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CHAPTER IV
VARIABLES. HYPOTHESES AND METHODOLOGY
DESIGN OF THE STUDY
VEFUABLES OF THE STUDY
TOOLS USED FOR MEASUREMENT
DESCRIPTION OF TOOLS
SAMPLE USED FOR THE STUDY
COLLECTION OF DATA
SCORING AND CONSOLIDATION OF DATA
STATISTICAL TECHNIQUES USED
DESCRIPTION OF THE STAISTICAL TECHNIQUES USED
OTHER DETAILS RELATING TO THE DESIGN
VARIABLES, HYPOTHESES, AND METHODOLOGY
This chapter deals with the methods and procedure followed in the
study. These include the design of the study, the variables, selection of
sample, description of the tools used, data collection and statistical
techniques made use of.
4.1.0. DESIGN OF THE STUDY
The study was conducted in three phases. The first phase includes
the selection of variables involved in the study and construction and
validation of tests to measure them. In the second phase, the sample
was selected and data were collected regarding the variables. In the
third phase the data were analysed by using suitable statistical procedures
and the conclusions drawn. in The diagrammatic representation of the
design of the study is given below :
TABLE 4.1 T H E DIAGRAMMATIC REPRESENTATION O F T H E
PHASE ONE
PHASE TWO
PHASE THREE
DESIGN O F T H E STUDY
This phase involved
a) the selection of variables
b) the formulation of hypotheses
c) selection of appropriate tools to measure the
following:
i) Intelligence
ii) Home Environment for Science Learning
iii) School Learning Environment
iv) Socio-economic Status
v) Parental Education
vi) Parental Occupation
vii) Parental Income
d) preparation of tools with psychometric
properties to measure the following :
i) POP
ii) Attitude towards Science Learning
iii) Science Learning Interest
a) selection of sample
b) collection of data
statistical procedures used to analyze the data
4.2.0. VARIABLES OF THE STUDY
The study is designed with POP as the dependent variable and a
select group of cognitive, affective, social and environmental variables
treated as independent variables.
The details relating to the variables of the study are presented
below :
4.2.1. DEPENDENT VARIABLE
Process Outcomes in Physics (POP). The major component abilities
of Process Outcomes in Physics (POP) as used in the study are :
i) recognizing and defining a problem
ii) formulating hypothesis
iii) collecting data
iv) interpreting data
V) evaluating hypothesis
vi) formulating generalizations
4.2.2. INDEPENDENT VARIABLES
Four broad groups of variables - cognitive variables, affective
variables, social variables, and environmental variables have been
included as independent variables of the study. The details of the different
variables under each major group are given below :
1. Cognitive variables
i) Cognitive variables used in the study are restricted to one
crucial variable, viz., Intelligence
2. Affective variables
Affective variables used in the study a re :
ii) Attitude towards Science Learning
iii) Science Learning Interest
3. Social variables
iv) Parental Education
v) Parental Occupation
vi) Parental Income
vii) Socio-economic Status
4. Environmental variables
viii) Home Environment for Science Learning
ix) Science Learning Environment-student initiated
x) Science Learning Environment-teacher provided
xi) Total Science Learning Environment
4.2.3. CRITERIA USED FOR SELECTING T H E INDEPENDENT VARIABLES
Variables which registered correlation with educational outcomes
in process tests in physics or product outcomes were scrutinized.
Reported studies relating to the variables influencing process outcomes
in different science subjects were also scrutinized. The selection of
independent variables was done on the basis of research evidence relating
these variables and dependent variable of the study or in some cases as
having a significant association with conventional outcomes in science
subject. Some additional considerations were also weighed in selecting
the independent variables for the study. The additional considerations
of this kind are :
i variables selected for the study should specifically fall into the
four major groups selected, viz., cognitive, affective, social or
environmental groups
ii variables selected should show significant association with
Process Outcomes in Science or conventional achievement in
science, either as a direct correlation or as an indirect cause-
effect relationship
iii the selected variables should be capable of being quantified
and lend themselves to objective group measurement
iv standardized tests should as far as possible, be available for
measuring the variables selected
v wherever standardized tests are not available, it should be
possible to develop psychometric tools within a reasonable
time.
The review of research studies reported earlier and the above criteria
were used simultaneously for identifying the variables.
4.3.0. TOOLS USED FOR MEASUREMENT
The following tools were used for the collection of data.
1. Test of Process Outcomes in Physics-TPOP-(to measure the
dependent variable).
2. The Kerala Non-Verbal Group Test of Intelligence for
Secondary Schools (to measure intelligence).
3. Scale of Attitude Towards Science Learning-SATSL-, (to
measure attitude towards science learning).
4. Science Learning Interest Inventory-SLII-, (to measure science
learning interest).
5. General Data Sheet (to measure Parental Education, Parental
Occupation, Parental Income and SES).
6 . Home Environment Inventory for Science Learning (to measure
Home Learning Environment).
7 . Science Learning Environment Inventory (to measure Science
Learning Environment-student initiated, Science Learning
Environment-teacher provided and Total Science Learning
Environment).
4.4.0. DESCRIPTION OF THE TOOLS
The details of the tools used to measure different types of variables
are given below.
4.4.1. TEST OF PROCESS OUTCOMES IN PHYSICS (TPOP)
The investigator with the help of her supervising teacher, developed
and standardized 'Test of Process Outcomes in Physics (TPOP) in order
to measure the dependent variable, Process Outcomes in Physics (POP).
The Process Outcomes in this test were operationalized on the basis of
the theoretical models developed by Obourn (1960) and Klopfer (1971)
and on the basis of consultation with experts in field of science teaching.
The investigator selected six major skills and sixteen sub-skills coming
under them to be used for developing Test of Process Outcomes in
Physics (TPOP). The details of the skills and sub-skills used for the
preparation of test are presented in the table 4.2.
TABLE 4.2 SKILLS AND SUB-SKILLS USED FOR MEASURING PROCESS
OUTCOMES.
1 .0 . Recognizing and defining a problem
1.1. Pupils recognize specific problem in a new situation
1.2. Pupils isolate the single major idea of a problem
1.3. Pupils state problem as definite and concise questions
2.0. Formulating hypothesis
2.1. Pupils suggest tentative solutions to the problem
3.0. Collecting data
3.1. Pupils select suitable test of the hypothesis
3.2. Pupils design experiment
3.3. Pupils select equipments for experiment
3.4. Pupils observe objects and phenomena
3.5. Pupils measure objects and changes
4.0. Interpreting Data
4.1. Pupils organize data collected
4.2. Pupils identify relationships
4 .3 . Pupils interpret relationships
5.0. Evaluating hypothesis
5.1. Pupils formulate conclusions, on the basis of relationships
found
5.2. Pupils evaluate hypothesis in relation to the data interpreted
6 . 0 . Formulating generalizations
6.1. Pupils apply conclusions to new situations
6 . 2 . Pupils formulate generalizations on the basis of relationship
identified and conclusions formed and applied.
