chapter-iii design of the study -...

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CHAPTER-III

DESIGN OF THE STUDY

Teaching is to research what Method is to teaching or in a sense what logic

is to thinking.

- Rusk

The main objective of the study is to ascertain the interactional effects

and the main effect of Advance Organizer Model (AOM), Biological Science

Inquiry Model (BSIM) and Traditional Method (TM) on the academic

achievement of students with regard to their Intelligence and Socio-

Economic Status (SES). In order to accomplish this, the experimental

method has been employed. The present chapter deals with the methodology

and procedure adopted to conduct the experiment to study the interactional

effects is that may be described to the combination of variables above and

beyond that which can be predicated from the variable considered singly.

III.1. METHODS OF THE STUDY :-

Experimentation is an attempt to control all essential factors except a

single variable which is manipulated of changed with a view to determining

and measuring the effects of its operation. In experimental studies the crucial

aspect is the rigor with which the attack is designed desired towards the

testing of hypotheses. It requires the development of a hypothesis suitable

research design or specification of operation for testing of a hypothesis under

given set of conditions. In an experimental approach the condition or

element which is being evaluated is referred to as the independent are called

dependent variable. In the present study the achievement of students

attributable the criterion test was considered as a dependent variable and

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level of Intelligence and Socio-Economic Status (S.E.S.) were taken as

independent variables. Three teaching methods Advance Organizer Model

(AOM), Biological Science Inquiry Model (BSIM) and Traditional Method

(TM) were the primary independent variable.

III.2. POPULATION :-

A population may be defined as the totality of particular

characteristics for any specified groups of individuals or objectives i.e. a

population of art graduates, a population of science graduates, a population

of science teachers, a population of art teachers, a population of medical

graduates, a population of medical books in library a population of university

teachers and a population of trained teachers etc. Usually this selection is

based on the some rule or plan.

In the present study, all the IX grade students of English medium

schools recognized by C.B.S.E. Board, New Delhi situated in Bhiwani

district have been selected to constitute the population.

III.3. SAMPLE OF THE STUDY :-

The main criterion of a spirit sample is that it should be the

representative of the target population because it is not possible to measure

the population. The population in a statistical research is arbitrarily defined

by naming its unique properties.

In this research, a sample of 240 students (120 Male & 120 Female) of

science stream from ten co-educational English medium schools affiliated to

C.B.S.E. Board of Bhiwani District have been taken by selecting randomly

from these schools. School-wise distribution of the students is given below

in the following Table No.-T.III.1 .

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TABLE No. – T.III.1

SCHOOL-WISE DISTRIBUTION OF SAMPLE

S.No. Name of the School Students Total

Male Female

1. K.C.M. SECONDARY SCHOOL, JHOJHU KHURD, BHIWANI (HR.)

12 12 24

2. ARYA SENIOR SECONDARY SCHOOL, JHOJHU KALAN, BHIWANI (HR.)

12 12 24

3. N.R.J. SECONDARY SCHOOL, JHOJHU KALAN, BHIWANI (HR.)

12 12 24

4. ARYAWART SENIOR SECONDARY SCHOOL, ADAMPUR, BHIWANI (HR.)

12 12 24

5. SHIV SECONDARY SCHOOL, CHARKHI DADRI, BHIWANI (HR.)

12 12 24

6. GYAN KUNJ SECONDARY SCHOOL, LOHARU (HR.)

12 12 24

7. M.L. SENIOR SECONDARY SCHOOL, LOHARU , HR

12 12 24

8. PRAGYA SECONDARY SCHOOL, BADHRA, BHIWANI (HR.)

12 12 24

9. SWAMI VIVEKANAND SECONDARY SCHOOL, BADHRA, BHIWANI (HR.)

12 12 24

10. BAISH SECONDARY SCHOOL, CHARKHI DADRI, BHIWANI (HR.)

12 12 24

Total 120 120 240

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DISTRIBUTION OF SAMPLE

TOTAL SAMPLE (240)

HIGH INTELLIGENT LOW INTELLIGENT (A1) (A2) (120) (120)

HIGH S.E.S. LOW S.E.S. HIGH S.E.S. LOW S.E.S.

(B1) (B2) (B1) (B 2)

(60) (60) (60) (60)

(20) (20) (20) (20) (20) (20) (20) (20) (20) (20)

(20) (20)

A.O.M. B.S.I.M. T.M. A.O.M.

B.S.I.M.

