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CHAPTER-III DESIGN OF THE STUDY 3

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CHAPTER-III
DESIGN OF THE STUDY
3.1 INTRODUCTION
The term “Methodology”, refers to the overall approaches and perspectives to the research process as a whole and is concerned with research design. Research design is a mapping strategy which is based on objectives, sampling, research strategy, tools and techniques for collecting evidences, analyzing the data and reporting the findings. Thus research design is the statement of the object of the inquiry and how a satisfactory culmination to be effected.
This chapter deals with the research process and elaborates the objectives to set, sampling procedure, the different types of data collection methods and strategies deployed in this research. The aim is to provide an appreciation of the detailed investigation that forms the frame work for this study, and to give an account of how the findings are drawn. The chapter starts with an outline of the design followed by a detailed explanation of the three phases chosen for the study. The chapter ends with an outline of the phases used to address issues of value integration in school mathematics text book of Tamil Nadu and the perception of mathematics teachers about the value integration in mathematics classroom.

In order to capture the different dynamics of content analysis in relation to value integration in school mathematics text books, the researcher chose qualitative research method. To critically analyze the perception of mathematics teacher about value integration in mathematics class room, the researcher chose both qualitative and quantitative research method.

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While emphasizing the fact that values are a subjective and continuously shifting concept , the researcher used multiple methods of data gathering to not only clarify the findings, but also to confirm the statements made by the same teachers in different periods and situations. Fidel(1993) asserts that subjective research should make use of multiple methods to measure the same qualities , each verifying the other.

3.2 Research questions
How areMathematical values, sociological values and personal values emphasized in Mathematics text books of Tamilnadu?
What are the Values identified and strategies suggested for integrating values in the branches of mathematics?
How do mathematics teachers understand the concept of value inculcation in mathematics teaching and learning?
What are the levels of perception of mathematics teachers with regard to the inculcation of mathematical, sociological, attitudinal, motivational and personal values?
What are the challenges constraining and suggestions to improve in inculcating values in mathematics teaching and learning?
and the research problem is stated as
3.3STATEMENT OF THE PROBLEM
“VALUES IN SCHOOL MATHEMATICS CONTENT AND STRATEGIES TO INTEGRATE VALUES IN MATHEMATICS TEACHING”
3.4. Operational definition of the terms
Values in School Mathematics Content
Value is a belief upon which a man acts by preferences, Values are principles or standards of behavior; one’s judgment of what is important in life. In this study, mathematical values, sociological values and personal values were identified in the content material of the subject matter which stands for quantity, shapes and measurement at the school level i.e. VI to X classes
Strategies to Integrate values in Mathematics teaching
Different design of activities,methods and models to incorporate values in to a unified whole content of mathematics while teaching and learning mathematics, refer to strategies to integrate values in mathematics teaching
3.5.OBJECTIVES OF THE STUDY
To critically analyze the different dimensions of values that could be integrated in different branches of mathematics
To suggest various strategies to adopt to inculcate values in different branches of mathematics
To identify the approaches that could be adopted in teaching math at school level
To study the perception of mathematics teachers to integrate values in mathematical classroom
To validate the findings from the three phases
3.6HYPOTHESIS
A research hypothesis is the statement created by researchers when they speculate upon the outcome of a research or experiment. There are various types of hypothesis, but in this study only null hypothesis is used.
Male and female teachers do not differ in their perception of mathematical values
Rural and urban teachers do not differ in their perception of mathematical values
Tamil medium and English medium teachers do not differ in their perception of mathematical values
Teachers do not differ in their perception of mathematical values with respect to their teaching experience
Teachers do not differ in their perception of mathematical values with respect to their type of school
Teachers of different age groups do not differ in their perception of mathematical values.
Teachers with different educational qualifications do not differ in their perception of mathematical values.
There is correlation among the various dimensions of values chosen for study.

Each hypothesis has been tested and the mean differences, t and F ratio has been found out. Co relational analysis was also done.Regression analysis and discriminant analysis were also taken up.

3.7METHOD OF ANALYSIS
The conduct of this study has been taken up by a research framework made up of three phases.
CONTENT ANALYSIS
The first two phases adopted the research design “content analysis”. Content Analysis is described as the scientific study of content of communication. It is the study of the content with reference to the meanings, contexts and intentions contained in messages. It is a research technique for the objective, systematic and quantitative description of the manifest concepts of communication. The steps of content analysis includes to prepare data, define unit of analysis, develop categories and coding scheme, test the coding scheme, draw conclusion from coded data and report the findings.

