analysis and interpretation -...

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ANALYSIS AND INTERPRETATION

5.1 INTRODUCTION

After the data collection is over, the next step in the realm of research is data

processing, the primary data collected in the field. The processing involves editing,

classification and coding of data. Editing is essential to identify the errors and omissions

of the collected data and rectify them in order to achieve homogeneity, consistency and

completeness. Data should be edited before being presented as information. This action

ensures that the information provided is accurate, complete and consistent. Data editing

can be performed manually, with the assistance of computer programming or a

combination of both techniques. Goode and Hatt (1952) define that ‘coding is an

operation by which data are organized into classes, and a number or symbols are given to

each item, according to the class in which it falls’. Each answer to a particular question

must be given a distinctive code or value. After the editing and coding of the collected

data, there is a need for classification of data for easy understanding. It is the first step in

the process of analysis and interpretation of data. The classification and tabulation of data

is essential for proper and systematic arrangement and presentation of data. Stockton and

Clark (1975) defined that the process of grouping a large number of individual facts of

observation on the basis of similarity among the item is called classification. Thus the

process of good classification should have clarity, homogeneity and equality of scale,

purposefulness and accuracy.

The method of investigation presented in the previous chapter helped the

investigator generate data for the present study. The generated data were coded and

grouped for verifying the hypotheses formulated for the present study. Factor analysis

and cluster analysis were employed for validation and grouping of data. Further

correlation and ‘t’ test were used to find out the relationship between the variables and to

find if there is any difference between the groups that emerged after clustering.

The analysis and interpretation in this chapter is preceded by a brief introduction

on the Factor analysis technique, and then it is followed by the analysis of hypotheses

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related to it. Next a brief description of cluster analysis is followed by it and the analysis

of hypotheses related to it and at last the test of significance and correlation test tables

with the hypotheses are displayed.

5.2 FACTOR ANALYSIS

Factor Analysis is a collection of statistical methods used to (a) analyse patterns

in a correlation matrix, (b) reduce large numbers of variables to a smaller number of

components or factors, (c) simplify analysis of highly correlated independent variables,

(d) explore observed data for the presence of theoretical variables, and (e) test hypotheses

about theoretical variables. Factor Analysis can be classified as Exploratory or

Confirmatory on the basis of the researcher’s objective. Exploratory Factor Analysis

(EFA) is used to gain insight into the structure or underlying processes that explain a

collection of variables. The term structure describes the relationships between latent

variables and measured variables. Confirmatory Factor Analysis (CFA) is used when a

researcher has a number of well- articulated theories about the latent structure of a set of

measured variables and wishes to test how well those models fit the data.

5.2.1 History of factor Analysis

The Concept of Factor Analysis can be traced back to Charles Spearman’s (1904,

1927, 1933) research on the structure of human intellect. Spearman theorized that each

measure of human ability contains a general factor, common to all other measures of

ability, and a specific component unique to itself. According to Spearman’s theory, the

only basis for a correlation between two ability measures is their shared influence of a

common factor that he called ‘g’. The earliest Factor Analysis were focused on

confirming Spearman’s general factor model and identifying tests that correlated the

highest with g, and thereby serving as measures of general intelligence. It soon became

apparent that Spearman’s one-factor theory did not accurately describe the factor

structure of ability tests.

Thurstone (1947) developed the method of multiple-factor analysis to analyse the

tests determined by more than one kind of intelligence. Unlike Spearman’s use of Factor

Analysis, Thurstone’s multiple factor analysis challenged researchers to ascertain the

number of factors required to explain a collection of test measures and then to interpret


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the factors. Modern exploratory Factor Analysis requires researchers to deal with these

same two issues, dimensionality (number of factors) and interpretability (ascribing

meaning to factors). With modern computers, exact principal-axis solutions to Factor

Analysis problems can be obtained promptly and easily. Principal-axis factors are

extracted from a correlation or covariance matrix in decreasing order of the variance

explained. The first factor explains more variance than any other possible factor; the

second factor explains the remaining variance than any other and so on.

Ad hoc decisions about the number of factors (dimensionality) were replaced with

precise rules for the number of factors (Cattell, 1958, Cattell and Vogelman,1977;

Guttman,1954; Kaiser, 1961), and transformations of the factors were introduced to

enhance interpretability (Carroll,1953; Kaiser 1958). The Kaiser- Guttman rule, which

states that a researcher should attempt to interpret the number of factors that have

eigenvalues greater than 1, became a standard. An eigenvalue measures the amount of

variance in the variables explained by a factor. Now it has become a computer program

default in the major statistical programs like SAS and SPSS.

Cattell’s (1958) Scree Test, a visual plot of eigen values, is another popular method

of determining the dimensionality of a set of variables that is the number of factors that

can be derived from the set. The most common interpretability transformation of factor

structures is Kaiser’s (1958) varimax criterion. The varimax criterion simplifies the factor

interpretation by rotating (transforming) the principal axis solution into uncorrelated

factors with maximum variation in the factor variable correlations. The varimax criterion

simplifies the interpretation of a factor by causing a separation in the variable factor

correlations. The varimax transformation, along with other analytical rotations is guided

by Thurstone’s (1947) concept of simple structure. In uncomplicated terms, a simple

structure occurs when each variable relates to only one factor.

In the second half of the 20th century, the mathematical and statistical basis of

Factor Analysis progressed to the point where rigorous tests of significance for

dimensionality and structure were possible (Bentler and Bonnet, 1980). That technical

development led to a solid statistical basis for Confirmatory Factor Analysis.

Confirmatory Factor Analysis is used when a researcher wants to evaluate a number of


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well-articulated theories about the underlying structure for a set of variables.

The researcher specifies the number of factors and how the variables relate to the factors.

Some of the key terms used in factor analysis are described below.

5.2.2 Purpose of Factor Analysis

The general purpose of factor analytic techniques is to find a way of condensing

(summarizing) the information contained in a number of original variables into a smaller

set of new composite dimensions (factors) with a minimum loss of information; that is, to

search for and define the fundamental constructs or dimensions assumed to underlie the

original variables. The four functions Factor Analysis technique can perform are as follows-

� Identify a set of dimensions that are latent in a large set of variables; that is also

referred to as R factor analysis.

� Devise a method of combining or condensing large numbers of people into

distinctly different groups within a larger population; this is also referred to as Q

factor analysis.

� Identify appropriate variables for subsequent regression, correlation or

discriminant analysis from a much larger set of variables.

� Create an entirely new set of a smaller number of variables to partially or

completely replace the original set of variables for inclusion in subsequent

regression, correlation or discriminant analysis.

5.2.3 Some of the key terms used in Factor Analysis

5.2.3.1 Factor– Factor Analysis operates by extracting as many significant factors from

the data as possible, based on the bivariate correlations between the measures. A factor is

a dimension that consists of any number of variables. Factor Analysis involves extracting

one factor and then evaluating your data for the existence of additional factors.

The successive factors extracted in Factor Analysis are not of equal strength. Each

successive factors account for less and less variance. Typically the first two or three

factors will be the strongest that account for the most variance.

5.2.3.2 Eigen value- The strength of a factor is indicated by its eigen value. Factors with

eigen values less than 1.0 usually are not interpreted.


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5.2.3.3 Factor loading- In order to determine the dependent variables constituting a

common factor, factor loadings are computed. Each factor loading is the correlation

between a measure and the underlying factor. A positive factor loading means that a

variable positively correlated with the underlying dimension extracted, whereas a

negative loading means that a negative correlation exists. By convention, loadings are

interpreted only if they are equal to or exceed plus or minus 0.30.