T.M. A.O.M.

B.S.I.M.

T.M. A.O.M.

B.S.I.M.

T.M.

(C1) (C2) (C3) (C1) (C2) (C3) (C1) (C2) (C3) (C1) (C2) (C3)

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III.4. TOOLS TO BE USED:-

As per objectives of the study, to measure the criterion variable of the

subjects, following tools have been used for collecting data –

Name of Tools Developed by

A Intelligence Test Prof. S. Jalota

B Socio-Economic Status ( Rev. - 2001) Prof. Beena Shah

C Achievement Test (2011) Researcher

D Advance Organizer Model – Syntax (2011)

Researcher

E Biological Science Inquiry Model – Syntax (2011)

Researcher

A. INTELLIGENCE TEST :-

To ascertain the variable as High and Low Intelligence groups in the

present experimental study an Intelligence test was administered on the

selected students. The sample was taken by the stratified random sampling

method. A Group Test of General Mental Ability–72, developed by S. Jalota

(ANNEXURE-I) was used in this study.

Description of the Scale :-

The need of a group test of mental ability decided to prepare such a

test as could be given to a group of student in an average school. In this test

there are only 100 items and maximum time for solving it is only 20

minutes. The classification of the items is given below-

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S. No. Constituent Total Time Allotted

1. Vocabulary – Similars

20 min.

2. Vocabulary – Opposites

3. Number Series

4. Classification

5. Best Answers

6. Inferences

7. Analogies

Reliability :-

The reliability of the test as given in the manual is +0.938.

Validity :-

The validity of the test as given in the manual, with correlating the

common criteria school examination marks, Ranged from +0.50 to +0.78.

Scoring:-

The wrong and left out questions are crossed out and then the number

of correct answers is counted which is known as raw scores. Here one mark

is allotted for one correct response and no marks are deducted for wrong

answer. The student gets maximum 100 marks in this test.

B. SOCIO-ECONOMIC STATUS :-

To ascertain the High and Low Socio-Economic Status (SES) in the

present experimental study a Socio-Economic Status (SES) test, developed

by Dr. Beena Shah has been used (ANNEXURE – II). A brief introduction

of this test is given below.

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SOCIO-ECONOMIC STATUS SCALE

FORM-A (URBAN)

Author : Dr. Beena Shah

Publisher : Agra Psychological Research Cell, Belanganj, Agra

Language : Hindi

DESCRIPTION OF THE SCALE :-

A living human being is so obviously as an active biological organism,

that we often overlook the influence of his mental functions in guiding or

directing the physical activities. In the past, many thinkers have tempted at a

times, to treat the mental as an irrelevant by product or they have shown but

limited respect for its obvious weaknesses, as its guidance or direction are

easily weighed down by the energy of physical needs. On the other hand, a

number of other eminent thinkers have tried to minimize the facts of physical

processes and gave the supremacy of the mental, as theirto and the

representative of the spirit. There is however a cautious third group, which

seems to follow the middle path; they seem to find some reason to accept the

role of both kinds of views for the fuller approval and proper understanding

of certain common experiences and events of every day living.

The psychologist tries to probe the function of Intelligence in different

types of tasks, and to see an individuals’ efficiency of performance in them,

to arrive at a reasonable estimate of his mental ability. The use of different

sub-test was eminently suited to such a task. We could easily assess the level

of ability in tasks like following directions, classification, analogies, number

series, etc. Also, we could then easily discover the character of their inter-

relations through suitable analytic procedures of correlations, factor analysis

etc. Hence, this prospect of using subtests has proved attractive to some

scholars. But all these purposes can also be met equally well by the use of

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compilation type tests, with the aid of suitable element analysis keys. Indeed,

this is the procedure commonly used with the scientific analysis of

personality questionnaires.


Showing for Item 10 (similar) % age of Responses to Alternative

Class 1 2 3 4

Xth 6.73 46.15 18.26 28.84

IXth 19.61 21.57 41.18 17.64

VIIIth 10.17 21.43 35.71 22.14

Again in the case of item 18 (similar) the right response is No.1, and

the wrong alternatives were scored as follows (in percentage) –


Showing for Item 18 (similar) % age of Responses to Alternative

Class 1 2 3 4

Xth 18.26 41.31 18.26 20.12

IXth 5.77 46.15 32.66 15.38

VIIIth 3.70 44.45 25.93 25.93

When we compare the responses of the girls and boys, to the above

two items, we get the following results (in percent scores)-


Comparing Responses by Girls and Boys

Item – 10 Item – 18

1 2 3 4 1 2 3 4

Girls 11.32 30.97 11.32 45.29 15.10 51.84 9.44 22.65

Boys 1.96 60.79 25.49 11.77 22.00 32.00 28.00 18.00

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It is evident from the above that the various responses to the items

are often very different for the different sex or educational groups. The

procedure of item-difficult assessment is primarily concerned with the

proportions of success failures only. If the proportion of success among

the items of a test-element is arranged in a descending order for each class,

then we can obtain the ascending orders of difficulty in each group and

select the required item.


