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RESEARCH METHODOLOGY & STATISTICAL TOOLSMASTER OF BUSINESS ADMINISTRATION(JNTU)A MATERIAL FORRESEARCHMETHODOLOGYANDSTATIST...
RESEARCH METHODOLOGY & STATISTICAL TOOLSUNIT-1RESEARCH METHODOLOGY:An IntroductionMeaning of Research:Research in common p...
RESEARCH METHODOLOGY & STATISTICAL TOOLS2. To portray accurately the characteristics of a particular individual, situation...
RESEARCH METHODOLOGY & STATISTICAL TOOLSmethod is that the researcher has no control over the variables; he can onlyreport...
RESEARCH METHODOLOGY & STATISTICAL TOOLSan important type of qualitative research. This type of research aims atdiscoverin...
RESEARCH METHODOLOGY & STATISTICAL TOOLS“All progress is born of inquiry. Doubt is often better than over-confidence, for ...
RESEARCH METHODOLOGY & STATISTICAL TOOLSIn addition to what has been stated above, the significance of research can also b...
RESEARCH METHODOLOGY & STATISTICAL TOOLSbetween variables. At the very outset the researcher must single out the problem h...
RESEARCH METHODOLOGY & STATISTICAL TOOLSundertake extensive literature survey connected with the problem. For this purpose...
RESEARCH METHODOLOGY & STATISTICAL TOOLSoccasionally we may encounter a problem where we do not need working hypothesis,es...
RESEARCH METHODOLOGY & STATISTICAL TOOLS5) Determining sample design: All the items under consideration in any field ofinq...
RESEARCH METHODOLOGY & STATISTICAL TOOLSFor example, if we have to select a sample of 300 items from a universe of15,000 i...
RESEARCH METHODOLOGY & STATISTICAL TOOLSto mathematical decisions on the basis of information yielded as surveyprogresses....
RESEARCH METHODOLOGY & STATISTICAL TOOLSto tackle this problem. One method of dealing with the non-response problem is tom...
RESEARCH METHODOLOGY & STATISTICAL TOOLSThe process of interpretation may quite often trigger off new questions which in t...
RESEARCH METHODOLOGY & STATISTICAL TOOLS4. Calculated ‘confidence limits’ must be mentioned and the various constraintsexp...
RESEARCH METHODOLOGY & STATISTICAL TOOLSExternal data: When data is collected from outside the organization, then this isc...
RESEARCH METHODOLOGY & STATISTICAL TOOLS(i) Questionnaires sent to post: in this case, the questionnaire is sent to a pers...
RESEARCH METHODOLOGY & STATISTICAL TOOLS1. Geographical classification: Here data are classified on the basic ofgeographic...
RESEARCH METHODOLOGY & STATISTICAL TOOLSDrafting of a good questionnaire is a highly specialized job and requires greatcar...
RESEARCH METHODOLOGY & STATISTICAL TOOLSthey tax the respondents’ memory. Further, questions involving mathematicalcalcula...
RESEARCH METHODOLOGY & STATISTICAL TOOLS How do you go to your place of duty?By bus [ ] By three wheeler scooter [ ]By yo...
RESEARCH METHODOLOGY & STATISTICAL TOOLS10) Pre-testing the questionnaire: From practical of view it is desirable to try o...
RESEARCH METHODOLOGY & STATISTICAL TOOLSWe give below the 1971 Census – Individual Slip which was used for a generalpurpos...
RESEARCH METHODOLOGY & STATISTICAL TOOLS14. Mother Tongue…………………………………………..15. Other Languages, if any……………………………………………………...
RESEARCH METHODOLOGY & STATISTICAL TOOLScentral – for certain projects and investigations where high degree of response is...
RESEARCH METHODOLOGY & STATISTICAL TOOLSrecorded by different enumerators. An attempt should be made to minimizethis varia...
RESEARCH METHODOLOGY & STATISTICAL TOOLSresearcher will have to decide one or more of such units that he has to selectfor ...
RESEARCH METHODOLOGY & STATISTICAL TOOLSCHARACTERISTICS OF GOOD SAMPLE DESIGN:From what has been stated above, we can list...
RESEARCH METHODOLOGY & STATISTICAL TOOLS4) Indeterminacy principle: Sometimes we find that individuals act different when ...
RESEARCH METHODOLOGY & STATISTICAL TOOLSchoose the particular units of the universe for consulting a sample on the basis t...
RESEARCH METHODOLOGY & STATISTICAL TOOLSfrequently in which procedure the element for the sample is returned to the popula...
RESEARCH METHODOLOGY & STATISTICAL TOOLSbetter estimate of the whole. In brief, stratified sampling results in more reliab...
RESEARCH METHODOLOGY & STATISTICAL TOOLSdistricts. This would represent a two-stage sampling design with the ultimate samp...
RESEARCH METHODOLOGY & STATISTICAL TOOLSmultiple sampling. But when the number of samples is more than two but it is neith...
RESEARCH METHODOLOGY & STATISTICAL TOOLSare meant and requires great amount of expertise, skill, and intelligence. Aninapp...
RESEARCH METHODOLOGY & STATISTICAL TOOLSa) Line Diagram: This is the simplest of all the diagrams. It consists in drawingv...
RESEARCH METHODOLOGY & STATISTICAL TOOLS01020304050607080901st Qtr 2nd Qtr 3rd Qtr 4th QtrEastWestNorth2) Two-Dimensional ...
RESEARCH METHODOLOGY & STATISTICAL TOOLSof such diagrams are “cubes, spheres, cylinders, blocks etc”. These diagrams aresp...
RESEARCH METHODOLOGY & STATISTICAL TOOLSanalysis, viz., to study slopes, rates of change and for forecasting wherever poss...
RESEARCH METHODOLOGY & STATISTICAL TOOLS5. False Base Line6. Ratio or Logarithmic Scale7. Line designs8. Source Note and N...
RESEARCH METHODOLOGY & STATISTICAL TOOLSB) FREQUENCY POLYGON: Frequency polygon is other device of graphicpresentation of ...
RESEARCH METHODOLOGY & STATISTICAL TOOLS(i) Less than Ogive: This consists in plotting the ‘less than’ cumulativefrequenci...
RESEARCH METHODOLOGY & STATISTICAL TOOLSmaximum information contained in the data in the minimum possible space, withoutsa...
RESEARCH METHODOLOGY & STATISTICAL TOOLSStubHeadingTotalColumnHeadColumnHeadColumnHeadColumnHeadColumnHeadBodyTotalFoot No...
RESEARCH METHODOLOGY & STATISTICAL TOOLSSPSS (STATISTICAL PACKAGE FOR THE SOCIAL SCIENCES)SPSS (Statistical Package for th...
RESEARCH METHODOLOGY & STATISTICAL TOOLS1970) has been described as Sociologys most influential book. In addition tostatis...
22538598 introduction-to-research-methodology-acccording-to-jntu-hyd-mba-syllabus
22538598 introduction-to-research-methodology-acccording-to-jntu-hyd-mba-syllabus
22538598 introduction-to-research-methodology-acccording-to-jntu-hyd-mba-syllabus
22538598 introduction-to-research-methodology-acccording-to-jntu-hyd-mba-syllabus
22538598 introduction-to-research-methodology-acccording-to-jntu-hyd-mba-syllabus
22538598 introduction-to-research-methodology-acccording-to-jntu-hyd-mba-syllabus
22538598 introduction-to-research-methodology-acccording-to-jntu-hyd-mba-syllabus
22538598 introduction-to-research-methodology-acccording-to-jntu-hyd-mba-syllabus
22538598 introduction-to-research-methodology-acccording-to-jntu-hyd-mba-syllabus
22538598 introduction-to-research-methodology-acccording-to-jntu-hyd-mba-syllabus
22538598 introduction-to-research-methodology-acccording-to-jntu-hyd-mba-syllabus
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22538598 introduction-to-research-methodology-acccording-to-jntu-hyd-mba-syllabus

  1. 1. RESEARCH METHODOLOGY & STATISTICAL TOOLSMASTER OF BUSINESS ADMINISTRATION(JNTU)A MATERIAL FORRESEARCHMETHODOLOGYANDSTATISTICAL TOOLS(According to JNTU Syllabus)Prepared by,S. Venkata Siva Kumar;MBA (HR/MRKTG), MSc (Statistics).1
  2. 2. RESEARCH METHODOLOGY & STATISTICAL TOOLSUNIT-1RESEARCH METHODOLOGY:An IntroductionMeaning of Research:Research in common parlance refers to a search for knowledge. Once can alsodefine research as a scientific and systematic search for pertinent information on aspecific topic. In fact, research is an art of scientific investigation. The advancedLearner’s Dictionary of current English lays down the meaning of research as “acareful investigation or inquiry especially through search for new facts in any branchof knowledge.” Redman and Mory define research as a “systematized effort to gainnew knowledge.” Some people consider research as a movement, a movement fromthe known to unknown. It is actually a voyage of discovery.Research is an academic activity and as such the term should be used in atechnical sense. According to “Clifford Woody, Research comprises defining andredefining problems, formulating hypothesis or suggested solutions; collecting,organizing and evaluating data; making deductions and reaching conclusions; and atlast carefully testing the conclusions to determine whether they fit the formulatinghypothesis. D. Slesinger and M. Stephenson in the encyclopedia of Social Sciencesdefine Research as “the manipulation of things, concepts or symbols for the purpose ofgeneralizing to extend, correct or verify knowledge, whether that knowledge aids inconstruction of theory or in the practice of an art.”Objectives of Research:The purpose of Research is to discover answers to questions through theapplication of scientific procedures. The main aim of research is to find out the truthwhich is hidden and which has not been discovered as yet. Though each research studyhas its own specific purpose, we may think of research objectives as falling into anumber of following broad groupings:1. To gain familiarity with a phenomenon or to achieve new insights into it(studies with this object in view are termed as exploratory or formulativeresearch studies);2
  3. 3. RESEARCH METHODOLOGY & STATISTICAL TOOLS2. To portray accurately the characteristics of a particular individual, situation ora group (studies with this object in view are known as descriptive researchstudies);3. To determine the frequency with which something occurs or with which it isassociated with something else (studies with this object in view are known asdiagnostic research studies);4. To test a hypothesis of a casual relationship between variables (such studies areknown as hypothesis-testing research studies).Motivation in Research:What makes people to undertake research? This is a question of fundamentalimportance. The possible motives for doing research may be either one or more of thefollowing:1. Desire to get a research degree along with its consequential benefits;2. Desire to face the challenge in solving the unsolved problems, i.e., concernover practical problems initiates research;3. Desire to get intellectual joy of doing some creative work;4. Desire to be of service to society.5. Desire to get Respectability.However, this is not an exhaustive list of factors motivating people toundertake research studies. Many more factors such as directives ofgovernment, employment conditions, curiosity about new things, desire tounderstand casual relationships, social thinking and awakening and the likemay as well motivate (or at times compel) people to perform researchoperations.Types of Research:The basic types of research are as follows:1. Descriptive Vs. Analytical Research: Descriptive research includes surveysand fact-finding enquiries of different kinds. The major purpose of descriptiveresearch is description of the state of affairs as it exists at present. In socialscience and business research we quite often use the term Ex post factoresearch for descriptive research studies. The main characteristic of this3
  4. 4. RESEARCH METHODOLOGY & STATISTICAL TOOLSmethod is that the researcher has no control over the variables; he can onlyreport what has happened or what is happening. Most ex post facto researchprojects used for descriptive studies in which the researcher seeks to measuresuch items as, for example, frequency of shopping, preferences of people, orsimilar data. Ex post facto studies also include attempts by researchers todiscover causes even when they cannot control the variables. The methods ofresearch utilized in descriptive research are survey methods of all kinds,including comparative and co-relational methods. In analytical research, onthe other hand, the researcher has to use facts or information already available,and analyze these to make a critical evaluation of the material.2. Applied Vs Fundamental Research: Research can either be applied (or action)research or fundamental (to basic or pure) research. Applied research aims atfinding a solution for an immediate problem facing a society or anindustrial/business organization, whereas fundamental research is mainlyconcerned with generalizations and with the formulation of a theory.“Gathering knowledge for knowledge’s sake is termed as ‘pure’ or ‘basic’research.” Research concerning some natural phenomenon or relating to puremathematics are examples of fundamental research. Similarly, research studies,concerning human behavior carried on with a view to make generalizationsabout human behavior, are also examples of fundamental research, but researchaimed at certain conclusion (say, a solution) facing a concrete social orbusiness problem is an example of applied research. Research to identifysocial, economic or political trends that may affect a particular institution orthe copy research or the marketing research or evaluation research areexamples of applied research. Thus, the central aim of applied research is todiscover a solution for some pressing practical problem, whereas basic researchis directed towards finding information that has a broad base of applicationsand thus, adds to the already existing organized body of scientific knowledge.3. Quantitative Vs Qualitative Research: Quantitative research is based on themeasurement of quantity or amount. It is applicable to phenomena that can beexpressed in terms of quantity. Qualitative research, on the other hand, isconcerned with qualitative phenomenon i.e., phenomena relating to orinvolving quality or kind. For instance, when we are interested in investigatingthe reasons for human behavior, we quite often talk of ‘Motivation Research’,4
