The following methodological considerations deal with that part of developmental psychology which is usually described as aging research. Aging research consists of observing samples of different age levels in order to obtain age-functional relationships. Since the concept of age is defined in this context by its chronological aspects, aging research may be seen as an interdisciplinary task. The research approaches of various disciplines such as biology, demography, medicine, and psychology differ only with respect to the measurement variables which are used. In the field of psychology, such age-comparative studies represent the bulk of developmental research. In fact, aging research is often thought of as being synonymous with developmental psychology. As KESSEN (1960, p. 36) put it: "a characteristic is said to be developmental if it can be related to age in an orderly or lawful way".

To date two types of research plans have been used to study age-functional relationships, (a) the cross-sectional method and (b) the longitudinal method. SCHAIE (1965) called these two methods conventional designs for the study of aging. Despite the importance of these conventional designs for developmental psychology, it is surprising that nowhere in the psychological literature a satisfactory comprehensive discussion can be found. Only recently some more intensive attempts have been made to analyse and refine these two research designs (BALTES, 1967a, 1967b; KESSEN, 1960; KUHLEN, 1963; RAO, 1966; SCHAIE, 1965; WELFORD, 1961). SCHAIE (1965), in particular, has made a singular contribution by presenting his general developmental model as a basis for formulating new strategies.

Two factors seem to be primarily responsible for the renewed interest in cross-sectional and longitudinal methodology. First, there is a general trend in developmental psychology towards formulating a methodology specifically suited to dealing with developmental problems (BRONFENBRENNER, 1963; GOTTSCHALDT et al., 1961; HARRIS, 1963; ZIGLER, 1963). Second, observed striking discrepancies in the results of cross-sectional and longitudinal investigations (cf. DAMON, 1965; KUHLEN, 1963) pointed to the need for reevaluating the assumptions underlying these two methods. For example, cross-sectional studies of intelligence produce the well-known aging curves which suggest that between the ages of twenty and thirty there is a plateau or a gradual decline in intellectual functioning. By contrast, longitudinal studies give no evidence of such an early plateau or decline (BAYLEY, 1955; BAYLEY and ODEN, 1955; GLANZER and GLASER, 1959; KALLMANN and JARVIK, 1959; OWENS, 1953; 1966). On the contrary, longitudinal studies suggest an increase in intellectual functioning until the ages of forty or even fifty. Similar discrepancies between cross-sectional and longitudinal data have been found in age studies of interests and attitudes (BENDER, 1958; NELSON, 1954) as well as in investigations of age changes in such biological variables as height, grip strength and vital capacity (DAMON, 1965; JURCENS, 1966). These discrepancies between cross-sectional and longitudinal findings require an explanation since both methods should be expccted to yield comparable age-functional relationships.

Definitions and History

The different strategy of cross-sectional and longitudinal methods can be defined as follows (BALTES, 1967a):

According to KESSEN'S (1960) formula R = f (A), age (A) is the independent variable in both designs. The dependent variable R (response) is defined by the kind of measurement instrument used and may be of a psychological, a biological or a medical nature. Furthermore, the dependent variable may consist of one or of several measurement variables. The former can be called a univariate, and the latter a multivariate design. The following discussion will deal only with the simpler case, that is, the univariate approach[2].

Because of their application in different fields, the cross-sectional and the longitudinal method, when viewed historically, are closely tied to the conceptualization of developmental strategies in various disciplines. This multidisciplinary history has not received sufficient attention, and further exploration would be fruitful. For example, the field of demography has for centuries been using cross-sectional designs to obtain age-statistics concerning mortality rates. In light of this long history, it is not surprising that the level of methodological sophistication is relatively advanced in demography. As early as the eighteenth century, SÜSSMILCH (1741, p. 226), one of the founders of demography, referred to some problems of generalizability of cross-sectional data, when he said: "daß man einige aufeinanderfolgende gute und mittelmäßige Jahre haben müsse, wenn man von denen sterbenden nach dem Alter etwas zuverlässiges bekommen will". Similarly, the sequential strategies to be presented later seem to have their roots in demography (JACOBY, 1958; OSNADIK, 1959; WHELPTON, 1954).

In the history of psychology, QUETELET (1835) and GALTON (1883) pioneered aging research by comparing age groups observed at the same time of measurement. Although this technique was used frequently around the 1900s, it was not specifically referred to as the cross-sectional method. In the 1910s, based on the biographical approach (DARWIN, PREYER, SCUPIN, SHINN, TIEDEMANN, etc.), an alternative technique of aging research was applied when observing the same individuals at several times. Only by following this development were both strategies finally given their present names, i.e. cross-sectional and longitudinal method. It is not clear, however, who first used these concepts in psychology[3]. GESELL (1925, p. 441) employed the term cross-section in the context of developmental stages. The term longitudinal study appeared in the work of BLATZ and BOTT (1927). Yet in both these instances, the authors failed to designate these terms as specific methods of developmental research. In his classical contribution to the methodology of developmental psychology, ANDERSON (1931) pointed out that the terms cross-section and longitudinal had been introduced recently as technical terms, but without citing any references as to their origin. The operations which underlie both strategies had been described earlier in connection with other concepts. In the case of the longitudinal method, for example, such terms as consecutive tests, continuous record, follow-up, repeated measurement, repeated re-examination, repeated testing, repeated tests, retests, etc., had been used.