First phase The first phase identified the distribution of values in school mathematics text books of Tamil Nadu. This was taken up as the content analysis of mathematics text books at school level.Mathematics text books of classes VI-X .Qualitative method is followed
Second phaseThe second phase analyzed value integration in the branches of mathematics and strategies are to be adopted to integrate values in the mathematical content. This is a document analysis of different branches of mathematics content in qualitative approach.
Third phase The third phase studied the perception of mathematics teachers about the feasibility of inculcation of values in mathematics classroom while teaching the subject mathematics.Quantitative analysis was used.
Interview is the technique used to validate the above findings
The study adopts both qualitative and quantitative method for analyzing the data.

FIRST PHASE
The first phase of the research included the identification of mathematical, personal, social values in mathematics text books. The analysis of text books belongs to a class of non-reactive research technique called content analysis. This technique is useful for this study as it “can reveal messages in a text that are difficult to see with casual observation.” (Neumann 1997)
The study is done on mathematics text books of classes VI to X of state board syllabus of Tamil Nadu. The content of these text books were taken for the study. These text books were analyzed based on semantic content analysis. Semantic content analysis is a method that finds out the main subject areas in material content, its dimension and special sub dimension about the areas and dimension (Tavsancil and asbn 2001). In this study, mathematical general values and its sub values were taken into consideration.

Without the luxury of time, all topics of each text book were critically analyzed. All the chapters of text books were grouped into different topics according to the strands Number system, Algebra, Measurement, Arithmetic, Statistics and geometry. Only content were analyzed which includes theorems, expository writing, definition, theorems, concepts, intricate sub topics, worked examples, exercise problems and activities for solving. Cover design, illustration, figures, charts and physical properties of the text. (eg, font size, font type, text length etc) were excluded in this study.

The aim of this analysis is to identify the explicit and implicit values that could be integrated in the branches of mathematics. The branches of mathematics fall under the category of general mathematics at school level. From these branches, the researcher started her analysis of values critically. In each branch there were some ten to twelve subtopics and these subtopics were taken for the study. Each subtopic was analyzed without any exception to integrate values possible in the content.
The broad category values such as social, economical, attitudinal, motivational and mathematical values could be integrated in the branches of mathematics. The school mathematics text books were scrutinized to find the distribution of mathematical values, personal values and social values. The types of mathematical values Rationality, Accurate, Logical and abstract values were taken for this study. The types of personal values and social values adjustment, co-operation, unity and discipline were taken for the investigation. The count of values was given for each sub topic and total was calculated to see the predominance of value which appears most. Each chapter of different standard was unique. And the value was distributed based on the nature of the sub topic.
The mathematical values persistence/existence can be easily traced upon, but the social and personal values were identified with care.

In the current study, the procedure adopted to identify the values incorporated in mathematics text books were analyzed as per the guidelines and definitions given by researchers.

General Categories of Values
Sam and Ernest(1997) classified the values of Mathematics education in to three as Epistemological values , Social and cultural values and Personal values.

Epistemological values
They are the values which are about theoretical side of mathematics learning and teaching such as accuracy, systematic, accuracy rationalism and analytics, problem solving.

Social and cultural values
They are values which indicate human responsibility about mathematics education for society such as compassion, adjustment, co-operation, gratitude etc.

Personal values
Values that affect a person as an individual or a learner such as curiosity, sharing and caring, trust etc.

Bishop(1996) classified values taught in mathematics into three different types making them more specialized. They are general Educational values, Mathematical values and Mathematical educational values.

For the present study, the classification of values were taken from Sam and Ernest(1997) and Bishop(1996) on mathematical values were taken as a frame of reference. The classification of values for the present study was based on the above classification and they were taken for investigation in the Indian context.

Category of values in the mathematics text book analysis is
Main category of value Sub category of value
Mathematical values Rationalism, logical, accuracy and abstract
Social values Adjustment and co-operation
Personal values Discipline, unity
The following definitions were taken from Bishop(1996) and Sam Ernest(1997) and classification of values and sub categories were included in this study in analysing the values embedded in the mathematics text books.