PREPARATION OF ITEMS
Since the Purpose of the TPOP was to measure the Process in
outcomes Physics achieved by the secondary school students of Kerala,
the items prepared were from the area of secondary school Physics.
The investigator took precautions to include the items, which have
practical applications in day-to-day life. Special care was given so that
the mental operation while answering the questions were the natural
outcomes of science teaching and learning in classroom situatioiis.
The following books and other forms of literature were freely used
as guidelines for preparing the test items.
1. Science Teaching and Testing (Nedelsky, 1965).
2. Handbook of Formative and Summative Evaluation of Students
Learning (Bloom, et. a]., 1971).
3. Science Education in Nineteen Countries-An Empirical Study
(Comber and Keeves, 1973).
4. Integrated Process Skills Test (Okey & Dillashow, 1979).
5. Middle Grades Integrated Process Skill Test (Padilla & Cronin,
1978).
6. Test of Process outcomes in Biology (Suresh, 1991)
7. Text Books in Physics for Standards VII, VIII and IX (Govt. of
Kerala, 1 9 9 2 & 1994).
The TPOP include six subtests. Each subtest measures the
acquisition of each major skill given in table 4.2. Each subtest contains
fifteen items of objective multiple choice type. For each item, four
alternative responses are given. The respondent has to select the correct
alternative. The choice of correct alternative by the respondent would
indicate that he/she has achieved the outcome in question. The
explanations given below regarding each skill served as guidelines for
the preparation of the items.
i) Recognizing and Defining a Problem
The test items under this head present problematic situations before
the respondent. The respondent has to identify the problem area, he
has to isolate the single major idea of a problem, and has to define the
problem using correct language.
ii) Formulating Hypotheses
In this subtest the subject is presented stated problems. He has to
suggest suitable solutions to the problem in hand, based on the conditions
presented in the items. The hypothesis should direct one to further
investigation. Four alternative hypotheses were given along with each
test item. The task of the subject is to decide which hypothesis is the
most suitable and reasonable one.
i i i ) Collecting Data
In this subtest, students are given actual learning situations for
particular problems. The tasks of the students are to identify the
manipulated variables, the responding variables and controlled variables
in the problem situations and to describe how variables are controlled.
The correct response to items under this category would indicate that
the student has attained the outcome in question.
iv) Interpreting Data
Here, the tasks assigned to the respondent are to describe the
collected data in verbal or nonverbal form, organize the data so as to
facilitate effective communication, to draw inference based upon the
collected data and to construct tables.
v) Evaluation of Hypotheses
In this subtest, the problem stated and the hypotheses formulated
are presented to the subject. He has to design an investigation for testing
the hypothesis, to select suitable test from the alternate tests given and
to evaluate the hypotheses on the basis of the given data. [The student
has to s ee whether t he evidence is consistent with t he logical
requirements of the hypothesis.]
vi) Formulating Generalizations
Here the tasks given to the respondent are to apply the conclusions
to new situations and formulate generalizations on the basis of
relationships identified.
Twenty items each were pooled initially for each subtest. Some of
the test items were adapted from school Physics text-books, published
texts and from the available literature cited earlier. A panel of physics
teachers was formed for establishing the face validity. Each item was
discussed at length in terms of its appropriateness, complexity, subject
matter and exactness of information. Based on the scrutiny of experts,
f if teen items were selected for each subtest, which were found
appropriate and valid. These subtests constitute the draft TPOP.
Instructions for the respondents, scoring key and appropriate form of
the response sheet were prepared.
The draft TPOP was 'pretriedout' to a group of 1 0 students of
ninth standard randomly selected from St. Thomas High School, Pala
in order to ensure the clarity of the wordings and directions.
Based on the pre-tryout, final draft TPOP consisting of ninety items,
fifteen items for each subtest was prepared and got printed.
Standardization of TPOP
The draft test was administered to a representative sample of 400
students drawn from standard IX of the secondary schools of Kottayam,
Kannur and Malappuram districts. The testing was done during the
academic year 1996-'97. One score each was given to the correct
response of each test item. The sum of the scores for the ninety items
was taken as the total score for the test. After rejecting incomplete
entries, only 3 7 8 answer sheets were available for item analysis. Further
eight answer sheets were rejected at random in order to bring down the
number to 370, to follow the psychometric procedures for item analysis.
The 370 answer scripts were arranged in the descending order of
the total score. The highest 27% and the lowest 27%, with respect to
the total scores were separated. There were 1 0 0 response sheets each
from upper and lower levels.
Each response sheet in the upper and lower level was examined.
The number of respondents in the upper and lower groups who answered
each item correctly was found out. The indices of item discrimination
and difficulty were estimated by using the procedure suggested by Ebel
(1965).
The difficulty level and discriminating power of each item were
estimated using the following formulae
u + L x l o o Index of item difficulty Dv = -- 2N u - L
Index of discrimination Di = -- N
Where
'U ' = the number of correct responses for any item in the upper
group.
'L' = the number of correct responses for any item in the lower
group.
' 2N ' = total number of answer scripts in the upper and lower levels.
'N ' = 100 , since the upper and lower groups stands for 27% of
the total group of 370 which is equal to 1 0 0 for both upper
and lower groups.
The item analysis data is given as Appendix I
On the basis of the indices of difficulty and discrimination, items
were rated. Items with difficulty index between 65 and 35 (on the
assumption that the items of difficulty level of 5 0 have the highest
discriminating power) were identified. From among these items, items
with highest discriminating power were selected. Only items of
discriminating power of 0.30 and above were selected for the final test.
Thus 10 items from each subtest were selected and they were arranged
in the increasing order of difficulty.
The final TPOP included a covering page with specific directions
for the guidance of the students and the six subtests containing 1 0
items each were got printed in the shape of a test booklet.
The draft and final TPOP are given as Appendices I1 & 111. The
response sheet and scoring key are provided as appendices IV & V,
the table of norms (percentile norms) for the test (worked out for the
final sample of 900) are presented as Appendix VI. The English
translation of final test is given as Appendix VII.
Validity and Reliability of TPOP
Content validity of the test, which requires the determination of
the adequacy of each item to be a sample of the process skills which
are supposed to be measured, was ensured through careful planning of
the test, satisfying the adequacy of sampling of test items by following
the standard theoretical models of the construct to be measured and
meticulous analysis of the test items by experts. In the final TPOP, all
the six subtests were given equal weightage by including equal number
of items in each.
