Thesis Writing

Chapter 1 THE PROBLEM AND ITS BACKGROUND

Chapter 1 of a thesis should contain a discussion of each of the following topics:

Introduction
Background of the study
Theoretical Framework
Conceptual Framework
Statement of the Problem
Assumptions and Hypotheses
Scope and Limitations of the Study
Significance or Importance of the Study
Definitions of Terms

The Introduction

Guidelines in writing the introduction. The introduction of a thesis should contain a
discussion of any or all of the following:

1. Presentation of the Problem. The start of the introduction is the
presentation of the problem, that is, what the problem is all about.
This will indicate what will be covered by the study. Example: Suppose
that the investigation is about the teaching of science in the high
schools of Province A. The discussion may start with this topic
sentence: There is no other period in world history when science has
been making its greatest impact upon humankind than it is today.
(Prolong the discussion citing the multifarious and wonderful benefits
that science is giving to humanity today. Later, in connection wit
science, the topic for inquiry may be presented as the teaching of
science in the high schools of Province A during the school year 1989-
1990 as perceived by the science teachers and students.)

2. The existence of an unsatisfactory condition, a felt problem that needs
a solution. Example: The teaching of science in the high schools of
Province A has been observed to be weak as shown by the results of
the survey tests given to the students recently. The causes must be
found so that remedial measures may be instituted. (The discussion
may be prolonged further)

3. Rationale of the study. The reason or reasons why it is necessary to
conduct the study must be discussed. Example: One of the Thrust of
the Department of Education, Culture and Sports and of the
government for that matter is to strengthen the teaching of science. It
is necessary to conduct this inquiry to find out how to strengthen the
instruction of science in the province. (This may be prolonged)

4. Historical background of the problem. For a historical background of
the research problem of the teaching of science, the first satellite to
orbited the earth, educational systems all over the world including that
the Philippines have been trying hard to improve their science
curricula and instruction, (This can be explained further)

5. A desire to have deeper and cleared understanding of a situation,
circumstance, or phenomenon. If the teaching of science in the high
schools of Province A is the topic, the researcher must explain his

earnest desire to have a deeper and clearer understanding of the
situation so that he will be in a better position to initiate remedial
measures.

6. A desire to find a better way of doing something or of improving a
product. The researcher must also explain his desire to find a better
way in teaching science in the high schools of Province A to improve
the outcome of instruction.

7. A desire to discover something. In connection with the teaching of
science in the high schools of Province A, the researcher may have the
desire to discover what is wrong with the instruction and a desire to
discover better ways of teaching the subject. He may discuss his
desire to discover such thing.

8. Geographical conditions of the study locale. This is necessary in
anthropological and economic studies. If the subject of investigation is
rice production, then the terrain, soil, climate, rainfall, etc. of the
study locale have to be described.

9. A link between the introduction and the statement of the problem. A
sentence or two should how the link between the introduction and the
conducting of the researcher. Example: The researcher got very much
interested in determining the status of teaching science in the high
schools of Province A and so he conducted this research.

Background of the study

This segment consists of statements on what led the investigator to launch the
study. A historical background may be given. Situations that may have spurred the
researcher to undertake the study are included. The background of the study may have
been generated by some empirical observations, the need to explore the problem and some
other relevant conditions.

Begin this section with a clear description of the background of the study and the
social, institutional context which will frame the project. Be careful to describe as clearly as
possible the problem intended to be addressed and refer to the relevant literature in the
field.

This section describes the history of the problem. That is, it is an overview of factors
which have led to the problem, comprise the problem and historical significance relative to
the problem. This should take between one (1) to one and a half (½) pages. (Salvador et
al.)

Theoretical Framework

This is the foundation of the research study. These are highly related theories and
principles that were established and proven by authorities which are very useful to the
present study. Almost all research studies that were conducted in the past were based on
universally accepted theories and principles.

Theoretical Framework means relating to or having the characteristic of the theory.
Theoretical Framework, therefore, refers to the set of interrelated construct, definitions, and
prepositions that presents a systematic view of phenomena by specifying relations among

variables. The theoretical framework becomes the basic of the research problem. It explains
the phenomena upon which the thesis investigation hopes to fill the vacuum in the stream
of knowledge.

Pursuing the linkage between the theory and the problem at hand, the researcher
views theoretical framework as an organized body that explains what has been done and
what has been said on the topic or problem being investigated. Moreover, the body of
knowledge establishes relationships among the variables concerned. The present study is
the missing link to the body of knowledge. Accordingly, if and when the research study is
consummated , the gap of missing link disappears since the study will have closed the gap.
The theoretical framework is now more complete until another researcher discovers another
gap, inconsistency, or weakness which will be the object of another investigation.

WHAT DATA MUST BE OBTAINED FROM A THEORY?

1. The name/s of author/s of the theory must be taken including the place and the time
/ year when he or she postulated such a principle or generalization.

2. Next, copy exactly the part or parts of the theory that are relevant to your study.
Make sure you will use a parenthetical reference to recognize the parts copied.

3. Finally, you will have to make a synthesis by relating to your findings what the
theory has to say about the phenomenon being studied. (Salvador et al.)

Conceptual Framework

From the review of related literature and studies, the researcher may formulate a
theoretical scheme for his research problem. This scheme is a tentative explanation or
theoretical explanation of the phenomenon or problem and serves as the basis for the
formulation research hypotheses. Thus, the conceptual framework consists of the
investigator’s own position on a problem after his exposure to various theories that have
bearing on the problem. It is the researcher’s new model which has its roots on the previous
models which the researcher had studied. (Sanchez, pp. 14-15)

The conceptual framework becomes the central theme, the focus, the main thrust of
the study. It serves as a guide in conducting investigation. Briefly stated, the conceptual
framework for the teaching of science can be: The effectiveness of a science instructional
program depends upon the qualifications of the teachers, the effectiveness of their methods
and strategies of teaching, the adequacy of facilities, the adequacy of supervisory
assistance, and the elimination of the problems hampering the progress.

Currently, however, most theses do not have a discussion of their conceptual
frameworks. Very few thesis writers endeavor to include an explanation of their conceptual
framework in their theses.

Paradigm. A paradigm is a diagrammatic representation of a conceptual
framework. It depicts in a more vivid way what the conceptual framework wants to convey.
Following are examples of a paradigm for the conceptual framework for the teaching of
science as mentioned above. A paradigm may take different diagrammatic forms.

Example 1

Inputs Process Outputs

Qualified
teachers Science Superior
science
Effective knowledge
methods
Instructional and
Adequate
facilities skills

Adequate Program of
Supervisory
assistance

Figure 8. Paradigm for science teaching in high school.

Statement of the Problem

There should be a general statement of the whole problem followed by the specific
questions or sub problems into which the general problem is broken up. These are already
formulated at the beginning of the study and so they should only be copied in this section.
(See the first section of the Statement of Problem, pp. 28-29, for further guidance in writing
the general problem and the specific questions pp. 29-30.)

Assumptions and Hypotheses

Historical and descriptive investigations do not need explicit hypotheses and
assumptions. Only experimental studies need expressly written assumptions and
hypotheses. Since these are already formulated at the start of the experiment, they are just
copied in this section. (See the sections Assumptions and Hypotheses, pp. 30-3, for further
guidance in writing assumptions and hypotheses).

Scope and limitations of the Study

Guidelines in writing the scope and delimitations. The scope and delimitations should
include the following:

1. A brief statement of the general purpose of the study.

2. The subject matter and topics studied and discussed.

3. The locale of the study, where the data were gathered or the entity to
which the data belong.

4. The population or universe from which the respondents were selected.
This must be large enough to make generalizations significant.

5. The period of the study. This is the time, either months or years,
during which the data were gathered.

Example: This investigation was conducted to determine the status of the teaching of
science in the high schools of Province A as perceived by the teachers and students
in science classes during the school year 1989-1990. the aspects looked into were
the qualifications of teachers, their methods and strategies, facilities forms of
supervisory assistance, problems and proposed solutions to problems.

General purpose: To determine the status of the teaching of science.
Subject matter: The teaching of science.
Topics (aspects) studied: Qualifications of teachers. Their methods and strategies,
facilities, form of supervisory assistance, problems and proposed solutions to the
problems.
Population or universe: teachers and students
Locale of the study: High schools of province A.
Period of the study: School year 1989-1990.