Research Designs

Based on the general terminology and classification of experimental designs (cf. CAMPBELL and STANLEY, 1963) both conventional strategies can be characterized as unifactorial designs, with age as the single factor (Table I).

The critical difference between the cross-sectional and the longitudinal designs lies in the use of independent sampling (S₁-S_n) in the cross-sectional method, and the use of dependent sampling (S₁) in the longitudinal method. In both models, differences between the observations on the different samples (S₁O₁-S_nO₁ and S₁O₁-S₁O_n) are attributed to the various levels of the factor age (A₁-A_n). Both designs are most powerful, if this interpretation is correct, i.e. if the differences between the age groups can be interpreted exclusively as age effects. In general, the significance of a plan with repeated measurement lies in its capacity to take into account intraindividual variation. As a result, a plan with dependent sampling (a) may be more sensitive, and (b) permits the analysis of individual trends. On the other hand, a plan using repeated observations also has some short-comings which are a consequence of the repeated measurement of the same individuals. The question of the choice between independent and dependent sampling will be dealt with in a subsequent section.

In the light of present standards of research methodology, both research designs appear to be relatively naive. CAMPBELL and STANLEY (1963) would not classify either model as a true experimental design. Their designation as pre-experimental designs implies that both models have serious methodological deficiencies which make questionable the interpretation of sample differences as pure age effects. The methodological deficiencies which are inherent to the conventional designs are possible a posteriori explanations for the divergent findings between cross-sectional and longitudinal studies. In this paper, the following problem areas will be discussed: (a) selective sampling, (b) selective survival, (c) selective drop-out, (d) testing effects, and (e) generation effects. The last two problem areas will receive closest attention since these sources of error can be controlled by the sequential models to be presented in a later section.

Most of these sources of error have as their basis the fact that the different age samples (S₁A₁-S_nA_n and S₁A₁-S₁A_n) do not differ only with respect to age but also with respect to other factors as well. As a result, the differences between age groups can not be interpreted as pure age effects. In the sense of CAMPBELL and STANLEY (1963), these sources of error may impair either the internal or the external validity of both research designs.

Selective sampling. Because of the repeated participation which is required of subjects in a longitudinal study, longitudinal samples almost always fail to meet criteria of representative sampling. Conversely, cross-sectional samples usually can fulfill this requirement without difficulty. Some empirical studies (BAKER, SONTAG and NELSON, 1958; KODLIN and THOMPSON, 1958; ROSE, 1965; STREIB, 1966) demonstrate that longitudinal samples already from their onset run the risk of being selectively biased in a positive direction. For example, subjects who volunteer for longitudinal studies tend to be of a higher average intelligence and tend to be of a higher socio-economic status. Such selective sampling biases in longitudinal studies impair (a) the comparability of cross-sectional and longitudinal investigations, and (b) the generalizability of longitudinal findings.

Selective survival. The phenomenon of selective survival applies to longitudinal as well as to cross-sectional samples. Selective survival implies that a given population at birth (cohort) changes in its composition in conjunction with the aging process as a result of death or incapacitation (BIRREN, 1959; CAMPBELL and STANLEY, 1963; DAMON, 1965; JARVIK and FALEK, 1963; RTEGEL, RIEGEL and MEYER, 1967a; 1967b). This population change is selective to the extent that the survival rate is correlated with the measurement variables. B1RREN (1959, p. 30) pointed out that "survivors might be, for example, taller or shorter, brighter or duller, happier or unhappier than their non-surviving cohort". This assumption of selective survival is further substantiated by the well-known fact that members of certain psychopathological groups have a shorter life expectancy. Subsequently, DAMON ( 1965) has demonstrated that alone on the basis of a negative correlation between height and life expectancy, the average height of older subjects tends to be less than that of younger subjects. RIEGEL, RIEGEL and MEYER (1967b) describe a gerontological study in which the survivors were on the average more intelligent, less dogmatic and less rigid than the non-survivors. In such cases of selective survival, the age samples no longer represent the population of birth cohorts and are therefore biased. As was suggested in the case of selective sampling, the effect of selective survival tends to be in the direction of positive selection.

Selective drop-out. Whereas theoretically the different age groups of a longitudinal study are completely homogeneous, in reality they become heterogeneous due to drop-outs. Such drop-outs, in the sense of CAMPBELL and STANLEY'S (1963) concept experimental mortality, occur during the course of the experiment as some subjects lose interest, change their residence, etc. This drop-out can be called selective if the loss of subjects does not follow a random pattern, i.e. if there is a correlation between the dependent variable and the characteristics related to drop-out. Selective drop-out, as defined here, is a characteristic of the sample under investigation and not a characteristic of the underlying population from which it was drawn. This is in contrast to the case of selective survival where attrition can be attributed to changes in both the underlying population and the sample.

