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Showing papers in "Review of Educational Research in 1974"


Journal ArticleDOI
TL;DR: A review of the research on the use of cooperative, competitive, cooperative, and individualistic goal structures on learning processes and outcomes can be found in this article, where the authors present a complete view of the conditions under which each type of goal structure should be used.
Abstract: Theories of instruction are prescriptive, in the sense that they set forth rules concerning or specifying the most effective way of achieving knowledge or mastering skills. Although there has been a great deal of debate concerning various aspects of the instructional situation, most educators seem to assume that there are no operational alternatives to the competitive goal structure in which students are expected to outperform their peers. There has been little recognition of the powerful effects the goal structure has upon student behavior, and the relevant social psychological research has never been fully reviewed. There are four possible goal structures which can be implemented in a learning situation: competitive, cooperative, individualistic, and no structure. Each type of goal structure has an implicit value foundation which is taught subtly, as an unconscious curriculum, to the student who interacts within it. There is a great deal of evidence that the process by which students learn (i.e., the way in which students interact and behave in learning situations) and the outcomes of learning are both largely determined by the goal structure implemented by educators. The purpose of this article is to present a review of the research on the use of cooperative, competitive, and individualistic goal structures on learning processes and outcomes. Before beginning the review the authors wish to make their bias clear. We believe that cooperative, competitive, and individualistic goal structures are all appropriate and effective under different conditions, that educators should use all three goal structures depending upon the specific instructional objectives, and that students should be taught the basic skills necessary to function in all three types of situations. There are some difficulties, however, with presenting a complete view of the conditions under which each type of goal structure should be used. There is little research comparing individualistic goal structures with cooperative and competitive goal structures and, therefore, the research on cooperation and competition dominates the review. Although there is a great deal of research comparing cooperative and competitive goal structures, this research has not clearly specified the conditions under which each is desirable. Much of the current literature on educational

473 citations


Journal ArticleDOI
TL;DR: A survey of research on the effectiveness of alternative instructional media can be found in this paper, where traditional classroom instruction (TI), instructional radio (IR), instructional television (ITV), programmed instruction (PI), and computer-assisted instruction (CAI).
Abstract: This survey provides an overview of research on the effectiveness of alternative instructional media. The media discussed are traditional classroom instruction (TI), instructional radio (IR), instructional television (ITV), programmed instruction (PI), and computer-assisted instruction (CAI). The effectiveness of these media is examined from a reasonably macroscopic point of view; the psychology of pupil-teacher interaction or the 'content variables' of ITV, to take two examples, are at a micro-level not considered. Achievement test scores constitute the measure of effectiveness most frequently used in this survey though, where available, results concerning the affective impact of the various media of instruction are included. Achievement test data, in most cases, were collected only on an annual basis, so they reveal no fine-grained detail about the learning process. Since this survey is relatively brief and its scope broad, a few caveats are in order. First, where literature surveys are available, their results have been cited to the extent possible and, frequently, original sources remain unchecked. Second, available knowledge of the effectiveness of the various media varies considerably; much more is known about TI and ITV than about the others. For this reason a survey such as this is inherently spotty in its conclusions. The third warning, related to the second, is that many of the evaluations fall short of (or lack entirely) scientific standards of analysis and reporting. For this reason, it was sometimes necessary to attempt to cull conclusions from essentially journalistic accounts of projects. Fourth, it should be noted that this survey is limited to instruction within a school setting. Finally, the survey excludes information on costs. Before beginning the literature survey, we present a paradigm for measurement of effectiveness and then discuss several less desirable alternatives that have actually been employed. In the surveys of the individual methods where adequate prior surveys are unavailable, results from a representative sample of individual evaluations are discussed.