Limitations of the Study

Limitations of the study include the weaknesses of the study beyond the control of
the researcher. This is especially true in descriptive research where the variables involved
are uncountable or continuous variables such as adequacy, effectiveness, efficiency, extent,
etc. The weaknesses spring out of the inaccuracies of the perceptions of the respondents.
For instance, library facilities may be rated as very adequate by 50 students, fairly adequate
by 30 students, inadequate by 20 students, and very inadequate by 15 students. Certainly,
with these ratings, not all of them could be correct in their assessment. Some could have
inaccurate if not entirely wrong perceptions.

Importance or Significance of the Study

Guidance in explaining the importance of the study. The rationale, timeliness, and/or
relevance of the study to existing conditions must contain explanations or discussions of any
or all of the following:

1. The rationale, timeliness and/or relevance of the study. The rationale,
timeliness and/or relevance of the study to existing conditions must be
explained or discussed. For instance, a survey test in science reveals
that the performance of the students in the high schools of Province A
is poor. It must be pointed out that it is a strong reason why an
investigation of the teaching in science in the said high schools is
necessary. Also, the study is timely and relevant because today, it is
science and technology that are making some nations very highly
industrialized and progressive. So, if science is properly studied and
taught and then applied, it can also make the country highly
industrialized and progressive.

2. Possible solutions to existing problems or improvement to
unsatisfactory conditions. The poor performance of the students in the
high schools of Province A in a survey test in science should be
explained as a problem and an unsatisfactory condition. So if the
inquiry is made the possible causes of the poor performance of the
students in the science survey test may be discovered so that remedial
measures may be instituted to solve the problem or the unsatisfactory
situation.

3. Who are to be benefited and how they are going to be benefited. It
must be shown who are the individuals, groups, or communities who

may be placed in a more advantageous position on account of the
study. In the inquiry conducted about the teaching of science, for
instance, some weaknesses of the instructional program may be
discovered. This will benefit the administrators of the high schools in
Province A because they can make the findings of the study as a basis
of formulating their supervisory plans for the ensuing year. They may
include in their plans some measures to correct the weaknesses so as
to strengthen the instruction. In turn, the students will also benefit for
learning more science. In the long run, the whole country will enjoy
the good results of the study.

4. Possible contribution to the fund of knowledge. If in the study it is
found out that the inductive method is very effective in the teaching of
science, it should be pointed out that this can be a contribution of the
study to the fund of knowledge.

5. Possible implications. It should be discussed here that the implications
include the possible causes of the problems discovered, the possible
effects of the problems, and the remedial measures to solve the
problems. Implications also include the good points of a system which
ought to be continued or to be improved if possible.

Definition of Terms

Guidelines in defining terms:

1. Only terms, words, or phrases which have special or unique meanings
in the study are defined. For instance, the term non-teaching facilities
may be used in the study of the teaching of science. Non-teaching
facilities may be defined as facilities needed by the students and
teachers but are not used to explain the lesson or to make instructions
clearer. Examples are toilets or comfort rooms, electric fans, rest
rooms or lounges, and the like. They may also be called non-
instructional facilities.

2. Terms should be defined operationally, that is how they are used in
the study. For instance, a study is made about early marriage. What is
meant by early marriage? To make the meaning clear, early marriage
may be defined as one in which the contracting parties are both below
eighteen years of age.

3. The researcher may develop his own definition from the characteristics
of the term defined. Thus, a house of light materials may be defined as
one with bamboo or small wooden posts, nipa, buri, or nipa walls; split
bamboo floor and cogon or nipa roof. This is also an operational
definition.

4. Definitions may be taken from encyclopedias, books, magazines and
newspaper articles, dictionaries, and other publications but the
researcher must acknowledge his sources. Definitions taken from
published materials are called conceptual or theoretical definitions.

5. Definitions should abe brief, clear, and unequivocal as possible.

6. Acronyms should always be spelled out fully especially if it is not
commonly known or if it is used for the first time.

Chapter 2 REVIEW OF RELATED LITERATURE AND STUDIES

Guidelines in Citing Related Literature and Studies

A. Characteristics of the Materials Cited

The following are the characteristics of related literature and studies that should be
cited: (Repeated for emphasis)

1. The materials must be as recent as possible. This is important because
of the rapid social, political, scientific, and technological changes.
Discoveries in historical and archeological research have also changed
some historical facts. Researchers in education and psychology are
also making great strides. So, finding fifteen years ago may have little
value today unless the study is a comparative inquiry about the past
and the present. Mathematical and statistical procedures, however, are
a little more stable.

2. Materials must be as objective and unbiased as possible. Some
materials are extremely one sided, either politically or religiously
biased. These should be avoided.

3. Materials must be relevant to the study. Only materials that have
some military to or bearing on the problem researched on should be
cited.

4. Materials must not too few but not too many. They must be sufficient enough
to give the researcher insight into his problem or to indicate the nature of the present
investigation. The number may also depend upon the availability of related materials. This is
especially a problem with pioneering studies. Naturally, there are few related materials or
even none at all. Ordinarily, from fifteen to twenty-five may do for a master’s thesis and
from twenty and above for a doctoral dissertation, depending upon their availability and
depth and length of discussions. The numbers, however, are only suggestive but not
imperative. These are only the usual numbers observed in theses and dissertations
surveyed. For an undergraduate thesis about ten may do.

B. Ways of Citing Related Literature and Studies

The following are the ways of citing related literature and studies:

1. By author or writer. In this method the ideas, facts, or principles,
although they have the same meaning, are explained or discussed
separately and cited in the footnote with their respective authors or
writers.

Examples: According to Enriquez, praise helps much in
learning, etc., (Enriquez, 1981)

Maglaque found out that praise is an important factor in
learning, etc., (Maglaque, 1984)

2. By topic. In this case, if different authors or writers have the same
opinion about the same topic, the topic is discussed and cited under
the names of the authors or writers. This is a summary of their
opinions. This is to avoid separate and long discussions of the same
topic.

Example: It has been found out that praise is an important aid
in learning of children. (Enriquez, 1981)

3. Chronological. Related materials may also be cited chronologically, that is,
according to the year they were written. Materials which were written earlier should be cited
first before those which were written later. This can be done especially when citation is by
author or writer. If citation is by topic, chronological citation can be done in the footnote.

C. What to Cite

It should be emphasized that only the major findings, ideas, generalizations,
principles, or conclusions in related materials relevant to the problem under investigation
should be discussed in this chapter. Generally, such findings, ideas, generalizations,
principles, or conclusions are summarized, paraphrased, or synthesized.
D. Quoting a Material

A material may be quoted if the idea conveyed is so perfectly stated or it is
controversial and it is not too long. It is written single spaced with wider margins at the left
and right sides of the paper but without any quotation marks.

Example: Suppose the following is a quotation: Said Enriquez,
Praise is an important factor in children’s learning. It
encourages them to study their lessons harder. Praise, however,
should be given appropriately.

Justification of the Study

It should be made clear that there is no duplication of other studies. The present
inquiry may only be a replication of another study. It should be stressed also that in spite of
similar studies, the present study is still necessary to find out if the findings of studies in
other places are also true in the locale of the present study. There may also be a need to
continue with the present investigation to affirm or negate the findings of other inquiries
about the same research problem or topic so that generalization or principles may be
formulated. These generalizations and principles would be the contributions of the present
investigation together with other studies to the fund of knowledge. This is one of the more
important purposes of research: the contribution that it can give to the fund of knowledge.

Synthesis

It should be emphasized in this area that the major findings, ideas, generalizations,
principles or conclusions in related materials relevant to the problem under investigation.
Generally, such findings, ideas, generalizations, principles or conclusions are summarized,
paraphrased, or synthesized.

Chapter 3 RESEARCH METHODOLOGY

Generally, the research design is explained in this chapter. Among those topics
included in the research design which need to be given some kind of explanations are the
following:

Methods of Research
Population, Sample Size, and Sampling Technique
Description of Respondents
Research instrument
Data-Gathering Procedure
Statistical Treatment of Data

Methods of Research

The method of research used whether historical, descriptive or experimental should
be explained briefly. The procedural part of the method, its appropriateness to the study,
and some of its advantages should be given attention and should be well discussed.