The construct validity of the test was estimated using average marks
obtained in Physics for the first and second terminal examination, of
standard IX pupils treated as the external criteria. The average marks
in physics of 1 0 0 pupils of standard IX was used for this purpose. The
scores obtained in the TPOP were correlated with the average physics
scores. The coefficient of correlation was found to be 0.77.
The split-half reliability was estimated for the whole test as well as
for the component tests. The coefficient of correlations corrected for
shortening using Spearman Brown formula are presented in Table 4.3.
TABLE 4.3. RELIABILITY COEFFICENTS CORRECTED USING SPEARMAN.
BROWN FORMULA FOR THE TPOP
Tests Reliability coefficient
Subtest I .92
Subtest 11
Subtest 111
Subtest IV
Subtest V . 9 2
Subtest VI
Whole test
Reliability using Kuder - Richardson formula was estimated.
The reliability by using this method (for N= 100) was found to be
0 .96 .
The validity and reliability coefficients reported here show that
TPOP used in the study is a reasonably valid and reliable tool for
measuring POP.
4.4.2. SCALE O F ATTITUDE TOWARDS SCIENCE LEARNING (SATSL)
This scale was developed by the investigator with the help of her
supervising teacher, inorder to measure the attitude of secondary school
students towards learning science. Attitude towards science learning is
the favourable or unfavourable disposition of the individual towards the
learning of science, which cannot be directly observed, but can be
inferred from overt behavior.
Since the investigator couldn't find an attitude scale which measures
the attitude of secondary school students towards science learning which
was meant for Indian sample, she, with the help of the supervising
teacher h z i s 4 constructed an attitude scale, namely Scale of Attitude
towards Science Learning (SATSL) applicable to the secondary school
students of Kerala state.
SELECTION OF STATEMENTS
After consulting with experts in the field and teacher educators, it
was decided to use the technique developed by Likert. The selection of
statements was done as follows.
The investigator reviewed books, periodicals, and other descriptive
materials to procure the material to construct the statements for the
attitude scale. Experts in the field were also consulted and their
suggestions were taken into consideration. It was decided to include
three dimensions of attitude towards science learning. These were views
on science learning, attitude towards scientists and the contributions of
science, and views on science as a process.
An initial pool of 60 statements was prepared. This pool of
statements was given to ten experienced and qualified teachers. Before
this the language was checked for ambiguity of wordings, if any. It was
also ascertained that the vocabulary used in the test item was appropriate
for secondary school students. The panel of teachers were asked to
evaluate the statements keeping in mind the following points :
1). whether there were enough statements under each of the
attitudinal dimension
2). accuracy and relevance of each statement
3). the level of language used for each statement
Based on their suggestions, those statements, which were complex,
vague, over-generalised, and not appropriate to measure the attitudinal
construct, were deleted. The remaining 4 0 statements formed the draft . -
form of the attitude scale
Out of the 4 0 statements 20 were of positive polarity and remaining
20 were of negative polarity. 14 statements were to rate the views on
science learning, 14, to rate the views on science as a process, and 1 2
to rate the attitude of the respondent towards scientists and their
contributions to science.
INITIAL TRY OUT
The 4 0 statements were arranged as in Likert type. To avoid any
error or tendency to a stereotyped response, items of positive polarity
and negative polarity were evenly arranged. Directions for the
respondents were also prepared. The students were asked to assign
any one of the five categories after carefully reading the statement.
The five categories were SA-strongly agree, A-Agree, U-undecided,
D-disagree and SD-strongly disagree. After the administration of the
scale, it was scored by keeping into consideration the scoring procedure
suggested by Likert, (Edwar+,1957)
for every S. A response 5
A response 4
U response 3
D response 2
S . D response 1
For items of negative polarity, the scoring system was reversed.
Appropriate response sheet was also prepared along with the draft form
of the scale.
ITEM ANALYSIS
The draft scale was administered to a representative sample of
1 8 0 ninth standard students. The sum of the scores of all the items
constituted the total score of the scale. 1 4 , incomplete entries were
exempted and the rest of 6 entries were rejected at random to bring
down the number to 160 for convenience.
The selection of items for the final form of scale, SATSL was done
as per the procedure suggested by Edwards (1957). The response sheets
of the individuals are arranged in the descending order of the total scores.
The highest 25% and the lowest 25% of the response sheets were
separated (N, = 4 0 and N, = 40). These were criterion groups in terms
of which to evaluate the individual statements. In evaluating the responses
of the high and low groups to the individual statements, the ratio was
found out using the formula,
where
XH = the mean score on a given statement for the high group - - the mean score on the same statement for the low group XL -
n = the number of subjects in the upper and low groups
X, = score for a given statement in the high group
X, = score for a given statement in the low group
The 't' value for each item was calculated by using the same formula.
The statements for which 't' value is grater than or equal to 1 .75 was
regarded as an item which possesses internal consistency and hence
discriminating power (Edwar&,1957). Items with 't' values from 3.02
to 6.60 were selected for the final form of the scale.
Thus 2 5 statements were selected for the final test. Out of the 2 5
statements, 13 were of negative polarity and 1 2 were of positive polarity.
Items with negative and positive polarity were distributed evenly in the
decreasing order of difference in means.
FINAL FORM
The final form of the SATSL contained 2 5 statements and specific
directions for the respondents. An appropriate response sheet was also
prepared. The scoring procedure for the items of positive polarity is as
follows :
for every S A response 5
A response 4
U response 3
D response 2
S D response 1
For the items of negative polarity the scoring procedure is as follows
for every S A response 1
A response 2
U response 3
D response 4
S D response 5
An illustrative item is given below.
There is no fault in doing other helpful matters in lieu of science
classes.
Since 'SD' is encircled, the score of the item is 5
The maximum and minimum scores, which the students may score
on SATSL, will be 1 2 5 and 25 respectively.
The construct validity of SATSL was estimated by using average
marks obtained in Physics, Chemistry and Biology for the first and second
terminal examinations of standard 1X pupils.The average marks in science
of 100 ninth standard students were used for that purpose. The score
obtained in the SATSL was correlated with achievement in science.
The coefficient of correlation was found to be 0.79.
The reliability of SATSL calculated by using split-half method and
corrected by using Spearman-Brown prophecy formula was found to be
0.87. The reliability of scale, calculated by test-retest method was found
to be 0.86. The high validity and reliability coefficients thus obtained
show that the scale is a reasonably valid and reliable one.
The Item analysis details SATSL are given as appendix VIII, The
draft form and final form of the scale are given as Appendices IX and X
respectively. The English translation of the final scale is given as appendix
XI and the percentile norm is given as appendix XII.