Mathematical values
Mathematical values are those that reflect the nature of mathematical knowledge. They are produced by mathematicians who have grown up in different cultures(Bishop et al., 1999)
Rationalism –Logic
This indicates the values that people have about mathematics. According to this value, mathematics has ideas, which depend on theory, logic, and hypothesis. Rationalism includes deductive logic and concern about correctness of results. Logic which means sequential and stepwise solution.

Abstract-Accuracy
It indicates mathematics and its own relation, pattern, sequence and surprises in its nature and accuracy which indicates the solution of the problems and theorems
Social Values
They are values that indicate human responsibilities about mathematics education for society such as adjustment and co-operation.
Personal values
Values that can affect person as an individual or learner such as discipline and unity.

SECOND PHASE
In the second phase, for subtopics of each branch, the strategies were suggested to integrate values in the mathematics classroom. The strategies were appropriately given by keeping in mind the concept of mathematics. In this phase, the researcher examined Arithmetic, Algebra, Geometry, which are the important branches of mathematics. In these branches of mathematics, certain topics from every branch, which were common for secondary and higher secondary class of state board of Tamil Nadu were taken for investigation. The different strategies and approaches of various categories were suggested according to the need of the classroom. The second phase concludes at this stage of development.

THIRD PHASE
The third phase gives detailed account of perception of mathematics teachers about the inculcation of values in mathematics class room. Quantitative and Qualitative approaches were adopted to analyze the data.

Data collected from inventory were analysed using statistical methods and percentage analysis.

VALIDATION PROCEDURES
The element of subjectivity in the analysis of content during this research was problematic. In order to reduce the risk of the own perspectives of the investigator dominating the data and overriding those of respondents, following strategies were used.

Expert opinion
The sample of the analysis of values was given to mathematics professors and mathematics teacher educators. This was to ensure the credibility and authenticity of the analysis without any bias from the researcher’s point of view. The comments given by the experts were taken in to account in the coding of values.

Triangulation
When conducting the key informant interviews, the data analyzed and the opinions collected were compared and clarified. To establish the consistency of the analysis, the suggested values were compared with the values practiced by teachers.

Peer review
The analyzed values of mathematical, personal, attitudinal and motivational were given to practicing mathematics teachers to give their suggestion about the integration of values in the content of mathematics of different standards. Modifications were made after many discussions and corrections.

Thick description
The content of the discussion and analysis with suggested values were briefly described as much detail as possible, so as not to omit any leading information. Thus the second phase concludes here at this stage of growth
3.8. SAMPLE
In research terms, a sample is a group of people, objects or items that were taken from a larger population for measurement. The sample should be representative of the population to ensure that we can generalize the findings from the research sample to the population as a whole. Purposive random sampling technique was adopted in this study.

The sample comprises of mathematics teachers handling classes VI to X working in high and higher secondary schoolsin Salem district. The participants of the study serving in schools with experience ranges from three years to twenty years of teaching mathematics in their respective schools at various levels. Mathematics teachersin the government, government aided, matriculation and CBSE schools were taken for the study. CBSE schools mathematics teachers were included, as it would be of help to note if the board of examination has an influence on value inculcation.The selection of the participants of this study were on the basis of longer tenure ship in teaching of mathematics as a profession and it is assumed that the longer in service, the better experience they had about mathematical knowledge and inculcation of values in their teaching. The sample consisted of undergraduate, postgraduate and mathematics teachers with M.Phil., qualification, which included headmasters and headmistress from some of the schools.Totally 300 teachers were selected by means of stratified random sampling method. B.T.Assistants and P.G. Assistants of Mathematics were chosen for the study from the selectschools. Totally 30 schools (approximately 35%) were chosen from the total population of 102 schools in Salem. Eight government schools, Seven government aided schools, Seven matriculation schools and eight CBSE schoolswere included. Math teachers handling classes VI-Xwith more years of teaching experience were included. The following table gives details of sample chosen. From these select teachers, 10% were selected purposively representing all demographic variables chosen. 10 under graduate teachers, 10 post graduateteachers,5Teachers with M.Phil. degree and 5 heads were in the interviewed group. Teachers with M.Phil.degree and the heads were highly experienced and in the age group greater than 35 years. In the other two groups, equal number of experienced and in experienced teachers were included for the interview.
Table- I showing Distribution of the Sample
S.No VARIABLES Number of Teachers
1 Gender Male 150
Female 150
2. Locality Rural 150
Urban 150
3. Medium of Instruction English 155
Tamil 145
4. Teaching Experience <10 years 120
10-15years years 100
>15 years 80
5. School Types Government 75
Government aided 80
Matriculation 75
CBSE 70
6. Age < 35 years 110
>35 years 190
7. Educational Qualifications U.G. 145
P.G. 85
M.Phil. 70
3.9.RATIONALE FOR THE CHOICE OF CATEGORICAL VARIABLES
The present study deals with the values prescribed in school mathematics content and the perception of mathematics teachers in integrating value system in the content in their teaching . The study itself talks only on mathematics subject matter and the teachers who deliver the subject.Hence purposive sampling technique is adopted. The common factors which influence the sample are Socio-demographic factors, Family factors, Employment factors and Income factors. Therefore these factors were taken for the current study.