251 citations


Journal ArticleDOI
TL;DR: Campbell and Stanley as discussed by the authors discussed the problems of describing independent variables, multiple-treatment interference, Hawthorne, novelty, and experimenter effects, pretest and posttest sensitization, interaction of history and treatment, and the measurement of dependent variables.
Abstract: A decade has passed since the publication of Campbell and Stanley's (1963) monumental treatise on experimental design in educational research. That document synthesized much prior thinking as well as original work and established clear principles for both designing and evaluating educational experiments. It provided a systematic study of quasi-experiments, i.e., useful compromises on the characteristics of true experimental designs. It also did much to develop the experimental attitude so apparent today among experienced and novice investigators alike. In analyzing threats to the validity of experiments, Campbell and Stanley distinguished between internal validity (i.e., interpretability) and external validity (i.e., generalizability), but they concentrated attention on internal validity. An important extension of their work was contributed by Bracht and Glass (1968), who elaborated considerably the concept of external validity. They dealt with two classes of threats to external validity, calling these population validity and ecological validity. Under the first heading, they examined the issues involved in generalizing from samples, through experimentally accessible populations of students, to ultimate target populations and reviewed the possibility that person characteristics might interact with experimental variables to limit generalizations about treatment effects. Under ecological validity, they discussed the problems of describing independent variables, multiple-treatment interference, Hawthorne, novelty, and experimenter effects, pretest and posttest sensitization, interaction of history and treatment, and the measurement of dependent variables. They closed their paper suggesting that extension of the list of threats and revision of experimental designs to control for such threats would be useful next steps. This paper explores some of these next steps. Initially, it seeks merely to reconstruct and extend some old ideas for inclusion in the field that might be called the "metatheory" or "comparative methodology" of educational research. In so doing, however, it suggests that some rather unconventional additions and revisions in the design and analysis of educational experiments may be needed. It becomes apparent that the biggest threat to external validity may come when the experiment does not fit the nature of the behavior being studied and,

204 citations


Journal ArticleDOI
TL;DR: In this paper, Rosenshine and Furst cite some 50 studies and propose 11 teacher-behavior variables they regard as ''the most promising of the variables studied.'' The variables proposed are: (1) clarity, (2) variability, (3) enthusiasm, (4) task-oriented and/or businesslike behaviors, (5) student opportunity to learn criterion material, (6) use of student ideas and general indirectness, (7) criticism, use of structuring comments, (8) types of questions, (10) probing, and (
Abstract: In recent years research and development in teaching have been strongly influenced by the idea of “ performance based teacher education,\" that is, the identification of operationallydefined teacher skills that are related to increased student achievement and the corresponding development of teacher training programs and materials (see Gage, 1972). Since hundreds of millions of dollars annually and substantial human resources are involved, the scientific basis for this movement is of considerable importance. In our opinion, an analysis of the research on the relation between specific teacher skills and student achievement fails to reveal an empirical basis for performance-based teacher education. The contribution by Rosenshine and Furst, \"Research on Teacher Performance Criteria\" in the book Research in Teacher Education: A Symposium, 1971 (edited by B. O. Smith), reviews a carefully selected set of studies. Rosenshine's several writings on this and related topics establish him as knowledgeable of this body of literature. Rosenshine and Furst cite some 50 studies and propose 11 teacher-behavior variables they regard as \"the most promising of the variables studied.\" The variables proposed are: (1) clarity, (2) variability, (3) enthusiasm, (4) task-oriented and/or businesslike behaviors, (5) student opportunity to learn criterion material, (6) use of student ideas and general indirectness, (7) criticism, (8) use of structuring comments, (9) types of questions, (10) probing, and (11) level of difficulty of instruction, in that order. The studies cited, and the teaching variables proposed, were carefully selected to represent the most conclusive and the \"best\" research to be found. Rosenshine and Furst (1971) say:

163 citations


Journal ArticleDOI
TL;DR: In this article, the authors discuss some propositions about the structure and incentive systems of public schools as they relate to the adoption of innovations and to their implementation in the schools, and they have certain systematic implications for educational research and development (R&D) policy and also for such broader questions as how to implement planned change in bureaucracies.
Abstract: Publisher Summary This chapter discusses some propositions about the structure and incentive systems of public schools as they relate to the adoption of innovations and to their implementation in the schools. These propositions may have certain systematic implications for educational research and development (R&D) policy and also for such broader questions as how to implement planned change in bureaucracies. A major focus of R&D policy should be, through experimentation and through incentives that encourage new patterns of institutional behavior, and to encourage a long-overdue diversity of approaches to schooling. Even with more sophisticated approaches to R&D management and to the realities of implementation, the task will be long, costly, and difficult. In the current state of knowledge, this process must be justified primarily on the grounds that an educational system that develops effective mechanisms for innovation is more likely to respond to changing social needs than one that is primarily centered on preserving the existing institutional order.

119 citations


Journal ArticleDOI
TL;DR: In this article, the authors discuss the relationship between psychological decision theory and various vocational decision-making theories and the population of decision situations with which people are faced, and suggest applications of theory to theoretical decision types.
Abstract: Vocational development has been described as the processes of preparation for and entry into a series of education and work roles over a lifetime. During the 1960's, a number of vocational theorists speculated that these processes could be understood better by employing concepts suggested by psychological decision theory. Indeed the promise that fundamental decision concepts have for enriching our understanding of vocational development received early acclaim (Blau, Gustad, Jesser, Parnes, & Wilcock, 1956; Brayfield, 1963, 1964; Super, 1961; Tyler, 1961). Recent reviews of vocational development theories have concluded that this promise remains largely unfulfilled (Crites, 1969; Kroll, Dinklage, Lee, Morley, & Wilson, 1970; Osipow, 1968.) One major problem in integrating this literature is that various theorists have not employed either the framework or the language of their predecessors. Several questions can be raised: Among the various theories, are there similarities in the basic concepts that are observed by the differences in language? Do the theories fit the same population of decision situations? Do certain theories better describe certain types of decisions? How do the theories vary in terms of assumptions about characteristics of decision-makers and their resources? The authors believe that psychological decision theory provides a useful framework for clarifying the relationships among various vocational decision-making theories and between these theories and the population of decision situations with which people are faced. This paper outlines psychological decision theory; summarizes eight prominent vocational decision-making (VDM) models; compares and contrasts VDM models on basic assumptions and fundamental concepts; and suggests applications of theory to theoretical decision types. Implications for research, theory, and practice are discussed.

107 citations


Journal ArticleDOI
TL;DR: Kohlbergian value education programs are based on ideas that have been around for some time; the programs integrate and concretize these basic ideas in new ways, although many further developments are necessary before one can claim to have successfully developed a distinctively new kind of educational program as discussed by the authors.
Abstract: The enthusiasm that Kohlberg and his associates have recently generated in value education programs lies not so much in new curriculum materials and new teaching techniques, nor in the demonstration of spectacular results in their pilot programs, but rather in the way they discuss their general directions and purposes in terms of philosophical and psychological theory and research. Kohlberg has characterized his efforts as "warmed-over Dewey," and refers to John Dewey as "the only modem thinker about education worth taking seriously" (Kohlberg, 1971a). Dewey laid out an educational program in broad philosophical terms. It was not, however, until Piaget's work that a psychology was begun which "developed the general premises of Dewey ... into a science of great richness and logical and empirical rigor." Following Piaget, Kohlberg has worked "to make Dewey's ideas concrete," and Kohlberg's associates, in turn, have worked on "an application of Kohlberg to a high school curriculum (Sprinthall, 1971b)." Educational programs with such a venerable lineage (DeweyPiaget-Kohlberg, and so forth), have created interest because of the intellectual heft behind them and the promise of initiating something more than a superficial, piecemeal, short-lived fad. A review of these current educational programs entails a consideration of the way in which the foundational ideas have been extended in educational practice and a consideration of their distinctive features. I shall not review the psychological research on which the programs are based but rather the way in which the conclusions from research are used to guide program construction. The gist of this review is that "Kohlbergian" value education programs are based on ideas that separately have widespread acceptance and that have been around for some time; the programs integrate and "concretize" these basic ideas in new ways, although many further developments are necessary before one can claim to have successfully developed a distinctively new kind of educational program. Some next steps in program development will be suggested.