  5. 5. RESEARCH METHODOLOGY & STATISTICAL TOOLSan important type of qualitative research. This type of research aims atdiscovering the underlying motives and desires, using in depth interviews forthe purpose. Other techniques of such research are word association tests,sentence completion tests, story completion tests and similar other projectivetechniques. Attitude or opinion research i.e., research designed to find out howpeople feel or what they think about a particular subject or institution is alsoqualitative research. Qualitative research is especially important in thebehavioral sciences where the aim is to discover the underlying motives ofhuman behavior. Through such research we can analyze the various factorswhich motivate people to behave in a particular manner or which make peoplelike or dislike a particular thing. It may be stated, that to apply qualitativeresearch in practice is relatively a difficult job and therefore, while doing suchresearch, one should seek guidance from experimental psychologists.4. Conceptual Vs Empirical Research: Conceptual research is that related tosome abstract idea(s) or theory. It is generally used by philosophers andthinkers to develop new concepts or to reinterpret existing ones. On the otherhand, empirical research relies on experience or observation alone, oftenwithout due regard for system and theory. It is data-based research, coming upwith conclusions which are capable of being verified by observation orexperiment. We can also call it as experimental type of research. In such aresearch it is necessary to get at facts first hand, at their source, and actively togo about doing certain things to stimulate the production of desiredinformation. In such a research, the researcher must first provide himself with aworking hypothesis or guess as to the probable results. He then works to getenough facts (data) to prove or disprove his hypothesis. He then sets upexperimental designs which he thinks will manipulate the persons or thematerials concerned so far to bring forth the desired information. Such researchis thus characterized by the experimenter’s control over the variables understudy and his deliberate manipulation of one of them to study its effects.Empirical research is appropriate when proof is sought that certain variablesaffect other variables in some way. Evidence gathered through experiments orempirical studies is today considered studies are today considered to be themost powerful support possible for a given hypothesis.Nature and Importance of Research:5
  6. 6. RESEARCH METHODOLOGY & STATISTICAL TOOLS“All progress is born of inquiry. Doubt is often better than over-confidence, for it leadsto inquiry, and inquiry leads to invention” is famous Hudson Maxim in context ofwhich the significance of research can well be understood. Increased amounts ofresearch make progress possible. Research inculcates scientific and inductive thinkingand it promotes the development of logical habits of thinking and organization.The role of research in several fields of applied economics, whether related tobusiness or to the economy as a whole, has greatly increased in modern times. Theincreasingly complex nature business and government has focused attention on the useof research in solving operational problems. Research, as an aid to economic policy,has gained added importance, both for government ad business.Research provides the basis for nearly all government policies in oureconomic system. For instance, government’s budgets rests in part on an analysis ofthe needs and desires of the people and on the availability of revenues to meet theseneeds. The cost of needs has to be equated to probable revenues and this is a fieldwhere research is most needed. Through research we van devise alternative policiesand can as well examine the consequences of each of these alternatives. Decision-making may not be a part of research, but research certainly facilitates the decisions ofthe policy maker. Government has also to chalk out programmes for dealing with allfacets of the country’s existence and most of these will be related directly or indirectlyto economic conditions. The plight of cultivators, the problems of big and smallbusiness and industry, working conditions, trade union activities, the problems ofdistribution, even the size and nature of defense services are matters requiringresearch. Thus, research is considered necessary with regard to the allocation ofnation’s resources.Research has its special significance in solving various operational andplanning problems of business and industry. Operations research and market research,along with motivational research, are considered crucial and their results assist, inmore than one way, in taking business decisions. Market research is the investigationof the structure and development of a market of the purpose of formulating efficientpolicies for purchasing, production and sales. Operations research refers to theapplication of mathematical, logical and analytical techniques to the solution ofbusiness problems of cost minimization or of profit maximization or what can betermed as optimization problems. Motivational research of determining why peoplebehave as they do is mainly concerned with market characteristics.6
  7. 7. RESEARCH METHODOLOGY & STATISTICAL TOOLSIn addition to what has been stated above, the significance of research can also beunderstood keeping in view the following points:1. To those students who are to write a master’s or Ph.D.thesis, research maymean a careerism or a way to attain a high position in the social structure;2. To professionals in research methodology, research may mean a source oflivelihood.3. To philosophers and thinkers, research may mean the outlet for new ideas andinsights;4. To analysts and intellectuals, research may mean the generalizations of newtheories.Thus, research is the fountain of knowledge for the sake of knowledge and animportant source of providing guidelines for solving different business, governmentaland social problems. It is a sort of formal training which enables one to understand thenew developments in one’s field in a battery way.RESEARCH PROCESS:The Research Process consists of series of actions or steps necessary toeffectively carry out research and the desired sequencing of these steps. The followingorder concerning various steps provides a useful procedural guideline regarding theresearch process:1. Formulating the Research problem2. Extensive Literature survey3. Development of working hypothesis4. Preparing the Research design5. Determining the Sample design6. Collection of data7. Execution of the project8. Analysis of data9. Hypothesis-testing10. Generalizations and interpretation11. Preparation of the report or the thesis1) Formulating the research problem: There are two types of research problems,viz., those which relates to states of nature and those which relate to relationships7
  8. 8. RESEARCH METHODOLOGY & STATISTICAL TOOLSbetween variables. At the very outset the researcher must single out the problem hewants to study i.e., he must decide the general area of interest or aspect of a subjectmatter that he would like to inquire into. Initially the problem may be stated in a broadgeneral way and then the ambiguities, if any, relating to the problem be resolved.Then, the feasibility of a particular solution has to be considered before a workingformulation of the problem can be set up. The formulation of a general topic into aspecific research problem, thus, constitutes the first step in a scientific enquiry.Essentially two steps are involved in formulating the research problem, viz.,understanding the problem thoroughly, and rephrasing the same into meaningful termsfrom an analytical point of view.The best way of understanding the problem is to discuss it with one’sown colleagues or with those having some expertise in the matter. In an academicinstitution the researcher can seek the help from a guide who is usually anexperimented man and has several research problems in mind. Often, the guide putsforth the problem in general terms and it is up to the researcher to narrow it down andphrase the problem in operational terms. In private business units or in governmentalorganizations, the problem is usually earmarked by the administrative agencies withwhich the researcher can discuss as to how the problem originally came about andwhat considerations are involved in its possible solutions.Professor W.A. Neiswanger correctly states that the statement of theobjective is of basic importance because it determines the data which are to becollected, the characteristics of the data which are relevant, relations which are to beexplored, the choice of techniques to be used in these explorations and the form of thefinal report. If there are certain pertinent terms, the same should be clearly definedalong with the task of formulating the problem. In fact, formulation of the problemoften follows a sequential pattern where a number of formulations are set up, eachformulation more specific than the preceding one, each one phrased in more analyticalterms, and each more realistic in terms of the available data and resources.2) Extensive literature survey: Once the problem is formulated, a brief summaryof it should be written down. It is compulsory for a research worker writing a thesis fora Ph.D. degree to write a synopsis of the topic and submit it to the necessaryCommittee or the Research Board for approval. At this juncture the researcher should8
  9. 9. RESEARCH METHODOLOGY & STATISTICAL TOOLSundertake extensive literature survey connected with the problem. For this purpose, theabstracting and indexing journals and published or unpublished bibliographies are thefirst place to go to. Academic journals, conference proceedings, government reports,books etc., must be tapped depending on the nature of the problem. In this process, itshould be remembered that one source will lead to another. The earlier studies, if any,which are similar to the study in hand, should be carefully studied. A good library willbe a great help to the researcher at this stage.3) Development of working hypothesis: After extensive literature survey,researcher state in clear terms the working hypothesis or hypotheses. Workinghypothesis is tentative assumption made in order to draw out and test its logical orempirical consequences. As such the manner in which research hypotheses aredeveloped is particularly important since they provide the focal point for research.They also affect the manner in which tests must be conducted in the analysis of dataand indirectly the quality of data which is required for the analysis. In most types ofresearch, the development of working hypothesis plays an important role. Hypothesisshould be very specific and limited to the piece of research in hand because it has to betested. The role of the hypothesis is to guide the researcher by delimiting the area ofresearch and to keep him on the right track. It sharpens his thinking and focusesattention on the more important facets of the problem. It also indicates the type of datarequired and the type of methods of data analysis to be used.How does one go about developing working hypothesis? The answer is byusing the following approach:a) Discussions with colleagues and experts about the problem, its origin and theobjectives in seeking a solution;b) Examination of data and records, if available, concerning the problem forpossible trends, peculiarities and other clues;c) Review of similar studies in the area or of the studies on similar problems; andd) Exploratory personal investigation which involves original field interviews ona limited scale with interested parties and individuals with a view to securegreater insight into the practical aspects of the problem.Thus, working hypothesis arise as a result of a priori thinking about the subject,examination of the available data and material including related studies and thecounsel of experts and interested parties. Working hypothesis is more useful whenstated in precise and clearly defined terms. It may as well be remembered that9