As a consequence of selective drop-out, the longitudinal sample as measured later in the experiment (S₁A_nO_n) is no longer comparable to the original sample (S₁A₁O₁). Again in the case of selective drop-out, it has been shown that the sample seems to become progressively more and more biased in a positive direction (AMES and WALKER, 1965; ANDERSON and COHEN, 1939).

Testing effects. The problem area of testing effects again applies primarily to the longitudinal method. The longitudinal designs, plans with repeated measurement, have as a basic assumption that the repeated observation of the same sample (S₁O₁-S₁O_n) has no effects on the dependent variable. This assumption is highly improbable for many psychological variables when one considers short- and long-term practice and satiation effects. Such effects have been demonstrated with achievement tests (cf. ANASTASI, 1958) as well as with personality tests (cf. WINDLE, 1954). In connection with the longitudinal design, practice effects combined with increased test-sophistication and deliberate coaching have been cited as sources of error (ANASTASI, 1958; ANDERSON, 1954; KODLIN and THOMPS0N, 1958; KUHLEN, 1963; MILES, 1934; OWENS, 1953; SONTAG, BAKER and NELSON, 1958; WELFORD, 1961; 1964). The importance of testing effects as confounding variables should not be underestimated since many longitudinal studies employ a high number of retests. For example, in the well-known Berkeley Growth Study the majority of subjects were tested no less than 38 times over a period of 18 years (BAYLEY, 1949).

As a matter of fact, it is relatively easy to control testing effects in longitudinal studies by introducing adequate control groups. For the purpose of controlling testing effects, it is necessary only to draw two or more equivalent samples at the beginning of a longitudinal study and to vary them systematically in terms of number of observations made in the sense of a "posttest-only control group design" (BALTES, 1967a; CAMPBELL and STANLEY, 1963; SCHAIE, 1965). In a later section dealing with the simultaneous application of longitudinal and cross-sectional sequences we will refer more explicitly to such a research plan.

Generation effects. The issue of generation effects as a source of error impairs the internal validity of cross-sectional studies and the external validity of longitudinal designs. With respect to the cross-sectional method it has been argued (BIRREN, 1959; DAMON, 1965; JEROME, 1959; KUHLEN, 1963; ROSLER, 1966; SCHAIE, 1965; WELFORD, 1964) that the age samples (S₁A₁-S_nA_n) differ not only with regard to age, but also simultaneously as to generations in the sense of cohorts. First formulated by KUHLEN (1940), this issue has been stated more precisely by ANASTASI (1958, p. 220): "Differences between 20- and 40-year-olds tested simultaneously (in 1940 or 1960) would reflect age changes plus cultural differentials, especially differences in the conditions under which the two age groups were reared". The relationships between age and generation effects in the cross-sectional design is presented in Figure 1.

The sample differences of a longitudinal study (S₁A₁O₁-S₁A_nO_n) have been obtained from a single generation. Consequently, the age effect of a longitudinal study is generation specific. Therefore, the internal validity of a longitudinal design is not attenuated by the existence of generation differences. The external validity of age effects, however, found in longitudinal studies is seriously restricted. If, for example, the results of the Berkeley Growth Study, begun in 1928, are to be generalized to the birth cohort 1965, the generation gap is almost 40 years.

In summary, one must conclude that the conventional methods are in no way adequate research designs for the assessment of age effects. Due to the various methodological deficiencies it is not legitimate to interpret the sample differences obtained in longitudinal and cross-sectional studies as pure age effects. Besides the age effects a number of other uncontrolled sources of variance are confounded. These uncontrolled factors are alternative explanations for the obtained sample differences. The picture can become very complicated indeed, since the effects need not occur in the same direction and to the same degree in different measurement variables. Because of the hopelessly confounded sources of error it does not seem feasible to make a posteriori statements with respect to differential validity of the results obtained by cross-sectional versus longitudinal investigations. If one considers the process of making at least one controlled comparison as the basis of securing scientific evidence (CAMPBELL and STANLEY, 1963), both conventional designs have such a total absence of control as to be of almost no scientific value. More differentiated research designs are needed to control these various deficiencies. In the following sections such research plans for the analysis and control of generation and testing effects will be presented.

General Developmentel Model of Schaie

The literature discloses a number of proposals to refine the conventional designs in order to eradicate one or another of the methodological shortcomings (ANASTASI, 1958; BELL, 1953; BIRREN, 1959; KESSEN, 1960; KUHLEN, 1963; MILES, 1934; RAO, 1966; SCHAIE, 1959; THOMAE, 1959a; WELFORD, 1961). In most cases, these proposals are not explicitly worked out. They consist either of the suggestion to perform several cross-sectional or longitudinal studies or to combine both conventional designs with one another.

