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power and resources, it is likely to have positive effects on mental health. Well-educated employed women have fewer mental symptoms than nonworking women; among working-class and low- er-class women, however, employment may actually increase anxiety and depression because it elevates demands at the same time that it produces only marginal increases in resources (Sales and Hanson Frieze 1984). Since employed women generally retain full responsibility for children, the demands of caring for children, particularly those under the age of 6, exacerbate work-related stress. Thus, male-female differences in power and resources produce differences in ability to control demands. Gender differences in control, in turn, shape perceptions of personal mastery; personal mastery is the psychological mechanism that connects gender differences in resources and demands to gender differences in mental illness (Rosenfield 1989).

The social selection perspective is valid only for explaining male-female differences in the relationship between marital status and mental disorder. The argument is that mental illness is more likely to select men out of marriage than women. (See Rushing 1979 for a related discussion.) According to this perspective, male forms of mental disorder—psychosis and antisocial personality, for example—prevent impaired men from satisfactorily discharging the traditional male obligation to be good economic providers, making them ineligible as marriage partners. In contrast, female forms of psychiatric impairment may go undetected for long periods of time and may not seriously interfere with a woman’s ability to fulfill the traditional housekeeping role. Thus, the higher rates of female disorder among the married may be a partial artifact of the differing probabilities of marriage for mentally disordered men and women.

The labeling explanation for male-female differences in psychiatric impairment begins by challenging the notion that women actually experience more symptoms and disorders than men do. Labeling theorists argue that women are overdiagnosed and overmedicated because of biases on the part of predominantly male psychiatrists and because of the male biases inherent in psychiatric nomenclature. Coupled with the greater willingness of females to admit their problems and to seek help for them, these biases simply

produce the illusion that women are more likely to be disordered than men. Scholars using the label- ing–societal reaction–critical perspective argue that the effects of gender biases are not benign and that they have consequences at two levels. First, individual women are unlikely to receive appropriate services for their real mental health problems. Second, and at a societal level, critics argue that psychiatry simply legitimates traditional gender roles, thereby buttressing the status quo (Chesler 1973).

A Theoretical Assessment. With the development of DSM-IV and with increases in the number of female mental health professionals, concern over the issues raised by labeling theorists has diminished somewhat. Trusting that the most blatant instances of sexism have been eliminated, researchers have turned their attention toward specifying the social psychological dynamics of the gender–mental health equation; considerable progress has been made in elucidating the circumstances under which women are most likely to experience symptoms of mental disorder. Nevertheless, it may be premature to close the question of gender bias in psychiatric disorders. In one study, male clinicians appeared to overestimate the prevalence of depressive disorders among women, a tendency that is certainly consistent with gender stereotypes. In the same study, black males were most likely to be diagnosed as paranoid schizophrenics, a view consistent with both gender and racial stereotypes (Loring and Powell 1988). In yet another study, male and female psychiatrists made similar diagnoses of male and female patients presenting severe Axis I conditions but made significantly different diagnoses for male and female patients with Axis II conditions, such as personality disorders (Dixon et al. 1995). Thus, advances of DSM-III (and IV) notwithstanding, the authors of these studies conclude that sex and race of client and psychiatrist continue to influence diagnosis even when psychiatric criteria appear to be clear-cut.

Age. Among adults, and with the exception of some types of dementia and other syndromes due to general medical conditions, rates of mental illness decrease with age. Rates of schizophrenia, manic disorder, drug addiction, and antisocial personality all peak between the ages of 25 and 44 (Robins et al. 1984). Furthermore, an older person

with a serious mental disorder is likely to have had a first psychiatric episode in young or middle adulthood. At least 90 percent of older schizophrenics experienced the onset of the disorder in earlier life. Similarly, about two-thirds of older alcoholics have a long history of alcohol abuse or dependence (Hinrichsen 1990). Depression is the disorder most likely to occur among the elderly, and a substantial proportion of older community residents do report some of its symptoms. In general, the relationship between age and depression appears to be curvilinear, with depression lowest among the middle aged, higher among younger and older adults, and highest among the oldest (Mirowsky and Ross 1992). Nevertheless, relatively few of these older individuals meet criteria for clinical depression (Blazer et al. 1987), and rates of major depression are lower among older adults than in younger age groups. Some older persons, however, are more vulnerable to depression than others. As is true throughout the life cycle, women, individuals with health problems, the unmarried, and those with lower socioeconomic status are at greater risk of depression in late life than their peers. Estimating the true prevalence of depression among the elderly is especially problematic because its symptoms are frequently confused with Alzheimer’s disease or other forms of dementia.

