that each element in the

population has a known probability of being

included in the sample (Sweeney, 2013). The

probability sampling procedures include simple

random, systematic, stratified, and cluster

(McMillan, 1996) as demonstrated in Figure 1.

The process of sample selection reveals such an

issue as sample size. Therefore, sample size has

attracted a lot of research efforts in all the research

Ahrens A. and Zaš

cerinska J..

A Framework for Selecting Sample Size in Educational Research on e-business Application.

DOI: 10.5220/0005020000390046

In Proceedings of the 11th International Conference on e-Business (ICE-B-2014), pages 39-46

ISBN: 978-989-758-043-7

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

Figure 1: Probability sampling procedures.

fields. In farmer surveys, sampling methods which

range from the practical to the mathematical are

focused on good practical points (Coe, 1996). In

organizational research, the procedures for

determining sample size for continuous and

categorical variables have been described by use of

Cochran’s (1977) formulas (Bartlett, Kotrlik,

Higgins, 2001). In management and economics

research, the emphasis is put on analysis of factors

influencing sample size (Kamau, Guandaru, Kariuki,

Nduati, 2012). In psychological research, analysis of

selection of sample size has contributed to three

criteria of sample size (Kroplijs, Raščevska, 2004).

Psychological research and educational research

are closely inter-connected as depicted in Figure 2.

Figure 2: Inter-relationship between psychological and

educational research.

Psychological research provides the basis for

pedagogical and, consequently, educational

developments in terms of organization of

educational environment, curriculum, institution

activities, and etc. In its turn, educational research

facilitates the promotion of psychologists’

professional knowledge, competences and behavior

aimed at ensuring new discoveries, innovations, etc.

Thus, in psychological and, consequently,

educational research, selection of sample size is

identified by the application of three criteria of

sample size (Kroplijs, Raščevska, 2004) such as

effort quantity or intensity of interaction with sample

components (subjects in educational research) or

elements; a number of topis investigated within a

particular educational research; subject matter within

a particular research. Hence, sample size has a two-

fold role in research as depicted in Figure 3: sample

size is inter-connected with statistical analysis of the

data and generalisation or theory formulation.

Figure 3: Relationship between sample size and statistical

analysis of the data and generalization in research.

In educational research, sample size has attracted

a lot of research efforts, too. Traditionally, selection

of sample size refers to empirical studies of

educational research as illustrated in Figure 4.

Figure 4: Relationship between research, empirical studies

and sample size in educational research.

However, little attention has been given to a

framework for selecting sample size in educational

research.

The research question is as follows: what shapes

sample size in educational research on E-Business

application? The aim of the research is to analyze

theoretically sample size shaping underpinning

elaboration of a framework for selecting sample size

in educational research on E-Business aplication.

The present research involves a process of

analysing the meaning of the key concepts statistical

analysis, generalisation, population, sample,

measurement procedures, probability sample,

information-oriented sample, case and factors.

Moreover, the study demonstrates how the key

concepts are related to the idea of “sample size”.

The methodological background of the present

contribution is based on the System-Constructivist

Theory. The System-Constructivist Theory is

introduced as the New or Social Constructivism

Pedagogical Theory. The System-Constructivist

Probability sampling

procedures

Cluste

Sample

random

Systematic

Stratified

Research

Educational

esea

Psychological

research

Research

Sample

size

Generalisation

Statistical

anal

sis of the

Research

Empirical study

Sam

le size

ICE-B2014-InternationalConferenceone-Business

Theory is formed by Parsons’s System Theory

(Parsons, 1976) on any activity as a system,

Luhmann’s Theory (Luhmann, 1988) on

communication as a system, the Theory of Symbolic

Interactionalism (Mead, 1973), the Theory of

Subjectivism (Groeben, 1986). The application of

this approach to learning introduced by Reich

(Reich, 2005) emphasizes that human being’s point

of view depends on the subjective aspect (Maslo,

2007):

 everyone has his/her own system of external

and internal perspectives (Ahrens, Zaščerinska,

2010) that is a complex open system

(Rudzinska, 2008) and

 experience plays the central role in the

knowledge construction process (Maslo, 2007).