4.4.5. SCIENCE LEARNING INTEREST INVENTORY (SLII)
The investigator developed a Science Learning Interest Inventory
(SLII) for the purpose of measuring interest of secondary school students
towards science learning. The details of the procedure involved in the
development are given below.
PREPARATION OF THE INVENTORY (DRAFT FORM)
Items in the inventory were presented in the form of triads and the
respondents were required to choose one of the three alternative
activities grouped under an item. It thus employed forced choice triad
type technique on the assumption that it reduces social desirability,
reduces bias, and the validity under forced choice technique is stable
over a period of time.
The investigator selected various activities, which have direct
relation with various school subjects. The activities were categorized
and put in each item on the basis of their nature as far as possible.
Each item included three activities. The task of the respondent was to
select the activity, which he/she likes the most. The items were prepared
in a way that out of the three activities, one is related to science and
the rest related to humanities. 6 0 items were prepared and subjected to
scrutiny by a panel of three experts. The items which were judged as
powerful to reflect the students' interest towards learning of science,
were selected. 30 items were selected for the draft inventory. Directions
for the respondents also were prepared along with the draft. The students
were asked to choose the activity, which was more preferred by them
than other activities in each item.
ITEM ANALYSIS
The inventory (draft form) was administered to a sample of 400
students of standard IX. For each item, i f the respondent selected the
activity showing some inclination towards the learning of science, 'one'
score was assigned and a 'zero' score for choosing other alternatives.
The sum of the scores of the 30 items constituted the total score of the
inventory. From the 400 responses, ten incomplete response sheets
were rejected and 390 response sheets were made available for item
analysis. 2 0 more response sheets were rejected randomly for bringing
down the number to 370, for the sake of convenience. The response
sheets were arranged in the descending order of scores. The performance
of the upper and lower 27% of the sample forming criterion groups,
compared to yield discriminating indices for 3 0 items.
The discriminating power of each item was calculated by applying
the formula given by Ebel (1965)
u - L Di = -----
N
Where 'Di' stands for Discriminating index (upper lower index)
'U' stands for number of respondents who select activities
related to science in upper group
'L' stands for the number of respondents who select activities
related to science in the lower group
' N ' stands for the number of respondents in each group
The data showed that all the items have significant discriminating
power. Even though, for ensuring the better quality of the inventory,5
items which have low discriminating index were rejected. Thus the final
inventory consisted of 2 5 items.
FINAL FORM OF T H E INVENTORY
In the final form of the inventory, 2 5 items in all, which possess
high discriminating power, were included. For each item 'one' score
was given, if a subject select the activity which shows some inclination
towards the learning of science and a 'zero' score for selecting other
alternatives. Thus a respondent could get a maximum of 2 5 scores in
this Inventory.
An illustrative item is given below:
Select one activity, which you like the most, from the set of three
activities given below, and put a cross mark in the proper column in the
response sheet.
A. Improvise a thermometer
B. Study the different methods of sculpture
C. Record speeches at public meetings
Since the cross mark is below 'A ' , it shows that the respondent
has interest in science learning than the other two activities. Hence a
score was assigned to that response.
Item number -
1
VALIDITY AND RELIABILITY O F T H E INVENTORY
The content validity of the inventory was ensured by subjecting the
items prepared for the initial tryout before a panel of 10 experts for
scrutiny. The items, which were certified by the experts as effective for
measuring science learning interest, were selected.
The construct validity of SLII was estimated by using the average
marks for science for the first and second terminal examinations, and
the validity coefficient was found to be 0 .72 ; (for N = 100)
A
X
B C
The reliability coefficient measured by test-retest method was 0.94.
The reliability coefficient estimated by using split-half method and
corrected by using Spearman-Brown prophecy formula was = 0.81 and
that by using Kuder Richardson formula was 0 .96 (for N = 40).
The opinion of the experts' high discriminating power and high
reliability and validity coefficients show that the inventory possesses
satisfactory psychometric properties.
The draft and final forms SLII and the English translation of its
final form are given as appendices XIII, XIV, and XV. The item analysis
data is given as appendix XVI. The percentile norm of Science Learning
Interest Inventory is given as appendix XVII.
4.4.4. GENERAL DATA SHEET
The investigator made use of a standard form of General Data
Sheet to collect basal information about respondents and to measure
the following variables, Parental Education, Parental Occupation,
Parental Income, and Socio-economic Status. A copy of the General
Data sheet used for the study is given as appendix XVIII.
The General Data sheet consisted of four sections. Section one
elicits the general information about the respondent (name of the
respondent, locality, age, sex, and name of the school etc.) Section two
is for collecting information regarding level of education of parents,
siblings and other members in the subject's family. Section three provides
information regarding the type of occupation of the parents and other
members in the family. Section four provides the details relating to the
income of family members. The school records were used for checking
the correctness of information entered in the General Data Sheet. The
details, which were not available in the school records, were collected
through direct questioning of the respondent during administration of
the test.
The information collected though the general data sheet helped to
classify subjects on the basis of Parental Education, Parental Occupation
and Parental Income.
4.4.5. THE KERALA SOCIO-ECONOMIC SCALE
The investigator used the Kerala Socio-Economic Scale developed
and standardized by Nair (1976), with necessary modifications (in scoring)
to measure the socio-economic status of the subjects. The Data needed
for the scale was obtained from General Data Sheet administered to
the subjects.
In this study Socio-economic Status is measured in terms of Parental
Occupation, Parental Education and Parental Income. Each of them is
divided into categories on the basis of the scoring scheme, revised by
the author (1996). Since scoring of income levels was based on old
classification, this revision was inevitable. The revision was done on the
basis of present salary pattern and cost-of-living index.
The details regarding the categories, scoring systems and
weightages are showed in Table 4.4
TABLE 4.4. CATEGORIES AND RESPECTIVE WEIGHTAGES OF THE
COMPONENTS OF THE KERALA SOCIO-ECONOMIC SCALE
CLASSlFlCATlON OF OCCUPATIONS
1. Unemployed : No permanent employment, and no special
qualifications or skills.
2. Unskilled : Coolies, ordinary labourers, watchmen, peons
and other low-level employees in establishments
and similar categories.
3. Semiskilled : Farmers , small scale merchan t s , l ibrary
attenders, office attenders.