According to some estimates, two to four million older Americans suffer some form of mental disorder due to a general medical condition. Of these, roughly half are diagnosed with Alzheimer’s, a disease that involves an irreversible, progressive deterioration of the brain. Approximately half of all nursing home residents are estimated to suffer from some form of dementia. Because there is no known treatment for most of these disorders, older mental patients receive little psychiatric care. Critics suggest, however, that many older persons are improperly diagnosed as having disorders of general medical origin. A sizable minority may actually be depressed; others may have treatable forms of dementia caused by medications, infection, metabolic disturbances, alcohol, or brain tumors. In some instances, then, the stereotype that senility is a concomitant of the aging process prevents appropriate diagnosis, intervention, and treatment.

Most explanations of the age–mental health relationship have focused on specific age groups.

Clinicians suggest, for instance, that anxiety and depression in middle age are a consequence of hormonal change or of changes in family and occupational roles. The personality disorders of young adulthood are often explained in terms of the stresses produced by the transition from adolescence to full adult roles. Among the elderly, explanations have focused on either organic or environmental factors. The dementias have recognized organic causes. Although neither is a normal part of the aging process, the two major causes of these disorders are (1) the deterioration of the brain tissue that is associated with Alzheimer’s disease and (2) cerebral arteriosclerosis. However, environmental factors also contribute to the onset of the dementias. They do so, in part, by increasing the likelihood of stroke or heart attack. In contrast, primary mental disorders, such as depression, personality disorders, and anxiety, depend more directly upon environmental factors. Some types of depression appear to have a genetic component, but the genetic link appears to be stronger in earlythan in late-onset cases. Individuals who have their first episode of clinical depression prior to the age of 50, for instance, are more likely to have relatives with depression than those who become depressed in later years (Hinrichsen 1990). Consequently, losses typical of late life—losses of health, occupation, income, and loved ones—ap- pear to be the primary causes of mental health problems among older adults.

Clearly, no single theory can adequately explain the etiology of mental disorder; at each stage of the life cycle, variables that are relevant to the onset of one type of disorder may be insignificant in the onset of other illnesses. Similarly, no single variable or set of variables is likely to explain age differences in overall rates of mental disorder. Nevertheless, efforts are under way to systematically explain the inverse relationship between age and primary psychiatric impairment. Gove and his associates have suggested that psychological distress decreases with age because individuals are able, over time, to find and settle into an appropriate social niche; as individuals move through life, they become less emotional and less self-absorbed, function more effectively in their selected roles, and generally become more content with themselves and with others. As a result, rates of mental disorder decrease from late adolescence through late life (Gove 1985; Gove et al. 1989).

Place of Residence. Sociologists have commonly assumed that rates of mental disorder are higher in urban than in rural areas. However, this assumption is based more on the antiurban bias of much sociological theory than it is on empirical research. In a thoughtful and systematic review, Wagenfeld (1990) has argued that there is little evidence in the mental health literature to suggest the superiority of rural life. In several of the rural community studies Wagenfeld cites, researchers report a ‘‘probable’’ case rate of depression and anxiety of 12 to 20 percent. Studies that explicitly compare rural and urban communities generally find that rates of psychosis are higher in rural communities and that rates of depression are somewhat higher in urban areas. Residents of metropolitan communities also appear more likely to have multiple diagnoses than do rural residents, leading Kessler et al. (1994) to conclude that ur- ban-rural differences in the prevalence of mental disorder probably reflect differences in comorbidity rather than differences in rates of individuals having a psychiatric condition. Differences in case definition and diagnosis, differences in how ‘‘rural place of residence’’ is defined and measured, and differences in the time period during which studies were conducted make it difficult, overall, to assess whether rural communities have significantly higher overall rates of pathology than urban areas. Results are sufficient, however, to suggest that rural life is not as blissful as it is often claimed to be. Recent declines in the rural economy, the out-migration of the young and upwardly mobile, and the relative paucity of mental health services are likely to be major contributing factors in the etiology of rural mental health problems.

