sufficient. The effect size of the replication and of the original study must be Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7 reported, It is not crucial which particular effect size is employed, but the same effect size should be reported for the replication and the original study. Complete discussions of various effect sizes and when they are useful are available from Cohen (1977, 1988) and elsewhere (e.g., Rosenthal, 1984). If the original study and its replication are reported in different effect size units these can usually be translated to one another (Cohen, 1977, 1988; Rosenthal, 1984; Rosenthal & Rosnow, 1984; Rosenthal & Rubin, in press). Especially if the results of either the original study or its replication were not significant, the statistical power at which the test of significance was made (assum- ing, for example, a population effect size equivalent to the effect size actually obtained) should be reported (Cohen, 1988). In addition to reporting the statistical power for each study separately, it would be valuable to report the overall probability that both studies would have yielded significant results given, for example, the effect size estimated from the results of the original and the replication | study combined. As an illustration of this procedure, consider the data of Table 4. Employing Cohen’s power tables tells us that given an effect size of d=.50, Smith’s power to Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7
reject at p=. 5, two-tailed was .60 while Jones's power was .18. shows that _ Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7 given these two levels of power there were only 11 chances in a hundred that both studies would reject the null hypothesis given the effect size d=.50. Indeed, the odds were three times greater (p=.33) that neither study would reject the null hypothesis than that both would reject! Insert Table 8 about here Such results are not at all unusual. It has often been documented that behav- ioral researchers are far fonder of making type II errors than of making type I errors (Cohen, 1962, 1988; Rosenthal & Rosnow, in press; Rosenthal & Rubin, 1985; Sedlmeier & Gigerenzer, in press). It has been suggested that it is part of our d udeo- Christian-Shinto tradition that we be deeply troubled that somewhere out there someone might be having a good time, could be getting a free ride, a significant result they don’t deserve, an .05 asterisk that was actually intended for someone else. A marvelous suggestion has been made by Donald Rubin that would go a long way toward helping us get over our problem with the relative risks of type II versus type Ierrors. Don has suggested that whenever we conclude that there is “no effect” Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7
we report the effect size along with that confidence interval around the elfect size Approved For Release 2000/08/10 : CIA-RDP96-00792R0 . that ranges from the effect size of zero to the equally Hae e Root Coe an the one we obtained. To return to Table 4, the “failure to replicate” by Jones provides a good example. Jones did not reject the null but obtained an effect size of d=.50. If Jones had been required to report that his d of.50 was just as close to a d of 1.00 as it was to a dof zero, Jones would have been less likely to draw his wrong conclusion. Meta-Analytic Procedures: An Evaluation Of course it was bound to happen. No discussion of replication and of the evaluation of the success of a particular replication could long avoid a more formal consideration of meta-analytic procedures. In the years 1980, 1981, and 1982 alone, well over 300 papers were published on the topic of meta-analysis (Lamb and Whitla, 1983), Does this represent a giant stride forward in the development of the behavioral and social sciences or does it signal a lemming-like flight to disaster? Judging from reactions to past meta- analytic enterprises, there are at least some who take the more pessimistic view. Some three dozen scholars were invited to respond to a meta-analysis of studies of interpersonal expectancy effects conducted by Don Rubin and myself (Rosenthal & Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7
Rubin, 1978). Although much of the commentary dealt with the substantive topic of Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7 interpersonal expectancy effects, a good deal of it dealt with methodological aspects of meta-analytic procedures and products. Some of the criticisms offered were accurately anticipated by Glass (1978) who had earlier received commentary on his meta-analytic work (Glass, 1976) and that of his colleagues (Smith & Glass, 1977; Glass, McGaw, & Smith, 1981). In the present discussion, the criticisms of our commentators are grouped into several conceptual categories, described, and discussed. Sampling Bias and the File Drawer Problem _ This criticism holds that there is a retrievability bias such that studies retrieved do not reflect the population of studies conducted. One version of this criticism is that the probability of publication is increased by the statistical signifi- cance of the results so that published studies may not be representative of the studies conducted. This is a well-taken criticism, though it applies equally to more traditional narrative reviews of the literature. Procedures that can be employed to address this problem have been described elsewhere (Rosenthal, 1979a; 1984, Chapter 5; Rosenthal & Rubin, 1988). Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7
