- 1. 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
- 2. 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
- 3. 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.
- 4. 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.
- 5. 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
- 6. 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.
- 7. 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)
- 8. 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.
- 9. 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;
- 10. 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.
- 11. 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.
- 12. 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.
- 13. 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
- 14. 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
- 15. 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
- 16. 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.
- 17. 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
- 18. 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.
- 19. 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.
- 20. 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.
- 21. 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 “ “ “ “ “ “
- 22. “ “ “ “ “ “ “ “ “ “ “ “ “ “ “ “ “ “ “ “ “ “ “ “ “ “ “ “ “ “ 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
- 23. 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.
- 24. 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.
- 25. 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
- 26. 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.
- 27. 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
- 28. 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.
- 29. 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
- 30. 700 600 500 400 300 200 100 0 1985-1986 1986-1987 1987-1988 1988-1989 1989-1990 Source: Principal’s Office Figure 3 Example of a horizontal bar graph is Figure 4. Enrolment of Pagasa High School 1989-1990 (By Curricular Year) Curricular Year 0 25 50 75 100 125 150 175 200 225 IV III II I Source: Principal’s Office 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. Enrolment of Pagasa High School 1985-1986 to 1989-1990 (By Curricular Year)
- 31. 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 Source: Principal’s Office 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
- 32. 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 Source: Treasurer’s Report 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.
- 33. 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 Source: Treasurer’s Report 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 Source: Principal’s Office
- 34. 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 Source: Principal’s Office 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.
- 35. Enrolment of Pagasa High School 1985-1986 to 1989-1990 600 500 400 300 200 100 0 1985-1986 1986-1987 1987-1988 1988-1989 1989-1990 Source: Principal’s Office 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.