Other factors. Epidemiologists have also explored the relationships between the incidence or prevalence of mental disorder and such variables as race and ethnicity, migration, social mobility, and marital status. In each case, results generally support the view that individuals with the fewest resources—both economic and social—are most likely to experience psychiatric impairment. However, most research has adopted a rather static view; few studies have assessed the extent to which relationships between each of these variables and mental disorder have changed over time. Given the significant changes in diagnostic practices and in the mental health professions over the last decades, this is a striking omission.

AN AGENDA FOR FUTURE RESEARCH

Since the early 1960s, psychiatric sociology has undergone enormous changes. During the 1960s and 1970s, much of the literature was sharply critical of psychiatry and of medical models of madness. Although sociologists were divided about the relative importance of labeling processes in the etiology of mental illness, most agreed that psychiatric diagnoses were unreliable and were influenced by social status and social resources, that long-term institutionalization had detrimental effects, and that at least some patients were hospitalized inappropriately. Such criticisms provided one impetus for the substantial change that took place in psychiatric care during the same period; laws were changed to make involuntary commitment more difficult; steps were taken to deinstitutionalize many mental patients; and a major effort was made to improve the reliability of mental diagnoses. By the time DSM-III was published in 1980, the most flagrant abuses and the sharpest criticism of psychiatry seemed to have disappeared. Consequently, many sociologists shifted their attention from concerns about the lives of people with serious mental disorder to the social correlates of psychological distress among the general population (Cook and Wright 1995). Using what is basically a medical model of impairment, researchers have focused on delineating the relationship between social variables (such as gender, age, race, social class, place of residence, life events, and stress) and specific diagnoses (most often depressive symptoms, anxiety, and substance abuse). Indeed, the psychiatric view of mental disorder is so well established in sociology that the growing literature on homelessness has generally accepted the assertion of mental health professionals that most of the homeless are simply individuals who have fallen through the cracks of the mental health care system. (For notable exceptions, see Bogard et al. 1999; Snow, Baker, and Anderson 1986.) It is surprising that sociologists have been so uncritical in their acceptance of this position; it is also surprising that in the decade of the 1990s, declared by the National Institute of Mental Health to be the ‘‘Decade of the Brain,’’ they have been so ready to accept the view that mental illness is primarily a problem of genetics or brain chemistry and that it can be treated just like any other disease. It is certainly true that enormous strides have been made in the diagnosis and psychopharmacological

treatment of mental disorder. It is also certainly true that biomedical factors are causally involved in some types of mental illness. Sociologists must, therefore, continue their efforts to develop a model of mental disorder that integrates medical, psychological, and social factors.

As some critics point out, however, the current emphasis on diagnoses, cases, and the medical model of mental illness has limitations. Acceptance of the psychiatric view of mental disorder leads to the acceptance of policy recommendations that are not yet firmly grounded in empirical research. It is far from clear, for instance, that deinstitutionalization of the mentally ill is the primary cause of homelessness in America. As Bogard et al. (1999) point out, conventional wisdom notwithstanding, very few homeless mothers are mentally ill; it can be reasonably argued, then, that the enormous resources that have been directed toward providing them with mental health care might more appropriately and effectively be used to provide safe, affordable housing. In a similar vein, Link and Phelan (1995) note that current attention to individual risk factors in disease gives rise to ‘‘personal policy’’ recommendations that leave totally unaddressed the fundamental social conditions that cause differential exposure to risk.