Loss of Information ae 8 Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7 Overemphasis on Single Values ‘Vhe first of two criticisms relevant to information loss notes the danger of trying to summarize a research domain by a single value such as a mean effect size. This criticism holds that defining a relationship in nature by a single value leads to overlooking moderator variables. When meta-analysis is seen as including not only con.bining effect sizes (and significance levels) but also comparing effect sizes in both diffuse and, especially, in focused fashion, the force of this criticism is removed (Rosenthal, 1984, Chapter 4). Overlooking negative instances. A special case of the criticism under discussion is that, by emphasizing average values, negative cases are overlooked. There are several ways in which negative cases can be defined: €.g.,p>.05, r=0, r negative, r significantly negative, and so on. However we may define negative cases, when we divide the sample of studies into negative and Positive cases we have merely dichotomized an underlying continuum of effect sizes or significance levels, and accounting for negative cases is simply a special case of finding moderator variables. Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7
Glossing over Details Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7 Although it is o:curate to say that meta-analyses gloss over details, it is equally as accurate to say that traditional narrative reviews do so, and that data analysts do so in every study in which any statistics are computed. The act of sum- marizing requires us to gloss over details. If we describe a nearly normal distribu- tion of scores by the mean and o we have neurly described the distribution perfectly. If the distribution is quadrimodal, the mean and o will not do a good job of summar- izing the data. It is the data analyst’s job in the individual study, and the meta- analyst’s job in meta-analysis, to “gloss well.’ Providing the reader with all the raw data of all the studies summarized avoids this criticism but serves no useful review function. Providing the reader with a stem-and-leaf display of the effect sizes | obtained, alon= with the results of the diffuse and focused comparisons of effect sizes, does some glossing, but it does a lot of informing besides. There is, of course, nothing to prevent the meta-analyst from reading each study as carefully and assessing it as creatively as might be done by a more traditional reviewer of a literature. Indeed, we have something of an operational check on reading articles carefully in the case of meta-analysis. If we do not read the results carefully, we cannot obtain effect sizes and significance levels. In traditional Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7
reviews, results may have been read carefully or not read at all, with the abstract or Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7 the discussion section providing “the results” to the more traditional reviewer. ’ Problems of Heterogeneity Heterogeneity of Method _ ‘The first of two criticisms relevant to problems of heterogeneity notes that meta-analyses average over studies in which the independent variables, the depen- dent variables, and the sampling units are not uniform. How can we speak of inter- personal expectancy effects, meta-analytically, when some of the independent variables are operationalized by (a) telling experimenters that tasks are easy versus hard; or by (b) telling experimenters that subjects are good versus poor task per- formers? How can we speak, meta-analytically, of these expectancy effects when sometimes the dependent variables are reaction times, sometimes IQ test scores, and sometimes responses to inkblots? How can we speak of these effects when sometimes the sampling units are rats, sometimes college sophomores, sometimes patients, sometimes pupils? Are these not all vastly different phenomena? How can they be pooled together in a single meta-analysis? Glass (1978) has eloquently addressed this issue--the apples and oranges issue. They are good things to mix, he wrote, when we are trying to generalize to fruit. Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7