Example: Suppose the descriptive method of research was used in the study of the
teaching of science in the high schools of Province A. Briefly the discussion follows:

The descriptive method of research was used in this study. Descriptive method of
research is a fact-finding study with adequate and accurate interpretation of the findings. It
describes what is. It describes with emphasis what actually exist such as current conditions,
practices, situations, or any phenomena. Since the present study or investigation was
concerned with the present status of the teaching of science in the high schools of Province
A, the descriptive method of research was the most appropriate method to use. (This can be
elaborated further)

Population, Sample size and Sampling Technique

The researcher describes how he selected places, products, situations, and
respondents. If regions were used, the different regions of the country are included in his
first list. The next question is: how did the researcher select the sample regions included in
the study? Are the selected regions representative of all the regions that make up the
Philippines? If barrios in a particular province were the focus of the study, how did the
researcher select the few barrios representative of all the barrios? On the other hand, if
ethnic groups were used, how did he arrive at the majority and minority ethnic groups of
the particular national survey? The researcher should describe how he went about selecting
the sampled places and sampled products and respondents in this part of the methodology.

The Sampling Design

Before the collection of data starts in any research project, the proportion of the
population to be used must have been determined already and the computation of the
sample must have been finished. So, what the researcher has to do here is to write about
the complete procedure he used in determining his sample. Among the things that he
should explain are:

a. The size of the population;
b. The study population;
c. The margin of error and the proportion of the study population used;
d. The type or technique of sampling used whether pure random
sampling, cluster sampling or a combination of two or more
techniques;

e. The actual computation of the sample; and
f. The sample

The researcher must explain very clearly how he selected his sample. He must be
able to show that his sample is representative of the population by showing that he used
the appropriate technique of sampling. This is very important because if it appears that his
sample is not representative, his findings and conclusions will be faulty and hence, not valid
and reliable.

To be able to discuss and explain very well his sampling procedures, the researcher
must review sampling procedures in Chapter 12. Everything about sampling has been
discussed in that part of the book.

Description of Respondents

The respondents are described as a small group or as a big group. Characteristics
may include sex, age level, socio-economic status, marital status, level of intelligence,
education, type of community (urban or rural, barrio or town), ethnic group, and other
characteristics sought by the researcher to describe his respondents. These characteristics
of respondents could be presented in table form.

Research Instrument

Instrument used for gathering data are described under Research Methodology. The
various aspects of the instruments are mentioned. Items in each instrument are described
too. If validation of the test was made, this is also mentioned. In some studies, several
instruments are used. These could be related following the order of administration. It is
desirables that writers mention how these instruments were used in the study. Could it be
that Instrument 1 is intended to shed light on Hypothesis 1; Instrument 2 on Hypothesis 2;
and so forth?

If the instrument is lengthy, this is generally placed in the appendix. Such placement
has to be mentioned in the text and labeled as Appendix A,B, or C, as the case maybe.

This part describes the tools used to measure the variables. In most cases, this
means detailing the survey used. If a researcher developed a survey on his own or modified
one which is in the literature, he needs to include this plus the cover letter in the appendix.
If he is using a well- researched questionnaire, reference it clearly. (Salvador et al.)

Data-Gathering Procedure

The method of collecting data and the development of the instrument for gathering
data must also be explained.

Example: the method of collecting data used was the normative survey. This is
concerned with looking into the commonality of some elements. Since the present research
is a status study, the normative survey was the most appropriate method to use in
gathering data.

The instrument used to collect data was the questionnaire. This was used because it
gathers data faster than any other method. Besides, the respondents were teachers and
students and so they are very literate. They could read and answer the questionnaire with
ease.

Development of the instrument. After reading and studying samples of questionnaire
from related studies, the researcher prepared his own questionnaire. He also consulted
some knowledgeable people about how to prepare one. The researcher saw to it that there
were enough items to collect data to cover all aspects of the problem and to answer all the
specific questions under the statement of the problem. Then he submitted the questionnaire
to his adviser for correction after which it was finalized.
For validation purposes, the questionnaire was given to ten high school science
teachers for them to fill up. These teachers did not participate in the study. After they have
filled up the copies they were interviewed by the researcher to find out their assessment of
the questionnaire. They were asked if all the items were clear and unequivocal to them; if
the number of items were adequate enough to collect data about all aspects of teaching of
science; if the questions were interesting and not boring; if all the items were objective and
not biased except for a few unavoidable essay questions; if all the items were relevant to
the research problem; and if the questionnaire were not too long. All of them said the items
were clear and unequivocal except a few, relevant, interesting and objective questions, and
the length was alright. The few questioned items were revised for more clarity and
definiteness.

The copies of the questionnaire were then distributed personally by the researcher to
the respondents. After a few days, all the copies distributed were retrieved also personally
by the researcher. (The discussion may be extended)

WAYS OF COLLECTING DATA

1. Mechanical devices include almost all tools (such as microscopes, telescopes,
thermometers, rulers and monitors) used in physical sciences.
2. Clerical tools are used when the researcher studies people and gather data on the
feeling, emotions, attitudes and judgment of the subject.

2.1 Questionnaire method
2.2 Interview method
2.3 Empirical observation method
2.4 Registration method
2.5 Testing method
2.6 Experiment method
2.7 Library method

Questionnaire Method. This is a list of planned, written questions, related to a
particular topic with space provided for indicating response to each question intended
for submission to a number of people for a reply. It is commonly used in normative
studies and in the measurements of attitudes and opinions.

Guidelines in the Formulation of Questions in a Questionnaire

1. Make all directions clear and unequivocal.
2. Use correct grammar.
3. Make all questions unequivocal.
4. Avoid asking biased questions.
5. Objectify the responses.
6. Relate all questions to the topic under study.
7. Create categories or classes for approximate answers.
8. Group the questions in local sequence.
9. Create sufficient number of response categories.
10. Word carefully or avoid questions that deal with confidential and embarrassing
information.
11. Explain and illustrate different questions.
12. State all questions affirmatively.
13. Place all space for replies at the left side.

Interview Method. This is a purposeful face-to-face relationship between person, one
called the interviewer who asks questions to gather information and to the other
called the interviewee or the respondent who supplies the information asked for.

This is feasible when a person interact is available. The research interview is a
research method that involves situations or conditions the respondent is in, although
it entails difficulty in tallying as the answers are varied. In other words, the answer is
entirely left at the discretion on the respondent.

In general, respondents do not like to answer open-ended questionnaires for aside
from giving multiple responses, they feel that they are taking an examination. Aside
from this, an open-ended questionnaire gives multiple responses, which makes
statistical analysis difficult. (Salvador et al.)

Statistical Treatment of Data

The last part of this chapter usually describes the statistical treatment of data. The
kind of statistical treatment depends upon the nature of the problem, especially the specific
problems and the nature of the data gathered. The explicit hypotheses particularly
determine the kind of statistics to be used.
The role of statistics in research. With the advent of the computer age, statistics is
now playing a vital role in research. This is true especially in science and technological
research. What functions do statistics perform in research? Some are the following:

1. Statistical methods help the researcher in making his research design,
particularly in experimental research. Statistical methods are always
involved in planning a research project because in some way statistics
directs the researcher how to gather his data.

2. Statistical techniques help the researcher in determining the validity
and reliability of his research instruments. Data gathered with
instruments that are not valid and reliable are almost useless and so
the researcher must have to be sure that his instruments are valid and
reliable. Statistics helps him in doing this.

3. Statistical manipulations organize raw data systematically to make the
latter appropriate for study. Unorganized data cannot be studied. No
inferences or deductions can be made from unorganized data.
Statistics organized systematically by ordered arrangement, ranking,
score distribution, class frequency distribution or cumulative
frequencies. These make the data appropriate for study.

4. Statistics are used to test the hypotheses. Statistics help the
researcher to determine whether these hypotheses are to be accepted
or to be rejected.

5. Statistical treatments give meaning and interpretation to data. For
Instance, if the standard deviation of the class frequency of a group is
small, we know that the group is more or less homogeneous but if it is
large, the group is more or less heterogeneous.

6. Statistical procedures are indispensable in determining the levels of
significance of vital statistical measures. These statistical measures are
the bases for making inferences, interpretations, conclusions or
generalizations.

Some guidelines in the selection and application of statistical procedures. The
researcher must have at least a rudimentary knowledge of statistics so that he will be able
to select and apply the appropriate statistical methods for his data. Some suggestions for
the selection and application of statistical techniques follows:

1. First of all, the data should be organized using any or all of the
following depending upon what is desired to be known or what is to be
computed: talligram (tabulation table), ordered arrangement of
scores, score distribution, class (grouped) frequency distribution, or
scattergram.

