Children and Parental Divorce: The Meaning of Small Effects - A Reply

BRYAN RODGERS The Australian National University

he commentary on my earlier review of Australian studies of parental divorce raises a number of important T points. One of these is the evaluation of strength of

association. I argue that the effect sizes found for the associ- ation between parental divorce and several social and psychological outcomes have been understated and can be shown to be equal to those of other important early-life and contemporary risk factors for mental health problems. A second issue is the research direction required to establish those factors which mediate or moderate the impact of parental separation for children. I suggest that the following questions need to be addressed: (a) What factors operating in childhood ameliorate or exacerbate the social and psycho- logical problems associated with parental divorce? (b) What behavioural signs identify those children who develop long- term problems? (c) What circumstances in adolescence and adulthood operate as risk and protective factors for the onset and persistence of adult difficulties?

Bums, Dunlop, and Taylor (1997) raise a number of impor- tant points in their commentary on my previous review of findings from Australian studies of children from divorced families (Rodgers, 1996~). Inevitably, my response tends to focus on areas of disagreement, so it is appropriate to preface this reply with an acknowledgment that many of their comments are uncontentious. This includes the view that “not all children of divorced families suffer adverse consequences”, and this has been stated in more detail elsewhere (Rodgers & Pryor, 1996). Indeed, my original review went further, indicating that “it is also necessary to acknowledge the possible benefits that can come from divorce, whether for particular individuals or for this group of children as a whole”. Further, Burns and colleagues’ main conclusion, “what we need is not generalised group compar- isons, but a greater understanding of the factors that act to protect or to harm children when their parents separate” is worthy of elaboration. My opinion is that this is not only a crucial issue (or set of issues) for the investigation of processes determining better or worse outcomes for children from divorced families, but that it also lies at the heart of the claim that this area of research has relevance for understand- ing so-called risk and protective factors in the development of children who experience comparable adversity in the

context of intact families. Rather than work through each of Bums and colleagues’ points in turn, I prefer to cover just two general issues. The first is the interpretation of effect sizes and other indices of strength of association. I believe this is an area of weakness in the social sciences, not just in the way results are formally presented, but also in the way we subjectively evaluate research findings. The second is the matter of risk and protective factors, already mentioned, which can incorporate factors acting during the childhood years, contemporary with or close to the experience of adversity, and those acting in subsequent years when disad- vantages become evident. Collectively, these mediating and moderating variables constitute the pathways linking early adversity to later outcomes.

Interpretation of Effect Sizes and Other Indices of Association It was only after about 15 years of working in epidemiologi- cal research that I reached the conclusion that social scien- tists were fickle in their appreciation of effect sizes. This recognition was especially painful because it was based predominantly on observations of myself. My view of the association between two variables was influenced by the form af presentation, for example, as a (Pearsm) correlation coefficient, as a difference between two means when one variable was dichotomised, or as a two-by-two contingency table when both variables were dichotomised. Even in circumstances when both variables were impeccably (i.e., normally) distributed and where the underlying relationship was linear, I gained a very different impression of the strength of association from these different modes of presen- tation. This encouraged me to (a) calculate effect sizes from my own analyses and from published studies; (b) present research findings in ways that allowed readers to calculate effect sizes, even if these were not made explicit; and (c) be sceptical of labels used to describe strength of association. Such labels are still necessary, however, and a useful start- ing point for discussion is the recommendation of conven- tional terms given in statistical texts. For example, Cohen (1988) uses “small” for effect sizes of d = 0.2, “medium” for 0.5, and “large” for 0.7. This is a good start, but there are considerable gaps between these values. Also, the equivalent values applied to different statistics (d, h, etc.) or to the same statistic derived from different research designs (e.g., h

Address for correspondence: Bryan Rodgers, NHMRC Psychiatric Epidemiology Research Centre, The Australian National University, Canberra ACT 0200, Australia.