  10. 10. RESEARCH METHODOLOGY & STATISTICAL TOOLSoccasionally we may encounter a problem where we do not need working hypothesis,especially in the case of exploratory or formulative researches which do not aim attesting the hypothesis. But as a general rule, specification of working hypothesis inanother basic step of the research process in most research problems.4) Preparing the research design: The research problem having been formulatedin clear cut terms, the researcher will be required to prepare a research design, i.e., hewill have to state the conceptual structure within which research would be conducted.The preparation of such a design facilitates research to be as efficient as possibleyielding maximal information. In other words, the function of research design is toprovide for the collection of relevant evidence with minimal expenditure of effort,time and money. But how all these can be achieved depends mainly on the researchpurpose. Research purposes may be grouped into four categories, viz.,a. Explorationb. Descriptionc. Diagnosisd. ExperimentationA flexible research design which provides opportunity for considering manydifferent aspects of a problem is considered appropriate if the purpose of the researchstudy is that of exploration. But when the purpose happens to be an accuratedescription of a situation or of an association between variables, the suitable designwill be one that minimizes bias and maximizes the reliability of the data collected andanalyzed. There are several research designs, such as, an experimental and non-experimental hypothesis testing. Experimental designs can be either informal design(such as completely randomized design, randomized block design, Latin squaredesign, simple and complex factorial designs), out of which the researcher must selectone for his own project.The preparation of the research design, appropriate for a particular researchproblem, involves usually the consideration of the following:I. The means of obtaining the information;II. The availability and skills of the researcher and his staff (if any);III. Explanation of the way in which selected means of obtaining information willbe organized and the reasoning leading to the selection;IV. The time available for research; andV. The cost factor relating to research, i.e., the finance available for the purpose.10
  11. 11. RESEARCH METHODOLOGY & STATISTICAL TOOLS5) Determining sample design: All the items under consideration in any field ofinquiry constitute a ‘universe’ or ‘population’. A complete enumeration of all items inthe ‘population’ is known as a census enquiry. It can be presumed that in such anenquiry when all the items are covered no element of chance is left and highestaccuracy is obtained. But in practice this may not be true. Even the slightest element ofbias in such an enquiry will get larger and larger as the number of observationsincreases. Moreover, there is no way of checking the element if bias or its extentexcept through a resurvey or use of sample checks. Besides, this type of inquiryinvolves a great deal of time, money and energy. Not only this, census enquiry is notpossible in practice under many circumstances. For instance, blood testing is doneonly on sample basis. Hence, quite often we select only a few items from the universefor our study purposes. The items so selected continue what is technically called asample.The researcher must decide the way of selecting a sample or what is popularlyknown as the sample design. In other words a sample design is a definite plandetermined before any data are actually collected for obtaining a sample from a givenpopulation. Thus, the plan to select 12 of a city’s 200 drugstores in a certain wayconstitutes a sample design. Samples can be either probability samples or non-probability samples. With probability samples each element has a known probabilityof being included in the sample but the non-probability samples do not allow theresearcher to determine this probability. Probability samples are those based on simplerandom sampling, systematic sampling, stratified sampling, cluster/area samplingwhereas non-probability samples are those based on convenience sampling, judgmentsampling and quota sampling techniques. A brief mention of the important sampledesigns is as follows.1. Deliberate sampling: Deliberate sampling is also known as purposive or non-probability sampling. This sampling method involves purposive or deliberateselection of particular units of the universe for constituting a sample whichrepresents the universe. When population elements are selected for inclusion inthe sample based on the ease of access, it can be called convenience sampling.2. Simple random sampling: This type of sampling is also known as chancesampling or probability sampling where each and every item in the populationhas an equal chance of inclusion in the sample and each one of the possiblesamples, in case of finite universe, has the same probability of being selected.11
  12. 12. RESEARCH METHODOLOGY & STATISTICAL TOOLSFor example, if we have to select a sample of 300 items from a universe of15,000 items, then we can put the names or numbers of all the 15,000 items onslips of paper and conduct a lottery.3. Systematic sampling: In some instances the most practical way of sampling isto select every 15thname on a list, every 10thhouse on one side of a street andso on. Sampling of this type is known as systematic sampling.4. Stratified sampling: if the population from which a sample is to be drawn doesnot constitute a homogeneous group, then stratified sampling technique isapplied so as to obtain a representative sample. In this technique, thepopulation as stratified into a number of non-overlapping subpopulations orstrata and sample items are selected from each stratum. If the items selectedfrom each stratum is based on simple random sampling the entire procedure,first stratification and then simple random sampling, is known as stratifiedrandom sampling.5. Quota sampling: In stratified sampling the cost of taking random samplesfrom individual strata is often so expensive that interviewers are simply givenquota to be filled from different strata, the actual selection of items for samplebeing left to the interviewer’s judgment. This is called quota sampling.6. Cluster sampling and Area sampling: cluster sampling involves grouping thepopulation and then selecting the groups or the clusters rather than individualelements for inclusion in the sample. Suppose some departmental store wishesto sample its credit card holders. It has issued its cards to 15,000 customers.The sample size is to be kept say 450. For cluster sample this list of 15,000card holders could be formed into 100 clusters of 150 card holders each. Threeclusters might then be selected for the sample randomly.7. Multi-stage sampling: This is a further development of the idea of clustersampling. This technique is mean for big enquiries extending to a considerablylarge geographical area like an entry country. Under multi-stage sampling thefirst stage may be to select large primary sampling units such as states, thendistricts, then towns and finally certain families within towns. If the techniqueof random sampling is applied at all stages, the sampling procedure isdescribed as multi-stage random sampling.8. Sequential sampling: This is some what a complex sample design where theultimate size of the sample is not fixed in advance but is determined according12
  13. 13. RESEARCH METHODOLOGY & STATISTICAL TOOLSto mathematical decisions on the basis of information yielded as surveyprogresses. This design is usually adopted under acceptance sampling plan inthe context of statistical quality control.6) Collecting the data: In dealing with any real life problem it is often found thatdata at hand are inadequate, and hence, it becomes necessary to collect data that areappropriate. There are several ways of collecting the appropriate data which differconsiderably in context of money costs, time and other resources at the disposal of theresearcher.Primary data can be collected either through experiment or through survey. Ifthe researcher conducts an experiment, he observes some quantitative measurements,or the data, with the help of which he examines the truth contained in his hypothesis.But in the case of a survey, data can be collected by any one or more of the followingways.1. By observation2. Through personal interview3. Through telephone interviews4. By mailing of questionnaires5. Through schedulers.7) Execution of the project: Execution of the project is a very important step in theresearch process. If the execution of the project proceeds on correct lines, the data tobe collected would be adequate and dependable. The researcher should see that theproject is executed in a systematic manner and in time. If the survey is to be conductedby means of structured questionnaires, data can be readily machine-processed. In sucha situation, questions as well as the possible answers may be coded. If the data are tobe collected through interviewers, arrangements should made for proper selection andtraining of the interviewers. The training may be given with the help of instructionmanuals which explain clearly the job of the interviewer at each step. Occasional fieldchecks should be made to ensure that the interviewers are doing their assigned jobsincerely and efficiently. A careful watch should be kept for unanticipated factors inorder to keep the survey as much realistic as possible. This, in other words, means thatsteps should be taken to ensure that survey is under statistical control so that thecollected information is in accordance with the pre-defined standard of accuracy. Ifsome of the respondents do not cooperate, some suitable methods should be designed13
  14. 14. RESEARCH METHODOLOGY & STATISTICAL TOOLSto tackle this problem. One method of dealing with the non-response problem is tomake a list of the non-respondents and take a small sub sample of them, and then withthe help of experts vigorous efforts can be made for securing response.8) Analysis of data: After the data have been collected, the researcher turns to thetask of analyzing them. The analysis of data requires a number of closely relatedoperations such as establishment of categories, the application of these categories toraw data through coding, tabulation and then drawing statistical inferences. The un-widely data should necessarily be condensed into a few manageable groups and tablesfor further analysis. Thus researcher should classify the raw data into some purposefuland usable categories. Coding operation is usually done at this stage through which thecategories of data are transformed into symbols that nay be tabulated and counted.Editing is the procedure that improves the quality of the data for coding. With codingthe stage is ready for tabulation. Tabulation is a part of the technical procedurewherein the classified data are put in the form of tables. The mechanical devices canbe made use of at this juncture. A great deal of data, especially in large inquiries, istabulated by computers. Computers not only save time but also make it possible tostudy large number of variables affecting a problem simultaneously.9) Hypothesis-testing: after analyzing the data as stated above, the researcher is in aposition to test the hypothesis, if any, he had formulated earlier. Do the facts supportthe hypothesis or they happen to be contrary? This is the usual question which shouldbe answered while testing hypothesis. Various tests, such as Chi-square test, t-test, F-test have been developed by statisticians for the purpose. The hypothesis may be testedthrough the use of one or more of such tests, depending upon the nature and object ofresearch inquiry. Hypothesis-testing will result in either accepting the hypothesis or inrejecting it. If the researcher had no hypothesis to start with, generalizationsestablished on the basis of data may be stated as hypothesis to be tested by subsequentresearches in times to come.10) Generalizations and interpretation: If a hypothesis is tested and upheldseveral times, it man be possible for the researcher to arrive at generalization, i.e., tobuild a theory. As a matter of fact, the real value of research lies in its ability to arriveat certain generalizations. If the researcher had no hypothesis to start with. He mightseek to explain his findings on the basis of some theory. It is knows as interpretation.14