The research done by MukhtarAlhajiLiman, MohdBurban Ibrahim, IyaAliyaGana, 2013, MukhtarAlhajiLiman,MohammedSalleh, Musa abdullahi, 2013, MukhtarAlhajiLiman, Mohd urban Ibrahim, JoharryOtman, 2012 focused on Measurement model for value inculcation in mathematical contents delivery included gender and service of teachers.

YukselDede, 2010, 2009, 2006,bWanzah Wan Ali, Rohani, Ahmad Tarmizi, Habsah Ismail, RamlahHarzah, 2007 ,Liz Bills, Chris Husbands, 2005,ChristineKeiti, 2003 analyzed on Values in Mathematics teachers’ length of service and locality of teachers.
As the studies reviewed were done in foreign countries, they didn’t include type of management and medium of instruction. To find the effect of these categorical variables, the current study included these variables.

The researches reviewed did not include age of the teachers as well their educational qualifications.The investigator has included these two variables in this study to fill in the research gap.

The current study has included gender, age and educational qualifications in socio-demographic variables.Locality as geographical factor.Medium of instruction and type of schools employed at ,length of service as employment factors..

3.10RESEARCH TOOL
Research tool is an instrument to gather data. It is described as a device to collect the data. It facilitates variable observation and measurement. The investigator prepared a mathematical value inventory as a research tool to collect data from the mathematics teachers.
3.10.1 DESCRIPTION OF THE TOOL
The mathematical value inventory was constructed by the researcher on a 5 point rating for each item. The tool consisted of five dimensions namely attitudinal, motivational, personal, mathematical and social value items. The inventory had five sections. Each section consisted ten items. There were totally ten items for each dimension, sum up to fifty items for five dimensions. Items1-10 addressed the perceptions of respondents about the mathematical values integration in teaching of mathematics. Item11-20 examined the perception of mathematics teachers about personal values to integrate in the mathematics teaching. Items21-30 gives detailed account of the perception of mathematics teachers about the social values to integrate in the teaching of mathematics. Items31-40 surveyed the perception of mathematics teachers about attitudinal values to be integrated in the mathematics teaching. Items 41-50 described the opinion of mathematics teachers about the motivational values to be integrated while teaching mathematics. Each item was self-explanatory and needed no description or clarification.
3.10.2 STANDARDIZATION OF THE TOOL
The tool is standardized by establishing reliability and validity of the tool. Validity
After drafting, the tool was given to a team of eminent professors for screening and edition. They ensured the appropriateness of language, relevance of items, essentiality of the items and conciseness of the statements. Some statements were reframed and some were modified for clarity. Thus the face validity and content validity of the tool was established.