5.2.3.4 Rotation of factor- After obtaining factor loadings, we need to interpret them.

The factor loadings computed initially are often difficult to interpret because they are

somewhat ambiguous. Factor rotation is used to make the factors distinct. Two types of

rotation are orthogonal and oblique rotation. In orthogonal rotation, the axes remain

perpendicular. In oblique rotation, the angles between the axes, as well as the orientation

of the axes in space, may change. Generally the orthogonal rotation is preferred over

oblique rotation because the results are easier to interpret. The most popular orthogonal

rotation method is varimax. This type of rotation maximises the variance of loadings on

each factor and simplifies factors (Tabachnick and Fidell, 2001).

5.2.3.5 Principal components and principal factors analysis

Two types of factor analysis are principal components analysis and principal

factors analysis. In principal components analysis, the diagonal of the completed

correlation matrix is filled with ones. In contrast the principal factors analysis completes

the correlation matrix by entering communalities along the diagonal. Communality is a

measure of a variable’s reliability and is fairly easy to obtain after Factor Analysis.

Various techniques have been proposed for estimating communalities. The choice

between principal components and principal factor analysis rests on the goals of the

analysis. If the goal is to reduce a large number of variables down to a smaller set and to

obtain an empirical summary of the data, then principle components analysis is most

appropriate. If the research goal is driven by empirical or theoretical predications, then

principal factor analysis is the best (Tabachnick and Fidell, 2001). In the absence of any

clear information on which technique is best, we should probably use principal

components in those situations in which you do not have any empirical or theoretical

guidance on the values of the communalities.


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5.2.3.6 Exploratory Factor Analysis versus Confirmatory Factor Analysis

Tabachnickand Fidell (2001) made distinction between exploratory Factor

Analysis and confirmatory Factor Analysis. Exploratory Factor Analysis is used when we

have a large set of variables that we want to describe in simpler terms and we have no a

priori ideas about which variables will cluster together. Exploratory Factor Analysis is

often used in the early stages of research to identify the variables that cluster together.

From such an analysis, research hypotheses can be generated and tested. Confirmatory

Factor Analysis is used in later stages of the research where the researcher can specify

how variables might relate given some underlying psychological process (Tabachnick

and Fidell, 2001).

5.2.4 Factor Analysis decision diagram

Figure (5.1) shows the general steps followed in any application of factor analysis

techniques. The starting point in Factor Analysis is the research problem, next the

calculation of the correlation matrix. The correlation matrix is chosen based on the

objectives of the problem at hand. At the next stage decision has to be taken on whether

the correlation to be done between the variables or between the respondents. Factor

Analysis when applied to a correlation matrix of the individual respondents is called ‘Q’

factor analysis and when it is applied to a correlation matrix of the variables is called ‘R’

factor analysis.

After identification of ‘Q’ factor analysis or ‘R’ factor analysis at the next level

the investigator has to decide on the Factor model to be chosen whether component

analysis or common factor analysis. The component model is used when the objective is

to summarize most of the original information in a minimum number of factors for

prediction purposes. In contrast, common factor analysis is used primarily to identify

underlying factors or dimensions not easily recognised. The flow chart depicting the

following steps in Factor Analysis is shown in figure 5.1.


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Figure (5.1) Factor Analysis decision Diagram

RESEARCH PROBLEM WHICH VARIABLES TO INCLUDE?

HOW MANY VARIABLES? HOW ARE VARIABLES MEASURED?

SAMPLE SIZE?

CORRELATION MATRIX (R VERSES Q)

FACTOR MODEL

UNROTATED FACTOR MATRIX

NUMBER OF FACTORS

COMPONENT

ANALYSIS COMMON FACTOR

ANALYSIS

EXTRACTION METHOD ORTHOGONAL?

OBLIQUE?

ROTATED FACTOR MATRIX FACTOR INTERPRETATION

FACTOR SCORES FOR SUBSEQUENT ANALYSIS:

REGRESSION DISCRIMINANT ANALYSIS

CORRELATION


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In addition to selecting the factor model the investigator has to specify how the

factors are extracted either orthogonal or oblique. In orthogonal solution the factors are

extracted in such a way that the factor axes are maintained at 90 degrees, meaning each

factor is independent of all other factors. Therefore the correlation between the factors is

arbitrarily determined to be zero. In oblique solution the extracted factors are correlated.

This is based on the needs of the research problem. At this stage the investigator is ready

to extract the initial unrotated factor matrix.

By examining the unrotated factor matrix, the investigator can explore the data

reduction possibilities for a set of variables and obtain the preliminary estimate of the

number of factors to be extracted. Final determination of the number of factors is done

after the factor matrix is rotated and the factors are interpreted. The researcher may stop with

the factor interpretation or proceed to calculate the factor scores and subsequent analysis with

other statistical techniques like correlation, discriminant analysis, regression etc.

With these basics of Factor Analysis the investigator identified cognitive

processing and self-perception of learning disabilities as variables to be included in

Factor Analysis and ‘R’ factor analysis was chosen, with principle component analysis as

Factor model. Orthogonal extraction method was employed with varimax rotation.

The varimax rotation yielded four factor solutions for cognitive processing which is

described in the following sections along with the concerned Hypothesis formulated.

5.3 ANALYSIS AND INTERPRETATIONS OF FACTORS

Hypothesis 1-There will be patterns of clustering of relationships among cognitive

processing of elementary inclusive school children.

To find the artificial dimensions of cognitive processing the data matrix of

23 × 100 was considered for factor solution. In order to arrive at the new independent

factors, the 23 × 23 correlation matrix of variables related to cognitive processing was

considered and reduced to 23× 4 factor solution, which explained 68.872 % of variance

of the original variables. It was further rotated using normal varimax rotation procedure

and the four factor emerged was considered for interpretation and description.

The rotated factor matrix explained the simplified factor structure with factor loading for

each variable. Here the signs of the loadings imply the direction of association. The size


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of each loading value indicates the degree of association of each variable with the

appropriate new independent dimension. The four new independent factors which

emerged explained 68.872% of the total variance. The share of the primary factor was

found to be higher than that of the other factors.

To find the best solution in terms of interpretability and theoretical sensibility, the

interpretability was investigated using Hatcher’s interpretability criteria (Hatcher, 1994)

which read- a given component contains at least three variables with significant loadings,

a loadings of ± 0.40 being suggested as cut off point, variables loaded on the same

component share the same conceptual meaning, variables loaded on different components

appear to measure different constructs, the rotated factor pattern demonstrates ‘simple

structure’ which means that most variables load relatively high on only one component

and low on the other components and most components have relatively high factor

loadings for some variables and low loadings for the remaining ones.

As a rule of thumb that has been frequently used by factor analyst, factor loadings

greater than ±0.30 are considered significant (n= 50 or larger), ±0.40 are considered more

important, and ±0.50 or greater are considered very significant. Thus the larger the

absolute size of the factor loading, the more significant the loadings is in interpreting the

factor matrix. Hence factor loadings with values of ±0.40 or greater have been

considered for interpretation and description. The variables are tabulated on the basis of

their absolute coefficient value in the descending order for all the 4 dimensions. The four

factor solution which emerged as a result of Factor Analysis with their loadings is

explained in the following sections.

FACTOR 1–Mental processing

The first factor which is considered as the primary factor is the most important

component among the four factors. The first factor is a general factor with highest

percentage of variance accounting to 23.798%. The variables highly loaded in this factor

are tabulated with their respective loadings in descending order.


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Table 5.1 Shows variable with significant loadings in cognitive processing for Factor 1

Variable Significant loadings

Receptive Attention part B 0.799

Matching numbers part E 0.759

Number detection part C 0.684

Planned connections part B 0.666

Matching numbers part D 0.638

Receptive Attention part A 0.618

Sentence questions 0.590

Planned connections part A 0.586

Planned codes part B 0.563

Non-verbal matrices 0.553

Figure memory 0.471

A total of 11 variables were loaded under this factor. This primary factor has high

loading on most of the variables related to general construct of cognitive processing

i.e., planning, attention, simultaneous and successive processing, relating to cognitive

processing otherwise called mental processing. Hence it is named as ‘mental processing’.