81 citations



Journal ArticleDOI
TL;DR: The idea of developing instructional programs in our schools to meet individual student needs is not a new theme in American education (Washburne, 1922; Wilhelms, 1962), but it has been only in the last decade that such programs have been implemented on any large-scale basis in the schools as discussed by the authors.
Abstract: The idea of developing instructional programs in our schools to meet individual student needs is not a new theme in American education (Washburne, 1922; Wilhelms, 1962), but it has been only in the last decade that such programs have been implemented on any large-scale basis in the schools. The basic argument in favor of individualizing instruction comes from a multitude of research and evaluation studies that suggest that students differ in interests, motivation, learning rate, goals, and capacity for learning, among other things; and, therefore, group-based instruction on a common curriculum is inappropriate to meet their educational needs. The necessity for change in our schools is evident when one notes, for example, that schools provide successful learning experiences for only about one-third of our students (Block, 1971). On the basis of Project TALENT data, Flanagan, Davis, Dailey, Shaycoft, Orr, Goldberg, and Neyman (1964) and Flanagan (1973) reported that our standard instructional programs are inadequate to handle the large individual differences in any age or grade group. In addition, these authors note that schools generally fail to help the student to cultivate a sense of responsibility for his educational, personal, and social development or to make realistic educational decisions and choices about his future.

55 citations


Journal ArticleDOI
TL;DR: The authors found evidence that the more militant labor unions are composed of members of occupations whose place of work and residence removed them from frequent contact with the middle-class world, and that the relationship between the social class composition of high schools and the educational plans of students suggest a peer influence explanation.
Abstract: The prolongation of adolescence in the United States suggests that the educational plans of adolescents may be more affected by peers than was formerly the case. Years ago, Karl Marx claimed that workers would become more class-conscious when they moved from rural areas and villages to the working-class districts of large cities. He foresaw a greater degree of mutual influence when workers were thus removed from the influence of persons of a different class. In a similar vein, Kerr and Siegel (1954) found evidence that the more militant labor unions are composed of members of occupations whose place of work and residence removed them from frequent contact with the middle-class world. An analogous situation has resulted in part from the long-term trend in high school attendance. In the United States in 1870, about two percent of persons seventeen years of age graduated from high school; today the figure is more than seventy percent. Today's adolescents are more likely to be influenced by each other than would be the case if they were to begin working soon after completing elementary school. While high school and college students are subject to adult influence, they are subject to that influence in the company of a large number of other adolescents. Indeed, the emergence of an \"adolescent subculture\" has been noted by a number of social observers, although there is some dispute as to the extent to which this is simply age-graded or adult-expected behavior or is behavior that conflicts with the expectations of adults. In sum, it seems highly probable that to a greater extent than formerly, adolescents in the United States are influenced by other adolescents. Whether this influence extends to a given kind of behavior does not automatically follow. However, some recent studies of the relationship between the social class composition of high schools and the educational plans of students suggest a peer influence explanation

42 citations


Journal ArticleDOI
TL;DR: The authors divided the article into three main parts, treating first problems of language and language development, second problems of concept formation and abstraction, and third problems of elementary mathematical skills, and made some effort to locate studies dealing with mathematical skills.
Abstract: important in training handicapped children for productive careers in society. It is also the set of skills most important for normal children. This does mean that to some extent I neglect the full range of psychological studies of concept formation in handicapped children. I am excluding the many studies on operant conditioning, reinforcement schedules, paired-associate learning and the like, especially in mentally retarded children. It is possible to make a case that these studies fall within the general area of cognition, but it is also reasonable to exclude them, and I have done so here. There have been a great many studies in the general area I am excluding, and the interested reader will find it easy to get into that literature from some of the survey references given below. I have divided the article into three main parts, treating first problems of language and language development, second, concept formation and abstraction, and third, elementary mathematical skills. As might be expected, the literature on language development, for example, is larger by an order of magnitude than the literature on the development of mathematical skills. I have made some effort to locate studies dealing with mathematical skills, but it will be clear to the

