The Study of Individual Differences: Statistical Approaches to Inter- and Intraindividual Variability

This chapter outlines some basic issues in research design and analysis. It is included to inform the reader about the manner in which researchers have typically explored relationships among environmental, task, or psychological stressors and specific biomarkers or performance outcomes. Although this standard approach has been invaluable up to the present, continued reliance on this approach to the exclusion of more complex, nonlinear methods may impede progress toward developing predictors that are reliable across unique individuals, times, and circumstances. To start, a discussion of the research hypothesis and its relationship to the partitioning of variance is presented. Attention is then shifted to the elements of a statistical test, followed by an examination of the selection perspective on research design and the distinction between inter- and intraindividual variability. A rationale for the use of multivariate, replicated, repeated-measures, single-subject designs in research with combat service members is offered. It is imperative to keep in mind that the most important aspect of any statistical test is the informed judgment of the researcher. As such, a clear understanding of these basic issues contributes greatly toward the appropriate design and analysis of experiments.

Biobehavioral research is among the most challenging of scientific endeavors. The study of interactions between living systems and their environment has tested the limits of research methodologies and theoretical models. The typical research design oversimplifies the complexity of these relationships and thus does not unambiguously allow for inferences about organism-environment interactions. Rather, these designs tend to obscure underlying processes by shrouding rich individual data with group data aggregation procedures (Glass and Mackey, 1988; O’Connor, 1990).

It is a truism in the biobehavioral sciences that no single measure or aspect of responding can adequately represent a complex latent construct (Nesselroade and

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2
The Study of Individual Differences: Statistical Approaches to Inter- and Intraindividual Variability
This chapter outlines some basic issues in research design and analysis. It is included to inform the reader about the manner in which researchers have typically explored relationships among environmental, task, or psychological stressors and specific biomarkers or performance outcomes. Although this standard approach has been invaluable up to the present, continued reliance on this approach to the exclusion of more complex, nonlinear methods may impede progress toward developing predictors that are reliable across unique individuals, times, and circumstances. To start, a discussion of the research hypothesis and its relationship to the partitioning of variance is presented. Attention is then shifted to the elements of a statistical test, followed by an examination of the selection perspective on research design and the distinction between inter- and intraindividual variability. A rationale for the use of multivariate, replicated, repeated-measures, single-subject designs in research with combat service members is offered. It is imperative to keep in mind that the most important aspect of any statistical test is the informed judgment of the researcher. As such, a clear understanding of these basic issues contributes greatly toward the appropriate design and analysis of experiments.
OVERVIEW
Biobehavioral research is among the most challenging of scientific endeavors. The study of interactions between living systems and their environment has tested the limits of research methodologies and theoretical models. The typical research design oversimplifies the complexity of these relationships and thus does not unambiguously allow for inferences about organism-environment interactions. Rather, these designs tend to obscure underlying processes by shrouding rich individual data with group data aggregation procedures (Glass and Mackey, 1988; O’Connor, 1990).
It is a truism in the biobehavioral sciences that no single measure or aspect of responding can adequately represent a complex latent construct (Nesselroade and

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Ford, 1987; Schwartz, 1986). Rather, such constructs must be represented by an entire pattern of manifestations (Cattell, 1966). In studying the behavior of living systems, a description and elucidation of the nature of underlying regulatory processes should precede any premature hypothesis testing with group means of individual variables (Barton, 1994). In view of the prevalence and importance of rhythmicity in biological regulatory mechanisms, inclusion of time-varying or temporal aspects of responding is crucial to accurately portray such activity (Glass and Mackey, 1988; Goldbeter and Decroly, 1983; Hrushesky, 1994).
Unfortunately, the analysis of variance (ANOVA) design, a staple of psychophysiological research, confuses temporal information by splitting physiological events into discrete epochs, thereby disrupting the continuity of responding (O’Connor, 1992). Furthermore, precise mapping of physiological activity from these distinct periods onto experimental manipulations is fraught with hazards, such as delayed physiological responses and compensatory homeostatic processes (Levenson, 1988). Alternatively, all recorded activity might be considered as relevant; functional relationships among ongoing physiological processes could then be extracted across observations (O’Connor, 1990).
In response to these various concerns, an alternative framework for research with combat service members is suggested: a multivariate, systems perspective that emphasizes the study of individuals. A distinctive feature of this approach is its focus on intraindividual variability in the behavioral and physiological processes of an organism. Moreover, within-group variance (typically treated as error in traditional experimental psychology) is also investigated since it contains a wealth of relevant information (Cronbach, 1957). Thus it is appropriate first to address these basic methodological issues in design and analysis for research involving combat service members.
SEX AND GENDER
Sex and gender factors, including genetic, hormonal, and behavioral factors, are important variables that contribute to differences in biological responses in all species. Sex and gender should therefore always be considered and taken into account when designing and analyzing studies at all levels of biomedical- and health-related research (IOM, 2001b). Data related to sex and gender variables in health and disease have been recently summarized in an Institute of Medicine report (IOM, 2001b). This report pointed out that incidence and severity of diseases vary between the sexes and may be related to differences in genetic, hormonal, cellular, or behavioral responses, as well as to differences in exposures, routes of entry, or the processing of a foreign agent. The report also underscored the importance of performing studies at different stages of the life span to determine how sex and developmental differences influence health, illness, and longevity.
Several examples of sexually dimorphic biomarkers are relevant to this report. For example, in the context of a military setting, it is known that the inci-