SCHAIE (1965) was the first to present a well explicated theoretical conception suitable to clarify the study of age effects. SCHAIE elaborated a general model for the study of developmental phenomena. This model provides a basis for the evaluation of certain characteristics of the conventional methods and for the formulation of new sequential research designs. Whereas the conventional methods are based on the unifactorial formula R = f (A), SCHAIE expanded this formula into a multifactorial one. He builds his general developmental model on three components: age (A), cohort (C), and time of measurement (T). Applied to a concrete example of human development the definitions and the interrelationships between the three components are illustrated in Table II. The example refers to the cohorts of 1880-2000, with an assumed life expectancy of 80 years per cohort. The corresponding time of measurement extends from 1880-2080, in 20 year intervals.

Figure 2
An example of the bifactorial developmental model with the components of age and cohort and its relationship to the conventional longitudinal (LO), cross-sectional (CS) and time-lag (TL) methods. Time of measurements are included for illustration only.

Age and generation effects. In the case of a parametric analysis, the bifactorial developmental model may be conceptualized as a bifactorial analysis of variance design. The components of age and cohort represent the factors in the sense of fixed factors, where number of age and cohort groups used is identical with the number of factorial levels respectively. Consequently, the arrangement in Figure 2 consists of a 7 x 5 bifactorial design since seven levels of cohort and five levels of age are employed. A 2 x 2 design, in which two cohorts are observed at the same two age levels, is the minimum bifactorial design which can be derived from the developmental model.

With respect to the factor age, the bifactorial analysis of variance might be conceived with independent as well as with repeated measurements. A repeated measurement design over the factor age is defined as one sample of the cohort y observed repeatedly, as is done in the case of the conventional longitudinal method. In contrast, independent measurements are present when several comparable samples are drawn from the cohort y which are all observed only once at a specific age level.

Such an analysis of variance design (Table III) permits the separation of the main effects of age and cohort. Simultaneously, in the presence of a significant interaction between age and cohort, it is possible to infer different age effects for different levels of cohorts. In other words, it is possible to examine the extent to which (a) the observed behavioral characteristic is affected significantly by age, (b) the observed behavioral characteristic is affected significantly by cohort, and (c) the extent to which the effect of age is different when age is combined with specific levels of cohort. By application of suitable a posteriori tests it is subsequently possible to localize the single effects more precisely within the levels of age and cohort. Furthermore, it might be tested whether the obtained age- and cohort-functional relationships fit to some developmental trends provided by theoretical considerations or other empirical studies.

The decision between a design with repeated and independent measurements is dependent upon various criteria. According to the general theory of experimental design, a design with repeated measurement is more adequate if it is feasible (a) to have a more sensitive test of significance, and (b) to analyse individual variation.

The increase in sensitivity seems worthwhile only if the effect of the factor under consideration (age) is expected to be relatively small, if the extent of confounding carry-over effects can be assumed to be negligible, and if it is not too difficult to observe the same individuals repeatedly. Therefore, a general decision between a design with repeated and independent observations to increase sensitivity does not seem reasonable. By considering the criteria of the extent of age, carry-over effects as well as of economy, a design with independent measurements, however, appears to be more often adequate for the study of age and generation effects. Age effects are generally considerable and testing effects are not to be underestimated in most psychological variables. In addition, because of selective drop-out, it is not easy to maintain the original samples over longer time intervals.

On the other hand, a design with repeated measurement is necessary for the analysis of individual trends and for the control of selective survival effects. The analysis of individual developmental trends corresponds largely to the advantage attributed often to the conventional longitudinal approach, namely that the longitudinal study alone is able to analyse the dynamics and individuality of developmental processes (cf. ANDERSON, 1954; BALDWIN, 1960; JONES, 1958; KESSEN, 1960; THOMAE, 1959a, 1959b). Besides the main effect of Ss (Table III) which indicates the existence of over-all individual differences, it is the interaction term Ss x Age in the repeated measurement design which provides information on the need for an idiographical kind of treatment of developmental trends. It is not yet sufficiently clarified to what extent it will be necessary to study developmental processes in an idiographic frame of reference. Should it be necessary, however, to adapt such an idiographic approach, this would have serious consequences for the generalizability of developmental findings.

Hypothetical examples. In Figure 3, six possible outcomes of a bifactorial design having three levels of each age (A1-A3) and cohort (C1-C3) are considered. It is usual (cf. WINER, 1962, p. 235) to illustrate the results of factorial analyses in the form of geometric representations of the sample means on the dependent variable.

Figure 3a-f
Six hypothetical outcomes of a 3 x 3 factorial design of the bifactorial developmental model (• = means, A₁-A₃ = three levels of age, C₁-C₃ = three levels of cohort).