Journal ArticleDOI
TL;DR: In a very brief survey during 1969 of twenty member countries, the O.E.C.D. as mentioned in this paper found 123 mathematical planning models with a status of either "finished" or "in progress" and not all educational planning models within each country were listed.
Abstract: Over the past ten to fifteen years, attempts have been made within various research institutes to develop mathematical models to help in educational planning. Recognition of the potential of models as planning tools has grown enormously over this period. In a very brief survey during 1969 of twenty member countries, the O.E.C.D. found 123 mathematical planning models with a status of either "finished" or "in progress"-and not all educational planning models within each country were listed (Kahn, 1970). This survey reflects the acceptance that the principle of the need to build models has achieved.

Journal ArticleDOI
TL;DR: A review of the use of environmental measures in college environments can be found in this article, with a focus on three major categories of decisions for which environmental information may be useful: decisions among institutions, decisions within institutions, and decisions concerning people.
Abstract: "How can I decide whether the present or the experimental dormitory arrangement is best?" "How can I choose the best college for me?" "How satisfied are our students with our professors?" "Which goals for our college have the greatest support in the community?" These questions are often heard by institutional researchers, psychologists, and sociologists. Asking these questions are students, administrators, and faculty. Implicitly, they all are asking for information that will help them make decisions. They want to choose, evaluate, or improve colleges. To do this, they need objective information that will help them choose between courses of action. So, they come to the researcher for help. What objective information can he provide that will be useful? If the researcher turns to current measures of college environments, he is likely to be frustrated. As recently suggested in a review (Baird, 1973), there is little in existing measures of the college environment to help in pragmatic decisions, and they are so atheoretical and global that they are unrelated to concepts that could suggest pragmatic actions. The purpose of this paper is to (1) review how environmental measures have been used and (2) suggest how environmental measures could be made more useful. The questions that researchers hear suggest the scope of purposes that environmental measures are asked to serve. These purposes may be grouped into several major categories of decisions for which environmental information may be useful: decisions among institutions, decisions within institutions, decisions concerning people, and decisions concerning nonpersonal resources. Decisions among institutions are those that involve the comparison of one institution with others, or of one type of institution with others, for example, when a high school student selects a college, or when a state legislator decides whether to spend more on universities or community colleges. Decisions within institutions are decisions that involve the comparison of one part of an institution with another, or of one way of doing things with another. Examples include comparing the teaching practices in the humanities with those in engineering and comparing an experimental curriculum with the regular curriculum. Decisions concerning people include those

Journal ArticleDOI
TL;DR: There have been many hypotheses concerning trie antecedents of poor school performance of lower-class black children as mentioned in this paper, and one of those most frequently mentioned concerns their language, however, as to the aspects of the language which cause the difficulty.
Abstract: There have been many hypotheses concerning trie antecedents of poor school performance of lower-class black children. One of those most frequently mentioned concerns their language. There is controversy, however, as to the aspects of the language which cause the difficulty. When intervention projects were being initiated in the early 1960's, several psychologists suggested that the language of the lower-class child was inadequate for learning the skills necessary for school or even for thinking (for statements of this sort see Brottman, 1968). That is, the inference was made that the language used by the lower-class child was inferior to that of the middle-class child. Linguists, psycholinguists, social linguists, and some psychologists, however, have taken issue with this position on several counts. First, linguists point out that the language of the lower-class child may be different, but there is no evidence that it is inferior. Indeed linguists have found that there are far more linguistic universals than differences. In fact, even the most primitive tribes have language systems as complicated as Standard English (SE). These linguists, for example, Chomsky, take the viewpoint that the ability to develop language is unique to the human being and that each child is endowed with a language acquisition device that makes it possible for him to acquire the rules that allow him to process and generate his language. Thus, there are no "inferior" languages. This position has received empirical support from a number of respected sources (Lenneberg, 1967; Chomsky, 1965, 1968; McNeill, 1970). Additional support of this position has been presented by sociolinguists who point out that many of the language samples gathered from lower-class subjects were recorded in school, not in situations where the lower-class children exhibit their most complex language behavior. When the lower-class black child is observed in a number of more natural settings, he exhibits a language that contains all of the complexities of the language spoken by middle-class white children (Houston, 1970; Labov, Cohen, Robins, & Lewis, 1968). Finally, there is some question as to the role that language itself plays in cognitive ability. More specifically, Piagetian theory and theorists have suggested that language may not be necessary for solving complex tasks.