Indeed, if we are willing to generalize over subjects within studies, why should we Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7 not be willing to generalize over studies? If subjects behave very differently within studies we block on subject characteristics to help us understand why. If studies yield very different results from each other, we block on study characteristics to help us understand why. It is very useful to be able to make general statements about fruit. If, in addition, it is also useful to make general statements about apples, about oranges, and about the differences between them, there is nothing in meta-analytic procedures to prevent us from doing so. Heterogeneity of Quality One of the most frequent criticisms of meta-analyses is that “bad” studies are thrown in with good. This criticism must be broken down into two questions: (a) What isa “bad” study?, and (b) What snall we do about “bad” studies? Defining “bad” studies. ‘Too often, deciding what is a “bad” study is a procedure richly susceptible to bias or to claims of bias (Fiske, 1978). “Bad” studies are too often those whose results we don’t like, or, as Glass, McGaw, and Smith (1981) have put it, the studies of our “enemies.” Therefore, when reviewers of research tell us they have omitted the “bad” studies, we should satisfy ourselves that this has been done by Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7
criteria we find acceptable. A discussion of these criteria (and the computation of Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7 their reliability) can be found elsewhere (Rosenthal, 1984, Chapter 3). Dealing with “bad” studies. The distribution of studies on a dimension of quality is, of course, not really dichotomous (good versus bad), but continuous with all possible degrees of quality. The fundamental method of coping with “bad” studies or, more accurately, variations in the quality of research, is by differential weighting of studies. Dropping studies is merely the special case of zero weighting. The most important question to ask relevant to study quality is that asked by Glass (1976): Is there a relationship between quality of research and effect size obtained? If there is not, thé inclusion of poorer quality studies will have no effect on the estimate of the average effect size though it will help to decrease the size of the confidence interval around that mean. If there is a relationship between the quality of research and effect size obtained, we can employ whatever weighting system we find reasonable (and that we can persuade our colleagues and critics also to find reasonable). Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7
Problems of Independence Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7 Responses Within Studies The first of two criticisms relevant to problems of independence notes that several effect size estimates and several tests of significance may be generated by the same subjects within each study. This can be a very well-taken criticism under some conditions and the problem has been dealt with elsewhere in some detail (Rosenthal, 1984, Chapter 2; Rosenthal & Rubin, 1986). Studies Within Sets of Studies Even when all studies yield only a single effect size estimate and level of significance, and even when all studies employ sampling units that do not also appear in other studies, there is a sense in which results may be nonindependent. That is, studies conducted in the same laboratory, or by the same research group, may be more similar to each other (in the sense of an intraclass correlation) than they are to studies conducted in other laboratories or by other research groups (Jung, 1978; Rosenthal, 1966, 1969, 1979b). The conceptual and statistical implications of this problem are not yet well worked out. Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7
Exaggeration of Significance Levels Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7 Truncating Significance Levels . It has been suggested that all p levels less than .01 (Z values greater than 2.33) be reported as .01 (Z2=2.33) because p’s less than .01 are likely to be in error (Elashoff, 1978). This truncating of Z’s cannot be recommended and will, in the long run, lead to serious errors of inference (Rosenthal & Rubin, 1978). If there is reason to suspect that a given p level <.01 isin error it should, of course, be corrected before employing it in the meta-analysis. It should not, however, be changed to p=.01 simply because it is less than .01. Too Many Studies It has been noted as a criticism of meta-analyses, that, as the number of studies increases, there is a greater and greater probability of rejecting the nul) hypothesis (Mayo, 1978). When the null hypothesis is false and, therefore, ought to be rejected, it is indeed true that adding observations (either sampling units within studies or new studies) increases statistical power. However, itis hard to accept as a legitimate criticism of a procedure, a characteristic that increases its accuracy and decreases its - error rate-- in this case, type I errors. Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7