The arrangement in Table IV permits the analysis of over-all testing effects. This analysis of testing effects is possible since for each age group of the repeated measurement design (C₁₁A₁-C₁₁A₅) a control group is available which has been observed only once at a specific age level (C₁₂A₁-C₁₆A₅). For the control of testing effects the observations, placed one beneath the other in Table IV, are therefore to be compared. For example, C₁₁A₂0₂ is compared with C₁₃A₂O₁. This control of testing effects can be expanded to all cohort and age levels of the bifactorial model under study. A problem is, however, that such a control group design contains simultaneously information with regard to selective drop-out effects. In other words, in the differences between the samples to be compared testing and drop-out effects might be confounded. Therefore, it should be recognized that even more complex research designs are needed to fully clarify these sources of error. The above example is intended only as a first attempt at developing the kind of experimental set-ups which are required for an adequate control of the effects of testing and selective drop-out.

Longitudinal and cross-sectional sequences. It remains to decide how to name the strategies of data collection when transforming the bifactorial developmental model into a research design. It seems reasonable to do this in terms of the conventional methods. Therefore, the relationship of the conventional methods to the bifactorial model will be clarified first.

The bifactorial developmental model can be separated into unifactorial designs. Such unifactorial designs consist of varying the levels of one factor only, while holding the second factor constant. The formulation of such unifactorial plans is legitimate since they produce effects which can be interpreted unambiguously. The status of the conventional methods has been illustrated already in Figure 2 (p. 158). It can be seen that both the conventional longitudinal and time-lag methods correspond to such unifactorial designs. In the case of the longitudinal method, the factor age is varied while the factor cohort is held constant. The reverse is true for a time-lag study where the factor cohort is varied while age is held constant. Therefore, both the conventional longitudinal and time-lag methods can be considered as adequate designs. Consequently, the effects of the longitudinal and time-lag methods can be interpreted as pure component effects, i.e. age or cohort effects. Within the bifactorial developmental model the findings of both methods are limited only with regard to their generalizability over the second factor, i.e. cohorts and ages respectively. The conventional cross-sectional method, however, must be considered as an inadequate research design. In a single cross-sectional study age and cohort conditions are varied simultaneously and consequently age and cohort effects are inevitably confounded. The suggestion to interpret the sample differences obtained by the conventional longitudinal and time-lag methods as pure component effects is contrary to the proposal made by SCHAIE (1965). On the basis of his trifactorial model, SCHAIE considered the sample differences of all three conventional methods as the confounded effect of two components.

After the status of the conventional methods within the bifactorial developmental model has been described we can proceed to designate the strategy of data collection needed to fill the cells of the bifactorial model. The kind of terminology should serve to distinguish between an independent and a repeated measurement design with regard to the factor age.

Figure 4
Examples for longitudinal (LOS) and cross-sectional sequences (CSS) as data collection strategies.

In the case of a design with independent observations with regard to the factor age, it is possible to obtain the required observations by performing successive cross-sectional studies. Therefore, this strategy of data collection may be called a cross-sectional sequence (Fig. 4). Again in the simplest case we are dealing with a 2 x 2 design with independent observations over both cohort and age. When applying a cross-sectional sequence one has to keep in mind, however, that a single cross-sectional study represents an inadequate design since it confounds age and cohort effects. For this reason, some of the single cross-sections, composing the total of the cross-sectional sequence, need not necessarily cover all age levels. From the first cross-section, for instance, only the results of the first age level are usable. From the second those of the first two age levels, and from the third cross-section the results of the first three age levels, etc., are usable for the bifactorial model. In principle, it is then possible to conceptualize the first cross-sectional studies over fewer age levels. If the first cross-sections, however, are expanded over all age levels under consideration, the obtained information is not necessarily useless. The observations might be applied to unifactorial designs in the sense of single longitudinal and time-lag methods[4].

When the bifactorial model is applied both with repeated as well as independent observations concerning the factor age some of the observations are applicable for both the cross-sectional and the longitudinal sequences. All samples which are observed for the first time in the course of the longitudinal designs may be used simultaneously for the cross-sectional sequences as well. Consequently, when longitudinal and cross-sectional sequences are applied simultaneously, the single cross-sections need not include the first age level of thc bifactorial model under consideration.

Discussion

The general developmental model and the sequential strategies based thereon were first presented by SCHAIE (1965). Their purpose was (a) to analyse critically the conventional methods in research on aging, and (b) to formulate more adequate research strategies. The present paper proposed a reformulation of SCHAIE'S developmental model and of the sequential strategies in an attempt to eliminate methodological deficiencies inherent to SCHAIE'S arguments. Furthermore, an adequate analysis and interpretation of the developmental model was sought. It is hoped that application of the longitudinal and cross-sectional sequences presented in this paper will clarify the puzzling discrepancies between cross-sectional and longitudinal findings and may contribute to the construction of more valid developmental gradients with regard to age as well as to cohort.

Since the proposed sequential strategies require such a great investment of time and energy, the question of utility might be raised. On the one hand, the amount of investment is mainly dependent upon the range and the number of intervals used regarding both factors age and cohort. On the other hand, the amount of investment depends on the choice of a design with independent and/or a design with dependent observations concerning the factor age. There is, however, no general rule to rely upon. In each single case, the investigator must make a new decision which will depend, for example, upon the kind of dependent variable under consideration, the underlying hypotheses with regard to the extent of age and cohort effects, and the intended range of generalizability.