Furthermore, few studies have assessed the extent to which changes in psychiatric diagnosis or changes in the civil rights guarantees of mental patients have affected the delivery and quality of mental health services. Consumers and families have voiced concern that the powerful new psychopharmacological drugs are being inappropriately used as forms of social control and chemical restraint at the same time that research continues to show that it is racial and ethnic minority consumers who are most likely to be so restrained (Cook and Wright 1995). Aside from the field trials used in their formulation, few studies have assessed the reliability and validity of DSM-IV diagnoses. However, results from several studies show that nonclinical factors such as gender, race, the availability of viable community housing and the presence of reliable caretakers significantly affect not only diagnosis but treatment protocols and outcomes. (See Cook and Wright [1995] for a review of these studies and these concerns.) It is far from clear, then, that lower-class women are any more likely to receive

appropriate care in 1999 than they were in 1950 or 1970. It is unclear whether urban-rural differences in rates of mental disorder have changed over time and, if so, to what extent changes in diagnostic systems or service availability are implicated. Evidence that rural residents may actually experience mental illness at approximately the same rates as urban residents coupled with an acute shortage of rural mental health providers suggest the importance of understanding the diagnostic practices of primary-care physicians and of providing appropriate training to them.

Research in the next century must adopt a more dynamic or process view of mental health issues. The consequences of changes in psychiatric diagnosis, of the increased reliance on drug therapies, of changes in mental health law and policy, and in the availability of mental health services must be assessed. Changes in the mental health system must be linked to changes in the composition of the pool of ‘‘potential clients’’ and to issues regarding the development of gender, age, class, and culturally appropriate systems of care.

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SUZANNE T.ORTEGA

SHARON L. LARSON

MERITOCRACY

See Affirmative Action; Equality of Opportunity.

META-ANALYSIS

Meta-analysis is the practice of statistically summarizing empirical findings from different studies, reaching generalizations about the obtained results. Thus, ‘‘meta-analysis’’ literally refers to analysis of analyses. Meta-analysis, a term coined by Glass (1976), is also known as research synthesis and quantitative reviewing. Because progress within any scientific field has always hinged on cumulating empirical evidence about phenomena in an orderly and accurate fashion, reviews of studies have historically proved extremely influential (e.g., Mazela and Malin 1977). With the exponential growth in the numbers of studies available on a given social scientific topic, the need for these reviews has increased proportionally, meaning that reviews are potentially even more important each day. The empirical evidence, consisting of multiple studies examining a phenomenon, exists as a literature on

the topic. Although new studies rarely replicate earlier studies without changing or adding new features, many studies can be described as conceptual replications that use different stimulus materials and dependent measures to test the same hypothesis, and still others might contain exact replications embedded within a larger design that adds new experimental conditions. In other instances, repeated tests of a relation accrue in a less systematic manner because researchers sometimes include in their studies tests of particular hypotheses in auxiliary or subsidiary analyses.

In order to reach conclusions about empirical support for a phenomenon, it is necessary to compare and contrast the findings of relevant studies. Therefore, accurate comparisons of study outcomes—reviews of research—are at the very heart of the scientific enterprise. Until recently these comparisons were nearly always made using informal methods that are now known as narrative reviewing, a practice by which scholars drew overall conclusions from their impressions of the overall trend of the studies’ findings, sometimes guided by a count of the number of studies that had either produced or failed to produce statistically significant findings in the hypothesized direction. Narrative reviews have appeared in many different contexts and still serve a useful purpose in writing that does not have a comprehensive literature review as its goal (e.g., textbook summaries, introductions to journal articles reporting primary research). Although narrative reviewing has often proved useful, the method has often proved to be inadequate for reaching definitive conclusions about the degree of empirical support for a phenomenon or for a theory about the phenomenon. One indication of this inadequacy is that independent narrative reviews of the same literature often have reached differing conclusions.

COMMON PROBLEMS WITH NARRATIVE

REVIEWS

Critics of the narrative reviewing strategy (e.g., Glass et al. 1981; Rosenthal 1991) have pointed to four general faults that frequently occur in narrative reviewing: (1) Narrative reviewing generally involves the use of a convenience sample of studies, perhaps consisting of only those studies that the reviewer happens to know. Because the parameters of the reviewed literature are typically

not explicit, it is difficult to evaluate the adequacy of the definition of the literature or the thoroughness of the search for studies. If the sample of studies was biased, the conclusions reached may also be biased. (2) Narrative reviewers generally do not publicly state the procedures they used for either cataloging studies’ characteristics or evaluating the quality of the studies’ methods. Therefore, the review’s claims about the characteristics of the studies and the quality of their methods are difficult to judge for their accuracy. (3) In cases in which study findings differed, narrative reviewing has difficulty in reaching clear conclusions about whether differences in study methods explain differences in results. Because narrative reviewers usually do not systematically code studies’ methods, these reviewing procedures are not well suited to accounting for inconsistencies in findings.