A related feature of meta-analysis appears to be that it may, in general, lead to Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7 a decrease in type I errors even when the number of studies is modest. Empirical support for this is provided in a study conducted by Cooper and Rosenthal (1980). Procedures requiring the research reviewer to be more systematic and to use more of the information in the data seem to be associated with increases in power, i.e., decreases in type I errors. Some Benefits of Meta-Analysis — From what has been said of the various criticisms of meta-analysis it will surprise no one to learn that I strongly support the increasing use of meta-analytic procedures. My reasons for that support go beyond the fact that the various criticisms of meta-analysis can be readily addressed. In the time that remains I want to note a number of special benefits of meta-analysis. Some of these benefits are well known, but some are not--indeed, some are almost secret benefits. Most Obvious Benefits Completeness. Meta-analytic consideration of a research domain is more complete and exhaustive though this does not mean that all studies found are . weighted equally. Indeed, every study should be weighted from zero to any desired Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7
number. These weights, of course, must be defensible. (It will not do to weight all Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7 my results +1.00 and all my enemies’ results 0.00). Explicitness. The quantitative nature of the process of obtaining effect sizes, standard normal deviates, and weights, forces explicitness on the analyst. Vague terms like “no relationship,” “some relationship,” a “strong relationship,” “very significant,” are replaced by numerical values. Power. Empirical work has shown that meta-analytic procedures increase power and decrease type 2 errors (Cooper & Rosenthal, 1980). Less Obvious Benefits Moderator variables. These are more easily spotted and evaluated in a context of a quantitative research summary. This aids theory development and increases empirical richness. Cumulation problems. Meta-analytic procedures address, in part, the chronic complaint that social sciences cumulate so poorly compared to the physical sciences. It should be noted that recent historical and sociological investigations have sug- gested that the physical sciences may not be all that much better off than we are - when it comes to successful replication (Collins, 1985; Hedges, 1987; Pool 1988). For example, Collins (1985) has described the failures to replicate the construction of Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7
TEA-lasers despite the availability of detailed instructions for replication. Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7 Apparently TEA-lasers could be replicated dependably only when the replication instructions were accompanied by a scientist who had actually built a laser. Least Obvious Benefits Decrease in overemphasis on single studies. One not so obvious benefit that will accrue to us is the gradual decrease in the overemphasis on the results of a single study. There are good sociological grounds for our monomaniacal preoccupation with the results of a single study. Those grounds have to do with the reward system of science where recognition, promotion, reputation, and the like depend on the results of the single study, also known as the smallest unit of academic currency. The study is “good,” “valuable,” and above all, “publishable” when pS .05. Our disci- plines would be further ahead if we adopted a more cumulative view of science in which the impact of a study were evaluated less on the basis of p levels, and more on the basis of its own effect size and on the revised effect size and combined probability that resulted from the addition of the new study to any earlier studies investigating the same or a similar relationship. This, of course, amounts to a call for a more meta- -analytic view of “doing science.” Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7
B. F Skinner has been eloquent in his comments on the overvaluation of the Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7 single study: “In my own thinking, I try to avoid the kind of fraudulent significance which comes with grandiose terms or profound ‘principles.’ But some psychologists seem to need to feel that every experiment they do demands a sweeping reorgan- ization of psychology as a whole. It’s not worth publishing unless it has some such significance. But research has its own values, and you don’t need to cook up spurious reasons why it’s important.” (Skinner, 1983, p. 39). “The new intimacy.” This new intimacy is between the reviewer and the data. We cannot do a meta-analysis by reading abstracts and discussion sections. We are forced to look at the numbers and, very often, compute the correct ones ourselves. Meta-analysis requires us to cumulate data, not conclusions. “Reading” a paper is quite a different matter when we need to compute an effect size and a fairly precise significance level--often from a results section that never heard of effect sizes, precise significance levels (or the APA publication manual)! The demise of the dichotomous significance testing decision. Far more than is good for us, social and behavioral scientists operate under a dichotomous null hypothesis decision procedure in which the evidence is interpreted as anti-nullifp = .05 and pro-nullifp > .05. If our dissertation pis < .05 it means joy, a Ph.D., anda Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7