For many variables of a physical or a biological nature, for instance, it might be feasible to restrict the number of levels with regard to the cohort factor, while in the same study the age factor might concentrate on the lower and higher age levels, or even on a specific smaller age range only. In other instances, as in the investigation of consumer motivation, it might be more interesting to select more levels of cohort and to concentrate on the age range of early adulthood. In the long run, nevertheless, we need in addition more systematic approaches covering wide ranges of age and cohort as well. This necessitates the cooperation of many people, institutions, and even members of different generations.

With regard to the choice between a design with independent and/or a design with dependent measurements over the factor age, this writer considers a design with independent observations as generally more feasible, at least in light of the current state of knowledge. A design with independent observations is in general more economical and as valid as a design with dependent observations. As a consequence, a design with repeated measurements seems worthwhile only when there are strong arguments for the need of a test with higher sensitivity concerning the factor age and/or strong arguments for the need of an idiographical kind of analysis. In this connection, it has to be recognized that in the realm of the bifactorial developmental model it is not the cross-sectional method which is the appropriate alternative to the longitudinal method but a design where different samples from the same cohort are observed, each at a specific age level.

The question of the relation between investment and utility of the bifactorial developmental model and the sequential strategies derived therefrom, therefore, cannot be answered a priori on a theoretical level. The answer is rather contingent on the intentions of the investigator, the empirical relevance of the postulated age, cohort and error effects, as on the need for the analysis of individual variation in the case of a repeated measurement design over the factor age. It might well be that the effects of generation differences, for instance, are very small or even absent in a specific case. Nevertheless, as long as this has not been proved empirically, the hypothesis of generation differences seems worthy of investigation with regard to all variables which might be dependent upon hereditary and/or environmental conditions.

Finally, regarding the utility of the sequential strategies, we should keep in mind that the scientific progress in aging research, as in any other discipline, is contingent largely upon the quality of its methodology. In dealing with continuous changes, as is true in the study of such time variables as age and cohort, we will have to become adapted to much more refined research planning. Strictly speaking, one could conclude that it will not be possible at all to investigate these levels of age and cohort which have not been studied to date, since the variation of age and cohort is of an ordered and irreversible nature. These restrictions with regard to the logical status of age and cohort as experimental variables underline the necessity for a careful methodology in the field of aging.

Summary

The conventional methods of aging research, the cross-sectional and longitudinal designs, are discussed in a historical frame of reference. An analysis of the research designs underlying both methods demonstrates that the two models exhibit serious deficiencies which make questionable the interpretation of sample differences as pure age effects. The following five methodological shortcomings are described: (a) selective sampling, (b) selective survival, (c) selective drop-out, (d) testing effects, and (e) generation effects.

Recently, SCHAIE has presented a general trifactorial developmental model consisting of the components age, cohort and time of measurement. This developmental model was the basis for deriving new strategies which SCHAIE called sequential designs. Some inconsistencies in the formal definitions and the measurability of the components sensu SCHAIE are pointed out. These inconsistencies necessitate a reformulation of the general developmental model and the sequential strategies derived therefrom. In order to obtain an adequate analysis and interpretation it is proposed that the trifactorial developmental model be transformed into a bifactorial model using only the components of age and cohort (generation). This bifactorial developmental model can be conceptualized as a design with independent as well as dependent measurements over the factor age. An analysis of variance design permits the separation of the main effects of age and cohort and their interaction.

The data collection strategies can be called in the case of independent measurement, cross-sectional sequences, and longitudinal sequences in the case of repeated measurement. In the frame of reference of the bifactorial model, the conventional longitudinal and time-lag methods can be considered as adequate unifactorial designs. However, the cross-sectional method must be considered as inadequate since it confounds age and generation effects.

Footnotes

References

AMES, C. B. and WALKER, R. N.: A note on school dropouts in longitudinal research with late adolescents. J. genet. Psychol. 107: 277-279 (1965).

ANASTASI, A.: Age differences. In: A. ANASTASI (Ed.) Differential psychology. pp. 216-265 (MacMillan, New York 1958).

ANDERSON, J. E.: The methods of child psychology. In: C. MURCHISON (Ed.) A handbook of child psychology. pp. 1-27 (Clark Univ. Press, Worcester 1931).

ANDERSON, J. E.: Methods of child psychology. In: L. CARMICHAEL (Ed.) Manual of child psychology. pp. 1-59 (Wiley, New York 1954).

ANDERSON, J. E. and COHEN, J. T.: The effect of including incomplete series in the statistical analysis of longitudinal measurements of children's dental arches. Child Develop. 10: 140-149 (1939).

BALTES, P. B.: Sequenzmodelle zum Studium von Altersprozessen: Querschnitt- und Längsschnittsequenzen. In: F. MERZ (Ed.) Bericht über den 25. Kongreß der Deutschen Gesellschaft fur Psychologie in Münster 1966. pp. 423-130 (Hogrefe, Göttingen 1967a).