  15. 15. RESEARCH METHODOLOGY & STATISTICAL TOOLSThe process of interpretation may quite often trigger off new questions which in turnlead to further researches.11) Preparation of the report or the thesis: Finally, the researcher has to prepare thereport of what has been done by him. Writing of report must be done with great carekeeping in view the following:1. The layout of report should be as follows:(i) The preliminary pages;(ii) The main text, and (iii) The end matterIn its preliminary pages the report should carry title and data followedacknowledgements and foreword. Then there should be a table of contents followed bya list of tables and list of graphs and charts, if any, given in the report.The main text of the report should have the following parts:(a) Introduction: It should contain a clear statement of the objective of theresearch and explanation of the methodology adopted in accomplishing theresearch. The scope of the study along with various limitations should as wellbe stated in this part.(b) Summary of findings: after introduction there would appear a statement offindings and recommendations in non-technical language. If the findings areextensive, they should be summarized.(c) Main report: the main body of the report should be presented in logicalsequence and broken-down into readily identifiable sections.(d) Conclusion: towards the end of the main text, researcher should again putdown the results of his research clearly and precisely. In fact, it is the finalsumming up.At the end of the report, appendices should be enlisted in respect of alltechnical data. Bibliography, i.e., list of books, journals, reports, etc.,consulted, should also be given in the end. Index should also be given speciallyin a published research report.2. Report should be written in a concise and objective style in simple languageavoiding vague expressions such as ‘it seems’, ‘there may be’, and the like.3. Charts and illustrations in the main report should be used only if they presentthe information more clearly and forcibly.15
  16. 16. RESEARCH METHODOLOGY & STATISTICAL TOOLS4. Calculated ‘confidence limits’ must be mentioned and the various constraintsexperienced in conducting research operations may as well be stated.COLLECTION OF DATAStatistical investigation: An investigation (or) inquiry means a “search forknowledge”. Statistical investigation means “search for knowledge with the help ofstatistical methods”.Stages of Investigation: A statistical investigation is a comprehensive which passesthrough the following steps:1. Planning the inquiry2. Collection of data3. Editing the data4. Presentation of data5. Analysis of data6. Presentation of final reportCollection of data: The first in the conduct of statistical investigation (or) inquiryis “collection of data”. The source of data can be represented as follows:Internal source: Internal data come from government and business organizationswhich generate them in the form of production, purchase, expenses etc.DATAINTERNALDATAEXTERNALDATAPRIMARYDATASECONDARYDATA16
  17. 17. RESEARCH METHODOLOGY & STATISTICAL TOOLSExternal data: When data is collected from outside the organization, then this iscollected from the external source. External data can be divided into two types.(i) Primary (ii) secondary(i) Primary data: It refers to the statistical material which the investigator originatesfor him for the purpose of the inquiry in hand in other words; it is one which iscollected by the investigator the first time.(ii) Secondary data: it refers to the statistical material which is not originated by theinvestigator himself but obtained from some one else records. This type of data isgenerally taken from news papers, magazines, bulletins, reports etc.Methods of collection of primary data: following methods may be used to collect theprimary data:1. Direct personal investigation2. Indirect personal investigation3. Information through correspondent4. Questionnaire method(a) Questionnaire step to post(b) Questionnaire step to investigators(1) Direct personal investigation: According to this method, the investigator obtainsthe data from personal interview or observation.Therefore, he contains the source of information directly and personally. Hewill contact cash and every possible source of information.(2) Indirect personal investigation: According to this method the investigator containsthird party’s witnesses who are use to collect the information directly or indirectly andor capable of supplying the necessary information. This method is generally adaptedby government committees to get views of the people relating to the inquiry.(3) Information through correspondent: Under this method, the investigator does notcollect the information from the persons directly. He appoints local agents in differentcards of the area under investigation. These local agents are called “correspondents”.This correspondents collect the information and pass it on to the investigate on time-to-time.(4) Questionnaire method: In this method, the necessary information is collected fromthe respondent’s through a questionnaire. A questionnaire is a set of questions relatingto the inquiry. The information can be collected through questionnaires in two ways.17
  18. 18. RESEARCH METHODOLOGY & STATISTICAL TOOLS(i) Questionnaires sent to post: in this case, the questionnaire is sent to a person andthe persons he fills the various answers to the various questions asked in it.(ii) Questionnaires sent to investigator: under this method, the investigators areappointed and contact the persons and get replace to the questionnaire and tell them intheir own hand writing in the questionnaire form.Sources of secondary data: sometimes it is not possible to collect information forresources in terms of money, time etc, in that solution secondary data is used. Thistype of data is generally available in magazines, journals etc. This secondary data canbe classified into two categories:(i) Published data(ii) Unpublished dataOrganization of data: the raw data in the form of unarranged figures are collectedthrough primary or secondary sources. The raw data practically gives no informationand hence there is a need for organization of data. In organization of data involves thefollowing ‘3’ stages:(1) Editing of data(2) Classification of data(3) Tabulation of data(1) Editing of data: Editing of data refers to detect possible errors and irregulatories committedduring the collection of data. If the data is not edited, then it may lead to wrong conclusions. Thereforeediting is essential to arrange the data in order.(2) Classification of data: The process of arranging the data in groups or classes according to theircommon characteristics is technically classified. Classification is the grouping of related facts into classes.Types of classification: broadly whole data can be classified into following factors:1. geographical classification2. chromo logical classification3. conditional classification4. qualitative classification5. quantitative classification18
  19. 19. RESEARCH METHODOLOGY & STATISTICAL TOOLS1. Geographical classification: Here data are classified on the basic ofgeographical area like village, city, states, and regions.2. Chromo logical classification: Here, this classification is done on thebasis of time likely hourly, daily, weakly, monthly etc.3. Conditional classification: This classification is done on the basis ofsome conditions such as literacy, intelligence, honesty, beauty and uglyetc.4. Qualitative classification: Here, this data is classified on the basis ofsome attributes (or) quality like literacy, honesty, beauty, intelligenceetc,. In this case the basis of classification is either presence or absenceof a quality.5. Quantitative classification: When the data classified on the basis ofthe characteristics which can be measured such as age, income, marks,height, weight, product is called “Qualitative classification”.(3) Tabulation of data: After the collection and classification of data process oftabulation begins. Tabulation is dependent upon classification. Tabulation is necessaryin order to make the data understandable or organize. By tabulation we make asystematic arrangement of statistical data in rows and columns. Rows are thehorizontal arrangements of data, where as the columns are the vertical arrangement ofdata.Tabulation tries to give the maximum information contained in the data inminimum possible space. It is mid way process between the collection of data andstatistical analysis.QUESTIONNAIRE AS A TOOL OF COLLECTING DATAThis method consists in preparing a questionnaire (a list of questions relating tothe field of enquiry and providing space for the answers to be filled by therespondents) which is mailed to the respondents with a request for quick responsewithin the specified time. The questionnaire is the only media of communicationbetween the investigator and the respondents and as such the questionnaire should bedesigned or drafted with utmost care and caution so that all the relevant and essentialinformation for the enquiry may be collected without any difficulty, ambiguity andvagueness.Drafting or Framing the Questionnaire:19
  20. 20. RESEARCH METHODOLOGY & STATISTICAL TOOLSDrafting of a good questionnaire is a highly specialized job and requires greatcare, skill, wisdom, efficiency and experience. No hard and fast rules can be laid downfor designing or framing a questionnaire. However, in this connection, the followinggeneral points may be borne in mind:1. The size of the questionnaire should be as small as possible. Thenumber of questions should be restricted to the minimum, keeping in view thenature, objectives and scope of the enquiry. In other words, the questionnaireshould be concise and should contain only those questions which would furnishall the necessary information relevant for the purpose. Respondents’ time shouldnot be wasted by asking irrelevant and unimportant questions. A large number ofquestions would involve more work for the investigator and thus result in delayon his part in collecting and submitting the information. These may, in addition,also necessarily annoy or tire the respondents. A reasonable questionnaire shouldcontain from 15 to 20-25 questions. If a still larger number of questions is a mustin any enquiry, then the questionnaire should be divided into various sections orparts.2. The questions should be clear, brief, unambiguous, non-offending, andcourteous in tone, corroborative in nature and to the point so that not much scopeof guessing is left on the part of the respondents.3. The questions should be arranged in a natural logical sequence. Forexample, to find if a person owns a refrigerator the logical order of questionswould be: “Do you own a refrigerator”? When did you buy it? What is its make?How much did it cost you? Is its performance satisfactory? Have you ever got itserviced? The logical arrangement of questions in addition to facilitatingtabulation work would leave no chance for omissions or duplication.4. The usage of vague and ‘multiple meaning’ words should be avoided.The vague works like good, bad, efficient, sufficient, prosperity, rarely,frequently, reasonable, poor, and rich, etc., should not be used since these maybe interpreted by different persons and as such might give unreliable andmisleading information. Similarly the use of words with multiple meanings likeprice, assets, capital, income, household, democracy, socialism, etc., should notbe used unless a clarification to these terms is given in the questionnaire.5. Questions should be so designed that they are readily comprehensiveand easy to answer for the respondents. They should not be tedious nor should20
  21. 21. RESEARCH METHODOLOGY & STATISTICAL TOOLSthey tax the respondents’ memory. Further, questions involving mathematicalcalculations like percentages, ratios, etc., should not be asked.6. Questions of a sensitive and personal nature should be avoided.Questions like “How much money you owe to private parties?” or “Do you cleanyour utensils yourself?” which might hurt the sentiments, pride or prestige of anindividual should not be asked, as far as possible. It is also advisable to avoidquestions on which the respondent may be reluctant or unwilling to furnishinformation. For example, the questions pertaining to income, savings, habits,addiction to social evils, age (particularly in case of ladies), etc., should be askedvery tactfully.7. Typed Questions: Under this head, the questions in the questionnairemay be broadly classified as follows:a) Shut Questions: In much questions possible answers are suggested bythe framers of the questionnaire and the respondent is required to tick one ofthem. Shut questions can further be sub-divided into the following forms.(i) Simple Alternative Questions: In such questions, therespondent has to choose between two clear cut alternatives like ‘Yes’ or‘No’; ‘Right’ or ‘Wrong’; ‘Either’ or ‘Or’ and so on. For instance, do youown a refrigerator? – Yes or No. Such questions are also calleddichotomous questions. This technique can be applied with elegance tosituations where two clear cut alternatives exist.(ii) Multiple Choice Questions: Quite often, it is not possible to define a clearcut alternative and accordingly in such a situation either the first method(Alternative Questions) is not used or additional answers between ‘Yes’or ‘No’ like ‘Do not know’, ‘No opinion’, Occasionally, Casually,Seldom, etc., are added. For instance to find a person smokes or drinks,the following multiple choice answers may be used: Do you smoke?Yes (Regularly) [ ] No (Never) [ ]Occasionally [ ] Seldom [ ] Which of the following modes of cooking you use?Gas [ ] Coal (Coke) [ ] Wood [ ]Power (Electricity) [ ] Stove (Kerosene) [ ]21