Journal ArticleDOI
TL;DR: Curriculum theorists have repeatedly stressed the importance of providing for structure in the curriculum (Bruner, 1960; Gagne, 1971; Goodlad & Richter, 1966; Johnson, 1969; Taba, 1962; Tyler, 1950) as mentioned in this paper.
Abstract: Curriculum theorists have repeatedly stressed the importance of providing for structure in the curriculum (Bruner, 1960; Gagne, 1971; Goodlad & Richter, 1966; Johnson, 1969; Taba, 1962; Tyler, 1950). Many theorists have not only exhorted curriculum developers to structure their curricula but have identified factors related to the extensiveness of curriculum structure.2 Such factors have included "continuity," "sequence," and "integration" (Tyler, 1950); "spiraling" (Bruner, 1961; Schrader, 1972); "hierarchical arrangement" (Briggs, 1968; Gagne, 1971); "flat" versus "vertical structure" (Briggs, 1968); "kinetic" versus "static structure" and "commonality" versus "progression" (Anderson, 1971); and "coherence" (Schrader, 1972). With such diverse terms as these in the literature and little or no

Journal ArticleDOI
TL;DR: The College Entrance Examination Board Scholastic Aptitude Test (SAT) is a widely used and highly useful measure of academic ability as mentioned in this paper, however, its use as a separate, independent measure has been justified primarily in terms of its supplementary nature.
Abstract: The College Entrance Examination Board Scholastic Aptitude Test (SAT) is a widely used and highly useful measure of academic ability. Yet, its use as a separate, independent measure has been justified primarily in terms of its supplementary nature. The College Board has consistently emphasized the inadvisability of using the test as a single, absolute measure of academic ability. The SAT's purpose, as stated explicitly by Donion and Angoff (1971), is \"to supplement the school record and other information about the student in assessing his competence for college work [p. 15] . \" Donlon and Angoff believe furthermore that the essential supplementary nature of the SAT is attested to in the way that the SAT's effectiveness is usually evaluated. They state:

Journal ArticleDOI
TL;DR: It would seem that a promising biochemical variable should satisfy at least three conditions: it should account for unexplained variance and should not be strongly correlated with ability or with psychological traits or variables for which the authors already have less cumbersome assessment procedures and which are already being used in predicting academic achievement.
Abstract: Our understanding of scholastic performance and achievement has reached a plateau, since it would appear that the major ability and motivational determinants (and the associated background and socioenvironmental factors) have been identified, assessed, and tested out for their predictive usefulness. A significant improvement in our understanding and prediction of scholastic achievement could come from the identification of new, relevant ability dimensions or from a considerable improvement in our assessment procedures of the more elusive motivational variables, but at the moment neither possibility appears very likely. Another strategy is to go to a radically different class of variables that have so far been largely unexplored, and to identify one or more variables which show promise of accounting for some of the unexplained variance in scholastic achievement. Biological or biochemical variables are such a class and, off and on in the past, educators have been intrigued and tantalized by them. Now, while it is true that the absence of any striking success from the previous sporadic work in this domain rules out any reasonable hints of an impending "breakthrough," it is also true that some of the work, such as with glutamic acid (Vogel, Broverman, Draguns, & Klaiber, 1966), shows more than minimal promise. Furthermore, promise of identifying a useful biochemical variable is enhanced if one starts out not blindly (or with the enthusiasm of a "dustbowl empiricist"), but with some approximate guidelines. It would seem that a promising biochemical variable should satisfy at least three conditions: (1) It should account for unexplained variance and should not be strongly correlated with ability or with psychological traits or variables for which we already have less cumbersome assessment procedures and which are already being used in predicting academic achievement. (2) The levels of the biochemical variable should be subject to experimental alteration through reasonably simple means and without serious side effects. (3) Existing knowledge about the biochemical should be able to generate a plausible explanation about the possible mechanism whereby human functioning and behavior may be influenced by this biochemical.