Therein, the subjective aspect of human being’s

point of view is applicable to the present research on

selection of sample size in educational research on

E-Business application.

2 THEORETICAL FRAMEWORK

By a theoretical framework, the unity of concepts,

their definitions and existing theories that are used

for a particular study are meant. A theoretical

framework is used to identify the specific viewpoint

(framework) taken into consideration while

analysing and interpreting the gathered data.

Educational research in general and sample size

in particular is initially shaped by educational

research paradigm (Taylor, Medina, 2013). A

paradigm is a comprehensive belief system, world

view, or framework that guides research and practice

in a field (Willis, 2007). Such educational research

paradigms are identified (Taylor, Medina, 2013) as

 the positivist paradigm that is commonly used

in research to test theories or hypotheses,

 the post-positivist paradigm that includes the

analysis of interaction between the researcher

and his/her research participants via use of such

quantitative methods as survey research and

qualitative methods as interviewing and

participant-observation (Creswell, 2008),

 the interpretive paradigm which aims to

understand other cultures, from the inside

through the use of ethnographic methods such

as informal interviewing, participant

observation and establishment of ethically

sound relationships,

 the critical paradigm which involves identifying

and transforming socially unjust social

structures, policies, beliefs and practices,

 the postmodern paradigm which holds that what

goes on in our minds and hearts is not directly

accessible to the world outside us,

 the multi-paradigmatic research by combining

methods and quality standards drawn from two

or more of the newer paradigms, and

 the new ‘integral paradigm’ that provides a

rationale for drawing upon multiple paradigms

to design new hybrid methodologies that

involve multiple epistemologies and their

accompanying quality standards.

Further on, sample size is framed by the research

methodology: quantitative methodology that

requires large, representative and precise sample,

and qualitative methodology that is based on a small

and non-representative sample.

Later, selection of sample size in educational

research involves analysis of access to the sample

which is a key issue in research (Cohen, Manion,

Marrison, 2003), and resources such as time,

personnel, technical support, competences,

experiences, etc (Flick, 2004). It should be noted

that research proposals are frequently based on an

unrealistic relationship between the planned tasks

and the personnel resources that can (realistically) be

asked for (Flick, 2004).

Then, selection of sample size is based on the

analysis of the inter-relationships between

 sample size and statistical analysis of the data,

 sample size and generalization.

For the analysis of the relationship between

sample size and statistical analysis of the data,

statistical analysis is identified as the unity of the

collection and processing of data and the results’

interpretation as demonstrated in Figure 5.

Figure 5: Elements of statistical analysis.

Below the relationship between sample size and

each element of statistical analysis is revealed.

Data collection implies use of measurement

procedures as depicted in Figure 6.

Statistical analysis

Data collection

Results’

interpretation

Data processing

AFrameworkforSelectingSampleSizeinEducationalResearchone-businessApplication

Figure 6: Relationship between data collection and

measurement procedures.

Analysis of the relationship between sample size

and measurement procedures in the present research

is based on measurement procedures defined as

measurement tools and scale as shown in Figure 7.

Figure 7: Elements of measurement procedures.

Such measurement tools as questionnaires as

well as measurement scales are fixed on one sample

and tested in a new sample (Gigerenzer, 2004) as

measurement tools and/or scales have to be cross-

validated in order not to provide non-precise data.

Therein, a sample is to be of such a size as, in the

measurement phase of the educational research, the

parameters of measurement tools and scales are kept

fixed when used by sample’s further components or

elements.

Traditionally, data processing includes two

methods (Geske, Grīnfelds, 2006) as illustrated in

Figure 8: method of descriptive statistics and method

of inferential statistics.