  22. 22. RESEARCH METHODOLOGY & STATISTICAL TOOLS How do you go to your place of duty?By bus [ ] By three wheeler scooter [ ]By your own vehicle [ ] By taxi [ ]By your own scooter [ ] On foot [ ]By your own car [ ] Any other [ ]Multiple choice questions are very easy and convenient for the respondentsto answer. Such questions save time and also facilitate tabulation. Thismethod should be used if only a selected few alternative answers exist to aparticular question. Sometimes, a last alternative under the category‘Others’ or ‘Any other’ may be added. However, multiple answer questionsof relatively equal importance to a given question.b) Open Questions: Open questions are those in which no alternativeanswers are suggested and the respondents are at liberty to express their frankand independent opinions on the problem in their own words. For instance,‘What are the drawbacks in our examination system?’; ‘What solution do yousuggest to the housing problem in Delhi?’; ‘Which program in the Delhi TVdo you like best?’ are some of the open questions. Since the views of therespondents in the open questions might differ widely, it is very difficult totabulate the diverse opinions and responses.8) Leading questions should be avoided: For example, the question ‘why do we use aparticular brand of blades, say, Erasmic blades’ should preferably be framed into twoquestions.(i) Which blade do you use?(ii) Why do you prefer it?Gives a smooth shave [] Readily available in the market []Gives more shaves [] Any other []Price is less (cheaper) []9) Cross checks: The questionnaire should be so designed as to provide internalchecks on the accuracy of the information supplied by the respondents by includingsome connected questions at least with respect to matters which are fundamental to theenquiry. For example in social survey for finding the age of the mother the question‘What is your age’? Can be supplemented by additional questions ‘What is your dateof birth?’ or ‘What is the age of your eldest child’? Similarly, the question, ‘Age atmarriage’ can be supplemented by the question ‘The age of the first child’.22
  23. 23. RESEARCH METHODOLOGY & STATISTICAL TOOLS10) Pre-testing the questionnaire: From practical of view it is desirable to try out thequestionnaire on a small scale (i.e., on a small cross-section of the population forwhich the enquiry is intended) before using it for the given enquiry on a large scale.This testing on a small scale (called pre-test) has been found to be extremely useful inpractice. The given questionnaire can be improved or modified in the light of thedrawbacks, shortcomings and problems faced by the investigator in the pre-test. Pre-testing also helps to decide upon the effective methods of asking questions forsoliciting the requisite information.11) A covering letter: A covering letter from the organizers of the enquiry should beenclosed along with the questionnaire for the following purposes:i. It should clearly explain in brief the objectives and scope of thesurvey to evoke the interest of the respondents and impress upon them torender their full co-operation by returning their schedule/questionnaire dulyfilled in within the specified period.ii. It should contain a note regarding the operational definitions tothe various terms and the concepts used in the questionnaire; units ofmeasurements to be used and the degree of accuracy aimed it.iii. It should take the respondents in confidence and ensure themthat the information furnished by them will be kept completely secret andthey will not be harassed in any way later.iv. In the case of mailed questionnaire method a self-addressedstamped envelope should be enclosed for enabling the respondents to returnthe questionnaire after completing it.v. To ensure quick and better response the respondents may beoffered awards/incentives in the form of free gifts, coupons, etc.vi. A copy of the survey report may be promised to the interestedrespondents.12) Mode of tabulation and analysis viz., hand operated, machine tabulation orcomputerization should also be kept in mind while designing the questionnaire.13) Lastly, the questionnaire should be made attractive by proper layout and appealingget up. We give below two specimen questionnaires for illustration.A MODEL OF QUESTIONNAIRE IN REGARDS TO CENSUS SURVEY:23
  24. 24. RESEARCH METHODOLOGY & STATISTICAL TOOLSWe give below the 1971 Census – Individual Slip which was used for a generalpurpose survey to collect:(i) Social and Cultural data like nationality, religion, literacy, mother tongue, etc.;(ii) Exhaustive economic data like occupation, industry, class of worker and activity, ifnot working;(iii) Demographic data like relation to the head of the house,sex, age, marital status, birth place, births and depths and the fertility of women toassess in particular the performance of the family planning programme.1971 CENSUS – INDIVIDUAL SLIP1. Name…………………………………………………..2. Relationship to the head of the family………………………………………3. Sex………………………..4. Age…………………………………..5. Marital status………………………..6. For currently married women only:a) Age at marriage……………b) Any child born in the last one year……………..7. Birth place:a) Place of birth……………b) Rural or urban…………….c) District…………………………….d) State/Country…………………………..8. Last Residence:a) Place of last residence…………………………………………b) Rural/Urban……………………………………….c) District………………………………….d) State/Country………………………………………9. Duration of present residence……………………………………..10. Religion………………………………………….11. Scheduled Caste/Tribe………………………………………12. Literacy………………………………………….13. Educational level………………………………………..24
  25. 25. RESEARCH METHODOLOGY & STATISTICAL TOOLS14. Mother Tongue…………………………………………..15. Other Languages, if any……………………………………………………….16. Main Activity:a) Broad Category:(i) Worker(ii) Non – Workerb) Place of work (Name of village/town)…………………………..c) Name of establishment………………………d) Name of Industry, Trade, Profession or Service…………………e) Description of work…………………………………..f) Class of worker………………………………..17. Secondary work:a) Broad Category………………………b) Place of work…………………………….c) Name of establishment……………………….d) Nature of Industry, Trade, Profession orservice………………………….e) Description of work…………………………………..f) Class of worker……………………………………………..SCHEDULES AS A TOOL FOR COLLECTING DATABefore discussing this method it is desirable to make a distinction between aquestionnaire and a schedule. As already explained, questionnaire in a list of questionswhich are answered by the respondent himself in this own handwriting while scheduleis the device of obtaining answers to the questions in a form which is filled by theinterviewers or enumerators (the field agents who put these questions) in a face to facesituation with the respondents. The most widely used method of collection of primarydata is the ‘schedules sent through enumerators’. This is so because this method is freefrom certain shortcomings inherent in the earlier methods discussed so far. In this theenumerators go to the respondents personally with the schedule (list of questions), askthem the questions there in and record their replies. This method is generally used bybig business houses, large public enterprises and research institutions like ‘NationalCouncil of Applied Economic Research (NCAER), Federation of Indian Chambers ofCommerce and Industries (FICCI) and so on and even by the governments – state or25
  26. 26. RESEARCH METHODOLOGY & STATISTICAL TOOLScentral – for certain projects and investigations where high degree of response isdesired. Population census, all over the world is conducted by this technique.Merits:1. The enumerators can explain in detail the objectives and aims of the enquiry tothe informants and impress upon them the need and utility of furnishing thecorrect information.2. This technique is very useful in expensive enquiries and generally yields fairlydependable and reliable results due to the fact that the information is recordedby highly trained and educated enumerators.3. Unlike the ‘Questionnaire method’, this technique can be used with advantageeven if the respondents are illiterate.4. As already pointed out in the ‘direct personal investigation’, due to personallikes and dislikes, different people react differently to different questions andas such some people might react very sharply to certain sensitive and personalquestions.Demerits:1. It is fairly expensive method since the team of enumerators is to be paid fordifferent services and as such can be used by only those bodies or institutionswhich are financially sound.2. It is also more time consuming as compared with the ‘Questionnaire method’.3. The success of the method largely depends upon the efficiency and skill of theenumerators who collect the information. The enumerators have to be trainedproperly in the art of collecting correct information by their intelligence,insight, patience and perseverance, diplomacy and courage. They shouldclearly understand the aims and objectives of the enquiry and also theimplications of the various terms, definitions and concepts used in thequestionnaire.4. Due to inherent variation in the individual personalities of the enumeratorsthere is bound to be variation, though not so obvious, in the information26
  27. 27. RESEARCH METHODOLOGY & STATISTICAL TOOLSrecorded by different enumerators. An attempt should be made to minimizethis variation.5. The success of this method also lies to a great extent on the efficiency andwisdom with which the schedule is prepared or drafted. If the schedule isframed haphazardly and incompetently, the enumerators will find it verydifficult to get the complete and correct desired information from therespondents.SAMPLE DESIGN AND SAMPLING PROCEDURESSAMPLE DESIGN:A sample design is a definite plan for obtaining a sample from a givenpopulation. It refers to the technique or the procedure the researcher would adopt inselecting items for the sample. Sample design may as well lay down the number oftimes to be included in the sample i.e., the size of the sample. Sample design isdetermined before data are collected. There are many sample designs from which aresearcher can choose. Some designs are relatively more precise and easier to applythan others. Researcher must select/prepare a sample design which should be reliableand appropriate for his research study.STEPS IN SAMPLE DESIGN:While developing a sample design, the researcher must pay attention to the followingpoints:1. Type of universe: The first step in developing sample design is to clearlydefine the set of objects, technically called the Universe, to be studied. Theuniverse can be finite or infinite. In finite universe the number of items iscertain, but in case of an infinite universe the number of items is infinite i.e.,we cannot have any idea about the total number of items. The population of acity, the number of workers in a factory and the like are examples of finiteuniverses, whereas the number of stars in the sky, listeners of a specific radioprogramme, throwing of a dice etc., are examples of infinite universes.2. Sampling Unit: A decision has to be taken concerning a sampling unit beforeselecting sample. Sampling unit may be a geographical one such as state,district, village, etc., or a construction unit such as house, flat, etc., or it may bea social unit such as family, club, school, etc., or it may be an individual. The27