2. When certain proportions of the population based on certain variables
such as age, height, income, etc. are desired to be known, frequency
counts with their frequency percents may be used. For further
analysis, cumulative frequencies (up and down) with their respective
cumulative frequency percents (up and down) may also be utilized.
For example, a specific question is “How the high school science
teachers of province A may be described in terms of sex?” The males
were counted and the females were also counted and their respective
percent equivalents were computed.

3. When the typical, normal, or average is desired to be known, the
measures of central tendency such as the median, the mean or the
mode may be computed and used.

4. When the variables being studied are abstract or continuous such that
they cannot be counted individually such as adequacy, efficiency,
excellence, extent, seriousness (of problems), and the like, the
weighted mean may be computed and used if the average is desired to
known. The variable is divided into categories of descending degree of
quality and then each degree of quality is given a weight. For instance,
the question is “How adequate are the facilities of the school?”
Adequacy may be divided into five degrees of quality such as “very
adequate” with a weight of 5, “adequate” with a weight of 4, “Fairly
adequate” with a weight of 3, “inadequate” with a weight of 2, and
“very inadequate” with a weight of 1. Then the weighted mean is
computed.

5. When the variability of the population is desired to be known, the
measures of variability such as the range, quartile deviation, average
deviation or the standard deviation may be computed and used. When
the measure of the variability or dispersion is small, the group is more
or less homogenous but when the measure of variability is large, the
group is more or less heterogeneous.

6. When the relative placements of scores or positions are desired to be
known, ranking, quartile or percentile rank may be computed and
used. These measures indicate the relative positions o scores in an
ordered arrangement of the scores.

7. When the significance of the trend of reaction or opinion of persons as
a group toward a certain issue, situation, value or thing is desired to
be known but in which there is a neutral position, the chi-square of
equal probability, single group, is computed and interpreted.

8. When the significance of the difference between the reactions, or
opinions of two distinct groups in which there is a neutral position is

desired to be known, the chi-square of equal probability, two-group, is
computed and used.
For instance, a group of 50 persons, 25 males and 25 females,
were asked to give their reactions may be “Strongly agree”, “Agree”,
“Undecided or No opinion”, “Disagree”, or “Strongly disagree”. If the
persons are considered as a group, the chi-square of equal probability,
single group is computed as in No. 7. However, if the significance of
the difference between the reactions of the males and those of the
females is to be studied, the chi-square of equal probability, two-
group, is applied as in No. 8.

9. To determine how one variable varies with one another, the coefficient
of correlation is computed, as for instance, how the scores of a group
of students in English test. This is also used to determine the validity
of a test by correlating it with a test of known validity. When the
coefficient of correlation between two tests is known and a prediction
is to be made as to what score a student gets in a second test after
knowing his score in the first, the so-called regression equation is to
be utilized.

10. If the significance of the difference between the perceptions of two-
groups about a certain situation is to be studied, the computation of
the difference between means is to be made. Example: Is there a
significant difference between the perceptions of the teachers and
those of the students about the facilities of the school? To answer this
question, the significance of the difference of two means is to used.
The statistical measure computed is called t.

The t is also used to determine the usefulness of a variable to
which one group called the experimental group is exposed and a
second group called control group is not exposed. For instance, the
question is: Does guidance improve instructions?” Create two matched
groups and expose one group to guidance while the control group is
not exposed to guidance. At the end of the experimental period, give
the same test to the two groups. Then compute the t which will show if
guidance is an effective aid to instruction.

11. To determine the relative effectiveness of the different ways of doing
things to which different randomized groups are respectively exposed
to and only a post test is given to the different groups, analysis of
variance is appropriate to use. For instance, a teacher wants to find
out the relative effectiveness of the following methods of
communication: pure lecture, lecture-demonstration, recitation-
discussion, and seminar type of instruction in science. Four groups of
students are formed randomly and each assigned to one method. The
four groups study the same lessons and after a certain period given
the same test. By analysis of variance, the relative effectiveness of the
four methods will be revealed.

If the four groups are given pre-test and a post-test, the
analysis of covariance is utilized.

12. To determine the effects of some variables upon a single variable to
which they are related, partial and multiple correlations are suggested
to be used. For example, the question is: Which is most related to the
passing of a licensing engineering examination: college achievement
grades, or percentile ranks in aptitude tests, general mental ability
test, vocational and professional interest inventory, or National College

Entrance Examination? The process of partial and multiple correlations
will reveal the pure and sole effect of each of the independent
variables upon the dependent variable, the passing of the licensing
examination.

13. To determine the association between two independent variables, the
chi-square of independence or chi-square of multiplication may be
used. The question answered by this statistical process is: Is there an
association between education and leadership? Or, the level of
education and the ability to acquire wealth? Or, between sociability
and economic status?

Indeed, there are lots of research situations in which different
statistical procedures may or can be used and if the researcher is not
so sure that he is in the right path, he better consult good statistical
books, or acquire the services of a good statistician plus the services
of a computer especially if the statistical procedures are complex ones.

Chapter 4 ANALYSES, PRESENTATION, AND
INTERPRETATION OF DATA

In this chapter, the researcher makes his analysis, presentation, and interpretation
of his data.

Analysis

Analysis is the process of breaking up the whole study into its constituent parts of
categories according to the specific questions under the statement of the problem. This is to
bring out into focus the essential features of the study. Analysis usually precedes
presentation.

Example: In the study of the teaching of science in the high schools of Province A,
the whole study may be divided into its constituent parts as follows according to the specific
questions:

1. Educational qualifications of the science teachers
2. Methods and strategies used in the teaching of science
3. Facilities available for the teaching of science
4. Forms of supervisory assistance
5. Differences between the perception of the teachers and those of the
students concerning the teaching of science
6. Problems encountered in the teaching of science
7. Proposed solutions to the problems
8. Implications of the findings

Each constituent part may still be divided into its essential categories. Example: The
educational qualifications of the teachers may further be subdivided into the following:

1. Degrees earned in pre-service education
2. Majors or specializations
3. Units earned in science
4. Teacher’s examinations and other examinations passed
5. Seminars, conferences, and other special trainings attended for the
teaching of science
6. Books, journals, and other materials in science being read
7. Advanced studies

8. Number of years in science teaching
9. Etc.

Then under degrees earned are

1. Bachelor of Arts
2. Bachelor of Science in Education
3. Master of Arts
4. Etc.

The other constituent parts may also be similarly divided and subdivided. The data
are then grouped under the categories or parts to which they belong.

Classification of data. Classification is grouping together data with similar
characteristics. Classification is a part of analysis. The bases of classification are the
following:

a. Qualitative (kind). Those having the same quality or are of the same
kind are grouped together. The grouping element in the examples
given under analysis is qualitative. See examples under analysis.

b. Quantitative. Data are grouped according to their quantity. In age, for
instance, people may be grouped into ages of 10-14, 15-19, 20-24,
25-29, etc.

c. Geographical. Data may be classified according to their location for
instance; the schools in the secondary level in Province A may be
grouped by district, as District 1, District 2, District 3, etc.

d. Chronological. In this, data are classified according to the order of
their occurrence. Example: The enrolments of the high schools of
Province A may be classified according to school years, as for,
instance, enrolments during the school years 1985-’86, 1986-’87,
1987-’88.

Cross-classification. This is further classifying a group of data into subclasses. This is
breaking up or dividing a big class into smaller classes. For instance, a group of students
may be classified as high school students as distinguished from elementary and college
students. Then they are further subdivided into curricular years as first, second, third, and
fourth years. Each curricular year may still be subdivided into male and female.

Arrangement of data or classes of data. The bases of arrangement of data or groups
of data are the same as those of classification.

a. Qualitative. Data may be arranged alphabetically, or from the biggest
class to the smallest class as from the phylum to specie in classifying
animals or vice versa, or listing the biggest country to the smallest one
or vice versa, or from the most important to the least important, or
vice versa, etc. Ranking of students according to brightness is
qualitative arrangement.

b. Quantitative. This is arranging data according to their numerical
magnitudes, from the greatest to the smallest number or vice versa.
Schools may be arranged according to their population, from the most
populated to the least populated, and so with countries, provinces,
cities, towns, etc.

c. Geographical. Data may be arranged according to their geographical
location or according to direction. Data from the Ilocos region may be
listed from north to south by province as Ilocos Norte, Abra, Ilocos Sur
and La Union.

d. Chronological. This is listing down data that occurred first and last
those that occurred last or vice versa according to the purpose of
presentation. This is especially true in historical research. For instance,
data during the Spanish period should be treated first before the data
during the American Period.