In this general factor the variables related to Planning as shown in Table 5.1 were

Matching Numbers, Planned connections and Planned Codes etc., and those related to

attention were Receptive attention, Number detection etc., and those related to successive

processing were sentence questions. Simultaneous processing included items like

Nonverbal Matrices and figure memory. The positive loadings signifies that all the variables

are positively associated with each other which implies the four dimensions namely planning,

attention, successive and simultaneous processing are positively related.

From the above Table 5.1 we can infer that the general construct of cognitive

processing has four dimensions namely Mental processing, Planning, Attention, and


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Simultaneous and Successive processing. So the present study goes along with the

theoretical description of cognitive processing by Das and his colleagues (1994b) which

involves the four tasks namely planning the task, paying attention to it and

simultaneously and successively processing the information to give the output.

FACTOR 2- Simultaneous and successive processing

The variables related to successive and simultaneous processing shows highly

significant positive loadings in the second factor. The positive loading is the result of the

positive correlation of some of the variables with the rest of the variates. This second

factor accounts for the second highest proportion of variance i.e. 20.588%. The variables

with factor loadings in descending order are described below in Table No. 5.2.



Word series part B 0.854

Word series part C 0.845

Sentence repetition 0.824

Word series part A 0.810

Expressive Attention 0.580

Spatial relations 0.534

Total variables loaded highly in this factor were 6. The first four variables listed

in Table 5.2 i.e., Word series Part A, Word series B and Word series C and Sentence

Repetition clearly indicates that it is related to successive processing and the last variable

spatial relations with simultaneous processing. The predominance of above variables

obviously becomes the basis for naming this component as ‘successive and simultaneous

processing’. The variable ‘Expressive Attention’ is also loaded here which indicates that

attention is related to successive and simultaneous processing.

From the above table we can conclude that Successive and Simultaneous

processing variables are positively associated with each other. From the above table it is


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seen that successive and simultaneous processing goes together as predicted in theory and

further these two should act together in an individual so as to bring out the result.

FACTOR 3- Planning

The third factor accounts for a total variance of 14.082%. There are significant

positive loadings in this factor also. Variables and its significant loadings are listed in

descending order in the Table 5.3 below.



Matching numbers part A 0.872

Matching numbers part B 0.861

Matching numbers part C 0.761

Matching numbers part D 0.527

Planned codes part A 0.455

Five variables were highly loaded in this factor. From the table it is evident that

all the variables i.e., Matching Numbers Part A, B, C, D and Planned Codes are related to

planning component of cognitive processing. Hence it is named as ‘planning’.

The positive loadings of the variables indicate that the variables present a positive

relationship in Factor 3. Matching Numbers Part D is highly loaded in Factor 1 (0.638)

and Planned codes part A is loaded highly in Factor 4 (0.619), but it is considered here

also to support the other variables of ‘planning’ component of cognitive processing.

It can be summarized from the above Table 5.3 that all the planning variables are

loaded in a single factor and also they are positively associated with each other. From this

we can say that children who performed well in matching number task have equally

performed in planned codes task. And planning is central to every activity. A child has to

plan his activity prior to the performance of the task and need attention, which help him

to simultaneously and successively process the information.


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FACTOR 4 - Attention

This factor which individually explains 10.404% of variance contains the

following variables with high positive loading.



Number detection part A 0.828

Number detection part B 0.705

Planned codes part A 0.619

Receptive Attention part A 0.410

The number of variable loaded in this factor was four. Based on the loading

pattern, this factor is called as ‘Attention’. The first two variables i.e. Number Detection

Part A and B and the last Receptive Attention listed in the Table 5.4 relates to attention

aspect of the cognitive processing. And hence it was named as ‘Attention’. The positive

loadings of the variables indicate that they have positive relationship with each other.

Receptive Attention part A is highly loaded in Factor 1 (0.618) and it is considered here

in Factor 4 to support the other variables related to attention factor. It is evident from the

table that the variable planned code is loaded here which indicates that Planning is

necessary condition for attention.

It can be inferred from the above table that the variables related to attention are

positively related and for a child to be attentive he needs to have a plan in mind.

Attention is very much necessary for a child to perform an activity and prior to it he has

to have a plan in mind and so as to process the information to put forth the result.

The multivariate approach to the concept of cognitive processing enabled the

investigator to bring out the underlying constructs of cognitive processing. This approach

helped the investigator to summarize the underlying dimensions in the structure of the

raw data – matrix. As a result it was possible to obtain four independent factors

representing the construct of cognitive processing. These four factors have been named


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accordingly taking into account the loadings of the variable in each factor. These four

independent factors have also brought out the significant relationships with most of the

chosen variables of the present study. Therefore hypothesis No.1 which describes

‘patterns of clustering of relationships in cognitive processing’ is retained.

To summarize the respondent’s cognitive processing skills falls under four

dimensions namely Mental processing, Planning, Attention, and Successive and

Simultaneous processing as in Figure 5.2. There were positive loading in all the four

independent factors, which implies that the variables are positively associated with each

other. Thus proving the theory put forth by Das and his colleagues (1994b).

Fig.5.2 Four dimensions of Cognitive processing

Hypothesis 2- There will be patterns of clustering of relationships among the self-perception

of learning disabilities of elementary inclusive school children.

PLANNING

ATTENTION

SIMULTANEOUS AND

SUCCESSIVE ROCESSING

MENTAL

PROCESSING

COGNITIVE

PROCESSING


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For establishing the artificial dimensions of self-perception of learning disabilities

after item extraction was prone to exploratory factor analysis and varimax rotation.

The rotated factor matrix explained the simplified factor structure with factor loading.

The total percentage of variance accounted was 54.7%. The share of the primary factor

was found to be higher than that of the other factors.

Factor 1- ‘Skill of Cognition’

The first factor is a general factor with highest percentage of variance accounting

to 15.07%. The significant loadings with the items are arranged in Table 5.5, in

descending order.

Table 5.5. Variables with Significant loadings in self-perception of learning disabilities

for Factor 1

Items Significant loadings

While reading I have difficulty in understanding important things 0.735

While speaking with friends I find It difficult to speak about a particular thing

0.664

I have difficulty in solving Maths word problems 0.638

I don’t get the right word to speak while speaking with friends 0.590

I have trouble in following directions that have more than one or two steps

0.553

I tend to be clumsy and unorganised 0.536

While writing copy book, I am not able to write within the four lines

0.508

I have a poor memory 0.487

I find it difficult to plan my time 0.480

A total of 9 variables (items) were loaded in this factor. This Primary factor has

highest loadings on reading, writing, arithmetic, organisation, memory etc. so it is named

as “perception of skill of cognition.” Further the loadings were all positive which implies

that there is positive association between the variables. This factor resembles the first

factor in the artificial dimensions of Cognitive processing (Hypothesis 1) i.e., ‘Mental


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processing’. Skill of Cognition involves perception and judgement on the part of the

child. For perception to take place he needs attention and planning skill and for the

judgement the simultaneous and Successive processing. Thus ‘Skill of cognition’ goes

along with mental processing in an individual.

It can be inferred from the above table that all the variables related to reading,

writing, arithmetic, memory and organisation are positively associated with each other.

And for all these aspects cognitive skills are necessary.

Factor 2- ‘Skill of Processing’

Six items were significantly loaded under factor 2, which accounted for a variance

of 14.27%. The items with their loadings are displayed in Table 5.6.

Table 5.6 Variables with Significant loadings in self-perception of learning disabilities

for Factor 2

From the Table 5.6 it is evident that the items are significant positive loadings and

they are closely associated with each other. These items i.e., ‘I am a poor speller’, ‘While

writing I don’t get ideas to put in’, ‘I am a poor reader’, ‘I am a poor at basic mathematics’, ‘I

make mistakes while reading’, ‘I can tell a story but cannot write it’, reflect the

processing skills in children. And hence it is named as “perception of skill of processing”.