  28. 28. RESEARCH METHODOLOGY & STATISTICAL TOOLSresearcher will have to decide one or more of such units that he has to selectfor his study.3. Source List: It is also known as ‘Sampling frame’ from which sample is to bedrawn. It contains the names of all items of a universe (in case of finiteuniverse only). If source list is not available, researcher has to prepare it. Sucha list should be comprehensive, correct, reliable and appropriate. It isextremely important for the source list to be as representative of the populationas possible.4. Size of sample: This refers to the number of items to be selected from theuniverse to constitute a sample. This major problem before a researcher. Thesize of sample should neither be excessively large, nor too small. It should beoptimum. An optimum sample is one which fulfills the requirements ofefficiency, representative-ness, reliability and flexibility. While deciding thesize of sample, researcher must determine the desired precision as also anacceptable confidence level for the estimate.5. Parameters of interest: In determining the sample design, one must considerthe question of the specific population parameters which are of interest. Forinstance, we may be interested in estimating the proportion of persons withsome characteristic in the population, or we may be interested in knowingsome average or the other measure concerning the population. There may alsobe important sub-groups in the population about whom we would like to makeestimates. All this has a strong impact upon the sample design we wouldaccept.6. Budgetary Constraint: Cost considerations, from practical point of view, havea major impact upon decisions relating to not only the size of the sample butalso to the type of sample. This fact can even lead to the use of a non-probability sample.7. Sampling Procedure: Finally, the researcher must decide the type of sample hewill use i.e., he must decide about the technique to be used in selecting theitems for the sample. In fact, this technique or procedure stands for the sampledesign itself. There are several sample designs out of which the researchermust choose one for his study. Obviously, he must select that design which, fora given sample size and for a cost, has a small sampling error.28
  29. 29. RESEARCH METHODOLOGY & STATISTICAL TOOLSCHARACTERISTICS OF GOOD SAMPLE DESIGN:From what has been stated above, we can list down the characteristics of a goodsample design as under:a) Sample design must result in a truly representative sample.b) Sample design must be such which results in a small sampling error.c) Sample design must be viable in the context of funds available for the researchstudy.d) Sample design must be such so that systematic bias can be controlled in abetter way.e) Sample should be such that the results of the sample study can be applied, ingeneral, for the universe with a reasonable level of confidence.CRITERIA OF SELECTING A SAMPLING PROCEDURE:In this context one must remember that two costs are involved in a samplinganalysis viz., the cost of collecting the data and the cost of an incorrect inferenceresulting from the data. Researcher must keep in view the two causes of incorrectinferences viz., systematic bias and sampling error. Systematic bias results from errorsin the sampling procedures, and it cannot be reduced or eliminated by increasing thesample size. At best the causes responsible for these errors can be detected andcorrected. Usually a systematic bias is the result of one or more of the followingfactors.1) Inappropriate frame: If the sampling frame is inappropriate i.e., a biasedrepresentation of the universe, it will result in a systematic bias.2) Defective measuring device: If the measuring device is constantly in error, it will return insystematic bias. In survey work, systematic bias can result if the questionnaire or theinterviewer is biased. Similarly, if the physical measuring device is defective there will besystematic bias in the data collected through such a measuring device.3) Non-respondents: If we are unable to sample all the individuals initially include in thesample, there may arise a systematic bias. The reason is that in such a situation the likelihoodof establishing contact or receiving a response from an individual is often correlated with themeasure of what is to be estimated.29
  30. 30. RESEARCH METHODOLOGY & STATISTICAL TOOLS4) Indeterminacy principle: Sometimes we find that individuals act different when keptunder observation that what they do when kept in non-observed situations. For instance, ifworkers are aware that somebody is observing then in course of a work study on the basis ofwhich the average length of time to complete a task will be determined and accordingly thequota will be set for piece work, they generally tend to work slowly in comparison to thespeed with which they work if kept unobserved. Thus, the indeterminacy principle may also bea cause of a systematic bias.5) Natural bias in the reporting of data: Natural bias of respondents in the reporting of datais often the cause of a systematic bias in many inquiries. There is usually a download bias inthe income data collected data by government taxation department, whereas we find anupward bias in the income data collected by some social organization. People in generalunderstate their incomes if asked about it for tax purposes, but they overstate the same if askedfor social status or their affluence. Generally in psychological surveys, people tend to givewhat they think is the ‘correct’ answer rather than revealing their true feelings.DIFFERENT TYPES OF SAMPLE DESIGNS:There are different types of sample designs based on two factors viz., therepresentation basis and the element selection technique. On the representation basisand the element selection technique. On the representation basis, the sample may beprobability sampling or it may be non-probability sampling. Probability sampling isbased on the concept of random selection, whereas non-probability sampling is ‘non-random sampling. On element selection bias, the sample may be either unrestricted orrestricted. When each sample element is drawn individually from the population atlarge, then the sample so drawn is known as ‘unrestricted sample’, whereas all otherforms of sampling are covered under the term ‘restricted sampling’. The followingchart exhibits the sample designs as explained above.Non-probability sampling: Non-probability sampling is that sampling procedurewhich does not afford any basis for estimating the probability that each item in thepopulation has of being included in the sample. Non-probability sampling is alsoknown by different names such as deliberate sampling, purposive sampling andjudgment sampling. In this type if sampling, items for the sample are selecteddeliberately by the researcher; his choice concerning the items remains supreme. Inother words, under non-probability sampling the organizers of the inquiry purposively30
  31. 31. RESEARCH METHODOLOGY & STATISTICAL TOOLSchoose the particular units of the universe for consulting a sample on the basis that thesmall mass that they so select out of a huge one will be typical or representative of thewhole. For instance, if economic conditions of people living in a state are to bestudied, a few towns and villages may be purposively selected for intensive study onthe principle that they can be representative of the entire state. Thus, the judgment ofthe organizers of the study plays an important part in this sampling design.Quota sampling: It is also an example of non-probability sampling. Under quotasampling the interviewers are simply given quotas to be filled from the different strata,with some restrictions on how they are to be filled. In other words, the actual selectionof the items for the sample is left to the interviewer’s discretion. This type of samplingis very convenient and is relatively inexpensive. But the samples so selected certainlydo not possess the characteristic of random samples. Quota samples are essentiallyjudgment samples and inferences drawn on their basis are not amenable to statisticaltreatment in a formal way.Probability sampling: Probability sampling is also known as ‘random sampling’ or‘chance sampling’. Under this sampling design, every time of the universe has anequal chance of inclusion in the sample. It is, so to say, a lottery method in whichindividual units are picked up from the whole group not deliberately but by somemechanical process. Here it is blind chance alone that determines whether one item orthe other is selected. The results obtained from probability or random sampling can beassured in terms of probability i.e., we can measure the errors of estimation or thesignificance of results obtained from a random sample, and this fact brings out thesuperiority of random sampling design over the deliberate sampling design. Randomsampling ensures the Law of Statistical Regularity which states that if on an averagethe sample chosen is a random one, the sample will have the same composition andcharacteristics as the universe. This is the reason why random sampling is consideredas the best technique of selecting a representative sample.Random sampling from a finite population to that method of sample selectionwhich gives each possible sample combination an equal probability of being picked upand each item in the entire population to have an equal chance of being included in thesample. This applies to sampling without replacement i.e., once an selected for thesample, it cannot appear in the sample again (sampling with replacement is used less31
  32. 32. RESEARCH METHODOLOGY & STATISTICAL TOOLSfrequently in which procedure the element for the sample is returned to the populationbefore the next element is selected. In such a situation the same element could appeartwice in the same sample before the second element is chosen).in brief, theimplications of random sampling (or simple random sampling) are:(a) It gives each element in the population an equal probability of getting into thesample; and all choices are independent of one another.(b) It gives each possible sample combination an equal probability of being chosen.COMPLEX RANDOM SAMPLING DESIGNS:Probability sampling under restricted sampling techniques, as stated above,may result in complex random sampling designs. Such designs may as well be called‘mixed sampling designs’ for many of such designs may represent a combination ofprobability and non-probability sampling procedures in selecting a sample. Some ofthe popular complex random sampling designs are as follows:(i) Systematic Sampling: In some instances, the most practical way of sampling is toselect every ithitem on a list. Sampling of this type is known as systematic sampling.An element of randomness is introduced into this kind of sampling by using randomnumbers to pick up the unit with which to start. For instance, if a 4 percent sample isdesired, the first item would be selected randomly from the first twenty-five andthereafter every 25thitem would automatically be included in the sample. Thus, insystematic sampling only the first unit is selected randomly and the remaining units ofthe sample are selected at fixed intervals. Although a systematic sample is not arandom sample in the strict sense of the term, but it is often considered reasonable totreat systematic sample as if it were a random sample.(ii) Stratified Sampling: If a population from which a sample is to be drawn does notconstitute a homogeneous group, stratified sampling technique is generally applied inorder to obtain a representative sample. Under stratified sampling the population isdivided into several sub-populations that are individually more homogeneous than thetotal population a (the different sub-populations are called ‘strata’) and then we selectitems from each stratum to constitute a sample. Since each stratum is morehomogeneous than the total population, we are able to get precise estimates for eachstratum and by estimating more accurately each of the component parts; we get a32
  33. 33. RESEARCH METHODOLOGY & STATISTICAL TOOLSbetter estimate of the whole. In brief, stratified sampling results in more reliable anddetailed information.(iii) Cluster Sampling: If the total area of interest happens to be a big one , aconvenient way in which a sample can be taken is to divide the area into a number ofsmaller non-overlapping areas and then to randomly select a number of these smallerareas (usually called clusters), with the ultimate sample consisting of all (or samples of) units in these small areas of clusters.Thus in cluster sampling the total population is divided into a number ofrelatively small subdivisions which are themselves clusters of still smaller units andthen some of these clusters are randomly selected for inclusion in the overall sample.Suppose we want to estimate the proportion of machine parts in an inventory whichare defective. Also assume that there are 20000 machine parts in the inventory at agiven point of time, stored in 400 cases of 50 each. Now using a cluster sampling, wewould consider the 400 cases as clusters and randomly select ‘n’ cases and examine allthe machine parts in each randomly selected case.Cluster sampling, no doubt, reduces cost by concentrating surveys in selectedsurveys. But certainly it is less precise than random sampling. There is also not asmuch information in ‘n’ observations within a cluster as there happens to be in ‘n’randomly drawn observations. Cluster sampling is used only because of the economicadvantage it possesses; estimates based on cluster samples are usually more reliableper unit cost.(iv) Area Sampling: If clusters happen to be some geographic subdivisions, in thatcase cluster sampling is better known as area sampling. In other words, clusterdesigns, where the primary sampling unit represents a cluster of units based ongeographic area, are distinguished as area sampling. The plus and minus points ofcluster sampling are also applicable to area sampling.(v) Multi-stage Sampling: Multi-stage sampling is a further development of theprinciple of cluster sampling. Suppose we want to investigate the working efficiencyof nationalized banks in India and we want to take a sample of few banks for thispurpose. The first stage is to select large primary sampling unit such as states in acountry. Then we may select certain districts and interview all banks in the chosen33