tenure-track position at a major university. Ifour pis > .05 it means ruin, despair, Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7 ard our advisor’s suddenly thinking of a new control condition that should be run. That attitude really must go. God loves the .06 nearly as much as the .05. Indeed, I have it on good authority that she views the strength of evidence for or against the null as a fairly continuous function of the magnitude of p. As a matter of fact, two .06 results are much stronger evidence against the null than one .05 result; and 10 p's of -10 are stronger evidence against the null than 5 p’s of .05. The overthrow of the omnibus test. It is common to find specific questions addressed by F tests with df > 1 in the numerator or by X? tests with df > 1. For example, suppose the specific question is whether increased incentive level improves the productivity of work groups. We employ four levels of incentive so that our omnibus F test would have 3 dfin the numerator or our omnibus xX? would be on at least 3 df. Common as these tests are, they reflect poorly on our teaching of data analytic procedures. The diffuse hypothesis tested by these omnibus tests usually tells us nothing of importance about our research question. The rule of thumb is unambiguous: Whenever we have tested a fixed effect with df > 1 for x? or for the numerator of F, we have tested a question in which we are almost surely not interested. Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7
The situation is even worse when there are several dependent variables as well Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7 as multiple 7/ for the independent variable. The paradigm case here is canonical correlation and special cases are MANOVA, MANCOVA, Multiple discriminant function, multiple path analysis, and complex multiple partial correlation. While all of these procedures have useful exploratory data analytic applications they are commonly used to test null hypotheses which are scientifically almost always of doubttul value. The effect size estimates they yield (e.g., the canonical correlation) are also almost always of doubtful value. This is not the place to go into detail, but one approach to the problem of analyzing canonical data structures is to reduce the set of dependent variables to some smaller number of composite variables using the principal-components- follov: ed-by-unit-weighting approach. Each composite can then be analyzed serially. Meta-analytic questions are basically contrast questions, F tests with df>1 in the numerator or X?’s with df >1 are useless in meta-analytic work. That leads to an additional scientific benefit: The increased recognition of contrast analysis. Meta-analytic questions require precise formulation of questions and contrasts are procedures for obtaining answers to such questions, often in an analysis of variance or table analysis context. Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7
Although most textbooks of statistics describe the logic and the machinery of Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7 contrast analyses, one still sees contrasts employed all too rarely. That is a real pity given the precision of thought and theory they encourage and (especially relevant to these times of publication pressure) given the boost in power conferred with the resulting increase in .05 asterisks (Rosenthal & Rosnow, 1985). A probable increase in the accurate understanding of interaction effects. Probably the universally most misinterpreted empirical results in psychology are the results of interaction effects. A recent survey of 191 research articles involving interactions found only two articles that showed the authors interpreting inter- actions in an unequivocally correct manner (i.e., by examining the residuals that define the interaction) (Rosnow & Rosenthal, 1989). The rest of the articles simply compared means of conditions with other means, a procedure that does not investigate interaction effects but rather the sum of main effects and interaction effects. Most standard textbooks of statistics for psychologists provide accurate mathematical definitions of interaction effects but then interpret not the residuals that define those interactions but the means of cells that are the sums of all main effects and all interactions. Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7