Educational Categories score
1 . Illiterate 5
2. Standard I to IV 1 0
3. Standard V to VII 15
4. Standard Vlll to X 2 0
5 . Pre-University/Pre-Degree/
T.T.C./lntermediate 2 5
6 . B.A.,B.Sc.,B.com., Engi-
neering Diploma etc. 3 0
7 . M.A./M.Sc./M.B.B.S.,M.Ed./
B.Sc.(Engg)/B.Sc.(Tech)/
L.L.B. 3 5
Occupational Categories score
Unemployed 5
Unskilled 1 0
Semi-skilled 15
Skilled 20
Semi-Professions 3 0
Full Professions 4 0
Income (monthly) score
- Below Rs.1000/- 5
Rs.1001/- 2000/-10
2001/- 4000/- 15
4001/- 7000/- 2 0
7001/- 10000/- 2 5
10001/- 25000/-30
above 25000/- 3 5
4. Skilled : Mechanics, fitters, field workers, electricians,
dr ivers , pho tog raphe r s , lab ass i s tan ts ,
carpenters, masons, document writers, vakil
clerks, head constables, village officers, and
similar categories.
5. Semi-Professionals: Chemists, druggists, qualified nurses, trained
teachers, managers, superintendents of offices,
smallscale land-owners, sub-inspectors of police/
equivalent, sub-registrars, assistant educational
officers, block-development officers, officers of
the sub-district level, public health workers and
similar categories.
6. Full Professionals : Ministers, judges, bank executives and officials,
doctors, engineers, lawyers, university teachers,
heads of research organizations, heads of Govt.
departments, secretaries to government, high
land owners and business executives and
equivalent categories.
Each subject was assigned score on each of the three subdivisions-
Parental Education, Parental Income and Parental Occupation. The three
independent scores added (with equal weights given to each) yielded
score on the Socio-economic Status for the family or for the respondent.
4.4.6. THE KERALA NON-VERBAL GROUP TEST OF INTELLIGENCE
To measure the intelligence of the subjects, the Kerala Non-Verbal
Group Test of Intelligence was used. This is a standardized group test
of intelligence developed by Nair (Nair, 1968) for the purpose of
appraising the general intelligence of secondary school pupils of Kerala.
The test provided a single score of general intelligence yielded by adding
the scores obtained in the four subtests.
The test battery consists of four subtests; Figure classification,
Figure series, Figure analogies, and Figure matrices. The details are
given in Table 4.5.
TABLE 4.5. TEST COMPONENTS AND OTHER DETAILS OF THE KERALA
NON-VERBAL GROUP TEST OF INTELLIGENCE.
DESCRIPTION OF SUBTESTS
i) Figure classification: This test measures the ability to perceive
relationship. This consists of five figures, four of which can be
Time limit in minutes.
5
5
5
5
grouped together according to some common rule. One figure will
not go with the group. The respondent has to identify this figure,
which will not fit in the group.
No. of items inclu- ding practice items
20
2 0
2 0
20
Subtest Number
I
I1
Il l
IV
An illustrative item is presented below:
Test Component
Figure classification
Figure series
Figure analogies
Figure matrices
The correct answer is E
There are twenty items in the subtest. Out of twenty, first four
items are practice items. The answers are also given along with the
test. The remaining 16 items are used for scoring. The subject has to
work out the sixteen items within the specific time limit of five minutes.
One score is given for each correct response.
ii) Figure series.
Each item of this subtest consists five small squares arranged in a
row. The first four squares contain small figures within, while the last
square is blank. The subject has to findout the figure from four alternative
answers given, which when placed in the blank square will complete the
design. The task of the subject is to identify the rule behind the four
figures and to findout the fifth, which follows the same rule from the
alternative answers given. An illustrative item is given below :
Problem Answers
A B C D
The correct answer is D
There are 4 practice items. The remaining 16 items are to be
answered in 5 minutes. One score is given for each correct response.
iii) Figure analogies
In each item of this subtest there are four squares in a row, arranged
into two sections. They are divided into two groups of two on the left
and two on the right. The first square in the right pair contains figures
and the second square is blank. The figures contained in the first pair
on the left imply a relationship. The same relationship is assumed to
hold for the pair of squares on the right as well. The subject has to find
out the relationship connecting the figure in the first two squares and
apply it to visualise the figure which when put in the blank square on
the right would imply the same relationship. The answer is to be selected
from a set of four alternatives given.
An illustrative item is presented below :
Problem Answers
The correct answer is C.
There are 16 items to be answered in 5 minutes.
iv) Figure matrices.
Each of the items of this subtest has nine squares arranged in the
form of 3 rows and 3 columns. The matrices of nine squares with the
figures inside form one design. The design is incomplete because the
bottom right-hand corner is left blank. The subject is asked to examine
the squares in each row or column and find out the relationship
connecting the figures in the first and second rows or columns. He has
to use this relationship to find out the figure that fits in the blank square
of third column (row), from a set of four alternative answers given.
An illustrative item is given below :
Problem
Answers A B C D
The correct answer is D.
There are 16 items in this subtest to be answered in 5 minutes
SCORING
The test is scored by assigning one score for correct answer.
Separate total for each subtest can be obtained and then the scores on
the four subtests are combined to yield the total score for non-verbal
group test of intelligence.
VALIDITY AND RELIABILITY O F TEST BATTERY
Validity: The validity of the test has been assessed using different tests
as external criteria. (Nair, 1971). Validity coefficient using Progressive
Matrices Test (PMT) as external criteria, r = 0.784 (for N=256) , with
Kerala Verbal group Test of Intelligence as external criteria, r = 0 . 5 2
(for N=504) and with total marks in S.S.L.C. Examination, r = 0.537
(for N= 324). Factor analysis of the battery with the Progressive Matrices
Test and Kerala Verbal Group Test of Intelligence as reference tests,
revealed the presence of a major general factor of intelligence in all the
tests of the battery.
Reliability
Test retest reliability of the test has been calculated with different
intervals in testing. For three months interval between tests, reliability
= 0.76 (for N = 246); one month interval between tests, reliability =
0.75 (for N = 124) and for one-week interval between tests, reliability
= 0.80; (for N = 121) .
Corrected split-half coefficient for the whole test battery and for
the component tests (for N= 237) are given in Table 4.6.
TABLE 4.6. SPLIT-HALF RELIABILITY COEFFICIENTS O F THE KERALA
NON-VERBAL GROUP TEST O F INTELLIGENCE.
Corrected value of reliability coefficient.
0 .92
0 .90
0 .88
0 . 8 8
0 .91
SI.No
1.
2.
3.
4.
Subtests
Figure classification
Figure series
Figure analogies
Figure matrices
Whole Test
Reliability estimated by the rational equivalence method was
0 .864 (for N= 100).
The values quoted above show that the test is a reliable and valid
instrument for measuring the general factor of intelligence, and could
therefore be treated as an appropriate tool for the purpose of the
investigation.
4.4.7. H O M E ENVIRONMENT INVENTORY FOR SCIENCE LEARNING (HEISL)
The learning environment provided by the parents and other
members of the subjects' family for the attainment of maximum learning
in science was measured by using Home Environment Inventory for
Science Learning. This questionnaire was developed and standardized
by Suresh (1 988).