BALTES, P. B.: Längsschnitt- und Querschnittsequenzen zur Erfassung von Alters- und Generationseffekten. Phil. Diss. (Photo-print, Saarbrücken 1967b).

BAKER, C. T., SONTAG, L. W. and NELSON, V. L.: Individual and group differences in the longitudinal measurement of change in mental ability. Monogr. Soc. Res. Child Develop. 23: 11-85 (1958).

BALDWIN, A. L.: The study of child behavior and development. In: P.H. MUSSEN (Ed.) Handbook of research methods in child development. pp. 3-35 (Wiley, New York 1960).

BAYLEY, N.: Consistency and variability in the growth of intelligence from birth to eighteen years. J. genet. Psychol. 75: 165-196 (1949).

BAYLEY, N.: On the growth of intelligence. Amer. Psychologist 10: 805-815 (1955).

BAYLEY, N. and ODEN, M. H.: The maintenance of intellectual ability in gifted adults. J. Geront. 10: 91-107 (1955).

BELL, R. Q.: Convergence: an accelerated longitudinal approach. Child Develop. 24: 115-152 (1953).

BENDER, I. E.: Changes in religious interest: a retest after 15 years. J. abnorm. soc. Psychol. 57: 41-46 (1958).

BIRREN, J. E.: Principles of research on aging. In: J. E. BIRREN (Ed.) Handbook of aging and the individual. pp. 3-42 (Univ. of Chicago Press, Chicago 1959).

BLATZ, W. E. and BOTT, E. A.: Studies in mental hygiene: I. Behavior of public school children - a description of method. Pedagog. Sem. 34: 552-582 (1927).

BRONFENBRENNER, U.: Developmental theory in transition. In: H. W. STEVENSON (Ed.) Child psychology. pp. 517-542 (Univ. of Chicago Press, Chicago 1963).

CAMERER, W.: Gewichts- und Längenwachstum der Kinder. In: M. PFAUNDLER and A. SCHLOSSMANN (Eds.) Handbuch der Kinderheilkunde. Vol. I. pp. 232-247 (Vogel, Berlin 1910).

CAMPBELL, D. T. and STANLEY, J. C.: Experimental and quasiexperimental designs for research on teaching. In: N. L. GAGE (Ed.) Handbook for research on teaching. pp. 171-246 (McNALLY, Chicago 1963).

CATTELL, R. B.: The fate of national intelligence in a test of a thirteen - year prediction. Eugen. Rev. 42: 136-148 (1951).

DAMON, A.: Discrepancies between findings of longitudinal and cross-sectional studies in adult life: physique and physiology. Hum. Develop. 3: 16-22 (1965).

EMMET, W. G.: The trend of intelligence in certain districts of England. Popul. Stud. 3: 324-337 (1950).

GALTON, F.: Inquiries into human faculty and its development (MacMillan, London 1883).

GESELL, A.: The mental growth of the preschool child. A psychological outline of normal development from birth to the sixth year, including a system of developmental diagnosis (MacMillan, New York 1925).

GLANZER, M. and CLASER, R.: Cross-sectional and longitudinal results in a study of age-related changes. Educ. psychol. Measmt. 19: 89-101 (1959).

GOTTSCHALDT, F.: (Ed.) Allgemeine und methodologische Fragen der Entwicklungspsychologie. Z. Psychol. 165: 4-156 (1961).

HARRIS, C. W.: (Ed.) Problems in measuring change (Univ. of Wisconsin Press, Madison 1963).

JACOBY, F..G.: Kohorten-Analyse insbesondere als Mittel zur Messung der Fruchtbarkeit. Allg. Stat. Arch. 42: 21-28 (1958).

JARVIK, LISSY, F. and FALEK, A.: Intellectual stability and survival in the aged. J. Geront. 18: 173-176 (1963).

JONES, H. E.: Problems of method in longitudinal research. Vita humana 1: 93-99 (1958).

JEROME, E. A.: Age and learning - experimental studies. In: J. E. BIRREN (Ed.) A handbook of aging and the individual. pp. 655-699 (Univ. of Chicago Press, Chicago 1959).

JÜRGENS, H. W.: Über das Wachstum der Korpergröße beim "erwachsenen" Menschen. Dtsch. med. Wschr. 91: 1881-1886 (1966).

KALLMANN, F. J. and JARVIK, L. F.: Individual differences in constitution and genetic background. In: J. E. BIRREN (Ed.) Handbook of aging and the individual. pp. 216-263 (Univ. of Chicago Press, Chicago 1959).

KESSEN, W.: Research design in the study of developmental problems. In: P. MUSSEN (Ed.) Handbook of research methods in child development. pp. 36-70 (Wiley, New York 1960).

KODLIN, D. and THOMPSON, D. J.: An appraisal of the longitudinal approach to studies in growth and development. Monogr. Soc. Res. Child Develop. 32: No. 67 (1958).