Classification, cross-classification and arrangement of data are done for purposes of
organizing the thesis report and in presenting them in tabular form. In tables, data are
properly and logically classified, cross-classified, and arranged so that their relationships are
readily seen.

Group-derived Generalizations

One of the main purposes of analyzing research data is to form inferences,
interpretations, conclusions, and/or generalizations from the collected data. In so doing the
researcher should be guided by the following discussions about group-derived
generalizations.

The use of the survey, usually called the normative survey, as a method of collecting
data for research implies the study of groups. From the findings are formulated conclusions
in the form of generalizations that pertain to the particular group studied. These conclusions
are called group-derived generalizations designed to represent characteristics of groups and
are to be applied to groups rather than to individual cases one at a time. These are
applicable to all kinds of research, be they social, science or natural science research. There
are several types of these but are discussed under four categories by Good and Scates.
(Good and Scates, pp. 290-298) The key sentences are of this author.
1. Generally, only proportional predictions can be made. One type of
generalization is that which is expressed in terms of proportion of the cases in a group,
often in the form of probability. When this type is used, we do not have enough information
about individual cases to make predictions for them, but we can nevertheless predict for a
group of future observations. As to individual event, however, we can say nothing;
probability is distinctly a group concept and applies only to groups.

Quality control in manufacturing is an example. Based on the recognition that
products cannot be turned out as precisely as intended, but that so long as a given
proportion of the cases fall within assigned limits of variation, that is all that is expected. In
the biological field, certain proportions of offspring, inherit certain degrees of characteristics
of parents, but individual predictions cannot be made. In the social field, in insurance
especially, based on demographic and actuarial data, life tables indicate life expectancies of
groups but nothing whatsoever is known about the life expectancy of any particular
individual.

Here is another example. Suppose in a certain school offering civil engineering, it is a
known fact that all through the years, bout 70% of its graduates with an average of 2.0 or
its equivalent or higher pass the licensing examination for civil engineers. On this basis, we
can predict that about 70% of the graduates of the school with an average of 2.0 or higher
will pass the next licensing examination for civil engineers but we cannot predict with
certainty the passing of a particular graduate even if his average grade is 1.25.

2. The average can be made to represent the whole group. A second type of
group-derived generalization results from using the average as a representation of the
group of cases and offering it as a typical result. This is ignoring the individuals comprising

the group or the variation existing in the group but the average represents the whole group.
Generally, the mean and the median are used to denote the averages of scale position but
other statistical measures such as the common measures of variation, correlation,
regression lines, etc. are also structurally considered as averages. These are group
functions conveying no sure knowledge about any individual case in the group.

3. Full frequency distribution reveals characteristics of a group. As a third type
of knowledge growing out of the study of the groups, we have the full-frequency distribution
– the most characteristics device, perhaps of all statistical work. Perhaps, too the most
inferential characteristics of frequency distribution are shape and spread. Frequency
distributions carry the implication of probability. One implication is as follows. Suppose the
heights of a Grade I pupils are taken and then grouped into a class frequency distribution,
using height as the trait or basis of distributions in groups. Then the suppliers of chairs and
tables for the pupils will be able to know the number of chairs and tables to suit the heights
of the pupils.

Here is another example which enables us to know certain characteristics of a group.
Suppose a test is given to a group of students. Then their scores are grouped into a class
frequency distribution. If the standard deviation, a measure of variability, is computed and
it is unusually large, then we know that the group is heterogeneous. If the standard
deviation is small, the group is more or less homogeneous. If the distribution is graphed and
the curve is bell-shaped, the distribution is normal, that is, there is an equal number of
bright and dull students with the average in the middle. If the curve is skewed to the right,
there are more dull students than bright ones, and if the distribution is skewed to th left
there are more bright students than dull ones.

4. A group itself generates new qualities, characteristics, properties, or aspects
not present in individual cases. For instance, there are many chairs in a room. The chairs
can be arranged in a variety of ways. However, if there is only one chair, there can be no
arrangement in any order. Hence, order and arrangement are group properties and they
represent relationships within a group, properties which can arise only if there are two or
more cases.

Other group properties that exist only in groups are cooperation, opposition,
organization, specialization, leadership, teaching, morale, reciprocal sharing of emotions,
etc. which vanish in individual cases.

Two or more categories of generalization may be added at this point.

1. A generalization can also be made about an individual case. For instance, a
high school graduating student is declared valedictorian of his class. We can generalize that,
that student is the brightest in his class. This is a group-derived generalization because it
cannot be made if there is only one student. Here is another example. A teacher declares
that Juan is the best behaved pupil in her class. This is a group-derived generalization
because this statement cannot be made if there is only one pupil. There are many instances
of this kind.

2. In certain cases, predictions on individual cases can be made. It has been
mentioned earlier that, generally, only proportional predictions can be made. However, in
correlation and regression studies, one variable can be predicted from another. Take the
case of the civil engineering graduate taking the licensing examination by the use of
regression equations. The accuracy of prediction is high if (1) there is linearity in the
relationship of the two variables if graphed, (2) the distributions in the two variables are
normal or not badly skewed, and (3) the spread or scatter of the two variables is the same
for each column or row in the correlation table. The process involves a complicated
statistical book especially that of Garrett, pp. 122-146 for linear correlation and pp. 151-165
for regression and prediction.

Preparing Data for Presentation

Before presenting data in accepted forms, especially in presenting them in the form
of statistical tables, they have to be tallied first in a tabulation diagram which may be called
talligram, a contraction of tally and diagram. The individual responses to a questionnaire or
interview schedule have to be tallied one by one.

How to construct a talligram. A talligram may be constructed as follows:

1. Determine the classes and their respective subclasses along with their
respective numbers. For instance, in the study about science teaching
in the high schools of Province A, anent the qualifications of the
teachers, suppose there are four degrees earned by the teachers such
as AB (Bachelor of Arts), BSCE (Bachelor of Science in Civil
Engineering), BSE (Bachelor of Science in Education) and MA (Master
of Arts with undergraduate courses). The subclasses are the
specializations or majors of the teachers. There are also four such as
English, History, Mathematics, and Science. The classes and their
subclasses are arranged alphabetically.

2. Make rows for the classes by drawing horizontal lines with appropriate
spaces between the lines and the number of the rows should be two
more than the number of classes. So in the example given in step no.
1, there should be six rows because there are four classes. The
uppermost row is for the labels of the subclasses, the bottom row is
for the totals, and the middle four rows are for the classes: AB, BSCE,
BSE, and MA.

3. Make columns for the subclasses by drawing vertical lines with
appropriate spaces between the lines and the number of columns
should be two more than the number of subclasses. So in the example
in No. 1 step there should six columns. The leftmost column is for the
labels of the class rows, the rightmost column is for totals, and the
four middle columns are for the four subclasses.

See Figure 1 for an example of talligram.

Degrees and Specializations of Teachers

Degrees Specializations (Majors) Total
English History Mathematics Science
AB 1 11 1111 1 1111 1111 11 21
BSCE 1111 4
BSE 11 11 1111 1111 1111 1111 1111 111 31
MA 1 11 3
Totals 3 4 25 27 59

Figure 1

How to tally data (responses) gathered through a questionnaire. Tallying responses
to a questionnaire in a talligram follows. Suppose a questionnaire gives the following data:

a. Teacher A is an AB graduate with a science major. Enter a tally in the
cell which is the intersection of the AB row and the Science column.
The tally is a short vertical bar. See Entry (1) in Figure 1.

b. Teacher B is an AB graduate with a science major. Enter a tally in the
cell which is the intersection of the AB row and the Science column.
See Entry (2) in Figure 1.

c. Teacher C is a BSE graduate with a science major. Enter a tally in the
cell which is the intersection of the BSE row and the Science column.
See Entry (3) in Figure 1.

d. Teacher D is a BSE graduate with mathematics major. Enter a tally in
the cell which is the intersection of the BSCE row and the Mathematics
column. See Entry (4) in Figure 1.
e. Teacher E is a BSCE graduate with mathematics major. Enter a tally in
the cell which is the intersection of the BSCE row and the Mathematics
column. See Entry (5) in Figure 1.

f. Continue the process until all the data needed are entered.