  34. 34. RESEARCH METHODOLOGY & STATISTICAL TOOLSdistricts. This would represent a two-stage sampling design with the ultimate samplingunits being clusters of districts.If instead of taking a census of all banks within the selected districts, we selectcertain towns and interview all banks in the chosen towns. This would represent athree-stage sampling design. If instead of taking a census of all banks within theselected towns, we randomly sample banks from each selected town, then it is a caseof using a four-stage sampling plan. If we select randomly at all stages, we will havewhat is known as ‘multi-stage random sampling design’.Ordinarily multi-stage sampling is applied in inquires extending to aconsiderable large geographical area, say, the entire country. There are two advantagesof this sampling design viz., (a) It is easier to administer than most single stage designsmainly because of the fact that sampling frame under multi-stage sampling indeveloped impartial units. (b) A large number of units can be sampled for a given costunder multistage because of sequential clustering, whereas this is not possible in mostof the sample designs.(vi) Sampling with probability proportional to size: In case the cluster samplingunits do not have the same number or approximately the same number of elements, itis considered appropriate to use a random selection process where the probability ofeach cluster being included in the sample is proportional to the size of the cluster. Forthis purpose, we have to list the number of the elements in each cluster irrespective ofthe method of ordering the cluster. Then we must sample systematically theappropriate number of elements from the cumulative totals.(vii) Sequential Sampling: This sampling design is some what complex sampledesign. The ultimate size of the sample under this technique is not fixed in advance,but we determined according to mathematical decision rules on the basis ofinformation yielded as survey progresses. This is usually adopted in case of acceptancesampling plan in context of statistical quality control. When a particular lot is to beaccepted or rejected on the basis of single sample, it is known as single sampling;when the decision is to be taken on the basis of two samples, it is known as doublesampling and in case the decision rests on the basis of more than two samples but thenumber of samples in certain and decide in advance, the sampling is known as the34
  35. 35. RESEARCH METHODOLOGY & STATISTICAL TOOLSmultiple sampling. But when the number of samples is more than two but it is neithercertain nor decides in advance, this type of system is often referred to as sequentialsampling.DIAGRAMATIC PRESENTATION OF DATAGeneral rules for Constructing Diagrams:(1) Neatness: Diagrams are visual aids for presentation of statisticaldata and are more appealing and fascinating to the eye and leave a lastingimpression on the mind. It is, therefore, imperative that they are made very neat,clean and attractive by proper size and lettering; and the use of appropriate deviceslike different colours, different shades (light and dark), dots, dashes, dotted lines,broken lines, dots and dash lines, etc., for filling the in between space of the bars,rectangles, circles, etc., and their components.(2) Title and Footnotes: As in the case of a good statistical table, eachdiagram should be given a suitable title to indicate the subject-matter and thevarious facts depicted in the diagram. The title should be brief and selfexplanatory, clear. If necessary the footnotes may be given at the left hand bottomof the diagram to explain certain points or facts, not otherwise covered in the title.(3) Selection of Scale: One of the most important factors in theconstruction of diagrams is the choice of an appropriate scale. The same set ofnumerical data if plotted on different scales may give the diagrams differingwidely in size and at times might lead to wrong and misleading interpretations.Hence, the scale should be selected with great caution.(4) Proportion between Width and Height: A proper proportionbetween the dimensions (height and width) of the diagram should be maintained,consistent with the space available.(5) Choice of a Diagram: A large number of diagrams are used topresent statistical data. The choice of a particular diagram to present a given set ofnumerical data is not an easy one. It primarily depends on the nature of the data,magnitude of the observations and the type of the people for whom the diagrams35
  36. 36. RESEARCH METHODOLOGY & STATISTICAL TOOLSare meant and requires great amount of expertise, skill, and intelligence. Aninappropriate choice of the diagram for the given set of data might give a distortedpicture of the phenomenon under study and might lead to wrong and fallaciousinterpretations and conclusions.(6) Source Note and Number: As in the case of tables, source note,wherever possible should be appended at the bottom of the diagram. This isnecessary as, to the learned audience of statistics; the reliability of the informationvaries from source to source. Each diagram should also be given a number forready reference and comparative study.(7) Index: A brief index explaining various types of shades, colors,lines, and designs used in the construction of the diagram should be given for clearunderstanding of the diagram.(8) Simplicity: Lastly, diagrams should be as simple as possible so thatthey are easily understood even by a layman who does not have any mathematicalor statistical background. If too much information is presented in a single complexdiagram it will be difficult to grasp and might even become confusing to the mind.Hence, it is advisable to draw more simple diagrams than one or two complexdiagrams.TYPES OF DIAGRAMS:A large variety of diagrammatic devices are used in practice to present statistical data.However, we shall discuss here only some of the most commonly used diagramswhich may be broadly classified as follows:(1) One-dimensional diagrams(2) Two-dimensional diagrams(3) Three-dimensional diagrams(4) Pictograms(5) Cartograms1) One-Dimensional Diagrams: These one-dimensional diagrams are classified intotwo types. They are:I. Line DiagramsII. Bar Diagram36
  37. 37. RESEARCH METHODOLOGY & STATISTICAL TOOLSa) Line Diagram: This is the simplest of all the diagrams. It consists in drawingvertical lines, each vertical line being equal to the frequency. The variate (x) valuesare presented on a suitable scale along the X-axis and the correspondingfrequencies are presented on a suitable scale along Y-axis. Line diagrams facilitatecomparisons though they are not attractive or appealing to the eye.0204060801001st Qtr 2nd Qtr 3rd Qtr 4th QtrEastWestNorthb) Bar Diagram: Bar diagrams are one of the easiest and the most commonly useddevices of presenting most of the business and economic data. These are especiallysatisfactory for categorical data or series. They consist of a group of equidistantrectangles, one for each group or category of the data in which the values or themagnitudes are represented by the length or height of the rectangles, the width ofthe rectangles being arbitrary and immaterial. These diagrams are called one-dimensional because in such diagrams only one dimension viz., height or length ofthe rectangles is taken into account to present the given values. There are varioustypes of Bar Diagrams. They are listed as follows:(i) Simple bar diagram(ii) Sub-divided or component bar diagram(iii) Percentage bar diagram(iv) Multiple bar diagram(v) Deviation or Bilateral bar diagram37
  38. 38. RESEARCH METHODOLOGY & STATISTICAL TOOLS01020304050607080901st Qtr 2nd Qtr 3rd Qtr 4th QtrEastWestNorth2) Two-Dimensional Diagrams: Line or Bar diagrams discussed so far are one-dimensional diagrams since the magnitudes of the observations are represented byonly one of the dimensions viz., height (length) of the bars while the width of the barsis arbitrary and uniform. However, in two-dimensional diagrams, the magnitudes ofthe given observations are represented by the area of the diagram. Thus, in the case oftwo-dimensional bar diagrams, the length as well as width of the bars will have to beconsidered. Two-dimensional diagrams are also known as “area diagrams or surfacediagrams”. Some of the commonly used two-dimensional diagrams are listed asfollows:They are: Rectangles Squares Circles Angular or pie diagrams3) Three-Dimensional Diagrams: Three-dimensional diagrams, also termed as‘volume diagrams’ are those in which three dimensions, viz., length, breadth, andheight are taken into account. They are constructed so that the given magnitudesare represented by the volumes of the corresponding diagrams. The common forms38
  39. 39. RESEARCH METHODOLOGY & STATISTICAL TOOLSof such diagrams are “cubes, spheres, cylinders, blocks etc”. These diagrams arespecially useful if there are very wide variations between the smallest and thelargest magnitudes to be represented. Of the various three-dimensional diagrams,‘cubes’ are the simplest and most commonly used devices of diagrammaticpresentation of data.4) Pictograms: Pictograms is the technique of presenting statistical data throughappropriate pictures and is one of the very popular devices particularly when thestatistical facts are to be presented to a layman without any mathematicalbackground. In this, the magnitudes of the particular phenomenon under study arepresented through appropriate pictures, the number pictures drawn or the size ofthe pictures being proportional to the values of the different magnitudes to bepresented. Pictures are more attractive and appealing to the eye and have a lastingimpression on the mind. Accordingly they are extensively used by government andprivate institutions for diagrammatic presentation of the data relating to a varietyof social, business or economic phenomena primarily for display to the generalpublic or common masses in fairs and exhibitions.5) Cartograms: in cartograms, statistical facts are presented through mapsaccomplished by various types of diagrammatic representation. They are speciallyused to depict the quantitative facts on a regional or geographical basis eg., thepopulation density of different states in a country or different countries in theworld, or the distribution of the rainfall in different regions of a country can beshown with the help of maps or cartograms. The different regions or geographicalzones are depicted on a map and the quantities or magnitudes in the regions maybe shown by dots, different shades or colors etc., or by placing bars or pictogramsin each region or by writing the magnitudes to be represented in the respectiveregions. Cartograms are simple and elementary forms of visual presentation andare easy to understand. They are generally used when the regional or geographiccomparisons are to be highlighted.GRAPHIC REPRESENTATION OF DATADiagrams are primarily used for comparative studies and can’t be used to study therelation ship between the variables under study. This is done through graphs.Diagrams furnish only approximate information and they are not of much utility to astatistician from analysis point of view. On the other hand, graphs are more obvious,precise and accurate than diagrams and can be effectively used for further statistical39