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from prospective and case-control studies) do, not necessar- ily indicate the same strength of relationship. In the absence of a clear convention, it is possible that the research community reaches consensus by less formal means. I was aware, however, that epidemiologists in some fields attached considerable importance to risk factors that increased the risk of a particular outcome by 20% (and sometimes 10% or less) while social scientists would describe increases of 50% or more as trivial. The contrast with some areas of biomedical research is even more extreme (Rosenthal, 1990). These differences did not appear to reflect the subjective importance of the dependent variables under consideration, for they applied as much to outcomes such as suicide attempts and alcoholism as to less severe problems. It is apparent that the labels applied to effect sizes actually exacerbate our difficulty in interpreta- tion. The message from this is to ignore the labels and focus on the indices of effect size. It is of no consequence that terms such as small are used to describe a doubling of the risk of suicide attempts, psychiatric hospital admissions, or alcoholism, for the terms themselves do not conceal the fact that the risk is indeed doubled.

It is not necessary to repeat here all the effect sizes given in my review, either from Australian or overseas studies. It is important, however, to correct the idea that the only point of departure for this review was Amato and Keith’s (1991b) meta-analysis of childhood outcomes, for their second meta-analysis of adult outcomes was given equal weight (Amato & Keith, 1991a). This second review has more direct relevance to Dunlop and Burn’s (1995) recent publication and to their present commentary, and it also provides a clue that effect sizes may be larger for adult outcomes than for childhood outcomes. The effect sizes given for psychological adjustment, which includes measures of anxiety and depression, were 0.32 and 0.08 respectively. I will return to this point later. I agree with Amato and Keith’s (1991a, 1991b) view, as represented in Bums and colleagues’ commentary, that many of the effect sizes in their meta-analysis were weak. I also agree with their conclusion that “the argument that parental divorce presents few problems for children’s long-term develop- ment is simply inconsistent with the literature on this topic” (Amato & Keith, 1991a). I used the term “not trivial” to describe effect sizes of the order of d = 0.3, as reported for a number of outcomes from the meta-analysis and from my own review, as I felt this would not unfairly exaggerate the effect size where a doubling of risk was found. I note that a recent paper by Amato (1996) reports the association between parental divorce and own divorce in adulthood. The effect size for this association, as found by a number of studies, is very similar to that found for the link with adult depression. Amato (1996) describes this association as “large enough to be nontrivial” so, at least, there appears to be some consensus here.

Another way of evaluating the relative strength of association is to make comparisons with effect sizes reported for other known risk factors that are generally accepted to be important. This is essentially the approach adopted by Bums et al. when they present figures for associ- ations with gender, father relations, mother relations, and father’s occupation to be compared with the equivalent associations for parental divorce (their Table 1). Unfortunately, this table is not very helpful, as no confi- dence intervals are presented for the mean differences. My own rough calculations suggest that the standard errors associated with these mean values are large by comparison with the differences between them. It is not the case, as Burns et al. suggest, that these figures indicate that the

power of their study “was adequate to pick up other effects in the data, compared to which the effects of parental divorce were very weak”. Power is determined by the design of a study and the presumed effect sizes, not by the findings. If the same study were repeated with a new sample, some previously significant results would then turn out to be nonsignificant and vice versa. To obtain more accurate estimates of effect sizes for the above risk factors, it is appropriate to turn to findings from studies with larger samples and, if possible, to reviews of such studies. For gender differences in depression, this is very simple, for the area has been reviewed extensively. The higher rates of depression in women compared to men is one of the most consistent and important findings in psychiatric epidemiol- ogy. This gender difference varies by age (Jorm, 1987) and, at its greatest, reaches a value of about d = 0.4 (for continu- ous measures) or h = 0.3 (for discrete measures). Recent studies of adults using DSM-III criteria (American Psychiatric Association, 1980) estimate the sex ratio for lifetime major depression as 2.7 in the United States and 1.9 in New Zealand, with effect sizes of h = 0.21 and 0.23 respectively (Smith & Weissman,. 1992). Overall, these effect sizes for gender are a little higher than those associ- ated with parental divorce. For relationships with parents, as measured by the Parental Bonding Instrument (Parker, Tupling, & Brown, 1979), my own work in Britain provides the best estimate of effect size. The multiple correlation for the association between all four scales of this instrument with a measure of depression and anxiety was found to be 0.15 in a sample of about 3,000 adults (Rodgers, 1996a). General population samples in this country show similar correlations (Mackinnon, Henderson, Scott, & Duncan- Jones, 1989). A correlation of 0.15 corresponds to an effect size slightly less than d = 0.30, and is therefore not quite as large as the effect size associated with parental divorce. It is not possible to obtain accurate estimates of effect sizes for the association between father’s socioeconomic status and depression in adulthood. This is a relatively neglected area of research, and studies show inconsistent findings (Power & Manor, 1992; Rodgers, 1990).