This inventory contains 25 items, covering different aspects of
Home Environment for Science Learning such as parents' help and
personal attention, the importance given to students' achievement to
his peers, parents' input in home assignments and discussions, parents'
control over their work habits and general behavior, and students'
freedom to work at his own pace and in his own style.
The subjects were asked to respond to each question by taking
against the entries of a three-point scale marked 'Always', 'Sometimes',
and 'Never'. The scoring procedure is as shown below:
Always - 2
Sometimes - I
Never - 0
VALIDITY AND RELIABILITY O F T H E INVENTORY
Validity
Criterion related validity of the test was estimated using average
class marks obtained in physics for 1st and 2nd terminal examination
of standard IX and intelligence (Non-verbal) treated as two criteria (for
N = 4 0 ) . The coefficient of correlat ion between home learning
environment score and average physics achievement score is 0.671.
The validity coefficient using Kerala Non-verbal Group Test of
Intelligence a s external criteria was 0 . 3 4 9 for the same sample
(for N=40).
Reliability
The internal consistency of the 'Home Environment Inventory for
Science Learning' determined by the Alpha coefficient is, 0.893.
The values of validity and reliability coefficients show that the tool
is a reasonably valid and reliable one for measuring Home Environment
for Science Learning.
A sample of the inventory is given as Appendix XIX.
4.4.8. SCIENCE LEARNING ENVIRONMENT INVENTORY (SLEI)
The different aspects of class room learning environment for science
learning-Science Learning Environment-student initiated and Science
Learning Environment-teacher provided-was measured by using 'Science
Learning Environment Inventory' developed and standardized by Suresh.
(Suresh, 1988).
This inventory contains 50 s ta tements , covering different
dimensions of science learning environment. Students' attentiveness,
students' social awareness, enjoyment of class, students' involvement
in class work and discussions, students' freedom to work at their own
pace and in their own style etc., are grouped under Science Learning
Environment -student initiated. Teacher's help and personal attention,
amount of stress placed on curricular and co-curricular activities, orderly
behaviour and organization of class, ' importance of students '
achievements to compare to that of their peers', difficulty of class work
and home assignments, teachers' control over students' work habits
and general behavior are grouped under 'Science Learning Environment-
teacher provided.
SCORING
The students are asked to respond to each question on a three
point scale- Always, Sometimes and Never. The score for each item
varied from 0 to 2. The weightages given for each item is shown below:
Positive item Negative item
Always - 2 Always - 0
Sometimes - 1 Sometimes - 1
Never - 0 Always - 2
RELIABILITY AND VALIDITY
The Alpha coefficient of homogeneity of the science Learning
Environment Inventory is 0.897. This index of homogeneity reveals
that all the items included in the questionnaire measure the same trait,
science learning environment.
The validity of the tool was established by validating it against the
total achievement in science subjects (physics, chemistry and biology)
for first and second terminal Examination of standard IX and also against
the Kerala Non-verbal Group Test of Intelligence. The validity coefficient
of the tool against the achievement in science subjects is 0 .587 (for
N=40) and that against the Non-verbal Group Test of Intelligence is
0 .385 (for N=40).
The validity and reliability coefficients indicate that the tool is
reasonably valid and reliable for measuring the Science Learning
Environment of Secondary school students.
A copy of the inventory is presented as Appendix XX
4.5.0. SAMPLE USED FOR THE STUDY
The population of the present study was secondary school students
(standard VIII, IX, and X) of Kerala. For the ease of preparing test of
process outcomes, the study was confined to students attending standard
IX of secondary schools of Kerala. Treating this as reference population,
the investigator had to take decisions regarding, size of the sample,
techniques of sampling, and factors to be represented in the sample.
The details are given below :
a) SIZE OF THE SAMPLE
Considering the special nature of the study and the type of statistical
procedures intended to be used, the size of the sample was tentatively
fixed as 1000 , eventhough, it is considerably larger than what was
suggested by social researchers for similar studies. The important
statistical procedures used for the study were.
1) Pearson's Product Moment Coefficient of Correlation 'r' to
estimate the association between the dependent variable-POP
- and each of the independent variables for the whole sample
and for subgroups HPA ,APA ,and LPA in POP.
2) Two-tailed test of significance of difference between means
for large independent groups.
3) Multiple regression equation to predict the POP, in terms of
independent variables, which have high correlation with the
dependent variable.
4) Multiple correlation coefficient 'R' to estimate the combined
effect of selected independent variables on the dependent
variable.
Size of the sample was such that, it should yield sufficiently large
subsamples for the different types of analysis. The question of
experimental mortality had to be considered. Also the possibility that
the investigator had to deal with individual student as the unit of study,
and the question of representing the factors which will yield a representa-
tive stratified sample had to be considered. Considering all these factors,
the size of the basal sample was dicided to keep around 1000.
b) SAMPLING TECHNIQUE
The population contains different strata of different sizes. Guilford
and Fruchter (1982) suggest "stratification is a step in the direction of
experimental control." A representative sample should contain individuals
drawn from each category, in accordance with the size of the group. So
proportionate stratified sampling technique was decided to be used
with individual student treated as the unit of testing for the present
study. This sampling technique was considered to be the best in view
of the highly heterogeneous nature of the sample.
C) FACTORS TO BE CONSIDERED FOR SELECTION OF THE SAMPLE
The widely accepted and popular procedure for stratification
recommended for the use of Indian social science researchers for studying
with school children, was adopted for the purpose of stratification.
According to this procedure, if representation is given for the following
basal variables, a most satisfactory representative sample of secondary
school pupils could be obtained.
The basal variables are:
1) sex of the subjects
2) rural/urban residence of the subject
3) instructional efficiency of the educational institution (roughly
estimated on the basis of pass percentage in the common
state examination at the end of the 10 years of schooling).
4) type of management of schools (govt. or private).
If these four basal variables are represented in the sample,it is
likely that other factors like cultural levels, socio- economic levels etc.,
get indirectly represented in the sample.
The official statistics kept by the Director of Public Instruction,
Government of Kerala was used for deciding the proport ionate
representation to be given for the four basal variables. The data for five
years, preceding the study was analyzed to obtain information regarding
the pupil enrolment, and pass percentage at the common secondary
school leaving certificate examination. The average figures for the five
years were taken up for estimating the proportions.
The estimated ratios were approximately as follows:
Boys : Girls = 9:10 (roughly)
Urban pupils : Rural pupils = 1:2 (roughly)
Pupils f rom government schools : Pupils f rom private
schools = 1:2
The five levels of pupils based on school efficiency,
A:B:C:D:E = 2:3:3:2:1
The letters A,B,C,D and E stand for the following level of
instructional efficiency.