The pilot study was carefully planned and carried out. In order to validate the scale, the draft tool was administered to 30 mathematics teachers working in schools. The researcher distributed and collected the filled in tool keeping in mind to cover the demographic variables approximately equal. The sample was derived using simple random technique. The recorded responses were scored as per the scoring key.
Pilot study
The tool consisted of 70 items out of which 50 were selected for final tool. Test-retest method was adopted to establish reliability. The tool of 70 items were administered to thirty samples to remove the ambiguous items. After 15 days, the same tool was administered to the same sample of 30 students. The items which need more construction were rectified. Some items were removed as per the requirement. The final tool consisted of 50 items of different dimensions. The reliability co-efficient found to be 0.82
TABLE – 2 SHOWING ITEM WISE CORRELATION
ITEM NO ‘r’ VALUE REMARK ITEM NO ‘r’ VALUE REMARK
1 0.456 Selected 35 0.602 Selected
2 0.445 Selected 36 0.528 Selected
3 0.302 Selected 37 0.666 Selected
4 0.689 Selected 38 0.456 Selected
5 0.765 Selected 39 0.745 Selected
6 0.166 Rejected 40 0.190 Rejected
7 0.677 Selected 41 0.203 Rejected
8 0.564 Selected 42 0.621 Selected
9 0.368 Selected 43 0.507 Selected
10 0.456 Selected 44 0.368 Selected
11 0.304 Selected 45 0.321 Selected
12 0.222 Rejected 46 0.304 Selected
13 0.364 Selected 47 0.222 Rejected
14 0.567 Selected 48 0.364 Selected
15 0.555 Selected 49 0.567 Selected
16 0.453 Selected 50 0.555 Selected
17 0.410 Selected 51 0.453 Selected
18 0.519 Selected 52 0.410 Selected
19 0.444 Selected 53 0.666 Selected
20 0.561 Selected 54 0.190 Rejected
21 0.345 Selected 55 0.300 Selected
22 0.216 Rejected 56 0.239 Rejected
23 0.012 Rejected 57 0.290 Selected
24 0.123 Rejected 58 0.532 Selected
25 0.145 Rejected 59 0.678 Selected
26 0.233 Rejected 60 0.096 Rejected
27 0.112 Rejected 61 0.505 Selected
28 0.101 Rejected 62 0.453 Selected
29 0.298 Selected 63 0.410 Selected
30 0.452 Selected 64 0.519 Selected
31 0.431 Selected 65 0.444 Selected
32 0.789 Selected 66 0.161 Rejected
33 0.654 Selected 67 0.015 Rejected
34 0.452 Selected 68 0.098 Rejected
69 0.021 Rejected 70 0.112 Rejected
To give high validity to the tool, the items with ‘r’ value above 0.25 was retained and the other items were rejected. Based on it 20 statements were deleted. The final tool contained 50 statements.

Reliability
Reliability of the tool was established using split half method. For computing the split half method, the entire tool was divided into two equal halves and the co – efficient of the reliability was calculated. A Cronbach ? analysis was calculated for each components of this scale. The Cronbach ? analysis could examine if the items were internally consistent, stable, and homogenous. In order to raise the reliability and lower the error, some unsuitable items would be deleted.Details are as given below.
Table-3 RELIABILITY OF MATHEMATICS VALUES INVENTORY
SCALE METHOD FORMULA RELIABILITY VALUE
Mathematics Values Inventory Split half reliability Cronbach’sAlapha 0.797(?)
Spearman – Brown prophency 0.816
Final Tool – Mathematics Value Inventory
The final scale Mathematics Value Inventory consisted 50 statements with five dimensions vizMathematical, Personal, Sociological, Motivational and computational dimensions
3.10.3 Scoring Procedure of the tool
The mathematical value inventory was rated on 5 point rating scale. The ratings given were strongly agree, agree, neutral, disagree, strongly disagree. The maximum value of 5 for strongly agree, and the minimum value of 1 for strongly disagree was given to each item. The maximum score for each dimension was 50.