Comparing Difficulty and Discrimination Values for X & IX classes

X Class IX Class

Ele

men

t

Item

No.

Diff

icul

ty

Dis

crim

inat

ion

Ele

men

t

Item

No.

Diff

icul

ty

Dis

crim

inat

ion

Ka 2 .985 .11 Ka 1 .973 .17

“ 6 .960 .32 “ 29 .950 .23

“ 22 .855 -.11 “ 22 .880 -.22

“ 17 .735 .60 “ 25 .653 .46

“ 22 .455 .04 “ 20 .653 -.1

“ 8 .160 .02 “ 14 .150 .31

Kha 4 .943 .10 Kha 3 .937 .23

“ 19 .937 .30 “ 22 .803 .40

“ 30 .469 -.20 “ 19 .847 -.47

“ 13 .108 .25 “ 13 .053 -.18

“ 20 .075 .26 “ 14 .053 .00

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Giving Products Moment Correlations between Item Difficulty (Success proportion) and Item Discrimination for the various test

Elements of the X and IX classes

Test Element X IX

Similar - .340 .159

Opposite - .232 .220

Classification - .537 .233

Number series - -.236 .040

Best Answers - .322 .121

Analogies - .634 .136

Reasoning - -.293 .432

Later, all the items were arranged according to their order of

increasing difficulty and we selected ten each for similar. Opposites, best

answer and reasoning, as well as twenty each for the test-elements of

classification, number series, and analogies, for our first empirical study

(1971). This followed the pattern of our first test decided upon in 1951. To

confirm the aforesaid hopes in a strong and ready manner, the total-scores

for the various test elements, in the different classes, were processed for

finding the Means and Standard Deviations. We find that there is an overlap

of M + SD scores of the VIII and the Means of the next higher class, the IX

class, this pattern is repeated with the result of the IX and X classes.

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Giving Means and Standard Deviations for the Preliminary Study of Test-Element-Sheet Scores

Class vavavava'k'k'k'k dddd [k[k[k[k XkXkXkXk ?k?k?k?k pppp NNNN tttt

VIII M 21.99 12.66 23.35 21.27 12.12 22.34 11.40

σ 2.76 2.97 5.03 12.43 3.65 7.62 2.64

IX M 14.94 17.19 26.22 28.16 15.51 23.69 11.77

σ 2.07 3.30 8.11 10.82 5.45 6.93 3.23

X M 15.08 18.35 31.18 36.18 15.92 27.92 13.47

σ 3.61 3.05 5.87 12.03 4.21 7.07 3.27


Giving Inter-Correlations between the Various Classes for Scores on the Test-Element Sheet (Similar)

Class VIII IX X

VIII - .826 .841

IX - - .938


Giving Inter-Correlations between the Various Classes for Scores on the Test-Element Sheet (Reasoning)

Class VIII IX X

VIII - .556 .645

IX - - .729

For additional confirmation the order of difficulty for the different

classes were correlated for verbal test-element of similars. To be further

assumed, a similar study was carried out with the test-element of reasoning.

We find from Table No. – T.III.7 that in our sample the correlation between

VIII and X is higher than that between VIII and X. However, the Correlation

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between the two orders of difficulty for IX and X is the highest. The same

pattern is repeated in Table No. – T.III.8; but the correlations are medium-

high, while in the former these are uniformly high. The processes of

“reasoning” are ex hypothesis more complex than those of ‘similars’. This

may be due to the fact that the complex processes obtain a larger range of

variation among the junior classes, and there are some what lower inter

corelations among the different classes.