When finished, the talligram will look exactly like Figure 2.

Degrees and Specializations of the Teachers

Degrees Specializations (Majors) Totals

English History Mathematics Science
AB 1 11 1111 1 1111 1111 11 21
BSCE 1111 4
BSE 11 11 1111 1111 1111 1111 1111 111 31
MA 1 11 3
Totals 3 4 25 27 59

Figure 2

Figure 2 may now ebe converted into a statistical table for data presentation.
Generally, all quantified data are tallied first in talligram which are then converted into
statistical tables for data presentation using Hindu-Arabic numerals in the cells in place of
tallies.

Presentation of Data

Presentation is the process of organizing data into logical, sequential, and meaningful
categories and classifications to make them amenable to study and interpretation. Analysis
and presentation put data into proper order and in categories reducing them into forms that
are intelligible and interpretable so that the relationships between the research specific
questions and their intended answers can be established. There are three ways of
presenting data; textual, tabular, and graphical.

Textual Presentation of Data

Textual presentation uses statements with numerals or numbers to describe data.
The main aims of textual presentation are to focus attention to some important data and to
supplement tabular presentation.

The disadvantage, especially if its too long, is that it is boring to read and the reader
may not even be able to grasp the quantitative relationships of the data presented. The
reader may even skip some statements.

Example: The following refers to the degrees earned by 59 science teachers in the
hypothetical study of the teaching of science in the high schools of Province A:

Of the 59 science teachers, 21 or 35.59 percent have earned a bachelor of Arts
degree with education units, four or 6.78 percent have earned a Bachelor of Science in Civil
Engineering degrees with education units, 31 or 52.54 percent a Bachelor of Science in
Education degree, and three or 5.08 percent a Master of Arts degree.

According to government regulations, all the teachers are qualified to teach in the
high school. (This is already a finding, interpretation, or inference)

Tabular Presentation of Data

Statistical table defined. A statistical table or simply table is defined as a systematic
arrangement of related data in which classes of numerical facts or data are given each a
row and their subclasses are given ach column in order to present the relationships of the
sets or numerical facts or data in a definite, compact, and understandable form or forms.

Advantages of tabular over textual presentation of data. The advantages of the
tabular over the textual presentation of data are:

1. Statistical tables are concise, and because data are systematically
grouped and arranged, explanatory matter is minimal.

2. Data are more easily read, understood and compared because of their
systematic and logical arrangement into rows and columns. The reader
can understand and interpret a great bulk of data rapidly because he
can see significant relationships of data at once.

3. Tables give the whole information even without combining numerals
with textual matter. This is so because tables are so constructed that
the ideas they convey can be understood even without reading their
textual presentation.

The major functional parts of a statistical table. The names of the functional parts of
a statistical table are shown in the following diagrams: (Bacani, et. Al, p. 55)

Table Number
Title
(Head note)

Stub Head Master Caption

Column Column Column Column
Caption Caption Caption Caption
Row Label Entry Entry Entry Entry
“ “ “ “ “ “

“ “ “ “ “ “
“ “ “ “ “ “
“ “ “ “ “ “
“ “ “ “ “ “
“ “ “ “ “ “
Total

The above illustration of a table is only a simple one. There are tables that are very
complicated. For instance, the column captions may further be subdivided into sub-column
captions which in turn may still be subdivided. This happens when the subject matter of the
table is classified, then the first classifications are further sub classified, and so on.

1. Table Number. Each table should have a number, preferably in Arabic, for
reference purposes. This is because only the table numbers are cited. The number is written
above the title of the table. Tables are numbered consecutively throughout the thesis
report. If there is only one table the number is unnecessary. See table 1 for illustration.

2. Title. The title should tell about the following:

a. The subject matter that said table deals with;
b. where such subject matter is situated, or from whom the data
about such subject matter were gathered;
c. when data about such subject matter were gathered or the
time period when such data were existent; and
d. sometimes how the data about such subject matter are
classified.

Usually, however, only the first two elements are mentioned in the title, and
occasionally only the subject matter. This is possible if the time period of the study as well
as the locale and respondents are well discussed in the scope and delimitation of the study.
Only the beginning letters of the important words in the title are capitalized. If the title
contains more than one line, it should be written like an inverted pyramid. See Table 1
below.

Table 1

Degrees and Specializations of the Teachers

Degrees Specializations (Majors) Totals
Earned a English History Mathematics Science
Fb % F % F % F % F %
AB 1 1.69 2 3.39 6 10.17 12 20.34 21 35.59
BSCE 4 6.78 4 6.78
BSE 2 3.39 2 3.39 14 23.73 13 22.03 31 52.54
MA 1 1.69 2 3.39 3 5.08
Totals 3 5.08 4 6.78 25 42.37 27 45.76 59 99.99c

3. Headnote or Prefatory Note. This is written below the title and it is usually
enclosed in parentheses. It explains some things in the table that are not clear. Suppose a
table entitled “Monetary Values or Properties of the High Schools in Province A” is to be
constructed and the entries in the table are in rounded millions of pesos. If the amount to
be entered is six million pesos, the entry is only 6, instead of entering 8,000,000 the entry
is only 8, etc. The Headnote that should be written below the title should be written below

the title should be “Millions of Pesos.” So, the entry of 6 is read six million pesos, the entry
of 8 should be read eight million pesos, etc.

4. Stub. The stub contains the stub head and the row labels. The stub head tells
what the stub contains, the row labels. Each row label describes the data contained in that
row. In the table given as example, Table 1, Degrees is the stub head and below it are the
degrees which are the row label: AB, BSCE, BSE, and MA. In the AB row all the teachers
listed there are AB graduates, in the BSCE row all BSCE graduates, in the BSE row, all BSE
graduates, and in the MA row, all MA graduates. Totals may be considered as part of the
stub.

5. Box Head. The box head contains the master caption, the column captions,
and the column sub captions. The master caption describes the column captions and the
column captions in turn describe the sub column captions. In Table 1, the master caption is
Specializations (Majors). The column captions are English, History, Mathematics, Science,
and Totals. The sub captions are F (frequency), and % (percent). The F indicates the
number of teachers under it and the symbol % indicates the proportion of the number under
F to the total, 59.

6. Main body, field or text. The main body, field or text of the table contains all
the quantitative and/or proportional information presented in the table in rows and in
columns. Each numerical datum is entered in the cell which is the intersection of the row
and the column of the datum. For instance, the 14 teachers who are BSE graduates and
who majored in mathematics are centered in the cell which is the intersection of the BSE
row and the mathematics column.

7. Footnote. The footnote which appears immediately below the bottom line of
the table explains, qualifies, or clarifies some items in the table which are not readily
understandable or are missing. Proper symbols are used o indicate the items that are
clarified or explained. In Table 1, a is used to indicate that all the teachers have enough
education units, b is used to indicate that all percents were computed with 59 as the base,
and c is used to indicate that the total percent does not equal 100.00 due to the rounding
off of the partial percents to two decimal places.

The footnote is not necessary everything in the table is clear and there is nothing to
clarify or explain.

8. Source note. The source note which is generally written below the footnote
indicates the origin or source of the data presented in the table. In Table 1, the sources of
the data are the Principals’ Offices. The purposes of placing the source note are:

a. To give credit or recognition to the author of the table or the
source or sources of the data;

b. To allow the user to secure additional data from the same
source;

c. To provide the user a basis for determining the accuracy and
reliability of the information provided by the table; and

d. To protect the maker of the table against any charge of
inaccuracy and unreliability.

The source note is not necessary if the sources of the data are the respondents to a
questionnaire or interview schedule.

Ruling and spacing in tables. Ruling is done in a table to emphasize or make clear
relationships. There are no fixed standard rules to follow in ruling and spacing tables.

Emphasis and clarity are the determining factors. However, the following guidelines are
generally followed in the construction of tables for a thesis report:
1. The table number is not separated by line from the title. It is written
two spaces above the title.

2. The title is separated from the rest of the table by a double line placed
two spaces below the lowest line of the title.

3. The stub, master caption, captions, sub-captions, and totals are
separated from one another by vertical and horizontal lines.

4. The rows and columns are not separated by lines. Major groups,
however, are separated by single lines. For purposes of clarity, rows
are separated by a double space and the columns are separated by as
wide a space as possible.