(4) Narrative reviewing typically relies much more heavily on statistical significance to judge studies’ findings than on the magnitude of the findings. Statistical significance is a poor basis for comparing studies that have different sample sizes, because effects of identical magnitude can differ widely in statistical significance. Because of this problem, narrative reviewers often reach erroneous conclusions about a pattern in a series of studies, even in literatures as small as ten studies (Cooper and Rosenthal 1980).

As the number of available studies cumulates, the conclusions reached in narrative reviews become increasingly unreliable because of the informality of the methods they use to draw these conclusions. Indeed, some historical scholars have attributed crises of confidence in central social scientific principles to apparent failures to replicate findings across studies (e.g., Johnson and Nichols 1998). Clearly, there will be practical limitations on the abilities of scholars to understand the vagaries of a literature containing dozens if not hundreds of studies (e.g., by 1978, there were at least 345 studies examining interpersonal expectancy effects, according to Rosenthal and Rubin 1978; and by 1983, there were over 1,000 studies evaluating whether birth order is related to personality, as reported by Ernst and Angst 1983). From this perspective, the social sciences might be considered victims of their own success: Although social scientists have been able to collect a myriad of data about a myriad of phenomena, they were forced to rely on their intuition when it came to assessing

the state of the knowledge about popular topics. Since the 1980s, however, as scholars have gained increasing expertise in reviewing research literatures, literatures that once appeared haphazard at best and fragile at worst now frequently are shown to have substantial regularities (Johnson and Nichols 1998). For example, although scholars working in the 1950s and on through the 1970s frequently reached conflicting conclusions about whether men or women (or neither) are more easily influenced by others, reviewers using meta-analytic techniques have found highly reliable tendencies in this same literature. For example, Eagly and Carli’s meta-analysis (1981) showed that men are more influenced than women when the communication topic is feminine (e.g., sewing), and that women are more influenced than men when the topic is masculine (e.g., automobiles). Moreover, contemporary meta-analysts now almost routinely move beyond relatively simple questions of whether one variable relates to another to the more sophisticated question of when the relation is larger, smaller, or reverses in sign. Thus, there is, indeed, a great deal of replicability across a wide array of topics, and inconsistencies among study findings can often be explained on the basis of methodological differences among the studies.

META-ANALYTIC REVIEWS OF EVIDENCE

Because of the importance of comparing study findings accurately, scholars have dedicated considerable effort to making the review process as reliable and valid as possible and thereby circumventing the criticisms listed above. These efforts highlight the proposition that research synthesis is a scientific endeavor—there are identifiable and replicable methods involved in producing reliable and valid reviews (Cooper and Hedges 1994). Although scientists have cumulated empirical data from independent studies since the early 1800s (see Stigler 1986), relatively sophisticated techniques for synthesizing study findings emerged only after the development of such standardized indexes as r-, d-, and p-values, around the turn of the twentieth century (see Olkin 1990). Reflecting the field’s maturation, Hedges and Olkin (1985) presented a sophisticated version of the statistical bases of meta-analysis, and standards for metaanalysis have grown increasingly rigorous. Metaanalysis is now quite common and well accepted because scholars realize that careful application of

these techniques often will yield the clearest conclusions about a research literature (Cooper and Hedges 1994; Hunt 1997).

Conducting a meta-analysis generally involves seven steps: (1) determining the theoretical domain of the literature under consideration, (2) setting boundaries for the sample of studies, (3) locating relevant studies, (4) coding studies for their distinctive characteristics, (5) estimating standardized effect sizes for each study, (6) analyzing the database, and (7) interpreting and presenting the results. The first conceptual step is to specify with great clarity the phenomenon under review by defining the variables whose relation is the focus of the review. Ordinarily a synthesis evaluates evidence relevant to a single hypothesis; the analyst studies the history of the research problem and of typical studies in the literature. Typically, the research problem will be defined as a relation between two variables, such as the influence of an independent variable on a dependent variable (e.g., the influence of silicon breast implants on connective tissure disease, as reported by Perkins et al. 1995). Moreover, a synthesis must take study quality into account at an early point to determine the kinds of operations that constitute acceptable operationalizations of these conceptual variables. Because studies testing a particular hypothesis typically differ in the operations used to establish the variables, it is no surprise that these different operations were often associated with variability in studies’ findings. If the differences in studies’ operations can be appropriately judged or categorized, it is likely that an analyst can explain some of this variability in effect size magnitude.