Showing the Inter-Correlation (Try out 71) among the Components of Verbal Ability

Opposites ¼[k½¼[k½¼[k½¼[k½ Classification ¼x¼x¼x¼x½½½½

Similar ¼d½¼d½¼d½¼d½ 0.523 0.510 Opposite ¼[k½¼[k½¼[k½¼[k½ - 0.549


Showing the Inter-Correlation (Try out 71) among the Components of Reasoning Ability

Opposites ¼[k½¼[k½¼[k½¼[k½ Classification ¼x½¼x½¼x½¼x½

Best Answers ¼p½¼p½¼p½¼p½ 0.860 0.606

Analogies ¼t½¼t½¼t½¼t½ - 0.790

We find the correlation fall within the range or .510 to .549 for the

verbal tasks, and from .606 to .860 for the reasoning tasks. The correlation

between the total scores for V and R was .695. Hence, we conclude that

there was a possible common element among the V-task, and another among

the R-task, and also, that there was one element with medium weight

common to the total performances of the V and R tasks.

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(C). ACHIEVEMENT TEST :-

In the present study, Researcher has been developed and standardized

properely three achievement tests on topic “Cell and Tissues” for IX grade

students. These achievements tests have to be used to measure the

knowledge of related subject (Biology) before and after the proper treatment.

The items taken in the Achievement test were based on the topics taught by

the researcher during the treatment. Achievement scores of selected students

in Biology have been taken with the help of achievement test (ANNEXURE

– III).

(D). ADVANCE ORGANIZER MODEL (AOM) :-

According to Ausubel whether or not material is meaningful depends

more on the preparation of the learner and on the organization of the material

than it does on the methods of presentation. If the learner beings with the

right ‘set’ and if the material is solidly organized, then meaningful learning

can occur.

Advance Organizers are the primary means of strengthening cognitive

structure and enhancing retention of new information. Ausubel describes

Advance Organizers as introductory material presented ahead of the learning

task and at a higher level of abstraction and indusiveness than the learning

task itself. Their purpose is to explain, integrate and inter-relate the material

in the learning task with the previously learned material (and also to help the

learner discriminate the new material from previously learned material).

According to Ausubel “The Advance Organizer Model (AOM) also

presented at a higher level of abstraction generality and inclusiveness; and

since the substantive content of a given organizers or series of organizers is

selected on the basis of its suitability for explaining, integrating and

interrelating the material they precede this strategy. Simultaneously satisfies

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the substantive as well as the programming criteria for enhancing the

organization strength of cognitive structure.”

Advance Organizer is used in good “Transmission” teaching e.g.

direct instruction. Such teaching is different from simple rote learning since

learners are encouraged to relate new knowledge to old knowledge (what

they already know). “Advance Organizer provide the necessary scaffolding

for students to either learn new and unfamiliar material (an expository

organizer which provides the basic concept at the highest level of

generalization) of integrate new ideas into relatively familiar ideas (a

comparative organizer which compares and contrasts old and new ideas).

According to Mayer “An Advance Organizers Information that is

presented prior to learning and that can be used by the learner to organize

and interpret new incoming information.

Ausubel contends that these organizing ideas which may be single

concepts or statements of relationship are themselves important content and

should be taught because they serve to organize everything that follows.

Advance Organizers are based on mazor concepts, generalizations, principles

and lavels of academic disciplines. By keeping the principles of Advance

Organizers Model in mind, Researcher has also been developed the lesson

plans on the selected topic “Celle and Tissues” in subject Biology for

providing the sufficient treatment to the selected students of English medium

(ANNEXURE – IV).

(E). BIOLOGICAL SCIENCE INQUIRY MODEL (BSIM) :-

Biological Science Inquiry Model (BSIM) is an inductive and learners

centered approaches of teaching based on Biological Science propounded by

J. Schwab (1965) to teach scientific knowledge and to develop interest in

scientific inquiry. Not only can the nature of science but process of research

in Biology also be introduced to students. They can also learn planning and

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execution of projects and self learning involving acquisition of knowledge

through observation of phenomena, creative thinking and activities. The

Biological Science Inquiry Model includes a number of activities which are

grouped into four phases.

START

Phase – I Area of investigation is posed to students

Phase – II Students structure the problem

Phase – III Students identify the problem in the investigation

Phase – IV Students speculate on ways to clear up the difficulty

START

(Fig.- 8:- Flow chart of Inquiry Process in BSIM)

In the first phase, an area of investigation is posed to the students that

include methodology used in the investigation. In the second phase, students

structure the problem so that they become aware of problem in the

investigation. However, difficulty may be one of data interpretation, data

generation, the control of experiments of making inferences etc. In the third

phase, students speculate about the problem and identify the difficulty

involved in the inquiry. In the last and fourth phase, students search ways to

clear up the difficulty by designing experiments, collecting data, organizing

data in different ways and finding the results. By keeping the different

phases of Biological Science Inquiry Model in mind, Researcher has also

been developed the lesson plans on the selected topic “Celle and Tissues” in

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subject Biology for providing the sufficient treatment to the selected students

of English medium (ANNEXURE – V).