  40. 40. RESEARCH METHODOLOGY & STATISTICAL TOOLSanalysis, viz., to study slopes, rates of change and for forecasting wherever possible.Graphs are drawn on a special type of paper, known as “graph paper”.Before discussing these graphs we shall briefly describe the technique ofconstructing graphs and the general rules for drawing graphs.TECHNIQUE OF CONSTRUCTION OF GRAPHS:QUADRANT II 5- QUADRANT IX-Negative 4- X-PositiveY-Positive 3- Y-Negative(-X, +Y) 2- (+X, +Y)1--5 -4 -3 -2 -1 0 1 2 3 4 5QUADRANT III -1- QUADRANT IVX-Negative -2- X - PositiveY-Positive -3- Y - Negative(-X, -Y) -4- (+X, -Y)-5-Graphs are drawn on a special type of paper known as “Graph Paper”, whichhas a fine network of horizontal and vertical lines; the thick lines for each division of acentimeter or an inch measure and thin lines for small parts of the same. In a graph ofany size, two simple lines are drawn at right angle to each other, intersecting at point‘O’ which is known as origin or zero of reference. The two lines are known as co-ordinate axes. The horizontal line is called X – axis and is denoted by X’OX. Thevertical line is called the Y – axis and is usually denoted by YOY’. Thus the graph isdivided into four sections, known as four quadrants.General Rules for Graphing: The following guidelines may be kept in mind fordrawing effective and accurate graphs.1. Neatness2. Title and Footnote3. Structural Framework4. Scale40
  41. 41. RESEARCH METHODOLOGY & STATISTICAL TOOLS5. False Base Line6. Ratio or Logarithmic Scale7. Line designs8. Source Note and Number9. Index10. SimplicityTYPES OF GRAPHS: A large number of graphs are used in practice. But they canbe broadly classified under the following two heads:(i) Graphs of frequency distributions.(ii) Graphs of time series.1) Graphs of Frequency Distributions: The reasons and the guiding principlesfor the graphic representation of the frequency distributions are precisely the sameas for the diagrammatic and graphic representation of other types of data. The so-called frequency graphs are designed to reveal clearly the characteristic features ofa frequency data. Such graphs are more appealing to the eye than the tabulated dataand are readily perceptible to the mind. They facilitate comparative study of two ormore frequency distributions regarding their shape and pattern. The mostcommonly used graphs for charting a frequency distribution for the generalunderstanding of the details of the data are:A) Histogram B) Frequency PolygonC) Frequency Curve D) “Ogive” or Cumulative Frequency CurveThe choice of a particular graph for a given frequency distribution largely depends onthe nature of the frequency distribution, viz., discrete or continuous.A) HISTOGRAM: It is one of the most popular and commonly used devices forcharting continuous frequency distribution. It consists in erecting a series ofadjacent vertical rectangles on the sections of the horizontal axis (X-axis), withbases (sections) equal to the width of the corresponding class intervals and heightsare so taken that the areas of the rectangles are equal to the frequencies of thecorresponding classes.The Histogram can be constructed in two cases. They are:Case (i): Histogram with equal classes.Case (ii): Histogram with un-equal classes.41
  42. 42. RESEARCH METHODOLOGY & STATISTICAL TOOLSB) FREQUENCY POLYGON: Frequency polygon is other device of graphicpresentation of a frequency distribution (continuous, grouped or discrete). In caseof discrete frequency distribution, frequency polygon is obtained on plotting thefrequencies on the vertical axis (Y-axis) against the corresponding values of thevariable on the horizontal axis (X-axis) and joining the points so obtained bystraight lines.C) FREQUENCY CURVE: A frequency curve is a smooth free hand curvedrawn through the vertices of a frequency polygon. The object of smoothing of thefrequency polygon is to eliminate, as far as possible, the random or erraticfluctuations that might be present in the data. The area enclosed by the frequencycurve is same as that of the histogram or frequency polygon but its shape is smoothone and not with sharp edges. Frequency curve may be regarded as a limited formof the frequency polygon as the number of observations (total frequency) becomesvery large and class intervals are made smaller and smaller.Types of frequency curves:Though different types of data may give rise to a variety of frequency curves, weshall discuss below only some of the important curves which, in general, describemost of the data observed in practice, viz., and the data relating to natural, social,economic and business phenomena.i) Curves of Symmetrical Distributionii) Moderately Asymmetrical (skewed) frequency distributioncurvesiii) Extremely asymmetrical or J – shaped curvesiv) U – curvev) Mixed curvesD) “OGIVE” OR CUMULATIVE FREQUENCY CURVE: Ogive, pronouncedas “Ojive”, is a graphic presentation of the cumulative frequency (C.F)distribution of continuous variable. It consists in plotting the cumulative frequency(along the Y – axis) against the class boundaries (along the X – axis). Since thereare two types of cumulative frequency distributions viz., “LESS THAN C.F” and“MORE THAN C.F”. We have accordingly two types of ogives, viz., (i) Less thanogive (ii) More than ogive.42
  43. 43. RESEARCH METHODOLOGY & STATISTICAL TOOLS(i) Less than Ogive: This consists in plotting the ‘less than’ cumulativefrequencies against the upper class boundaries of the respective classes. The pointsso obtained are joined by a smooth free hand curve to give “Less than Ogive”.Obviously, “less than ogive” is an increasing curve, sloping upwards from left toright and has the shape of an elongated S.(ii) More than Ogive: Similarly, in “more than ogive”, the “more than”cumulative frequencies are plotted against the lower class boundaries of therespective classes. The points so obtained are joined by a smooth ‘free hand’ curveto give “more than ogive”. “More than Ogive” is a decreasing curve and slopesdownwards from left to right and has the shape of an elongated S, upside down.2) Graphs of Time Series: The Time Series data are represented geometrically bymeans of times series graph which is also known as “Histogram”. The various typesof Time Series graphs are:i) Horizontal Line Graphs or Histogramsii) Silhouette or Net Balance Graphsiii) Range or Variation Graphsiv) Components or Band GraphsTABULATION OF DATAMeaning and Importance of Tabulation: By Tabulation we mean the symmetricpresentation of the information contained in the data, in rows and columns inaccordance with some salient features or characteristics. Rows are horizontalarrangements and columns are vertical arrangements. In the words of A.M. Tuttle.“A Statistical table is the logical listing of related quantitative data in verticalcolumns and horizontal rows of numbers with sufficient explanatory and qualifyingwords, phrases and statements in the form of titles, headings and notes to make clearthe full meaning of data and their origin”.Professor Bowley, in his manual of statistics prefers to Tabulation as “theintermediate process between the accumulation of data in what ever form they areobtained, and the final reasoned account of the result shown by the statistics”.Tabulation is one of the most important and ingenious device of the presentingthe data in a condensed and readily comprehensible form and attempts to furnish the43
  44. 44. RESEARCH METHODOLOGY & STATISTICAL TOOLSmaximum information contained in the data in the minimum possible space, withoutsacrificing the quality and usefulness of the data. It is an intermediate process betweenthe collection of the data on one hand and statistical analysis on the other hand. Infact, Tabulation is the final stage in collection and compilation of the data and formsthe gateway for further statistical analysis and interpretations. Tabulation makes thedata comprehensible and facilitates comparisons (by classifying data into suitablegroups), and the work of further statistical analysis, averaging, correlation, etc. Itmakes the data suitable for further Diagrammatic and Graphic representation.GENERAL RULES FOR CONSTRUCTING A TABLEThe various parts of a table vary from problem to problem depending upon the natureof the data and the purpose of the investigation. However, the following are a must ina good statistical table:1. Table Number2. Title3. Head Notes (or) Prefatory Notes4. Captions and Stubs5. Body of the Table6. Foot-Note7. Source NoteFORMAT OF A BLANK TABLETable No: # TITLE[Head Note or Prefatory Note (if any)]CaptionSub Heads Sub Heads44
  45. 45. RESEARCH METHODOLOGY & STATISTICAL TOOLSStubHeadingTotalColumnHeadColumnHeadColumnHeadColumnHeadColumnHeadBodyTotalFoot Note:Source Note:TYPES OF TABULATION: The Tables are constructed in many ways.1. Objectives and Scope of the enquiry.General Purpose or Reference TableSpecial Purpose or Summary Table2. Nature of Enquiry.(i) Original or Primary Table(ii) Derived or Derivative Table3. Extent of Coverage given in the Enquiry.Simple TableComplex Table45
  46. 46. RESEARCH METHODOLOGY & STATISTICAL TOOLSSPSS (STATISTICAL PACKAGE FOR THE SOCIAL SCIENCES)SPSS (Statistical Package for the Social Sciences) has now been in development formore than thirty years. Originally developed as a programming language forconducting statistical analysis, it has grown into a complex and powerful applicationwith now uses both a graphical and a syntactical interface and provides dozens offunctions for managing, analyzing, and presenting data. Its statistical capabilities alonerange from simple percentages to complex analyses of variance, multiple regressions,and general linear models. You can use data ranging from simple integers/binaryvariables to multiple response or logarithmic variables. SPSS also provides extensivedata management functions, along with a complex and powerful programminglanguage.STATISTICS PROGRAMSPSS (originally, Statistical Package for the Social Sciences) was released in its firstversion in 1968 after being developed by Norman H. Nie and C. Hadlai Hull. NormanNie was then a political science postgraduate at Stanford University, and nowResearch Professor in the Department of Political Science at Stanford and ProfessorEmeritus of Political Science at the University of Chicago. SPSS is among the mostwidely used programs for statistical analysis in social science. It is used by marketresearchers, health researchers, survey companies, government, education researchers,marketing organizations and others. The original SPSS manual (Nie, Bent & Hull,TYPESOFTABLESOBJECTIVESAND THESCOPE OFTHEENQUIRIESNATURE OFTHEENQUIRYEXTENT OFCOVERAGEGIVEN INTHEENQUIRYGeneralPurpose orReferenceTableSpecial Purposeor SummaryTableOriginal orPrimary TableDerived orDerivativeTableSimple Table Complex Table46
  47. 47. RESEARCH METHODOLOGY & STATISTICAL TOOLS1970) has been described as Sociologys most influential book. In addition tostatistical analysis, data management (case selection, file reshaping, creating deriveddata) and data documentation (a metadata dictionary is stored in the data file) arefeatures of the base software.Statistics included in the base software:• Descriptive statistics: Cross tabulation, Frequencies, Descriptive, Explore,Descriptive Ratio Statistics• Bi-variate statistics: Means, t-test, ANOVA, Correlation (bi-variate, partial,distances), Nonparametric tests• Prediction for numerical outcomes: Linear regression• Prediction for identifying groups: Factor analysis, cluster analysis (two-step,K-means, hierarchical), DiscriminantThe many features of SPSS are accessible via pull-down menus or can be programmedwith a proprietary 4GL command syntax language. Command syntax programminghas the benefits of reproducibility; simplifying repetitive tasks; and handling complexdata manipulations and analyses. Additionally, some complex applications can only beprogrammed in syntax and is not accessible through the menu structure. The pull-down menu interface also generates command syntax, this can be displayed in theoutput though the default settings have to be changed to make the syntax visible to theuser; or can be paste into a syntax file using the "paste" button present in each menu.Programs can be run interactively or unattended using the supplied Production JobFacility. Additionally a "macro" language can be used to write command languagesubroutines and a Python programmability extension can access the information in thedata dictionary and data and dynamically build command syntax programs. ThePython programmability extension, introduced in SPSS 14, replaced the less functionalSAX Basic "scripts" for most purposes, although Sax Basic remains available. Inaddition, the Python extension allows SPSS to run any of the statistics in the freesoftware package R. From version 14 onwards SPSS can be driven externally by aPython or a VB.NET program using supplied "plug-ins".SPSS places constraints on internal file structure, data types, data processing andmatching files, which together considerably simplify programming. SPSS datasets47

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