Figure 8: Two methods of data processing.

Figure 9 demonstrates methods of descriptive

statistics (Geske, Grīnfelds, 2006).

In educational research such a method of

inferential statistics as significance test is closely

inter-connected with sample size while null

hypothesis testing relates to two measured

phenomena, and variance analysis – to

a variable's

values.

Figure 9: Methods of descriptive statistics.

Figure 10 shows elements of central tendencies

(Geske, Grīnfelds, 2006).

Figure 10: Elements of central tendencies.

In its turn, Figure 11 demonstrates methods of

inferential statistics (Geske, Grīnfelds, 2006) in

educational research.

Figure 11: Methods of inferential statistics.

For the analysis of the relationship between

sample size and significance test, a sampling

distribution is required. Sampling distribution is

connected with probability distribution: the sampling

distribution of the mean is a probability distribution

of the possible values of the mean that would occur

if we were to draw all possible samples of a fixed

size from a given population (Plonksy, 1997).

Knowledge of the sampling distribution is necessary

for the construction of an interval estimate for a

population parameter (Sweeney, 2013). This is why

a probability sample is needed; without a probability

sample, the sampling distribution cannot be

determined, and an interval estimate of a parameter

cannot be constructed (Sweeney, 2013).

Sampling distribution is usually examined by the

Kolmogorov-Smirnov test. Statistical Package for

the Social Sciences (SPSS) Exact Tests also offers

Data collection

Measurement procedures

Measurement

tools

Measurement

scale

Data processing

Descriptive

statistics

Inferential

statistics

Statistical analysis

Variance,

skewness,

tos

Frequencies,

percentage

Central tendency

Median

Mean

Inferential statistics

Null

hypothesis

testing

Significance test

Variance

analysis

Mode

ICE-B2014-InternationalConferenceone-Business

the asymptotic version of the Kolmogorov-Smirnov

test to reach correct conclusions with small samples

(Statistical Package for the Social Sciences, 2009).

A sampling distribution is considered within the

framework of deviation of the empirical distribution.

Deviation of empirical distribution is significant if

Significance p or Asymp. Sig. (2-tailed) is smaller

than 0.05 (Lasmanis, 2003). The Kolmogorov-

Smirnov test identifies that if the deviation of

empirical distribution is greater than 0.05, sampling

distribution is normal, or if the deviation of

empirical distribution is smaller than 0.05, sampling

distribution is non-normal. Normal empirical

distribution implies the use of parametric methods in

the empirical study, and non-normal empirical

distribution - the use of non-parametric methods.

However, the use of normality tests does not

determine automatically whether or not to use a

parametric or non-parametric test: they can help

make the decision (GraphPad Software, 2007). For

example, non-parametric tests have little or no

power to find a significant difference if there is a

tiny sample (a few subjects in the group) (GraphPad

Software, 2007).

In comparison to theoretical sampling which

relates not to the sample size determination, but to

the analysis of the necessity in the increase of the

sample size for the enrichment of theory developed

from the data obtained in a previous sample

(Kroplijs, Raščevska, 2004) in psychological and,

consequently, educational research, empirical

sampling distributions are not true sampling

distributions, since all possible samples are not

chosen (Plonsky, 1997), as well as some differences

exist between any natural groups (Gigerenzer,

2004). Therein, a sample is to be of such a size as, in

the data processing phase of the educational

research, the tests carried out on a given set of data

allow extracting the required information in an

appropriate form such as diagrams, reports, or

tables.

For the analysis of the relationship between

sample size and results’ interpretation, interpretation

and judgement are part of the art of statistics

(Gigerenzer, 2004). Thus, a sample is to be of such a

size as, in the statistical analysis phase of the

empirical study within educational research, the

information extracted from the obtained data

processing ensures a possibility to make conclusions

and generalisations.

