Includes bibliographical references."In any comprehensive research project, there are essentially five steps. First, one starts with a literature review with regard to a particular research question. Second, one seeks to develop a theory. Third, the research question is finalized, frequently in the form of a hypothesis to be tested. Fourth, data are collected. Fifth, the subject matter of this paper, the data are analyzed in order to come to a resolution of the research question. There are two general approaches to analyzing research data. If the data were gathered concerning a 'research question,' a description of the data may be sufficient. However, if the data were gathered to accept or reject a formal hypothesis, statistical analysis is usually in order. This paper briefly surveys the principal data analysis methodologies that are available.

Brighton, Gerald D.

Michaelson, Robert H.

English

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jHR' '§liUNIVERSITY OfILLINOIS LIBRARYAX UREANA CHAMPAIGNSTACKSDigitized by the Internet Archivein 2011 with funding fromUniversity of Illinois Urbana-Champaignhttp://www.archive.org/details/dataanalysis540brig-of i^Faculty Working PapersCollege of Commerce and Business AdministrationUniversity of Illinois at U rba n a - Cha m p a ig nFACULTY WORKING PAPERSCollege of Commsrce and Business AdministrationUniversity of Illinois at Urbana-ChampaignJanuary 16, 19TJDATA ANALYSISGerald D, Brighton, Professor, Department ofAccountancyRobert H. Michaelson, Graduate Student inAccountancy#5A0Summary:In any comprehensive res-E.^'rch project, there are essentially five steps.First, one starts with a li'"i="::ture review with regard to a particularresearch question. Second, one seeks to develop a theory. Third, theresearch question is finalized, frequently in the form of a hypothesisto be tested. Fourth, data are collected. Fifth, the subject matterof this paper, the data are analyzed in order to come to a resolution ofthe research question. There are two general approaches to analyzingresearch data. If the data were gathered concerning a "research question,"a description of the data may be sufficient. However, if the data weregathered to accept or reject a formal hypothesis, statistical analysisis usually in order. This paper briefly surveys the principal dataanalysis methodologies that are available.tli.-:r.-.'-?,;;t:1. IntroductionIn any comprehensive research project, there are essentially fivesteps. First, one starts with a literature review ^rf.th regard to aparticular research question. Second, one seeks to develop a theory.Third, the research question is finalized, frequently in the form ofa hypothesis to be tested. Fourth, data are collected. Fifth, the sub-ject matter of this paper, the data are analyzed in order to come toa resolution of the research question.There are two general approaches to analyzing research data. Ifthe data were gathered concerning a "research question," a descriptionof the data may be sufficient. Also, data may be so obvious that astatistical test is not really necessary. However, if the data weregathered to accept or reject a formal hypothesis, statistical analysisis usually in order.Since this is a brief paper intended only to remind the aspiringresearcher of the principal data analysis methodologies that are avail-able, it of necessity includes some "technical jargon" that is notfully explained. To help in the solution of that potential problem,we have cited a general reference just below and are citing specificreferences in each section of the paper.General reference: Kerlinger, Fred N., Foundations of BehavioralResearch,New York: Holt, Rinehart , & Winston, 1973,II. Nonstatistical MethodsOnce data have been collected concerning a study, it will alwaysbe necessary to arrange these data in a logical manner, whether or notstatistical analysis is employed, so that the relationships of the re-search problem can be studied. If statistical analysis is not employed,-2-the data are still analyzed in a descriptive manner, often with the useof frequency distributions, crossbreaks, and graphs. Once the data areproperly analyzed, interprenation can proceed so that conclusions canbe drawn concerning the res(;arch relationships studied.In addition to informal description, formalized methods of nonsta-tistical data analysis have been developed. This formalization concernsthe manner In which the data are measured, categorized, ordered, andsummarized. For example, scales are employed to measure variables. Ascale is a set of symbols o-.: numerals so constructed that they can beassigned by rule to individuals to whom the scale is applied, the