Table- 4 showing Scoring procedure of the inventory
Options Score
Strongly agree 5
Agree 4
Neutral 3
Disagree 2
Strongly disagree 1
3.10.4 Method of administering the tool
The tool was administered to three hundred mathematics teachers of secondary and higher secondary level. The inventory was self explanatory. The prelude instructions were given to illumine the vision of mathematics teachers. The teachers were given enough time to appropriately choose the options and mark it. If the participants mark it as “Strongly agree”, he/she was given the point “5” in which that particular, value predominates, like wise from each participant the data was collected.
3.10.5. INTERVIEW
The other tool which was adopted to collect opinion about integration of values in mathematics was “Interview”. Interview involves either structured or unstructured verbal communication, between the researcher and subject, during which information is obtained for a study.
3.10.5.1 Conduct of the interview
Interview was conducted at the convenient time of the participant. This took from one hour to two hours. This was mixed approach of structured and unstructured verbal communication. The questions for interview was based on the study conducted by MuktharAlhajiLiman, Mohammed JohdiSalleh, and Musa Abdullahi (2013) on, ” Sociological and Mathematical Educational Values: An Intersection of Need for effective Mathematics Instructional Contents Delivery”
The interview questions were
What is your understanding about mathematical value inculcation ?
How do you perceive inculcation of mathematical, attitudinal, sociological values in your teaching?
How do you inculcate mathematical values in your mathematics teaching?
What are the challenges constraining your capacity to inculcate mathematical value.
What is your suggestion to improve the inculcation of mathematical values in daily teaching?
3.10.5.2 KEY INFORMANTS OF THE INTERVIEWS
The interview involved persons who have been central in the subsequent development of the mathematical values. The interviews were conducted on a one-to-one basis and, in most circumstances, in the work place of the interviewee. The process and data gathered during the interviews was exceptional in providing the background and impact of the prevailing social, cultural and political environment on values education. The face to face interview offered the possibility of checking interesting responses and allowed the interviewer to investigate underlying principal topic of the study. The data was collected and analyzed objectively by giving it to 3 raters of experts. The analysis was based on qualitative approach.
One interview was particularly insightful, in the sense that the investigator recorded key interviewees as she sought to interpret the interesting situation that happened in classroom while integrating values in mathematics classroom.
The key informant interviews afforded the investigator the opportunity to get first hand information of the controversy, conflict, and emotions that accompanied and influenced the value integration in mathematics. Anonymity was guaranteed in the individual interviews and this increased the richness and depth of information gathered. It is highly unlikely that it would have been possible to gather such information from the neatly packaged structured / unstructured questions. The response rate for the key interviews was high, and in some instances the respondents remained in touch with the investigator.
“Snowball” sampling technique was used the selection of interviewees. The sample comprises of thirty mathematics teachers of secondary and higher secondary level. Ten higher secondary teachers and 20 secondary teachers were taken for the study. The interviewees were those who had either been directly involved in the value education in mathematics or those who had involved in administration of value education in mathematics. This strategy not only assisted the researcher in gaining access to value education, but in some instances afforded access to highly placed educators.
The direct interviews, in contrast to survey questionnaires, allowed to seek clarification and to prompt the interviewee if a question seemed unclear. The interview sessions concentrated not only on identifying values in mathematics as opposed to current practice, but also the factors that determine the challenges of value education in mathematics. The session provided a more detailed account of the meanings of the official pronouncements of the goal of integrating value education in mathematics. The information gathered increased the understanding of the original intentions of inculcating values in mathematics, as well as the challenges they have faced in trying to achieve the goal.
3.10.5.3 Ethical Consideration
This study explored the analysis of the content and personal understanding of how teachers interpreted and implemented the value integration in the content of mathematics while teaching mathematics. The fact that values as a concept touches the personal lives of teachers meant that the researcher was seeking information that has been largely been considered private and sensitive. It was therefore critical that the researcher maintained a high level of sensitivity and confidentiality towards the issues under observation.

From the start of the study, the investigator explained the aim of the study in detail to the participating teachers, also assured them that the information would not be used in any way to discredit themselves or their school. The investigator therefore used pseudonyms in the text and has presented the information in the appropriate form, according to the stratification adopted in the sampling that is, government, government-aided and CBSE private schools involved in this study. This style ensures anonymity and at no time any one can make a connection to the respective schools or teachers. The number of schools in the different clusters renders such an exercise impossible.

3.11.STATISTICAL TECHNIQUES USED FOR THE STUDY
Differential, correlational , regression, discriminant and percentage analyses were done.
Method of Data Analysis
The data analysis consisted of examining the branches of mathematics, the content of mathematics and the opinions of mathematics teachers about the value inculcation in mathematics. The first two phases involved the document analysis and content analysis. The opinions of mathematics teachers were carefully analysedqualitatively. The perception of mathematics teachers were analysed using statistical analysis.

3.12 CONCLUSION
This chapter summarized the procedure of research design, objectives, different phases of research design, tool adopted , select sample and the statistical techniques used to analyze the data. The next chapter vividly presents the data analysis.

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