The above figures do not provide an empirical basis for claiming that the effect sizes associated with other risk factors exceed those found for parental divorce. The design of the Dunlop and Bums (1995) study was such that it had 80% power (the level conventionally used in grant applica- tions, for example) to detect an effect size of around 0.70 for differences between subjects from divorced and intact families. The only measures of childhood adversity that have been demonstrated to have effect sizes as large as or larger than this are reports of the more severe forms of sexual and physical abuse. Only one of the 15 effect sizes in Bums and colleagues Table 1 exceeds the value of 0.70. Furthermore, I know of no adult risk factor in common use in psychiatric epidemiology (aside from Ylier assessments of symptomatology or such personality measures as neuroti- cism) that has an effect size as large as 0.70, and factors such as stressful life events and social suppofl have effect sizes smaller than this. Estimates from my own analyses of risk factors for depressive symptoms gave effect sizes of 0.59 for unemployment in men and 0.36 for single-parent status in women (Rodgers, 1991), and these were chosen as the factors likely to show the strongest associations with depression in men and women respectively.

My review mentioned two other ways of evaluating the associations between risk factors and outcomes. The first is the concept of attributable risk, used in epidemiology, which takes account of the frequency of a risk factor in the general population as well as its effect size. It is therefore of

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CHILDREN AND PARENTAL DIVORCE: THE MEANING OF SMALL EFFECTS -A REPLY

value in providing a public health perspective. Attributable risk is a useful concept because it provides a measure of association at the population level, which can be used in conjunction with measures focusing on the level of individ- ual differences. I estimated that, if the risk of depressive illness in the offspring from separated families could be reduced to the level found in the rest of the population, then the prevalence in the total population would fall by around 17%. This seemed more than a small effect.

The final suggestion for evaluation of associations was to consider the range of adverse outcomes linked to a partic- ular risk factor. The outcomes implicated in my review included: nervous and mental disorders, poor self-control, and lower reading skill in primary children; psychiatric symptoms, poor body image, impulsivity, early sexual activity, a range of substance abuse, delinquency, recidi- vism, and poor educational achievement in adolescence; and neurotic disorders, attempted suicide, alcoholism, and crimi- nal convictions in adulthood. Although I know of no published Australian findings, it seems likely that own divorce in adulthood is also associated with parental divorce, for such intergenerational continuity has been found in several other countries (Amato, 1996). It is clear that the long-term disadvantages associated with parental divorce are not confined to a particular area of wellbeing.

Mediating and Moderating Factors Linking Parental Divorce with Later Outcomes As indicated earlier, I think Bums et al. have identified a key area for future research endeavour in this field. There are several strands to the line of work required, and I suggest the inclusion of the following important research questions: (a) What factors operating in childhood amelio- rate or exacerbate the social and psychological problems associated with parental divorce? (b) What behavioural signs identify those children who develop long-term problems? (c) What circumstances in adolescence and adult- hood operate as risk and protective factors for the onset and persistence of adult difficulties?

It is beyond my expertise to go into detail on the f i s t of these questions. As a starting point, it seems reasonable to consider that risk factors observed in the general population are applicable to children from divorced families; therefore, conflict, hostility, parental neglect, parental psychopathol- ogy, and outright abuse are likely to be involved. Reviews over a number of years indicate that we have learned something of the factors that underlie the association between parental divorce and psychological adjustment in childhood (Amato, 1993; Emery, 1982; Pryor & Seymour, 1996; Rutter, 1971). To what extent this knowledge gener- alises to longer term outcomes is not clear. The British work on parental style provides a cautionary note, for it was found that the association between parental affectionless control and adult depression, observed in the sample as a whole, might not apply to children who experienced particu- lar childhood adversities, including parental divorce (Rodgers, 1996a). For these children, parental style was not a significant predictor of adult symptomatology. It remains to be seen whether this is a genuine replicable finding or perhaps reflects some inappropriateness of the Parental Bonding Instrument for certain subgroups of the population.