KUHLEN, R. G.: Social change: a neglected factor in psychological studies of the life span. School Soc. 52: 14-16 (1940).

KUHLEN, R. G.: Age and intelligence: the significance of cultural change in longitudinal vs. cross-sectional findings. Vita humana 6: 113-124 (1963).

MILES, C. C.: Influence of speed and age on intelligence scores of adults. J. genet. Psychol. 10: 208-210 (1934).

NELSON, E. N. P.: Persistence of attitudes of college students fourteen years later. Psychol. Monogr. 68: No. 2 (1954).

OSNADIK, L.: Über das Verfahren der Kohorten-Analyse. Allg. Stat. Arch. 43: 65-68 (1959)

OWENS, W. A. Jr.: Age and mental abilities: a longitudinal study. Genet. Psychol. Monogr. 48: 3-54 (1953).

OWENS, W. A.: Age and mental abilities: a second adult follow-up. J. educ. Psychol. 57: 311-325 (1966).

QUETELET, A. L.: Sur l'homme et le développement de ses facultés (Bachelier, Paris 1835).

RAMSEY, C. E. and NELSON, L.: Change in values and attitudes toward the family. Amer. sac. Rev. 21: 605-609 (1956).

RAO, M. N. and RAO, C. R.: Methods for determining norms and growth rates. A study amongst indian school-going boys. Gerontologia, Basel 12: 200-216 (1966).

RIEGEL, K. F., RIEGEL, R. M. and MEYER, G.: Socio-psychological factors of aging: a cohort-sequential analysis. Hum. Develop. 10: 27-56 (1967a).

RIEGEL, K. F., RIEGEL, R. M. and MEYER, G.: A study of drop-out rates in longitudinal research on aging and the prediction of death. J. Pers. soc. Psychol. 5: 324-348 (1967b).

ROSE, C. L.: Representativeness of volunteer subjects in a longitudinal aging study. Hum. Develop. 8: 152-156 (1965).

ROSLER, H. D.: Acceleration and intelligence capacity in adult (abstract). Ber. 18. Intern. Congr. Psychol. Moskau 3: 54 (1966).

SCHAIE, K. W.: Cross-sectional methods in the study of psychological aspects of aging. J. Geront. 14: 208-215 (1959).

SCHAIE, K. W.: A general model for the study of developmental problems. Psychol. Bull. 64: 92-107 (1965).

Scottish Council for Research in Education (Ed.). The trend of Scottish intelligence: a comparison of the 1947 and 1932 surveys of the intelligence of eleven-year-old pupils (Univ. London Press, London 1919).

SIXTL, F. and BALTES, P. B.: Multivariate longitudinal and cross-sectional sequences (in preparation).

STREIB, C. F.: Participants and drop-outs in a longitudinal study. J. Geront. 21: 200-209 (1966).

SÜSSMILCH, J. P.: Die göttliche Ordnung in den Veränderungen des menschlichen Geschlechtes, aus der Geburt, dem Tod und der Fortpflanzung desselben erwiesen (Realschulbuchhandlung, Berlin 1741).

THOMAE, H.: Forschungsmethoden der Entwicklungspsychologie. In: H. THOMAE (Ed.) Entwicklungspsychologie. pp. 46-76 (Hogrefe, Göttingen 1959a).

THOMAE, H.: Die Bedeutung der Längsschnittuntersuchung für die Entwicklungspsychologie und Pädagogik. In: J. DERBOLAV und H. ROTH (Eds.) Psychologie und Pädagogik. pp. 177-206 (Quelle und Meyer, Heidelberg 1959b).

TUDDENHAM, R.D.: Soldier intelligence in World Wars I and II. Amer. Psychologist 3: 54-56 (1948).

WELFORD, A. T.: Méthode longitudinale et transversale dans les recherches sur le vieillissement. In: Colloques internationaux du Centre de la Recherche Scientifique (Ed.) Le vieillissement des fonctions psychologiques et psycho-physiologiques. pp. 31-44 (Centre National, Paris 1961).

WELFORD, A. T.: Vieillissement et aptitudes humaines (Presses Universitaires de France, Paris 1964).

WHEELER, L. R. A.: A comparative study of the intelligence of East Tennessee mountain children. J. educ. Psychol. 33: 321-334 (1942).

WHELPTON, P. K.: Cohort Fertility (native white women in the United States) (University Press, Princeton 1951).

WINDLE, C.: Test - retest effect on personality questionnaires. Educ. psychol. Measmt. 11: 617-633 (1954).

WINER, B. J.: Statistical principles in experimental design (McGraw-Hill, New York 1962).

ZIGLER, E.: Metatheoretical issues in developmental psychology. In: M. H. MARX (Ed.) Theories in contemporary psychology. pp. 341-369 (MacMillan, New York 1963).

Paul B. Baltes
Director, Center for Lifespan Psychology
Max Planck Institute for Human Development
Lentzeallee 94
14195 Berlin
Germany
sekbaltes(at)mpib-berlin.mpg.de