Visual processing skills should be helpful when solving geometry problems that must be

solved by looking at the problem as a whole, sequential visual processing skill should be


I am a poor speller 0.787

While writing I don’t get ideas to put in 0.737

I am a poor reader 0.654

I am a poor at basic mathematics 0.649

I make mistakes while reading 0.606

I can tell a story but cannot write it 0.558


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instrumental in reading and writing and also when solving word problems and organizing

calculations that must be solved in a sequential fashion. This factor resembles the Factor

2- ie ‘Simultaneous and successive processing’ in the artificial dimensions of cognitive

processing of elementary school children. Visual sequential as well as simultaneous

processing skills are necessary in mastering reading, writing, arithmetic etc. If these skills

are impaired children cannot write or read properly.

To summarize items in the second factor ‘the skill of processing’ are positively

associated with each other. This factor resembles the second factor in the cognitive

processing of elementary inclusive school children. Processing skills are very much

essential in mastering the three r’s i.e. reading, writing and arithmetic.

Factor 3- ‘Skill of Expression’

Under factor 3 nine items got significantly loaded. The items were arranged in

descending order of their loading values. This factor accounted for a total variance of

12.98%. The items in the Table 5.7 below show positive loadings and so they are

positively associated with each other.

Table 5.7. Variables with Significant loadings in self-perception of learning disabilities

for Factor 3


I find it difficult to tell the alphabets in order 0.698

I find it difficult to tell the months of the year in order 0.663

It is difficult for me to write about myself 0.584

My homework is not neat 0.566

My handwriting is poor 0.534

I have difficulty in solving Maths word problems 0.505

I reverse letters when I read 0.494

While writing, I give no space between words 0.466

I learn something today but do not remember it for the next day. 0.455


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The items in Table 5.7 reflect the expressive skills in children namely oral and

written. And so it is named as “perception of skill of expression”. Expressive skills are

required to convey message to others through words, facial expressions, and body

language or in writing. Expressive language skills or the ability to express one’s thoughts,

feelings and knowledge is extremely important in the educational setting. Poorly

developed expressive language skills create a barrier to student participation and create

difficulty in assessing how much the student actually has learned. Expressive language

deficits are seen in children with autism and other learning disabilities.

The skill of expression requires prior planning by the child. So the factor three

i.e., Planning in the artificial dimensions of cognitive processing ability is related with

this factor. If a child want to read or write (express) he has to plan first which part he has

to read or write and how he has to do it either by part method or whole method and what

are the aspects to be covered in it etc. So Planning is an essential component in the ‘skill

of expression’ whether it is oral or written aspect.

To conclude all the items in Factor 3, ‘skill of expression’ has high loadings and

is positively associated with each other. This Factor is related with the Planning aspect of

cognitive processing ability in elementary school children. In school, expressive language

difficulties will impact a student’s performance both in written and spoken language.

Without good expressive language, the child will have great difficulty showing people

what he or she actually knows. A person with an expressive language issue may actually

know the answer, but not be able to put it into words. Therapy can help with this problem

using stories, games and a variety of other methods and strategies.

Factor 4- Skill of Memory

Six items were loaded under factor 4. The total variance accounted by this factor

is 12.38 %. The items with their positive loadings are displayed in Table No.5.8 below in

descending order.


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Table 5.8 Variables with Significant loadings in self-perception of learning disabilities

for Factor 4

Items Significant loading

I cannot remember the words I have read 0.723

I while reading I interchange the letters in words 0.681

My note book is not neat 0.631

I forget what I am saying right at the middle of saying it 0.512

It is hard for me to memorize things for school 0.499

I often do not write down the assignments and forget what to do 0.449

Most of the items resemble memorization skill in children and hence it is named as

perception of ‘skill of memory”. It is evident from the table that most of the items are

positively loaded which implies that there is positive association between the items.

Memorization is an important concept in learning, and so it is important in skill of

reading, writing, maths etc. This factor is related with the fourth Factor i.e., ‘Attention’ in

cognitive processing ability of the elementary school children. Only if a child is attentive

he can store important things in the memory.

It can be inferred from the above table that items in Factor 4 reflect ‘skill of

Memory’ which are positively associated with each other. And this factor is related with

the Factor 4, ‘Attention’ of the cognitive processing abilities of elementary school

children. Only if the child is attentive he can store information in the memory i.e., short

term memory or long term memory. And also the stored up information which has to be

coded and stored can be retrieved, recalled or recognised only if the child is attentive in

this process. If the child is inattentive there may be gap in the information storage so that

the correct retrieval won’t take place.

It is seen from the above discussion of the four independent factor solution that

the first factor which is a general factor items loaded were related to reading, writing,

arithmetic, organisation, memory etc. named as ‘skill of cognition’. Next three factors

were specific factors related to ‘skill of processing’, ‘skill of expression’ and ‘skill of


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memory’. All the items in each of the independent factors were loaded positively which

implies that there were positive association between the items. Hence there are patterns of

clustering in self-perception of learning disabilities of elementary school children. So the

hypothesis 2 is accepted and retained.

More over Factor 1,2,3 and 4 in self-perception of learning disabilities is related

with Factor 1,2,3, and 4 of cognitive processing of elementary school children i.e.,

‘mental processing’ is related with ‘skill of cognition’; ‘simultaneous and successive

processing’ with ‘skill of processing’; ‘Planning’ with ‘Skill of expression’; and ‘Attention’

with ‘skill of memory’. The theory suggested by Das and his colleagues (1994b) that is

cognitive processing has four dimensions namely Planning, Attention, Simultaneous and

Successive Processing in PASS theory of Cognitive Processing is proved here that

Planning, Attention, Simultaneous and Successive Processing are components of

cognitive processes. The four dimensions of the self-perception of learning disabilities is

depicted in figure 5.3.

The factors which emerged from cognitive processing and self-perception of

disabilities were taken for further analysis in the following sections.

Fig. 5.3. Factorial dimension of self-perception of learning disabilities

SKILL OF COGNITION

SELF-PERCEPTION OF

LEARNING DISABILITIES

SKILL OF MEMORY

SKILL OF EXPRESSION

SKILL OF PROCESSING


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5.4 CLUSTER ANALYSIS

Cluster analysis is the name of a group of multivariate techniques whose primary

purpose is to identify similar entities from the characteristics they possess. It identifies

and classifies objects or variables so that each object is very similar to others in its cluster

with respect to some predetermined selection criteria. The resulting object clusters should

then exhibit high internal within cluster homogeneity and high external between cluster

heterogeneity. Cluster analysis is a multivariate statistical technique that can be used to

group individuals or objects into clusters based on particular characteristics that they

possess (Hair et al., 1995). When clustering individuals, the ultimate goal is to arrive at

clusters of people with homogeneous characteristics who thereby exhibit small within-

cluster (internal) variation, but at the same time exhibit large between cluster (external)

variations (Aldenderfer and Blashfield, 1984; Hair et al., 1995).

The main advantage of cluster analysis is that it enables the researcher to define a

cluster variate (i.e., the characteristic variables included in the comparison) which then

determines the commonalities and differences among and between groups and leads to

natural groupings (Hair et al., 1995). Furthermore, this approach provides an opportunity

to explore structures existing in data prior to attempting to explain why they exist.

Finally, taxonomy can be developed to help describe a population. These techniques have

been variously referred to as techniques of cluster analysis, Q-analysis, typology,

grouping, clumping, classification, numerical taxonomy and unsupervised pattern

recognition. This variety of nomenclature is due to its application in the field of diverse

disciplines such as Psychology, Zoology, Biology, Botany, Sociology, Artificial

Intelligence and Information Retrieval. Although the names differ across disciplines, they

all have a common dimension: classification according to natural relationships.