III.5. PROCEDURE OF THE STUDY :-

A sample of 240 (120 Male & 120 Female) science stream students of

class IX with the mean age of 14 years (13-15 yrs) has been selected through

random sampling from the population. These selected students have divided

into two groups on the basis of their Intelligence (High & Low). Again these

groups were divided into two group of students each on the basis of their

SES (High SES & Low SES). At last for preparing Experimental & Control

groups, students of High & Low SES have also been divided into three

groups of 20 students each. After the proper categorization of the students,

appropriate treatment with the help of Advance Organizer Model (AOM),

Biological Science Inquary Model (BSIM) & Traditional Method (TM) has

been given to them. After the completion of the treatment an Achievements

test have been applied to know the achievements of student on particular

topics. On the basis of achievements scores and other related scores of

Independent variables, Effectiveness of the Teaching Methods (AOM, BSIM

& TM) have been calculated with the help of suitable statistics.

III.6. DESIGN OF THE STUDY :-

The selection of a design is partly dependent upon the researcher’s decision

regarding whether he is going to use one or more than one group of subjects in the

proposed experiment. If researcher decides that there will be only one group of

subjects who will be tested under different values or conditions or treatments of

the independent variable, the resulting experimental design is known as the within-

groups design or repeated treatment designs. If, on the other hand, the researcher

decides to use a separate group for each value of the independent variable, the

resulting designs are also known as between-groups design. A schematic

presentation of research design i.e. experimental deign is given in the following

figure-

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(Fig.-9:- Experimental Designs)

The present study will be conducted through experimental method. It will

be based on 2 x 2 x 3 factorial design. When more than one independent variable is

considered in an experimental study a factorial design is usually employed. Thus,

in the present study three independent variables – Instructional Method,

Intelligence and Socio-Economic Status will be used and 2 x 2 x 3 factorial design

refers more to the assignment of subjects to group to the measurement employed

and to the statistical analysis techniques than to what is done in subjects. In the

present research the instructional methods Advance Organizer Model (AOM),

Biological Science Inquiry Model (BSIM) and Traditional Methods (TM) was the

primarily independent variable. The test of Intelligence and Socio-Economic

Status was the other secondary independent variables. The main objective was to

ascertain the interectional effects between the independent variable – primary and

secondary and dependent variable of criterion variable.

LAYOUT OF THE FACTORIAL DESIGN :-

In the present study a mixed factorial design of 2 x 2 x 3 order has

been used. The complete layout of this research design is given is given on

the next page –

Between-groups

design

Within-groups

design

Experimental Design

Complete Incomplete Factorial

design

Matched-

Group design

Two-

randomized

More than two

randomized group

Randomized

Group-

design

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LAYOUT OF THE FACTORIAL DESIGN

HIGH INTELLIGENT LOW INTELLIGENT

(A1) (A2)

HIGH S.E.S. LOW S.E.S. HIGH S.E.S. LOW S.E.S.

(B1) (B2) (B1) (B 2)

� 2 CATEGORY OF INTELLIGENCE (HIGH & LOW)

� 2 LEVEL OF S.E.S. (HIGH & LOW)

� 3 METHOD OF TEACHING (A.O.M., B.S.I.M. & T.M.)

2 x 2 x 3

A.O.M. B.S.I.M. T.M. A.O.M.

B.S.I.M.

T.M. A.O.M.

B.S.I.M.

T.M. A.O.M.

B.S.I.M.

T.M.

(C1) (C2) (C3) (C1) (C2) (C3) (C1) (C2) (C3) (C1) (C2) (C3)

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III.7. STATISTICAL TECHNIQUES USED :-

To analyze the collected data from the students of class IX of English

Medium Schools of Bhiwani District in Hariyana State, with reference to the

specific objectives and hypothesis, the following stastistical techniques have

been used.

(i). Mean

(ii). Standard Deviation (S.D.)

(iii). CR/“t” Value

(iv). Analysis of Variance (ANOVA)

(i). MEAN :- " The mean is the sum of the individual scores or measures

divided by their number.”