In addition, users of SPSS, SAS, BMDP, and virtually all other data-analytic Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7 software are poorly served in the matter of interactions since virtually no programs provide convenient tabular output giving the residuals defining interaction. The only exception to that of which I am aware is a little-known package called Data- Text developed by Arthur Couch and David Armor for which William Cochran and Donald Rubin provided the statistical consultation. Since many meta-analytic questions are by nature questions of interaction (for example, that opposite sex dyads will conduct standard transactions more slowly than wili same sex dyads), we can be hopeful that increased use of meta-analytic procedures will bring with it increased sophistication about the meaning of interaction. Meta-analytic procedures are applicable beyond meta-analyses. Many of the techniques of contrast analyses among effect sizes, for example, can be used within a single study (Rosenthal & Rosnow, 1985). Computing a single effect size from correlated dependent variables, or comparing treatment effects on two or more dependent variables serve as illustrations (Rosenthal & Rubin, 1986). The decrease in the splendid detachment of the full professor. Meta-analytic work requires careful reading of research and moderate data analytic skills. We Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7
cannot send an undergraduate research assistant to the library with a stack of 5x8 Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7 cards to bring us back “the results.” With narrative reviews that seems often to have been done. With meta-analysis the reviewer must get involved with the actual data and that is all to the good. Conclusion I hope that this paper has provided some comfort to the afflicted in showing that many of the findings of our discipline are neither as small nor as unimportant from a practical point of view as we may have feared. Perhaps I hope, too, that there may have been some affliction of the comfortable in showing that in our views of replication and of the cumulation of the wisdom of our field there is much yet remaining to be done. Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7
References Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7 Barnes, D. M. (1986). Promising results halt trial of anti-AIDS drug. Science, 234, 15-16. Canadian Multicentre Transplant Study Group. (1983). A randomized clinical trial of cyclosporine in cadaveric renal transplantation. New England Journal of Medicine, 309, 809-815. Centers for Disease Control Vietnam Experience Study. (1988). Health status of Vietnam veterans: 1. Psychosocial characteristics. Journal of the American Medical Association, 259, 2701-2707. Cohen, J. (1962). the statistical power of abnormal|-social psychological research: A review. Journal of Abnormal and Social Psychology, 65, 145-153. Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences, 2nd ed., Hillsdale, NJ: Lawrence Erlbaum Associates. Collins, H. M. (1985). Changing Order: Replication and Induction in Scientific Practice. Beverly Hills, CA: Sage. Cooper, H. M., & Rosenthal, R. (1980). Statistical versus traditional procedures for summarizing research findings. Psychological Bulletin, 87,442-449. Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7
Elashoff, J. D. (1978). Box scores are for baseball. The Behavioral and Brain Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7 Sciences, 3,392. Fiske, D. W. (1978). The several kinds of generalization. The Behavioral and Brain Sciences, 3, 393-394. Glass, G. V. (1976). Primary, secondary, and meta-analysis of research. Educational Researcher, 5, 3-8. Glass, G. V. (1978). In defense of generalization. The Behavioral and Brain Sciences, 3, 394-395. Glass, G. V., McGaw, B., & Smith, M. L. (1981). Meta-Analysis in Social Research. Beverly Hills, CA: Sage. Hedges, L. V. (1982). Estimation of effect size from a series of independent experiments. Psychologica! Bulletin, 92, 490-499. Hedges, L. V. (1987). How hard is hard science, how soft is soft science? American Psychologist, 42, 443-455. Jung, J. (1978). Self-negating functions of self-fulfilling prophecies. The Behavioral and Brain Sciences, 3, 397-398. Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7
Lamb, W. K., & Whitla, D. K. (1983). Meta-Analysis and the Integration of Research Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7 Findings: A Trend Analysis and Bibliography Prior to 1983. Unpublished manuscript, Harvard University, Cambridge. Mayo, R. J. (1978). Statistical considerations in analyzing the results of a collection ofexperiments. The Behavioral and Brain Sciences, 3, 400-401. Nelson, N., Rosenthal, R., & Rosnow, R. L. (1986). Interpretation of significance levels and effect sizes by psychological researchers. American Psychologist, 41, 1299-1301. Pool, R. (1988). Similar experiments, dissimilar results. Science, 242, 192-193. Rimland, B. (1979). Death knell for psychotherapy? American Psychologist, 34, 192. Rosenthal, R. (1966). Experimenter Effects in. Behavioral Research. New York: Appleton-Century-Crofts. Rosenthal, R. (1969). Interpersonal expectations. In R. Rosenthal and R. L. Rosnow (Eds.), Artifact in Behavioral Research (pp. 181-277). New York: Academic Press. | Rosenthal, R. (1979a). The “file drawer problem” and tolerance for null results. Psychological Bulletin, 86,638-641. Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7