Cluster Analysis (CA) is a technique which seeks to separate data into constituent

groups. This technique is used for grouping of objects or individuals under investigation.

The objects which are subjected to cluster analysis are termed ‘entity’ or ‘ individual’.

The measurements taken on each entity are generally referred to as variables, characters

or attributes. The result of a Cluster Analysis will be number of groups, clusters, types or

classes.


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5.4.1 Objectives of Cluster Analysis

The goals of various users of clustering technique are frequently dissimilar.

Ball (1971) lists seven possible uses of clustering technique- Finding a true typology,

Model fitting, Prediction based on groups, Hypotheses testing, Data exploration,

Hypothesis generating and Data reduction. Cluster Analysis can be used to perform data

reduction procedure objectively by reducing the information from an entire population or

to set information about specific smaller subgroups. Cluster Analysis may be used to

generate hypotheses concerning the nature of the data and useful in shedding light on

previously made hypotheses. In some investigations Cluster Analysis methods may be

used to produce groups which form the basis of classification scheme useful in later

studies for predictive purposes of some kind. In general the technique of Cluster Analysis

which is a useful tool for data analysis can be used to search for natural groupings in the

data, to simplify the description of a large set of multivariate data, to generate hypotheses

to be tested on future samples and to verify the previously stated hypotheses.

5.4.2 Types of Cluster Analysis technique

The technique for Cluster Analysis seeks to separate a set of data into groups or

clusters. Cluster Analysis technique may be classified into types as follows-

• Hierarchical techniques- In Hierarchical techniques the classes themselves are

classified into groups, the process being repeated at different levels to form a tree.

• Optimization-partitioning techniques- In this technique the clusters are formed by

optimization of ‘clustering criterion’. The classes are mutually exclusive, thus

forming a partition of the set of entities.

• Density or mode - seeking techniques- In this the clusters are formed by searching

for regions containing a relatively dense concentration of entities.

• Clumping techniques- In this technique the classes or clumps can overlap.

These types are not necessarily mutually exclusive, and several clustering

techniques could be placed in more than one category. For the present study the

investigator has employed the hierarchical clustering technique and so it is presented in

detail in the following sections.


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5.4.3 Hierarchical clustering techniques

Hierarchical clustering techniques may be subdivided into agglomerative methods

which proceed by a series of successive fusions of the N entities into groups, and divisive

methods which partition the set of N entities successively into finer partitions. The results

of both agglomerative and divisive techniques may be presented in the form of a

dendrogram, which is a two-dimensional diagram illustrating the fusions or partitions

which have been made at each successive level. Since all agglomerative hierarchical

techniques ultimately reduce the data to a single cluster containing all the entities, and the

divisive technique will finally split the entire set of data into N groups each containing a

single entity, the investigator must decide at what stage in the analysis he wishes to stop

which may be based on some criteria.

5.4.3.1 Agglomerative methods-The basic procedure with all these methods is similar.

They begin with the computation of a similarity or distance matrix between the entities.

The end product of the methods is a dendrogram showing the successive fusions of

individuals, which culminates at the stage where all the individuals are in one group.

For this reason agglomerative procedures are sometimes referred to as build-up methods.

At any particular stage the methods fuse individuals or groups of individuals which are

closest (or most similar). Differences between methods arise because of the different

ways of defining distance (or similarity) between an individual and a group containing

several individuals or between two groups of individuals. Seven popular agglomerative

procedures used to develop clusters are Single linkage, Complete linkage, Unweighted

pair-group average, Weighted pair-group average, Unweighted pair-group centroid

method, Weighted pair-group centroid (median) and Ward’s method.

Single linkage (nearest neighbour) method - In this method the distance between two

clusters is determined by the distance of the two closest objects (nearest neighbours) in

the different clusters. This rule will, in a sense, string objects together to form clusters,

and the resulting clusters tend to represent long "chains."

Complete linkage (furthest neighbour) method - In this method, the distances between

clusters are determined by the greatest distance between any two objects in the different


139

clusters (i.e., by the "furthest neighbours"). This method usually performs quite well in

cases when the objects actually form naturally distinct "clumps". This method is

inappropriate, if the clusters tend to be somehow elongated or of a "chain" type nature.

Unweighted pair-group average method - In this method, the distance between two

clusters is calculated as the average distance between all pairs of objects in the two

different clusters. This method is also very efficient when the objects form natural

distinct "clumps," however, it performs equally well with elongated, "chain" type

clusters. Sneath and Sokal (1973) introduced the abbreviation UPGMA to refer to this

method as unweighted pair-group method using arithmetic averages.

Weighted pair-group average method- This method is identical to the unweighted

pair-group average method, except that in the computations, the size of the respective

clusters (i.e., the number of objects contained in them) is used as a weight. Thus, this

method (rather than the previous method) should be used when the cluster sizes are

suspected to be greatly uneven. Sneath and Sokal (1973) introduced the abbreviation

WPGMA to refer to this method as weighted pair-group method using arithmetic

averages.

Unweighted pair-group centroid method- The centroid of a cluster is the average point

in the multi-dimensional space defined by the dimensions. In a sense, it is the center of

gravity for the respective cluster. In this method, the distance between two clusters is

determined as the difference between centroids. Sneath and Sokal (1973) used the

abbreviation UPGMC to refer to this method as unweighted pair-group method using the

centroid average.

Weighted pair-group centroid (median) method - This method is identical to the

previous one, except that weighting is introduced into the computations to take into

consideration differences in cluster sizes (i.e., the number of objects contained in them).

Thus, when there are (or we suspect there to be) considerable differences in cluster sizes,

this method is preferable to the previous one. Sneath and Sokal (1973) use the

abbreviation WPGMC to refer to this method as weighted pair-group method using the

centroid average.


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Ward's method- This method is distinct from all other methods because it uses an

analysis of variance approach to evaluate the distances between clusters. In short, this

method attempts to minimize the Sum of Squares (SS) of any two (hypothetical) clusters

that can be formed at each step. In general, this method is regarded as very efficient;

however, it tends to create clusters of small size.

5.4.4 Steps in cluster analysis

The objective of cluster analysis is to group observations into clusters such that

each cluster is a homogenous as possible with respect to the clustering variables.

The various steps in cluster analysis are-

• Select a measure of similarity

• Decision is to be made on the type of clustering technique to be used

• Type of clustering method for the selected technique is selected

• Decision regarding the number of clusters

• Cluster solution is interpreted

No generalisation about cluster analysis is possible as vast number of clustering

methods have been developed in several different fields with different definitions of

clusters and similarities. There are many kinds of clusters namely-

• Disjoint cluster where every object appears in single cluster

• Hierarchical clusters where one cluster can be completely contained in another

cluster, but no other kind of overlap is permitted.

• Overlapping clusters

• Fuzzy clusters, defined by a probability of membership of each object in one

cluster.

With these basics of cluster analysis in mind the investigator moved on with the

classification of elementary inclusive school children based on their cognitive processing

and self-perception of learning disabilities using the hierarchical clustering technique in

line with the hypotheses formulated in the methodology of investigation.


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5.5 ANALYSIS AND INTERPRETATION OF CLUSTERS

Hypothesis 3- Different groups based on the cognitive processing will emerge from the

elementary inclusive school children.

To classify the 100 subjects based on their cognitive processing skills the multivariate

statistical technique cluster analysis was employed. The descriptive typologies of the 100

subjects were obtained through computing the similarity coefficients among the subjects

considered for the study. This analytical procedure was carried out based on hierarchical

clustering agglomerative method to obtain homogeneous classifications based on cognitive

processing in elementary inclusive school children with as many groups as possible.