Journal ArticleDOI
TL;DR: There seemed to be general consensus that the threefold purpose of drug education was to increase knowledge about drugs, promote healthy attitudes toward the use of drugs, and decrease (potential) drug abuse behavior in the general population.
Abstract: Drug education differs considerably from crisis intervention and treatment. Workers in the latter fields find themselves involved in bringing people down from bad trips, in tending to those who have overdosed, and in helping addicts be rid of their habits through, for example, methadone maintenance or behavior therapy (e.g., Harris, 1973; Wisocki, 1973). Drug education, on the other hand, focuses on drug abuse prevention. Its programs are broader in scope, dealing for the most part with as yet non-drug-involved populations. The drug educator of the 1960's had a lot in common with Christopher Columbus. Both were seeking a newer world, but then again, both started out not knowing where they were going; both ended up not knowing where they had been, and both did it all on government money. In the early 1970's, however, there seemed to be general consensus that the threefold purpose of drug education was to (1) increase knowledge about drugs, (2) promote healthy attitudes toward the use of drugs, and (3) decrease (potential) drug abuse behavior in the general population (Horan, Shute, Swisher, & Westcott, 1973; Warner, Swisher, & Horan, 1973). But even this academic entente is fraught with conceptual and empirical problems.

Journal ArticleDOI
TL;DR: In this paper, the problem of unbalanced data analysis has been studied in a wide range of settings, e.g., linear models where the numbers of observations in the subclasses are unequal.
Abstract: Increasing interest has been expressed, particularly by social scientists, in the analysis of unbalanced data occurring in models not of full rank, i.e., linear models where the numbers of observations in the subclasses are unequal. The various discussions of this problem that have appeared in the psychological and educational literature differ depending upon the intent of the author(s). For example, some writers (Gourlay, 1955; Steinhorst & Miller, 1969; Tsao, 1942, 1946; Williams, 1972) have examined and at times compared different types of solutions, including approximate solutions, for the unbalanced case. Other writers (Overall & Spiegel, 1969; Rawlings, 1972) have focused upon the difficulty which arises in interpreting the results of unbalanced data analyses because the estimable functions involved in tests of hypotheses are not orthogonal. Though not specifically addressed to the unbalanced case but important in this regard is the work of Bottenberg and Ward (1960), Cohen (1968), Hurst (1970), and Jennings (1967) that demonstrates the equivalence of linear regression and the fixed-effects analysis of variance by the use of regression on dummy variables. This diversity in purpose, combined with the relative narrowness of the individual efforts, has resulted in a fragmented treatment of the problem of unbalanced data and in some cases confusion and controversy regarding methodology, e.g., the role of constraints in obtaining a solution for models not of full rank or the calculation of reductions in sums of squares (Overall & Spiegel, 1973; Rawlings, 1973; Smith, 1973). In response, at least one writer (Joe, 1971) has been prompted to call for a greater understanding and more detailed presentation of the models employed. Some of the more important issues encountered in the analysis of unbalanced data will be examined here within a single framework. These issues are broadly defined as (1) solutions to the normal equations for linear models where the incidence or design matrix is not of full column rank, (2) estimable functions of the parameters and tests of hypotheses, and (3) reductions in sums of squares and interpretation of results. Because of the increased availability of computer hardware and sophisticated least squares routines, the various approximate solutions for analyzing unbalanced data are not considered here.