Level A = Superior schools - pass percentage above 80 .
Level B = Above average schools -pass percentage below 8 0 and
above 60 .
Level C = Average schools - pass pe rcen tage below 6 0 and
above 40 .
Level D = Below average schools -pass percentage below 4 0 and
above 2 0
Level E = Inferior schools - pass percentage below 2 0
The approximate number of pupils to be covered from each
category was worked out, keeping in view the ratios fixed for each
category. A tentative break- up was roughly estimated on the assumption
that the total sample is 1000 and it will be covered by testing 2 4 class
divisions each with arround 4 5 pupils. This is represented in table 4 .7 .
TABLE 4.7. BREAK-UP OF THE TENTATIVE SAMPLE BASED ON SEX AND
PLACE OF RESIDENCE
The number of pupils fall in each efficiency level was estimated.
The values are given below.
Sex -
Boys
Girls
Total -
TABLE 4.8. NUMBER OF PUPILS SELECTED FOR THE SAMPLE FROM EACH
EFFICIENCY LEVEL OF THE SCHOOL
Urban
158
1 7 5
333
The approximate number of class divisions t o be covered is
estimated as 24 on the assumption that the strength of each class division
is 45. The schools were selected on the basis of the break-up given in
the table 4 . 7 and table 4.8.
Rural
316
35 1
6 6 7
LEVEL A
1 8 2
4.6.0 COLLECTION OF DATA
After selection and preparation of tools, and selection of sample,
the next phase to be accomplished was the collection of required data
from the sample by using the tools.
The investigator studied the basic literature relating to the tools
and test-booklets in detail to famiiiarise with the testing procedures and
possible eventualities before the commencement of the actual testing.
Total
4 7 4
5 2 6
1000
LEVEL C
2 7 3
LEVEL B
272
LEVEL D
182
LEVEL E
91
A schedule was prepared for the collection of data after visiting
the heads of the schools and teacher-in charge of the classes selected
for the collection of data. Their support was sought. The tools, test-
booklets and score sheets were got printed in adequate number.
The testing procedure followed a pre-fixed pattern in every school.
Firstly, the general data sheet was given to the subjects and got filled.
Then the TPOP was administered. After this an interval of 10 minutes
was allowed. Then the SATSL was administered. The next tool to be
used was SLII. The testing procedure for the fore-noon section was
over by the administration of SLII.
After lunch-break, The Kerala Non-verbal Group Test of Intelligence
was administered followed by Home Environment Inventory for Science
Learning (HEISL) and Science Learning Environment Inventory (SLEI).
The investigator herself visited the selected schools and collected
the data. Before administration of the tools, the aim and importance
of the study were explained to the students, for ensuring their active
participation and co-operation. Rules and procedure described already
were strictly followed in all schools for the uniformity of the testing
procedure.
While administering each test, the investigator was particular to
follow certain steps. They were:
1) distributing test-booklets together with instructions
2) explaining the directions given in the instruction
3) distributing the response sheets
4) making the students familiar with response sheet and mode
of entering responses
5) clearing the doubts of the students and giving directions
regarding time limit
6 ) collecting back the test booklets and response sheets
These steps were invariably followed in the administration of each
test. An interval of five minutes was given to the children before the
next tool, if they were administered consecutively.
4.7.0. SCORING AND CONSOLIDATION OF DATA
Scoring of the response sheets were done according to the
directions given in the test manuals and conventional procedures.
Punched cards were used for the scoring of The Kerala Non-
verbal Group Test of Intelligence, TPOP, and SLII in order t o speed
up scoring. During Scoring, incomplete entries were eliminated. Only
the data, which are complete in all respects were selected. This left the
investigator with 948 subjects. Further, 4 8 items were randomly rejected
to brind down the number to 900 , for convenience.
The school- wise break-up of the final sample is presented in table
4.9. The scores o n different tools and other data were tabulated
on a consolidated data sheet . The total sample was classified on
the basis of pre-determined basal variables, such a s gender, rural/
urban residence, type of management, and school efficiency. Each
subject was assigned a number and the whole data corresponding
TABLE 4.9. DETAILS OF THE SCHOOL-WISE BREAK-UP OF THE FINAL SAMPLE
S1.No. Name of the School
1. Govt. Girls H.S. Ettumanoor
2. St. Ann's H.S. Kurianadu
3. Holy Cross H.S. Cherpunkal
4. St. Thomas H.S. Thudanganad
5. St. Antony's H.S. Vellikulam
6. St. Augustin's H.S. Karimkunnam
7. St. Mary's B.H.S. Kuravilangad
8. St. Ma1y'sG.H.S. Kuravilangad
9. Sivapuram H.S. Sivapuram
10. St. Pauls's H.S. Valiyakumaramangalam
11. Govt. Model H.S. Calicut University Campus
12. St. George H.S. Aruvithura
13. St. George H.S. Koottickal
Locality
Rural
"
Typeof
School
Girls
Co-Edn.
Boys
Girls
Co-Edn.
Boys
Co-Edn.
Boys
Co-Edn.
No. of
Boys
-
20
18
14
25
27
28
-
11
34
30
34
17
Typeof
management
Govt
Private
"
Govt
Private
"
School
efficiency
Average
Superior
Above Avg.
Average
Below Avg.
,.
No. of Girls
40
18
22
16
25
26
-
35
22
-
20
-
19
Total
40
38
40
30
50
53
28
35
32
34
50
34
36
SI.No. Name of the School
14. KoothuparamhaH.S. Koothuparamha
15. Govt. V.H.S.S. Kadirur
16. Govt. H.S. Erattupetta
17. Govt. H.S. Thirurangadi
18. St. Thomas H.S. Pala
19. St. Augustine's H.S. Muvattupuzha
20. St.AntonySs H.S. Kacheripady
21. St. Mary's H.S. Ernakulam
22. St. Albert's H.S. Ernakulam
23. Govt. Model H.S. Muvattupuzha
24. Govt. G.H.S. Kaloor,
Total
- 2
Locality
Rural
Urban
,,
,,
,,
,,
,,
Type of School
Co-Edn.
,,
,,
,,
Boys
&Is
,,
,,
Boys
Co-Edn.
Girls
Type of
management
Private
Govt.
,,
Private
,,
,,
,,
,,
Govt.
Govt.
Schoof
efficiency
Below Avg.
,,
Inferior
Superior
,,
AboveAvg.
Average
Inferior
No. of
Boys
15
16
27
21
40
40
15
432
No. of
Girls
21
22
17
18
49
29
28
14
28
468
Total
36
38
44
39
40
49
29
28
40
29
28
900
to that subject was coded in different columns headed with suitable
codes to identify each, against the number.