This procedure resulted in identifying exclusive and mutually exhaustive groups or

typologies. Further as a result of this procedure, 100 subjects has been clustered in terms

of the taxonomic distances as computed between the pairs which are illustrated in the

form of a linkage tree called Dendogram figure 5.4.

The different groups of the subjects were arrived at by drawing cut-off lines

across the dendogram. This procedure has been adopted because of the fact that there are

no accepted standards or norms of the taxonomic distance values that could be considered

as characteristic indicator to establish taxonomic category or the cluster status. In the

present analysis one cut-off line was drawn across the linkage tree figure 5.4 at the mean

of the taxonomic distance. There is no analytical solution which exists for identifying the

number of distinct groups or classes. The cut-off line drawn at the mean yielded two

major groups or clusters of the subjects. Table 5.9 shows the number of subjects clustered

in each of the groups and their mean values of cognitive processing. Further two isolates

were also present in the group. These isolates were considered for purpose of

interpretation by including in the nearest and approximate group. The different groups

then evolved are considered for further interpretation. The two major groups evolved

contained within themselves a few homogenous subgroups.

Analysis of group 1

From the Figure 5.4 and Table 5.9 it is evident that the groups and subgroups

have several unique features. When we consider the cognitive processing at the group1

level it is comprised of 52 subjects arranged themselves into distinct subgroups of


142

different sizes based on taxonomic distances. Here there were two sub groups viz.,

subgroup one with 36 subjects and subgroup 2 with 16 subjects. However considering the

mean scores of cognitive processing of these subgroups of group 1 reveals that there is

negligible difference in mean scores which emphasises the homogeneity of the sub

groups with respect to the personal variables such as age, grade, mother’s education and

occupation, father’s education and occupation etc. But when we consider the mean scores

of various subjects we find that there is large variation between the subgroups, within

group1.Group 1 is considered as high cognitive processing group as mean scores of the

subjects in this group is high compared to the group 2.

Analysis of group 2

At the group 2 level as shown in figure there were 48 subjects. Based on the

difference of the taxonomic distances it was further divided (next level) into two major

subgroups with 18 subjects in the first subgroup and 30 subjects in the second. From the

table 5.9 of mean scores of two sub groups, it is evident that there is no much variation in

the mean scores of personal variables, but there is significant variation in the mean scores

of the achievement scores. The 18 subjects in the first major subgroups at next level were

divided into two sub groups with 8 subjects in the first subgroup and 10 subjects in the

second. The 30 subjects in the second subgroup at the next level were divided into three

subgroups with 14 subjects in the first and second subgroups respectively and two in the

third. These two in the third subgroups were considered as isolates. The subgroups also

possesses the same characteristics as found in the first group namely the mean scores of

cognitive processing which have not shown much difference between the subgroups of

group 2. Hence it was considered that these subgroups are homogeneous within the

group2.

The above description of classification of subjects based on their cognitive

processing resulted in identifying 2 distinct groups of cognitive processing in elementary

inclusive school children, thus confirming the hypothesis 2 i.e., different groups based on

cognitive processing will emerge from the elementary inclusive school children.

Therefore hypothesis 2 is retained.


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Table 5.9 Cognitive processing Taxonomic group means

Sl. No

Groups Group 1 Group 2

Subgroups Subgroup 1 Subgroup 2 Subgroup 1 Subgroup 2

Description Mean Scores

Std. Dev.

Mean Scores

Std. Dev.

Mean Scores

Std. Dev.

Mean Scores

Std. Dev.

1 Age 11.22 0.832 12.06 1.29 11.78 1.11 11.63 1.19

2 Grade 6.44 0.504 6.75 0.447 6.61 0.502 6.33 0.479

3 Mother’s education

1.28 0.513 1.06 0.250 1.06 0.236 1.00 0.00

4 Father’s education

1.25 0.500 1.00 0.00 1.28 0.669 1.03 0.183

5 Mother’s occupation

2.97 1.341 3.69 0.602 3.61 0.778 3.70 0.466

6 Father’s occupation

2.50 0.811 2.94 0.250 2.61 0.778 2.97 0.183

7 Science marks (%)

81.50 11.60 63.40 23.28 58.74 22.80 36.73 16.31

8 Maths (%) 80.45 13.38 60.24 23.88 59.17 25.81 38.42 18.09

9 Malayalam (%) 79.93 15.57 66.61 23.08 63.45 21.83 36.87 17.40

10 Social science (%)

80.52 14.33 59.22 23.40 63.14 20.89 36.86 16.43

11 English (%) 82.46 10.60 63.60 23.20 58.25 23.91 35.91 17.58

12 Hindi (%) 75.83 19.06 56.95 27.02 53.53 24.46 35.89 16.83

13 Avg. (%) 80.13 12.15 61.67 22.50 59.38 21.77 35.79 15.91

14 Total no. of subjects

36 16 18 30

From the figure 5.4 it is evident that the subgroup of group1 has the following

subjects of the elementary inclusive school children representing each of the sub groups.

A thorough introspection of the data set of the subjects of cognitive processing subgroups

clearly indicates the homogeneous characteristics of the cognitive processing within each


144

of the subgroups or sub clusters. Further the analysis of mean scores of the variables of

the subgroups with the major group I and II Table No 5.9 clearly reveals there is

homogeneity.

Finally from Table 5.9 and Figure 5.4 of the subgroups and major groups it is

clear that the elementary inclusive school children have grouped themselves based on

their similarity of cognitive processing characteristics. They were grouped themselves

due to their individual characteristics. In this study the 100 elementary inclusive school

children at the highest level has emerged as a single homogeneous group. This implies

that they are related to each other in planning, attention or simultaneous and successive

processing dimensions of cognitive processing.

Based on the above typological description which resulted in two homogeneous

groups of elementary inclusive school children i.e., the low cognitive processing group and

the high cognitive processing groups, which confirms hypothesis 2. Hence hypothesis 2 is

retained i.e., different groups emerged from the elementary inclusive school children

based on their cognitive processing skill/abilities. Also two isolates were also spotted out

who are very weak in their processing skills but they join the subgroup in certain unique

characteristics.

Hypothesis 4- Different groups based on the self-perception of learning disabilities will

emerge from the elementary inclusive school children.

In order to find out the typologies of elementary inclusive school children on self-

perception of learning disabilities, Taxonomic procedure cluster analysis (CA) was

carried out. Based on the 32 items of self-perception of learning disabilities the subjects

were found to cluster themselves into groups. The result obtained through Cluster

Analysis is presented in the form of a linkage tree Figure 5.5.

Cut of lines were drawn at the mean of the taxonomic distances to get clear and

distinct groups. By this two major groups were formed at the first level. Different groups

and subgroups emerged from the subjects are shown in the linkage tree Figure 5.5 and in

the Table 5.10. The 100 subjects cluster themselves at the first level, to form two major

groups, with 50 subjects in the first major group and the other 50 in the second. The first

major group (50 subjects) cluster into subgroups at the second level, with 36 subjects in


145

the first subgroup and 14 subjects in the second. At the third level the subgroups with 36

subjects are clustered into 3 more subgroups with 24 subjects in the first, 3 subjects in the

second and 9 subjects in the third. The second major groups (50 subjects) are clustered into 3

subgroups at the second level with 14 subjects in the first, 17 subjects in the second and 19

subjects in the third subgroup. At the third level the 14 subjects group clustered into 2

subgroups with 6 and 8 subjects in each, the 17 subjects groups clustered into 4 subgroups

with 2 subjects in the first, 4 subjects in the second, 7 in the third and 4 in the fourth.

Table 5.10 Showing Taxonomic group means based on self-perception of learning

disabilities

Sl. No.

Groups Group 1 Group 2

Subgroups Subgroup1 Subgroup2 Subgroup1 Subgroup2

Description Mean scores

Std. Dev.