For the analysis of the relationship between

sample size and generalisation, generalisation is

traditionally considered as a central aim of science,

as a process of theory formulation for further

applications (Mayring, 2007). Types of

generalisation include universal laws, statistical

laws, rules, context specific statements, similarities

and differences, descriptive studies, explorative

studies, and procedures to come to results (Mayring,

2007) as illustrated in Figure 12.

Figure 12: Eight types of generalisation.

Generalisation can be arrived by different

strategies which also include analysis of total

population and samples (Mayring, 2007). Therein,

Figure 13 demonstrates that sample is part of

population.

Figure 13: Relationship between total population and

sample.

A population is a group of elements or cases,

whether individuals, objects, or events, that conform

to specific criteria and to which we intend to

generalize the results of the research (McMillan,

1996). This group is also referred to as the target

population or universe (McMillan, 1996). It is also

important to distinguish the target population from a

list of elements from which a group of subjects is

selected (McMillan, 1996). The list is termed the

survey population or sampling frame (McMillan,

1996). The sample is the group of components,

elements, or a single element, from which data are

obtained (McMillan, 1996). By an individual who

participates in a research study or is someone from

Total population

Sam

Eight types of generalization

Universal

laws

Similarities and

differences

Statistical

laws

Descriptive

studies

Context specific

statements

Procedure

Explorative

studies

Rules

AFrameworkforSelectingSampleSizeinEducationalResearchone-businessApplication

whom data are collected, subjects or cases are meant

(McMillan, 1996). The term subject may also

identify individuals whose behavior, past or present,

is used as data, without their involvement in some

type of treatment or intervention (McMillan, 1996).

The focus in selecting the cases has changed to

information-oriented sampling, as opposed to

random sampling (Flyvbjerg, 2006). This is because

an average case is often not the richest in

information. In addition, it is often more important

to clarify the deeper causes behind a given problem

and its consequences than to describe the symptoms

of the problem and how frequently they occur

(Flyvbjerg, 2006). Random samples emphasizing

representativeness will seldom be able to produce

this kind of insight; it is more appropriate to select

some few cases chosen for their validity (Flyvbjerg,

2006).

In educational research, it is usually impractical

and unnecessary to measure all the elements in the

population of interest (McMillan, 1996). Typically, a

relatively small number of subjects or cases is

selected from the larger population (McMillan,

1996). In educational research, a sample should

include more than 30 subjects due to the “central

limit theorem” (Mayring, 2007), a sample which

involves less than 30 subjects is small (Arhipova,

Bāliņa, 2003), and a sample which consists of a few

subjects is tiny (GraphPad Software, 2007). It should

be noted that generalization can be drawn from a

single case study, too (Mayring, 2007). However, for

the result confirmation and drawing more general

conclusions, the case basis is to be widened

(Mayring, 2007) up to three-ten single cases (Yin,

2005). Therein, a sample is to be of such a size as, in

the analysis phase of the research, sample’s further

components or elements do not change conclusions

or generalisations drawn from the obtained data

(Kroplijs, Raščevska, 2004).

Hence , selection of sample size is shaped by the

following framework: in the educational research, a

sample is to be of such a size as

 in the measurement phase, the parameters of

measurement tools and scales are kept fixed

when used by sample’s further components or

elements,

 in the data processing phase, the tests carried

out on a given set of data allow extracting the

required information in an appropriate form

such as diagrams, reports, or tables,

 in the statistical analysis phase, the information

extracted from the obtained data processing

ensures a possibility to make conclusions and

generalisations.

 in the analysis phase, sample’s further

components or elements do not change

conclusions or generalisations drawn from the

obtained data (Kroplijs, Raščevska, 2004).

3 EMPIRICAL RESEARCH

The present part of the paper demonstrates the

design of the empirical research, survey results and

findings of the empirical study.

3.1 Research Design

The design of the present empirical research

comprises the purpose and question, sample and

methodology of the present empirical study.