assign-ment being indicated by the individual's possession of whatever attrib'-*"'the scale is supposed to measure. As an example of a particular appli-cation, a scaling technique that has been used to analyze the decisionsof Tax Court judges is a cumulative attitude scale called the Guttmanscale. ;Guttman scaling postulares that if the responses to a set of itemsreferring to an attitude area can be arranged in certain specified ways,that area is scalable and a respondent's rank makes it possible to pre-dict exactly which iteiTis were answered favorably. If a set of data isscalable, scalogram analysis will establish an order among the data andpinpoint deviations from thii group. This m.ethod is simpler than sophis-ticated statistical methods, but does not provide their detailed speci-fication of pivotal factors.Reference: Edwatds, A., Techniques of Attitude Scale Construction ,:'New York: Appletoi, 1957.-3~Again, even if statistical methods are being applied, it is alwaysnecessary first to sort and arrange the data in some logical order.This may be as simple as tables of data. It is a mistake, therefore,to think that nonstatistical analysis methods are not important. Thereal point is that increasingly they are not sufficient.The emphasis in research on statistical methods is because statis-tical methods are a more scientific approach and consequently increasethe acceptability of the results. The remainder of this discussion con-cerns statistical methods of data analysis.III. Modern Statistical MethodsA. Situations With Only One Independent and Dependent Variable (orOnly Two Groups )The most common situations with one independent and dependent variableinclude comparison of a mean, variance, correlation coefficient, orproportion of a sample with the same property of another sample or ofthe population. Because of the simplicitj' in experimental design thatis required for such statistics, they are often inapplicable.Reference: Glass, G. , and Stanley, J,, Statistical Methods inEducation and Psychology,Englewood Cliffs, N.J.: Prentice-Hall, Inc., 1970.B. Situations With More Than One Independent or Dependent Variable (orMore Than Two Groups )In more complex situations, three basic approaches are available:analysis of variance, regression analysis, and factor analysis. Each ofthese approaches is superior to the others in a particular set of circum-stances. In the remainder of this discussion, the question of when eachof these approaches is preferred will be briefly sketched.-4-1. Analysis of variance (anova)Analysis of variance is a method of identifying, breaking down, andtesting for statistical significance the variances in the dependentvariable that come from different sources of variation. According toKerllnger (general reference, p. 238), analysis of variance is the pre-ferable method of data analysis for the following reasons. It:(1) Permits us to test several hypotheses at one time.(2) Permits us to test hypotheses that cannot be tested in any otherway, at least with precision.(3) Gives insight into research approaches and methods by focusingsharply and constantly on variance thinking, by making clear theclose relationship between research problems and statistical methodsand inference, and by clarifying the structure of research design.Although analysis of variance would virtually always be preferableif It were applicable, applicability Is a serious problem. In general,anova is best suited to experimental research In which the subjects canbe randomly assigned to cells (groups), the group n's thus kept equaland the assumptions behind the method more or less satisfied (Kerllnger,general reference, pp. 268-269). Anova is not nearly so well suited toexpost (data retrieval or field study) research, or experimental re-search that uses a number of nonexperimental (attribute) variables,for the following reasons:(1) In such cases, interaction can be caused by some extraneous, un-wanted, uncontolled effect.(2) If the n's in the cells of a factorial design are not equal orproportionate, the independence of the Independent variables is-5-Itnpaired. While adjustments can be made, they are awkward and nottoo satisfactory. In nonexperimental anova, the n's get beyondthe control of the researcher. Also, In experiments with morethan one categorical variable (like race and sex), n's almost nec-essarily become unequal.A brief description of the various types of anova follows: -a. Factorial AnovaFactorial anova is the statistical method that analyses the inde-pendent and interactive effects of two or more Independent variables ona dependent variable.Reference: Kirk, R,,Experlm-ental Design; Procedures for