Rosenthal, R. (1979b). Replications and their relative utilities. Replications in Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7 Social Psychology, 1(1), 15-23. Rosenthal, R. (1984). Meta-Analytic Procedures for Social Research. Beverly Hills, CA: Sage. Rosenthal, R. (1986). Nonsignificant relationships as scientific evidence. Behavioral and Brain Sciences, 9, 479-481. Rosenthal, R., & Gaito, J. (1963). The interpretation of levels of significance by psychological researchers. Journal of Psychology, 55, 33-38. Rosenthal, R., & Gaito, J. (1964). Further evidence for the cliff effect in the interpretation of levels of significance. Psychological Reports, 15,570. Rosenthal, R., & Rosnow, R. L. (1984). Essentials of Behavioral Research: Methods and Data Analysis. New York: McGraw-Hill. Rosenthal, R., & Rosnow, R. L. (1985). Contrast Analysis: Focused Comparisons in the Analysis of Variance. New York: Cambridge University Press. Rosenthal, R., & Rosnow, R. L. (in press). Essentials of Behavioral Research: Methods and Data Analysis, 2nd ed., New York: McGraw-Hill. Rosenthal, R., & Rubin, D.B. (1978). Interpersonal expectancy effects: The first 345 studies. The Behavioral and Brain Sciences, 3, 377-386. Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7
Rosenthal, R., & Rubin, D. B. (1979). Comparing significance levels of independent Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7 studies. Psychological Bulletin, 86, 1165-1168. Rosenthal, R., & Rubin, D. B, (1982a). Comparing effect sizes of indepenaent studies. Psychological Bulletin, 92,500-504. Rosenthal, R., & Rubin, D. B.(1982b). Asimple, general purpose display of magnitude of experimental effect. Journal of Educational Psychology, 74, 166- 169. Rosenthal, R., & Rubin, D. B. (1985). Statistical analysis: Summarizing evidence versus establishing facts. Psychological Builetin, 97,527-529. Rosenthal, R., & Rubin, D. B. (1986). Meta-analytic procedures for combining studies with multiple effect sizes. Psychological Bulletin, 99, 400-406. Rosenthal, R., & Rubin, D. B. (1988). Comment: Assumptions and prucedures in the file drawer problem. Statistical Science, 3, 120-125. Rosenthal, R., & Rubin, D. B. (in press). Effect size estimation for one-sample multiple-choice-type data: Design, analysis, and meta-analysis. Psychological Bulletin. Rosnow, R. L., & Rosenthal, R. (1989). Definition and interpretation of interaction effects. Psychological Bulletin, 105, 143-146. Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7
* Author Notes S Approved For Release 2000/08/10 : CIA-RDP96- p07 s2R001001 S000 This paper was presented as an EPA Distinguished Lecture at ¢ Meeting of the Eastern Psychological Association, Boston, April 2, 19/ tion of this paper was supported in part by the National Science Founc the author was a Fellow at the Center for Advanced Study in the Behavioral Sciences. I am grateful for financial support provided by the John D. and Catherine T. MacArthur Foundation, and for improvements suggested by Lynn Gale, Deanna Knickerbocker, Harold Luft, and Lincoln Moses. Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7
Appmuad For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7 Effects of Aspirin on Heart Attacks Among 22,000 Physicians No Heart Heart Attack Attack Total I. Raw Counts _ Aspirin 104 10,933 11,037 Placebo 189 10,845 11,034 Total 293 21,778 22,071 Il. Percentages Aspirin 0.94 99.06 100 Placebo 1.71 98.29 100 Total 1.33 . 98.67 100 Il. Binomial Effect Size Display Aspirin 48.3 51.7 100 Placebo . 51.7 48.3 100 Total 100 100 200 Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7
Appiaved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7 Other Examples of Binomial Effect Size Displays I. Vietnam Service and Alcohol Problems (r = .07) Problem No Problem Total Vietnam Veteran 53.5 46.5 100 Non-Vietnam Veteran 46.5 53.5 100 Total 100 100 200 Il. AZT in the Treatment of AIDS (r = .23) Death Survival Total AZT 38.5. - 61.5 100 Placebo 61.5 38.5 100 Total 100 100 200 Ill. Benefits of Psychotherapy (r = .32) Greater Less Benefit Benefit Total Psychotherapy 34 66 100 Control 66 34 100 Total 100 100 200 A Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7
Tabkpproved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7 Common Model of Successful Replication: Judgment is Dichotomous and Based on Significance Testing First Study p> .05* p< .05 A B p< .05# Failure to Successful Replicate Replication Second Study Cc D p> .05 Failure to Failure to Establish Effect _ Replicate *By convention .05 but could be any other given level, e.g, .01. “In the same tail as the results of the first study. Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7
Table4 TAppratied Kesn Re tfascE200 618i 0anG [és REA881007 92R000100130006-7 Investigator I. Smith Il. Jones Combined. Treatment Mean 38 36 376 Control Mean .26 24 256 Difference 12 12 120 t 2.21 1.06 2.45 df 78 18 — 96 two-tail p .03 .30 02 effect size d® . .50 .50 50 effect size r> 24 24 24 standard normal Z 2.17° 1.03° 2.40 95% Confidence intervals From: 01 ~-.12 .02 Mean differences To: .23 36 22 From: .02 -.23 04 Effect size r's To: 44 62 42 “Obtained from 2tW df. > Obtained from V t?/(#?+df). ¢ These significance levels differ at Z=.81, p=.42 from (Z,-Z,V2. Approved For Release 2000/08/10 : CIA-RDP96-00792R000100130006-7