The second research question seems vital if we are ever to be in the position of providing genuine preventive services to children or adolescents, for the cost of primary prevention for all children from divorced families would be prohibitive. Unfortunately, the longitudinal research neces- sary for this is difficult and expensive to carry out. Existing

research is sparse and has produced disappointing results (Rodgers, 1994). It is possible that this reflects an overem- phasis on psychopathology and that attempts to identify developmental antecedents of adult interpersonal behaviour problems, whether applying to intimate relationships or more general social contacts, may prove more fruitful (Amato, 1996; Aro & Palosaari, 1991; McLeod, 1991; Rodgers, 1996b; Rodgers, Power, & Hope, in press).

The third research question stems from the apparent greater effect sizes observed for adult outcomes compared with childhood outcomes. I share Dunlop and Burns’ (1995) scepticism regarding the notion of a sleeper effect as a passive mechanism. However, Amato and Keith (1991b) pointed out that “the long-term consequences of parental divorce for adult attainment and quality of life may prove to be more serious than the short-term emotional and social problems in children that are more frequently studied. Further research on adult children of divorce - in particu- lar, longitudinal studies of children as they enter adulthood - would be of great value in understanding this phenome- non.” (p. 40). I think the key to this question is understand- ing the way in which the onset of problems over this part of the lifespan is contingent on the circumstances which adolescents and young adults have to contend with.

In recent work with the British National Child Development Study (NCDS), we have established that the association between parental divorce and adult depressive symptoms is evident in early adulthood (by age 23) and shows little change thereafter (Rodgers et al., 1997). The effect size at age 33 (in 1991) was d = 0.33 (0.31 after adjustment for childhood socioeconomic status), comparing 870 offspring from divorced families with 7,765 from intact‘ families. This can be compared with the value of 0.32 from the meta-analysis of adult outcomes (Amato & Keith, 1991a). It is larger than effect sizes found in studies of children and adolescents (Amato & Keith, 1991b; Aseltine, 1996). A different pattern was found for the association between parental divorce and alcohol consumption. This was known from a previous study to be nonsignificant at age 23 (Estaugh & Power, 1991), but was found to be highly significant at age 33 (Hope, Power, & Rodgers, 1997b). Effect sizes for heavy drinking (35 units per week for men and 20 units per week for women) were h = 0.17 and 0.13 for men and women respectively. It is interesting that one Australian study has reported parental divorce to be a risk factor for a range of substance abuse in adolescence, but not for alcohol use (Bell & Champion, 1979), whereas a link with alcoholism has been identified for adults (Koller & Castanos, 1969; Koller & Williams, 1974). Using the NCDS, we are pursuing the hypothesis that factors in early adulthood are implicated in the manifestation of the risks associated with parental divorce and have concentrated so far on the role of own marital careers. This appears to be particularly important for women, for whom the combina- tion of parental divorce and own divorce seems especially problematic (Rodgers, 1994). Our new longitudinal analyses show that this also applies in the NCDS sample, and that women from divorced families of origin have high levels of depressive symptomatology in the years preceding and following their own separation, and show a marked rise in alcohol consumption after their separation (Hope, Power, & Rodgers, 1997a). These relationships are not observed in women from intact families of origin. This work is at an early stage, but the results so far have been promising. They are consistent with the idea that difficulties in intimate relationships can mediate the link between parental divorce and mental health problems in adulthood.

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The Interplay Between Large-scale and Fine-grained Studies I think it appropriate to conclude with a brief consideration of the interplay between different research methods within this subject area. It is evident that past advances in this field have depended on the use of a diverse mix of research strategies, involving individuals from different disciplines pursuing different goals. This has been a strength of the area, and one which will bring rewards in the future. The focus on effect sizes and statistical power in this reply appears to favour large-scale epidemiological studies. This, however, overlooks the extent to which the ideas that drive research often flow from investigators who take the time and trouble to gather the in-depth information that cannot be obtained in large-scale studies. Those, like myself, who work in the latter paradigm are essentially parasites in this process, but hopefully return something to their hosts. The sample that has been followed painstakingly by Dunlop and Burns (1984, 1995) over so many years is clearly one that can provide rich information in both quantitative and quali- tative forms. I personally look forward to the products from their study.

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