Mean scores

Std. Dev.

Mean scores

Std. Dev.

Mean scores

Std. Dev.

1 Age 11.28 0.944 11.86 1.10 11.50 1.22 11.81 1.17

2 Grade 6.44 0.504 6.64 0.497 6.36 0.497 6.53 0.506

3 Mother’s education

1.28 0.513 1.00 0.00 1.00 0.00 1.06 0.232

4 Father’s education

1.33 0.586 1.00 0.00 1.00 0.00 1.08 0.368

5 Mother’s occupation

3.00 1.37 3.71 0.726 3.86 0.363 3.56 0.557

6 Father’s occupation

2.42 0.874 2.93 0.267 2.93 0.267 2.89 0.398

7 Science marks (%)

82.12 10.61 67.36 20.87 31.77 9.72 48.99 22.53

8 Maths (%) 79.61 15.30 67.16 22.44 32.83 10.22 50.33 24.09

9 Malayalam (%)

82.74 10.39 66.31 25.56 32.44 10.70 50.84 22.70

10 Social science (%)

80.88 11.51 65.85 23.23 31.22 10.72 50.50 22.61

11 English (%) 80.05 14.17 71.48 21.77 32.07 11.49 49.46 24.12

12 Hindi (%) 75.63 18.56 63.26 24.16 31.43 9.62 45.37 24.20

13 Avg. (%) 80.18 11.11 66.91 21.56 31.97 8.96 49.25 22.07

14 Total no. of subjects

36 14 14 36


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At level three the 19 subject group is clustered into 2 subgroups with 6 subjects

and 13 subjects in each group. At the fourth level the 6 subjects subgroups are clustered

into 2 subgroups with 3 subjects in each and the 13 subject’s subgroups formed 3

subgroups with 5, 3, and 5 subjects in each. Finally from the Table 5.10 and Figure 5.5,

it is clear that based on their similarities and differences over the 32 items of

self-perception of disabilities after applying the classification procedure individually are

found to form groups of different sizes of elementary inclusive school children. Two major

groups emerged with two isolates seen in the second group, which joins with the others to

form a subgroup. The presence of isolates indicates that they have characteristics

different from the subgroups. But in certain unique characteristics they join with the other

subgroup.

Analysing the data set of the subjects who fall between different levels and

different subgroups they are mostly homogeneous in their raw scores on self-perception

of disabilities. Also it is seen that each level differs in their raw scores but differences are

not much, because of small distance between the subjects. Also from the table of mean

scores it is seen that there is not much variation in the mean scores of the personal

variables such as age, grade, mother’s education and occupation, father’s education and

occupation etc., taken for the study but a large variation is seen between the achievement

scores of the subgroups and the groups formed after cluster analysis. This is further

proved in the last two hypotheses.

To conclude from the above analysis pertaining to the data of elementary school

children yielded homogenous groups based on self-perception of learning disabilities.

Hence the Hypothesis 4 is accepted and retained i.e., different groups will emerge from

the elementary inclusive school children based on self-perception of learning disabilities.

5.6 ANALYSIS AND INTERPRETATIONS OF RELATIONSHIPS

Hypothesis 5: There will be significant relationship between achievement and the factors

that emerged from cognitive processing among the elementary inclusive school children


147

Table 5.11Correlation Coefficients of achievement and cognitive processing factors

Achievement

Factors

Science Maths Malayalam Social science English Hindi

F1 (mental processing)

0.782** 0.730** 0.713** 0.743** 0.770** 0.647**

F2 (simultaneous and successive Processing)

0.712** 0.644** 0.676** 0.686** 0.687** 0.598**

F3 (Planning )

0.513** 0.464** 0.458** 0.481** 0.476** 0.381**

F4 (Attention)

0.515** 0.495** 0.488** 0.518** 0.503** 0.417**

** Correlation significant at the 0.01 level (2tailed)

Table 5.11 above shows the correlation coefficients of cognitive processing i.e.,

planning, attention and simultaneous and successive processing and achievement scores

in the subjects Science, Maths, Malayalam, Social science, English and Hindi of the

elementary inclusive school children. It is evident from the table that the correlation

coefficients are high and positive and also significant at 0.01 level (2 tailed), which

implies that as planning, attention, simultaneous and successive processing of an

individual increases the achievement increases. This shows that if the cognitive

processing of a child is high, his achievement also will be high.

It can be summarized from the above table that there is a positive relationship

between cognitive processing and achievement. Hence the Hypothesis that there will be

significant relationship between the achievement and cognitive processing factors is

retained. Further if a child’s cognitive processing skill is high he will have high planning,

attention, and simultaneously and successively process the information. He will be able to

perform well in the academics.


148

Hypothesis No.6: There will be significant relationship between achievement and factors

of self-perception of learning disabilities among the elementary inclusive school children.

Table 5.12 Correlation coefficients of achievement and self-perception of learning disabilities

Achievement

Factors

Science Maths Malayalam Social

Science English Hindi

F1 (skill of cognition)

-0.635** -0.553** -0.637** -0.568** -0.559** -0.495**

F2 (skill of processing )

-0.781** -0.748** -0.729** -0.738** -0.754** -0.668**

F3 (skill of expression)

-0.639**

-0.566** -0.655** -0.605** -0.599** -0.532**

F4 (skill of memory)

-0.653** -0.584** -0.633** -0.618** -0.617** -0.542**

** Correlation significant at the 0.01 level (2tailed)

Table 5.12 displays the correlation coefficients of achievement and self-perception

of learning disabilities (factors) among the elementary school children. There is

significant high negative correlation between self-perception of learning disabilities

factors i.e., skill of cognition, skill of processing, skill of expression and skill of memory

and the achievement scores in the subjects Science, Maths, Malayalam, Social science,

English and Hindi among the elementary inclusive school children. And it is significant

at 0.01 level of significance (2 tailed). This implies that as self-perception of learning

disabilities increases the achievement decreases and vice versa.

It can be inferred from the above table that the high negative correlation signifies

that as perception of learning disabilities in the skill of cognition, processing, expression

and memory decreases their achievement increases and vice versa which implies that

students who perceived their learning disabilities in reading, writing, arithmetic etc. as

low are good performers in academic achievement rather than the high perceivers.

In general, students who experience disabilities in reading, writing, arithmetic etc., have

low perception on learning and hence are low achievers.


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5.7 ANALYSIS AND INTERPRETATIONS OF MEAN DIFFERENCE S (t test)

Hypothesis 7: There will be significant mean score difference in achievement between

the high and low groups in factors that emerged in cognitive processing (CP) among the

elementary inclusive school children.

Table 5.13 Mean scores difference in achievement between high and low groups of

factors in Cognitive Processing

Factors Groups N df Mean SD ‘t’ value Level of

significance (0.01 level)

Mental processing (F1)

low 51 98

43.70 19.63 9.80 significant

high 49 77.86 14.79

Successive and simultaneous processing (F2)

low 50 98

45.06 21.50 8.10 significant

high 50 75.82 16.06

Planning (F3) low 52 98

48.13 21.49 6.16 significant

high 48 73.78 20.08

Attention (F4) low 51 98

48.97 24.44 5.45 significant

high 49 72.38 17.91

The above Table 5.13 presents the mean; Standard Deviation in achievement

between high and low groups of factors that emerged from cognitive processing in

elementary inclusive school children. It is evident from the table that for all the factors

i.e., mental processing, simultaneous and successive processing, planning and attention

the mean scores of the high group i.e., 77.86, 75.82, 73.78 and 72.38 is higher than the

low group i.e., 43.70, 45.06, 48.13 and 48.97. Also there is not much variation in the

Standard Deviation’s. It is clear from this that the high group on the factors of cognitive

processing has high academic achievement rather than the low group. The ‘t’ values for

factor 1, factor 2, factor 3 and factor 4 are 9.80, 8.10, 6.16 and 5.45 respectively are

found to be higher than the table value at 0.01 level of significance. And so they are

significant at 0.01 level of significance.