The most common way to test competing explanations is to examine how findings pattern across studies. Specifically, a theory might imply that a third variable should influence the relation between the independent and dependent variables: The relation should be larger or smaller with a higher level of this third variable. Treating this third variable as a potential moderator of the effect, the analyst would code the studies for their status on the moderator. This meta-analytic strategy, known as the moderator variable approach, tests whether the moderator affects the examined relation across the studies included in the sample. This moderator variable approach, advancing beyond the simple question of whether the independent variable is related to the dependent variable,

addresses the question of when the magnitude or sign of the relationship varies. In addition to this moderator variable approach to synthesizing studies’ findings, other strategies have proved to be useful. In particular, a theory might suggest that a third variable serves as a mediator of the critical relation because it conveys the causal impact of the independent variable on the dependent variable. If at least some of the primary studies within a literature have evaluated this mediating process, mediator relations can be tested within a metaanalytic framework by performing correlational analyses that are an extension of path analysis with primary-level data (Shadish 1996).

Clearly, only some studies will be relevant to the conceptual relation that is the focus of the meta-analysis, so analysts must define boundaries for the sample of studies, the second step in conducting a meta-analysis. Decisions about the inclusion of studies are important because the inferential power of any meta-analysis is limited by the methods of the studies that are integrated. To the extent that all (or most) of the reviewed studies share a particular methodological limitation, any synthesis of these studies would be limited in this respect. As a general rule, research syntheses profit by focusing on the studies that used stronger methods to test the meta-analytic hypotheses. Nonetheless, it is important to note that studies that have some strengths (e.g., manipulated independent variables) may have other weaknesses (e.g., deficiencies in ecological validity). In deciding whether some studies may lack sufficient rigor to include in the meta-analysis, it is important to adhere to methodological standards within the area reviewed. Although a large number of potential threats to methodological rigor have been identified (Campbell and Stanley 1963; Cook and Campbell 1979), there are few absolute standards of study quality that can be applied uniformly in every meta-analysis. As a case in point, although published studies are often thought to be of higher quality than unpublished studies, there is little basis for this generalization: Many unpublished studies (e.g., dissertations) have high quality, and many studies published in reputable sources do not. It is incumbent on the analyst to define the features of a high-quality study and to apply this definition toall studies in the literature, regardless of such considerations as the reputation of the journal.

Analysts often set the boundaries of the synthesis so that the methods of included studies differ dramatically only on critical moderator dimensions. If other, extraneous dimensions are thereby held relatively constant across the reviewed studies, moderator variable analyses can be more clearly interpreted. Nonetheless, an analyst should include in the sample all studies or portions of studies that satisfy the selection criteria, or, if an exhaustive sampling is not possible, a representative sample of those studies. Following this principle yields results that can be generalized to the universe of studies on the topic.

Because including a large number of studies generally increases the value of a quantitative synthesis, it is important to locate as many studies as possible that might be suitable for inclusion, the third step of a meta-analysis. To ensure that a sufficient sample of studies is located, reviewers are well advised to err in the direction of being extremely inclusive in their searching procedures. As described elsewhere (e.g., Cooper 1998; White 1994), there are many ways to find relevant studies; ordinarily, analysts should use all these techniques. Because computer searches of publication databases seldom locate all the available studies, it is important to supplement them by (1) examining the reference lists of existing reviews and of studies in the targeted literature, (2) obtaining published sources that have cited seminal articles within the literature, (3) contacting the extant network of researchers who work on a given topic to ask for new studies or unpublished studies, and (4) manually searching important journals to find some reports that might have been overlooked by other techniques.