∑ X = Sum of Individual Scores M = Mean N = Number of Scores

(ii). STANDARD DEVIATION: -

The Standard Deviation is the square root of the arithmetic average of

the squared deviations of various values from their arithmetic mean.

Standard Deviation (S.D.) of any series can be calculated from the

following formula -

SD = Standard Deviation. I = Class Interval ∑fd2 = Sum of the product the frequencies and square of

deviation from assumed mean. ∑fd = Sum of the product of frequencies and deviation from

assumed mean. N = Number of Scores.

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(iii). CR/t VALUE:-

CR value is a critical ratio in which a more exact estimate of the σd is

used t is a CR but all CR’s are not ‘t’s. The sampling distribution of ‘t’ is not

normal when N is smaller than 30.

M1 = Mean of the first group.

M2 = Mean of the second group.

SD1 2 = Square of SD of the first group.

SD2 2 = Square of SD of the second group.

N1 = Size of the first group.

N2 = Size of the second group.

(iv). ANALYSIS OF VARIANCE (ANOVA) :-

The weighted average of simple effect for all levels of the control

variable is known as the ‘main’ effects of the treatments. ‘Simple’ effect may

be interpreted as the treatment effect for a given level of independent

variable. In simple words, the main effects of factious are the mean squares

for the levels of factors.

In addition to the main effects of the three factors, there is a possibility

that there are interactions between the factors. “Interaction is a measure of

the non-additively of the main effects.” The significance of ‘F’ test is

determined by reference to Seducer’s table. In using this table, we have to

consider the two different df values. For the numerator of the ‘F’ we look for

the df at the left of a row. Three way of analysis of variance (ANOVA)

technique was used to study the main effects and interaction effects.

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ANALYSIS OF VARIANCE (ANOVA) TABLE :-

The analysis of variance table used in the present study has been

provided in following table.


THE TABLE OF ANOVA USED IN THE ANALYSIS OF DATA

Source df Sum of Squares (SS)

A – Instructional Method

B – Intelligence

C – S.E.S.

Error (b)

A – 1

B – 1

C – 1

Abc (n – 1)

SSA

SSB

SSC

SS error

Between subject Abc – 1 SSbs

AxB Interaction of two

BxC Interaction of two

AxC Interaction of two

AxBxC Interaction of three

Error (w)

(a-1) (b-1)

(b-1) (c-1)

(a-1) (c-1)

(a-1) (b-1) (c-1)

SSAB = SSAB – SSA-SSB

SSBC=SSBC-SSB-SSC

SSAC=SSAC-SSA-SSC

SSABC=SSABC-SSA-SSB

-SSC-SSAB-SSBC-SSAC

SS error CW-SS ous (w)

With in subject SSw = SS1-SSb

Total abc – 1 SS1

MEASURES OF ANOVA:

The present study was conducted on the Model of factorial design for

analyzing the main effects of three factors-Instructional Methods,

Intelligence test, and Socio-Economic Status (SES). The ‘F’ test was applied

for analyzing the main effects of these three facts. The weightage average of

simple effects for all levels of the control variable is known as ‘Main’ effects

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of treatment. ‘Simple’ may be interpreted as the treatment effect for a given

level of independent variable. Thus, the main effects of factors are the mean

square for the level of factors.

FORMULA FOR COMPUTING SIGNIFICANE OF MEANS AMONG

GROUPS:-

Correction factor = C

T2

Step – I C = ------------

N

Total sum of square = SST

Step – II SST = [(X1)2 + (X2)

2 + ……………. + (Xn)2] –C

Step – III Sum of Square of Treatment = SSA - C

Sum of Square of Total Cells = 8

(A1C1B1)2 + …… + (AnCnBn)2

Step – IV Cells = ---------------------------------- - C

m

Step – V Sum of Square of Treatment = SSB – C

Sum of Square of Treatment = SSC – C

Sum of Square of Treatment = SSBC - C

Step – VI Sum of Square of Treatment = SSAB – C

Sum of Square of Treatment = SSAC – C

Sum of Square of Treatment = SSABC – C

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ANOVA (2 X 2 X 2) factorial design:-

Source of Variation

df Sum of Square

Mean of square

F – ratio

Between group

df1 SSb SSb / df1 Mean of Square between groups

Mean of Square within groups

Within groups

df2 SSw SS2 / df2

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chapter-iii design of the study -...

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