theBehavioral Sciences,Belmont, Calif.: Brooks/Cole, 196S.b. Nonparametric AnovaNonparametric statistics use properties of data other than thestrictly quantitative. These statistics are based on properties ofdata that can be tested against chance expectation: rank, range,periodicity, distribution, etc.Reference: Slegel, Nonparametric Statistics for the BehavioralSciences,New York: McGraw-Hill, 1956.c. Analysis of Covariance (Ancova)Ancova is used when it is necessary to study groups as they are;when subjects cannot be matched or assigned at random. Ancova teststhe significance of the differences hetvjeen means of final experimentaldata by taking into account the correlation between the dependentvariable and one or more covariates, and by adjusting initial mean dif-ferences in the experimental groups.Reference: Kirk, R. , Experimental Design: Procedures for theBehavioral Sciences, Belmont, Califs : Brooks/Cole, 1968.d. Multivariate AnovaMultivariate anova is the generalization of anova to any number ofindependent variables and any number of dependent variables.Reference: Tatsuol<:a, M.,Multivariate Analysis; Techniques forEducational and Psychological Research ^ New York: Wiley, 1*971.2. Regression AnalysisRegression analysis is a method for studying the effects and themagnitude of the effects of one or more independent variables on one ormore dependent variables using principles of correlation and regression.According to Kerlinger (general reference, p. 268), regression analysisis the best method for analyzing data when the unequal n problem (dis-cussed under anova) appears. Tnis problem is most common with expost(data retrieval or field study) research, or experimental researchthat uses a number of nonexperimental (attribute) variables.A brief description of the various types of regression analysisfollows:a. Multiple Regression AnalysisMultiple regression analysis is a method for studying the effectsand the magnitudes of the effects of more than one independent variableon one dependent variable using principles of correlation and regres-sion. This analysis can be applied to cross-sectional data, time-seriesdata, or a combination of both.Reference: Kerlinger, F. , and Pedhazur, E. , Multiple Regressionin Behavioral Research , Nevv? York: Holt, Rinehart and Winston,1973.b. Discriminant AnalysisA discriminant function is a regression equation with a dependentvariable that represents group membership. The function maximally-7-dlscriminates the members of the group; It tells us to which group eachmember probably belongs. In short, if we have two or more independentvariables and the members of say, three groups, the discriminant func-tion gives the "best" prediction, in the least squares sense, of thecorrect group membership of each member of the sample. The discriminantfunction, then, can be used to assign individuals to groups on the basisof their scores on two or more measures. The discriminant approachgenerally provides the most accurate predictions in the sense of quan-tity right divided by predictions made.Reference: Tatsuoka, M. , Discriminant Analysis: The Study ofGroup Differences , Cham.paign, 111.: Institute for Personalityand Ability Testing, 1970.c. Canonical CorrelationThis is simply multiple regression analysis with more than onedependent variable. There are limitations in the interpretation ofthe results it yields.Reference: Cooley, w. , and Lohnes , P., Multivariate Data Analysis,New York: Wiley, 1971.3. Factor AnalysisFactor analysis is a method for determining the number and natureof the underlying variables among larger numbers of measures. It servesthe cause of scientific parsimony. It reduces the multiplicity of testsand measures toward greater simplicity. It tells us, in effect, whattests or measures belong together—which ones virtually measure the samething, and hov? much they do so. It thus is a technique to reduce thenumber of variables with which the scientist must cope.Reference: Harraan, H. , Modern Factor Analysis,2nd ed., Chicago:University of Chicago Press, 1967.IV. ConclusionObviously, no one method of data analysis is appropriate in all cir-cumstances. The best method must be determined on a project by projectbasis using the following considerations: i1. Nature of the data available. See discussion under anova.2. Intent or essence of the hypothesis or research question.3. Feasibility.4. Cost.5. Skill of the researcher.Finally, since data analysis is the last of five steps In the re-search process, it will need to be appropriate to the establishing ofthe validity of the data resulting from the preceding steps.,D/16.f\^.

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