The empirical study was aimed at evaluating

the framework for selecting sample size in

educational research on E-Business aplication.

The empirical research’s guiding question was

as follows: What is the expert evaluation of the

framework for selecting sample size in educational

research on E-Business application?

The present empirical study involved four

experts from different countries in February - April

2013. All the respondents have been awarded PhD

Degree in different fields of educational science.

As the respondents with different cultural

backgrounds and diverse educational approaches

were chosen, the sample was multicultural. Thus,

the group (age, field of study and work, mother

tongue, etc.) is heterogeneous. The sample of four

experts consisted of two researchers in the field of

educational research, Educational Research

Association, "Freie Universität" (Free University),

Berlin, Germany, a researcher in the field of

educational research, Latvia University of

Agriculture, Jelgava, Latvia and a researcher in the

field of applied research in education, CAH -

Vilentum University of Applied Sciences, Dronten,

the Netherlands. In order to save the information of

the study confidential, the respondents’ names and

surnames were coded as follows: two researchers

from Germany were given the codes of E1 (Expert

1) and E2 (Expert 2), a researcher from Latvia was

pointed as E3 (Expert 3), a researcher from the

Netherlands was considered as E4 (Expert 4).

Interpretive research paradigm that corresponds

to the nature of humanistic pedagogy (Luka, 2008)

was used in the present empirical study.

Interpretive paradigm is characterized by the

researchers’ practical interest in the research

question (Cohen, Manion, Marrison, 2003).

ICE-B2014-InternationalConferenceone-Business

Researcher is the interpreter.

Exploratory research was employed in the

empirical study (Phillips, 2006). Exploratory

research is aimed at generating new questions and

hypothesis (Phillips, 2006). The exploratory

methodology proceeds from exploration in Phase 1

through analysis in Phase 2 to hypothesis

development in Phase 3 as demonstrated in Figure

14.

Figure 14: Methodology of the exploratory research.

The qualitatively oriented empirical study

allows the construction of only few cases

(Mayring, 2004).

The choice of experts was based on two criteria

such as recognized knowledge in the research

topic, absence of conflict of interests (Lopez,

Salmeron, 2011) as depicted in Figure 15.

Figure 15: Criteria of choosing experts.

The number of experts depends on the

heterogeneity of the expert group: the greater the

heterogeneity of the group, the fewer the number of

experts (Okoli, Pawlovski, 2004). Thus, four is a

good number of experts for the study (Lopez,

Salmeron, 2011). Therein, the non-structured

interviews comprised four experts who were

researchers from different countries. It should be

noted that all the researchers were professors in the

fields connected with educational research. All the

four researchers had received extensive research

experience.

3.2 Survey Results

In order to analyse the framework for selecting

sample size in educational research on E-Business

aplication, non-structured inteviews were caried out.

Non-structured interviews with experts were

conducted in order to search for the main categories

of the research field (Kroplijs, Raščevka, 2004).

Expert 1 thanked the authors for the interesting

abstract submitted to the conference where Expert 1

was acting as a reviewer.

Expert 2 underlined that the authors had tried to

summarize a study and identify the main

characteristics of this study.

Expert 3 was interested in the continuation of the

study.

Expert 4 assumed that the factors play a key role

in forming the sample size in educational research.

3.3 Findings of the Empirical Study

Summarizing content analysis (Mayring, 2004) of

the data reveals that experts positively evaluated the

framework for selecting sample size in educational

research on E-Business aplication.

4 CONCLUSIONS

The empirical findings of the research allow drawing

the conclusions on the experts’ positive evaluation

of the framework for selecting sample size in

educational research on E-Business aplication.

The following research question has been

formulated: what are the principles of selection of

sample size in educational research?

The role of sample size it plays in research is to

be re-considered in further studies. Further research

tends to focus on empirical studies to be carried out

in other institutions. And a comparative research of

different countries could be carried out, too.

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conflict

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