Once the sample of studies is retrieved, analysts code them for their methodological characteristics, the fourth step in the process. The most important of these characteristics are potential moderator variables, which the analyst expects on an a priori basis to account for variation among the studies’ effect sizes, or which can provide useful descriptive information about the usual context of studies in the literature. In some cases, reviewers recruit outside judges to provide ratings of methods used in studies. Because accurate coding is crucial to the results of a meta-analysis, the coding of study characteristics should be carried out by two or more coders, and an appropriate index of interrater reliability should be calculated.

To be included in a meta-analysis, a study must contain some report of a quantitative test of the hypothesis that is under scrutiny in order to convert summary statistics into effect sizes, the fifth step of the process. Most studies report the examined relation by one or more inferential statistics (e.g., t-tests, F-tests, r-values), which can be converted into an effect size (see Cooper and Hedges 1994b; Glass et al. 1981; Johnson 1993; Rosenthal 1991). The most commonly used effect size indexes in meta-analysis are the standardized difference and the correlation coefficient (see Rosenthal 1991, 1994). The standardized difference, which expresses the finding in standard deviation units, was first proposed by Cohen (1969) in the following form:

where MA; and MB; are the sample means of two compared groups, and SD is the standard deviation, pooled from the two observations. Because this formula overestimates population effect sizes to the extent that sample sizes are small, Hedges (1981) provided a correction for this bias; with the bias corrected, this effect estimate is conventionally known as d. Another common effect size is the correlation coefficient, r, which gauges the association between two variables. Because the sampling distribution of a sample correlation coefficient tends to be skewed to the extent that the population correlation is large, it is conventional in metaanalysis to use a logarithmic transform of each correlation in statistical operations (Fisher 1921). The positive or negative sign of the effect sizes computed in a meta-analysis is defined so that studies with opposite outcomes have opposing signs. When a study examines the relation of interest within levels of another variable, effect sizes may be calculated within the levels of this variable as well as for the study as a whole. In addition to correcting the raw g and r because they are biased estimators of the population effect size, analysts sometimes correct for many other biases that accrue from the methods used in each study (e.g., unreliability of a measure; see Hunter and Schmidt 1990). Although it is unrealistic for analysts to take into account all potential sources of bias in a meta-analysis, they should remain aware of biases that may be important within the context of their research literature.

Once the effect sizes are calculated, they are analyzed, the sixth step of the process, using either fixedor random-effects models. Fixed-effects models, which are the most common analysis used, assume that there is one underlying, but unknown, effect size and that study estimates of this effect size vary only in sampling error. Random-effects models assume that each effect size is unique and that the study is drawn at random from a universe of related but separate effects (see Hedges and Vivea 1998 for a discussion). The general steps involved in the analysis of effect sizes usually are:

(1) to aggregate effect sizes across the studies to determine the overall strength of the relation between the examined variables; (2) to analyze the consistency of the effect sizes across the studies;

(3)to diagnose outliers among the effect sizes; and

(4)to perform tests of whether study attributes moderate the magnitude of the effect sizes. Although several frameworks for modeling effect sizes have been developed (for reviews, see Johnson et al. 1995; Sánchez-Meca and Marín-Martínez 1997), the Hedges and Olkin fixed-effect approach (1985) appears to be the most popular and therefore will be assumed in the remainder of this discourse. These statistics were designed to take advantage of the fact that studies have differing variances by calculating the nonsystematic variance of the effect sizes analytically (Hedges and Olkin 1985). Because this nonsystematic variance of an effect size is inversely proportional to the sample size of the study and because sample sizes typically vary widely across the studies, the error variances of the effect sizes are ordinarily quite heterogeneous. These meta-analytic statistics also permit an analysis of the consistency (or homogeneity) of the effect sizes across the studies, a highly informative analysis not produced by conventional, primary-level statistics. As the homogeneity calculation illustrates, analyzing effect sizes with specialized meta-analytic statistics rather than the ordinary inferential statistics used in primary research allows a reviewer to use a greater amount of the information available from the studies (Rosenthal 1991, 1995).

As a first step in a quantitative synthesis, the study outcomes are combined by averaging the effect sizes with each weighted by its sample size. This procedure gives greater weight to the more reliably estimated study outcomes, which are in general those with the larger sample sizes (see