5. Both ends of the table are unruled.

6. There is always a line, either ingle or double, at the bottom of the
table.

Unity in a table. There should always be unity in a table. To achieve this, presenting
too many ideas in a single table should be avoided. One subject matter is enough, one that
can be divided into categories which in turn can be divided into common classifications. In
Table 1, for instance, the subject matter is degrees and majors. Degrees are divided into
similar categories such as AB, BSCE, BSE, and MA. The sub classes such as English, History,
Mathematics, and Science are common to the degree categories.

Textual presentation of tabular data. Generally, there should be a textual
presentation of table which precedes the table or the table may be placed within the textual
presentation. The table and its textual presentation should be placed as near as possible to
each other. Textual presentation is mixing words with numbers in statements.

There are two ways of making a textual presentation of a table:

1. All the items in the table are textually presented. This manner enables
the reader to comprehend the totality of the data even without
consulting the table. This is alright if the data are not so many.
However, if the data are so numerous, reading becomes boring and
the reader may even skip some of the items.

2. Only the highlights or important parts of the data are textually
presented.

The basic principles that should be remembered in the textually presentations of a
table are:

1. The textual presentation of a table should be as complete as possible
so that the ideas conveyed in the table are understood even without
referring to the table itself.

2. Textual Presentation is generally followed by interpretation, inference
or implication. This is done after the data from the table have been
textually presented.

3. Findings in the present study should be compared with the findings of
other studies as presented in the related literature and studies. This
enables the researcher to make some generalizations if there are
enough data to support such generalizations.

Following is the textual presentation of Table 1:

(Complete) Table 1 shows that there were 59 science teachers in the high schools of
Province A. of this number, 21 or 35.59 percent were AB graduates. Of the AB graduates,
one or 1.69 percent majored in English, two or 3.39 percent in History, six or 10.17 percent
in Mathematics, and 12 or 30.34 percent in Science.

There were only four or 6.78 percent who were BSCE graduates, all majoring in
Mathematics.

There were 31 or 52.54 percent who were BSE graduates and of this number, two or
3.39 percent majored in English, the same number in History, 14 or 23.73 percent in
Mathematics, and 13 or 22.03 percent in Science.

Summarizing the majors, three or 5.08 percent were majors in English, four or 6.78
percent in History, 25 or 42.37 percent in Mathematics, and 27 or 45.76 percent in Science.

Summarizing the majors, three or 5.08 percent were majors in English, four or 6.78
percent in History, 25 or 42.37 percent in mathematics, and 27 or 45.76 percent in Science.

(Only the highlights) Of the 59 teachers, the AB and BSE graduates constituted the
most number. Twenty-one or 35.39 percent were AB graduates and 31 or 52.54 percent
had BSE degrees or a total of 52 or 88.13 percent. Of the majors, 27 or 45.76 percent of
the teachers were majors in Science, 25 or 42.37 percent in Mathematics, and three or 5.08
percent in English and four or 6.78 percent in History.

Findings. Findings are the original data, quantitative or otherwise, derived taken
from the original sources and which are results of questionnaires, interviews, experiments,
tests, observations and other data gathering instruments. Data presented in tables and their
textual presentations are examples of findings. Findings do not directly answer the specific
questions asked at the beginning of the investigation or the explicit hypotheses but the
findings provide the bases for making the answers. Hence, the main functions of the
findings are to provide bases for making the conclusions.

Implication, inference, interpretation. These three terms are synonymous if not
exactly the same in meaning. They are used interchangeably. Each is a statements of the
possible meaning, probable causes and probable effects of a situation or condition as
revealed by the findings plus a veiled suggestion to continue the situation if it is good or to
adopt some remedial measures to eradicate or minimize its bad effects. Those who are to
be benefited and those who are going to suffer the bad effects should also be mentioned.

Implication, inference, or interpretation has at least four elements, namely,
condition, cause, effect, and continuance or remedial measure.

(1) Statement of the condition or situation. The condition or situation is
stated based upon the findings, whether satisfactory or unsatisfactory.

(2) Probable cause of the condition. Usually, also every condition has a
cause but, there must be also a logical and valid relationship between
the condition and its cause.

(3) Probable effects of the condition. Usually, also every condition has an
effect, either bad or good. However, there must also be a logical and

valid relationship between the condition and its effect and this must be
clearly given.

(4) A veiled suggestion for continuance or remedial measure, if the
possible effect is bad. If the effect of condition is good, then there
must be a hint for the continuance of the existence of the condition.
However, if the effect is deleterious there must be some suggestions
for the adoption of measures aimed at minimizing the harmful effects.

The interpretation of Table 1 and its textual presentation is as follows: All the science
teachers were qualified to teach in the high school as per regulation. Unfortunately, more
than half of them were not science majors and therefore cannot teach science. Taking all
other things equal, a teacher with a science major can teach better than one with a non-
science major. Consequently, it can be assumed that the teaching of science in the high
schools of Province A is weak. As a result, the students and the whole country will suffer
and the whole consequences will be far-reaching. There is a need to encourage the teachers
who are non-science majors to increase their science units by attending evening or summer
courses or by attending more science seminars.

Graphical Presentation of Data

A graph is a chart representing the quantitative variations or changes of a variable
itself, or quantitative changes of variable in comparison with those of another variable or
variables in pictorial or diagrammatic form.

The quantitative variations or changes in the data may refer to their qualitative,
geographical, or chronological attributes. For instance, if the number of teachers teaching
science in the high schools of Province A is graphed according to their degrees, the graphing
is qualitative; if their number is graphed according to their assignments in the towns where
the high schools are located, the graphing is geographical; and if their number is graphed
according to school year, the graphing is chronological.

Purpose of graphing. The purpose of graphing is to present the variations, changes,
and relationships of data in a most attractive, appealing, effective and convincing way.

Advantages of the graphic method. (Bacani, et al., pp. 54-55) According to Bacani,
et al. the following are the advantages of the graphical method:

1. It attracts attention more effectively than do tables, and, therefore, is
less likely to be overlooked. Readers may skip tables but pause to look
at charts.

2. The use of colors and pictorial diagrams makes a list of figures in
business reports more meaningful. (Also in thesis reports)

3. It gives a comprehensive view of quantitative data. The wandering of a
line exerts a more powerful effect in the reader’s mind than tabulated
data. It shows what is happening and what is likely to take place.

4. Graphs enable the busy executive of a business concern to grasp the
essential facts quickly and without much trouble. Any relation not seen
from the figures themselves is easily discovered from the graph.
Illustrations, including attractive charts and graphs, are now
considered by most businessmen as indispensable accompaniment to
good business reports.

5. Their general usefulness lies in the simplicity they add to the
presentation of numerical data.

Limitations of graphs. (Bacani, et al., pp. 55) If there are advantages there are also
disadvantages of the graph. Some of these are:

1. Graphs do not show as much information at a time as do tables.

2. Graphs do not show as much information at a time as do tables.

3. Charts require more skill, more time, and more expense to prepare
than tables.

4. Graphs cannot be quoted in the same way as tabulated data.

5. Graphs can be made only after the data have been tabulated.

Types of graphs or charts. Graphs may be classified into the following types:

1. Bar Graphs

a. Single vertical bar graph
b. Single horizontal bar graph
c. Grouped or multiple or composite bar graph
d. Duo-directional or bilateral bar graph
e. subdivided or component bar graph
f. Histogram

2. Linear Graphs

a. Time series or chronological line chart
b. Composite line chart
c. Frequency polygon
d. Ogive
e. band chart

3. Hundred per cent graphs or charts

a. Subdivided bar or rectangular bar graph
b. Circle or pie graph

4. Pictograms

5. Statistical maps

6. Ratio charts

Construction of individual graphs. Stated herein are the principles to be followed in
the construction of individual graphs.

1. The bar graph. The bar graph is often used for the graphic
presentation of data. It is generally used to make comparison of
simple magnitudes very much more clearly and more distinctly
perceptible to the eye. Each bar is drawn to a height or length equal to
the magnitude it represents as indicated in the scale (Y-axis). The bars
are separated from each other by a space equal to one-half the width
of a bar. However, there are no fixed rules that govern the

construction of graphs and the maker may only be guided by
aesthetic, proportional, and symmetrical considerations and for
convenience.