The total group of 900 subjects was divided into High Process
Achievers (HPA), Average Process Achievers (APA), and Low Process
Achievers (LPA) with appropriate cut off in terms of the scores of the
total group in the dependent variable.
4.8.0 STATISTICAL TECHNIQUES USED
The following statistical techniques were employed for analysing,
interpreting and testing different hypotheses of the study.
a) Pearson's Product- moment Coefficient of Correlation 'r': This
was employed to study the association between the dependent
variable- POP- and each of the independent variables for the
whole sample and for the three subgroups Viz., HPA, APA,
and LPA.
b) Two-tailed Test of Significance of the difference between
means for large independent groups: This was used to compare
the three groups, (HPA-APA); (APA-LPA); and (HPA-LPA)
obtained on the basis of the scores in POP with respect to
each independent variable.
c) Multiple Regression Equation: This was developed to predict
POP in terms of a few select independent variables, which
have high correlation with the dependent variable.
d) Multiple Correlation Coefficient 'R ' . This was used to estimate
the combined effect of few select independent variables on
POP. Only those variables, which register high correlations
with the dependent variable, were used for this calculation.
4.9.0 DESCRIPTION OF THE STATISTICAL TECHNIQUES USED
a) Two-tailed test of significance of the difference between means
for large independent groups.
The ability of each of the independent variables- cognitive, affective
social, and environmental- to discriminate between the three groups of
POP - HPA, APA, and LPA - when taken in pairs (viz., HPA-APA;
APA-LPA; HPA-LPA) was determined by testing the significance of
the difference between means of these paired groups.
The procedure is to work out the t-values (critical ratios) given by
t = M, -M2 the formula
sE (MI - m) (Garrett, 1981)
where M, = Mean test score of the first group.
M, = Mean test score of the second group
and SE (MI-,,, = the standard error of the difference between
means MI and M,.
SE ,Ml*2, was estimated by using the formula
sE (Ml-t.12, = .\IsE'~, +sE',,
where SE & SE .,were the standard error of the mean scores
MI and M, respectively.
If N, and N, are the size of the samples under comparison and
o, and o, their respective standard deviations
0 1
then SE - - - m
The obtained t -value (critical ratio) was then treated as belonging
to a normal distribution. If the obtained 't' value falls between + 1. 9 6
and -1.96 the difference of means were treated as not being significant
at . 0 5 level. If the 't'-value falls outside the interval k 1.96, then the
difference between means was considered as significant at .05 level.
If the estimated 't'value falls inside the interval k 2 .58 , then the
difference between means was considered as not being significant at
.O1 level and if it falls outside the range k 2.58, it was considered as
significant.
b) Product moment coefficient of correlation.
Product momen t coefficient of co r r e l a t i on be tween two
variables x and y when they are given a s ungrouped pairs is
calculated by the formula
- - rxY
N C X Y - C X Z Y
J(NZX~ - ( Z X ) ~ ) (NZY~ - ( z Y ) ~ ) (Garrett, 1981)
where CX = Sum of all X scores
XY = sum of all Y scores
E X Y = sum of the product of the corresponding scores of X and Y
EX2 = sum of the squares of all X scores
CY2 = sum of the squares of all Y scores
The obtained correlation coefficients were interpreted by means
of the following approaches:
1) test of significance of the correlation coefficient
1 If the obtained correlation exceed -x1.96 or then it was JG
considered as significant at . 05 and .01 levels respectively
2) the .O1 confidence interval of 'r's
The limits of the . 0 1 confidence interval was estimated using the
formula r + - 2.58 SEr, where SEr is the standard error of 'r ' . SEr was
1 - r 2 calculated by using the formula, SEr = m where 'r' is the obtained
correlation
3) Verbal descriptions
Garrett's (1981) classification was used for the interpretation of
values of 'r ' ie., 'r ' from 0.0 to k 0.20 denotes indifferent or negligible
relationship.
' r ' from + .20 to + .40 denotes low correlation,
'r ' from + .40 to .70 denotes substantial or marked relationship.
'r' from + .70 to k 1.0 denotes very high relationship
4) Percen tage variance : This was est imated by finding out
rZ x 100; r being the obtained correlation coefficien (Fox, 1969) .
c ) MULTIPLE REGRESSION EQUATION
A multiple regression equation was derived to predict the
achievement of the students in POP by using four high influencing
independent variables.
The regression equation of X, (the criterion variable) on the
independent variable X,, X3, X4 and X5 in the deviation form is given by
- '1 12345) - b 1 2 . 345 '2 + b13.245 '3 + b14.235X4 + b15.234 '5.
(Garrett, 198 1)
In the score form the above equation becomes
Where b ~ ~ . 3 4 ~ , b13.2451 b14.2351 and b ~ ~ , , 3 4 a r e the regression
coefficients; MI, M,, M3, M4, M5 the mean scores on the variables
XI, X,, X3, X,, and X, respectively.
The regression coefficients are given by the formulae:
In these
The Coefficient of Multiple Correlation 'R'
T h e Multiple corre la t ion coefficient R of t h e variable
(r 1.2345 XI on variables X,,X,,X, and X, is given by Rl,,345, - - i r in
0 1
which s;,,,,is the standard deviation of the variable XI , when the effect
of the variables X,, X,, X, and X, are held constant.
The coefficient of multiple correlation indicates the strength of the
relationship between one variable and two or more others combined
with optimal weights.
Multiple 'R' is interpreted in the same way as simple correlation
' r ' . RZ, the coefficient of multiple determination tells us the proportion
of variance in the criterian variable; i.e. X,, that is dependent upon,
associated with or predicted by X,, X,, X, and X,, combined with the
regression weights used.
4.10.0 OTHER DETAILS RELATING T O T H E DESIGN
Procedure used for categorizing the whole sample in to groups
based on different levels of POP viz., High Process Achievers (HPA),
Average Process Achievers (APA), and Low Process Achievers (LPA) is
given below.
The total sample was divided into three groups on the basis of
scores obtained in the dependent variable POP For this, the scores of
the total sample of 900 subjects in POP was used in order to calculate
mean and standard deviation of the score distributions.
Assuming that M is the mean score and a the standard deviation
of 900 subjects in POP, the groups were labeled as below. A subject
whose score on the TPOP fell between (M + o) and (M -a) was classified
as Average Process Achiever (APA). A subject whose score was below
(M - a) was classified as Low Process Achiever (LPA). A subject whose
score was above (M + a) was classified as High Process Achiever (HPA).
The above Statistical techniques are made use of for the analysis
of data, the details of which are contained in a separate chapter-Chapter
V- Analysis, Interpretations, and discussion.
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