150

Considering the mean scores it is seen that for all the factors the group with high

cognitive processing is better in achievement than the low cognitive processing groups.

This shows that cognitive processing has influence on achievement. Hence Hypothesis 7

is accepted i.e., there will be significant difference in achievement between the high and

low groups on cognitive processing.

This implies that the two groups which differ in their cognitive processing also

differ in their achievement scores. It can be inferred from the above table that the two

groups on cognitive processing differ significantly in their achievement scores; also high

cognitive processing group has higher achievement than the low cognitive processing

group. In general we can say that if cognitive processing skill/abilities of an individual

increases his academic achievement also increases.

Hypothesis 8: There will be significant mean score difference in achievement between

the high and low groups in factors that emerged from self-perception of learning

disabilities among the elementary inclusive school children.

Table 5.14 Mean scores difference in achievement between high and low groups in

factors that emerged from self-perception of learning disabilities

Factors Groups N df Mean SD ‘t’ value Level of

significance 0.01 level

Skill of cognition (F1)

low 44 98

76.60 15.50 7.24 significant

high 56 47.74 22.59

Skill of processing (F2)

low 49

98

77.62 15.10

9.54 significant

high 51 43.93 19.80

Skill of expression (F3)

low 51 98

71.68 18.51 5.31 significant

high 49 48.74 24.43

Skill of memory(F4)

low 55 98

73.49 17.96 7.31 significant

high 45 44.49 21.69


151

The above table 5.14 describes the mean; SD of achievement scores of high and

low groups in factors that emerged from self-perception of learning disabilities in

elementary inclusive school children. It is seen from the above table that for all the

factors i.e., ‘skill of cognition’, ‘skill of processing’, ‘skill of expression’ and ‘skill of

memory’ the mean scores of the low group are 76.60, 77.62, 71.68 and 73.49 respectively

and found to be higher than the high group i.e., 47.74, 43.93, 48.74, and 44.49

respectively. Also there is no much variation in SD. The ‘t’ values for factor 1, factor 2,

factor 3 and factor 4 are 7.24, 9.54, 5.31, and 7.31 respectively are found to be significant

at 0.01 level of significance. It is clear from this that the high group on self-perception of

disabilities has low academic achievement scores rather than the low group. The ‘t’ value

is found to be higher than the table value for all factors and so it is significant at 0.01

level of significance. So the self-perception of learning disabilities has influence on the

achievement.

Further considering the mean scores it is evident that for all the factors the group

with low perception of learning disabilities have high achievement than the group with

high perception. This shows that self-perception influences achievement. This implies

that the two groups which differ in their self-perception of learning disabilities also differ

in their achievement scores.

It can be inferred from the above table that the two groups on self-perception of

learning disabilities differ significantly in their achievement scores. Hence hypothesis 8 is

accepted i.e., there will be significant mean score difference in achievement scores

between the high and low groups in factors that emerged from self-perception of learning

disabilities among the elementary inclusive school children. Also high perception group

has lower achievement score than the low perception group. It can be generalised from

the above that if self-perception of learning disabilities of an individual increases his

academic achievement decreases and vice versa.

Hypothesis 9: There will be significant mean score difference in achievement scores

between the high and low groups based on cluster in cognitive processing (CP) among

the elementary inclusive school children.


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Table 5.15 Mean scores difference in achievement between high and low groups of CP

Cognitive processing Groups (based on cluster)

N Mean SD Df ‘t’ value Level of significance

Low 48 45.26 21.20 98 7.437 Significant at 0.01 level (2 tailed)

High 52 74.45 18.00

The above table displays the mean; SD of achievement scores of high and low

groups of cognitive processing in elementary inclusive school children. The mean scores

of the high group on cognitive processing is found to be higher (M1=74.45) than the low

group (M2=45.26) .It is clear from this that the high group on cognitive processing has

high academic achievement scores rather than the low group. The ‘t’ value is found to be

higher than the table value and so it is significant at 0.01 level of significance. So the

cognitive processing has influence on the achievement score. Hence hypothesis 9 is

accepted and retained.

This implies that the two groups which differ in their cognitive processing also

differ in their achievement scores. It can be inferred from the above table that the two

groups on cognitive processing differ significantly in their achievement scores. Also high

cognitive processing group has higher achievement score than the low cognitive

processing group. In general we can say that if cognitive processing skill/abilities of an

individual increases his academic achievement also increases.

Hypothesis 10: There will be significant mean score difference in achievement scores

between the high and low groups (based on cluster) in self-perception of learning

disabilities among the elementary inclusive school children.

Table 5.16 Mean scores difference in achievement between high and low groups of

self perception of learning disabilities

Self-perception of disabilities

(learning) Groups (based on cluster)

N Mean SD Df ‘t’ value Level of significance

Low 50 76.47 15.74 98 8.701 Significant at 0.01 level (2 tailed)

High 50 44.41 20.75


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The above table displays the mean; SD of achievement scores of high and low

groups of self-perception of learning disabilities in elementary inclusive school children.

The mean scores of the high group is found to be lower (M1=44.41) than the low group

(M2=76.47). It is clear from this that the high group on self-perception of learning

disabilities has low academic achievement scores rather than the low group. The ‘t’ value

is found to be higher than the table value and so it is significant at 0.01 level of

significance. So the self-perception of learning disabilities has influence on the

achievement score. Hence hypothesis 10 is accepted and retained.

This implies that the two groups which differ in their self-perception of learning

disabilities also differ in their achievement scores. It can be inferred from the above table

that the two groups on self-perception of learning disabilities differ significantly in their

achievement scores. Also high perception group has lower achievement score than the

low perception group. In general we can say that if self-perception of learning disabilities

of an individual increases his academic achievement decreases and vice versa.

5.8 SUMMARY

The objectives and hypotheses stated in the methodology were analysed and

tested in this chapter based on the data generated after administering the tools. Four

factors emerged from each cognitive processing and self-perception of learning

disabilities. These factors scores were taken for further analysis i.e., correlation and ‘t’

test. With the cluster analysis two groups emerged each from cognitive processing and

self-perception of learning disabilities. The two groups were the high ability group on

cognitive processing and the low ability group. In self-perception of learning disabilities

using Cluster Analysis yielded the high perceivers on learning disabilities and the low

perceivers. The ten hypotheses formulated based on the study objectives were accepted

and retained.

This chapter puts forth light on the aspect that the PASS theory of cognitive

processing as stated by Das and his colleagues that PASS theory of intelligence is a

viable method in assessing the cognitive functions in children and Cognitive processing

has four dimensions namely - planning, attention, simultaneous and successive

processing. In addition to that this study yields one primary factor which includes all the


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three i.e. planning, attention, simultaneous and successive processing namely ‘mental

processing’. And these dimensions are highly correlated with each other i.e., as one

aspect increases other also increases and vice versa.

It is seen that as cognitive processing of an individual increases the achievement

also increases i.e., there is a positive relationship between the two. Considering the

self-perception of learning disabilities it is evident that it has a high negative correlation

with achievement, which implies that as self-perception of learning disabilities of an

individual increases his achievement decreases and vice versa. Also two groups emerged

from cognitive processing of elementary school children –the high and the low, which

were subjected to further analysis to find out if there exists any difference between the

groups. There existed a natural grouping based on self-perception of learning disabilities

i.e., the low perceived group and the high. Based on the grouping there existed a

difference in their achievement scores and self-perception.

It can be concluded from the analysis and interpretations that cognitive processing

and self-perception are related with achievement and there is significant difference in

achievement between the two groups i.e. high and low on cognitive processing and self-

perception of learning disabilities.


analysis and interpretation -...

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