Comparison in bar graphs is linear. It is the length of each bar that determines the
size of a magnitude it represents and the relative position of that magnitude in a series of
like and related magnitudes.

a. The single vertical graph. In the single vertical graph, the bars are
constructed vertically and they portray the magnitudes of the
categories into which data have been classified. See figure 3 as an
example of bar graph. Vertical bars are usually used to depict time
series data.

b. Single horizontal bar graph. In this graph, the bars are constructed
horizontally and are used to compare magnitudes of the different
categories into which the data are classified. The horizontal bar graph
is usually used to compare magnitudes of categories.

Construction of graphs. In constructing graphs, two straight lines are drawn
perpendicular to each other, intersecting at a point called the point of origin and marked 0
(zero).

The horizontal line is called baseline, coordinate, or X-axis. It represents the
variables involved or the classes’ categories of the variable involved.

The vertical line is called ordinate or Y-axis. It represents the quantities of the
variables involved or the classes or categories of a variable involved. The Y-axis is divided
into unit distances with each unit distance represents 4,2 unit distances represent 8,3 unit
distances represents 12, etc. This is called the scale.

The distance measured to any point parallel to the X-axis from the Y-axis is called
the abscissa of the point and the distance of that point parallel to the Y-axis from the X-axis
is the ordinate of the point. The abscissa and the ordinate of a point are called the
coordinates of the point.

Plotting the graph means locating the meeting point of the abscissa and the ordinate.

Essentials of a graph. The essential parts of a graph are the following:

1. Number. Charts or graphs are also numbered for reference purposes.
The general is to write the number as Figure 1, Figure 2, Figure 3, etc.
at the bottom of the graph.

2. Title. The same price principles hold in graphs as in tables. The title is
usually written above the graph.

3. Scale. The scale indicates the length or height unit that represents a
certain amount of the variable which is the subject of the graph. The
scale enables the reader to interpret the significance of a number of
length or height units. Thus, if a length or height unit is equal to 2,
two lengths or height units’ equal 4, 3 length or height units equal to
6, etc. The Y-axis represents the scale.

4. Classification and arrangement. The principles of classification and
arrangement are the same in graphs as in tables.

5. Classes, categories, or time series are indicated at the X-axis and the
scale units are indicated at the Y-axis.

6. Symmetry of the graph. The whole chart or graph should be about
square; otherwise the length should be a little greater than the height.
The chart should be placed on the page in such a way that the margins
at the left and at the right should be about the same, or the margin at
the left is a little wider.

7. Footnote. The footnote, if there is any, should be placed immediately
below the graph aligned with the left side of the graph.

8. Source. The source of data, if there is any, should be written just
below the footnote, if there is any, but it should be above the graph
number.

An example of a vertical bar graph is figure 3, the data of which are taken from the
following table, Table 2.

Table 2
Enrollment of Pagasa High School
1985-1986 to 1989-1990
(By Curricular Year)

School Years
Curricular 1985-1986 1986-1987 1987-1988 1988-1989 1989-1990 Total
Years F % F % F % F % F % F %
I 85 36 144 46 173 41 192 38 221 34 815 38
II 57 24 77 24 132 32 148 29 179 28 593 28
III 53 23 49 16 69 16 114 22 138 22 423 20
IV 40 17 45 14 46 11 56 11 102 16 289 14
Total 235 100 315 100 420 100 510 100 640 100 2120 100

Source: Principal’s Office

Enrollment of Pagasa High School
1985-1986 to 1989-1990

Number of
Students

700

600

500

400

300

200

100

0

1985-1986 1986-1987 1987-1988 1988-1989 1989-1990

Figure 3
Example of a horizontal bar graph is Figure 4.

Enrolment of Pagasa High School
1989-1990

Curricular
Year
0 25 50 75 100 125 150 175 200 225

IV

III

II

I

Figure 4
c. Grouped (Multiple or Composite) Bar graph. The grouped bar graph is used in
comparing two or more categories of a variable during a specified period or over successive
periods of time when the subgroups of the categories have common attributes. Figure 5
shows the comparison of the enrolments over five successive years of the curricular years of
the students of Pagasa High School, Table 2.

1985-1986 to 1989-1990

NumberoofoStudents

250

200

150 First year
Second year
Third year
100
Fourth year

50

0
1985-'86 1986-'87 1987-'88 1988-'89 1989-'90

Students

Figure 5

d. Duo-directional or bilateral bar graph. This graph is used to present data in
the form of assets, profits, and positive numbers, liabilities, losses and
negative numbers. If the baseline is vertical, the bars at the left of the
baseline represents liabilities, losses or negative numbers and those at the
right side represent assets, profits, or positive numbers. If the baseline is
horizontal, the bars above it represent assets, profits, or positive number and
those below represents liabilities, losses, or negative numbers. An example of
a bilateral graph is Figure 6 which is derived from Table 3 just below.

Table 3
Financial Operations of Pagasa High School
1985-1986 to 1988-1989
(In Thousands of Pesos)

Results of School Years
Operations 1985-1986 1986-1987 1987-1988 1988-1989 Total

Earnings 310 450 470 600 1830

Expenses 250 390 510 510 1660

Profits 60 60 90 210

Loss 40 40

Source: Treasurer’s Report

Profits and Loss of Pagasa High School
1985-1986 to 1988-1989

Thousands
Of Pesos

90

60

30

0

-
30

-
60

-
90

1985-1986 1986-1987 1987-1988 1988-1989


Figure 6

e. Subdivided (or Component) bar graph. Subdivided bar graphs are used to
show the variations or changes of the component parts of a whole and the whole itself.
Cross-comparison of the proportionate distribution of the different parts can be made easily.
Figure 7 is an example of a subdivided bar graph showing the earnings, expenses, and
profits and loss of the Pagasa High School for a number of years.

Financial Operations of Pagasa High School
1985-1986 to 1988-1989

Thousands
Of Pesos

700
600
500 Earnings
400 Expenses
300 Profit
200 Loss

100
0
1985-1986 1986-1987 1987-1988 1988-1989


Figure 7

f. Histogram. A histogram is composed of bars placed side by side whose
heights indicate the magnitudes of their respective classes or categories. It is
used with grouped or class frequency distributions. Figure 8 is an example.
The heights of the bar indicate the number of students in certain age groups.
Data are taken from Table 4.

Table 4
Age Distribution of Pagasa High School Students
School Year 1989-1990

Cumulative Cumulative
Age Groups Frequency Frequency Frequency
Upward Downward
20-21 53 640 53
18-19 162 587 215
16-17 211 425 426
14-15 150 214 576
12-13 64 64 640
________
N = 640


Age Distribution of Pagasa High School Students
School Year 1989-1990

Number of
Students

250

200

150

100

50

0
12-13 14-15 16-17 18-19 20-21
Age in Years


Figure 8

2. Linear graphs. Linear graphs are good devices to show variations of values
over successive periods of time. Changes in the data are indicated by the linear curves.

Advantages of linear graphs or charts. The advantages of the linear graph or chart
are the following: (Bacani, et al., p. 67)

a. The curve shows data as continuous line; hence, it is continuous in its effect.

b. The wandering line of the curve tells the whole story. At a glance one can
see just what the situation is and what is likely to happen.

c. Its preparation requires less time and skill.

Construction. Linear graphs are constructed in much the same way as many other
graphs are. A slight difference lies in the process of locating the intersections of the abscissa
representing a class or category of a variable and the ordinate representing the magnitudes
of the classes or categories of the variable. The intersections of the abscissa and the
ordinate are marked by bold dots and then joined successively by either straight lines or
curved lines to show the variations of a variable or the variable in relation to that of
another.

a. Time series linear charts. (single line) Time series linear single line charts
depict the variations of a variable over a period of time. Generally, the abscissa represents
the periods of time and the Y-axis represents quantitative values of the variable. The
intersections of the X-axis representing time and the Y-axis representing magnitude are
located and marked and then joined successively by straight or curved lines. The resulting
line, a broken straight line or a curved line, shows the variations of the variable. An
example of this chart is Figure 9 which shows the enrolment of Pagasa High School for five
school years. See table 2 for exact data.

1985-1986 to 1989-1990

600

500

400

300

200

100

0
1985-1986 1986-1987 1987-1988 1988-1989 1989-1990


Figure 9

b. Time series composite or multilinear charts. These charts are used when
comparisons are made between or among categories of the same variables or variations of
two or more variables over periods of time. Figure 10 is an example comparing the
enrolments of the curricular years over a period of five years in the Pagasa High School.
Exact data are found in Table 2.

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