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dence of stress fractures during military training is significantly higher in females than in males (Shaffer, 1997; Stoneman, 1997). Furthermore, recent research indicates that stress responses differ in males and females, and that the hormonal stress response (hypothalamic-pituitary-adrenal axis) is modulated by sex hormones. Conversely, stress hormones modulate the sex hormone axis (hypothalamic-pituitary-gonadal axis) (Castagnetta et al., 2003; Cutolo et al., 2003). Clinically relevant conditions related to this interplay between these axes that could apply to a military setting include amenorrhea in female athletes. Pain responses also differ in males and females (Sternberg et al., 2001), as do cognitive and behavioral differences in response to sleep deprivation (IOM, 2001a). The committee therefore emphasizes that sex- and gender-related differences at the biological level will impact outcome measures of all the biomarkers considered in this report; therefore when designing and analyzing relevant studies, consideration should be always be given to these differences.
RESEARCH: WHAT ARE WE REALLY TRYING TO DO?
Variance Partitioning and Hypothesis Testing
The research enterprise is primarily concerned with the detection of systematic relationships amidst the morass of variability in biobehavioral responses. This task calls for the partitioning of observed variability into systematic and random components, which in turn will reveal patterns of associations such that events can be described, predicted, controlled, and ultimately understood. In the simplest case, a research question or hypothesis is tested by an investigation of the existence, direction, and magnitude of a relationship between an independent or predictor variable (IV) and a dependent or criterion variable (DV).
It is a basic and often implicit assumption of most scientific research that the whole is equal to the sum of its parts. It then follows that the partitioning of observed variability will lead to an explicit set of relationships between IVs and DVs. This premise is the basis of all common statistical procedures and is the foundation of the general linear model, that is, the presumption of linearity allows for unambiguous partitioning of variability. As such, small causes lead to small effects and large causes lead to large effects. This concept of proportionality is a cornerstone of the general linear model (West, 1990). However, linearity, and thus this ability to neatly partition variance, often does not hold in nature, and so arose the impetus for contemporary work on nonlinear dynamics: the science of complexity, also called chaos theory (Gleick, 1987). In spite of the notoriety that has been attained by this field, most research methodologies are based on the presumption of linearity.

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Variance Partitioning in a Linear World
When trying to assess the relative importance of a particular association, one typically asks if the systematic relationship is large relative to random fluctuations. In a simple t-test or one-way, between-subjects ANOVA, this question becomes a test of the ratio of two variances: one representing systematic variability (between-subject variance) and the other representing unsystematic variability (within-subject variance). In the one-way, between-subjects ANOVA, this ratio is expressed as:
F=between-subject variance/within-subject variance
When this ratio is much greater than one, with the appropriate degrees of freedom (df), there is evidence for a statistically significant association between the IV and DV. However, in numerous situations there are many possible systematic relationships, only some of which will be of interest. Thus it is preferable to think of a statistical test as the ratio of the variance of interest to the variance of noninterest:
F=variance of interest/variance of noninterest
Another important consideration is the magnitude or size of the effect. Since one is not only attempting to estimate the probability, but also the direction and magnitude of relationships, a direct index of the latter is very useful. Unfortunately, the tradition of null-hypothesis testing has tended to divert the focus of research away from the dimension of magnitude. In fact, any significance test represents the confluence of four mathematical components: (1) the size of the study, which refers to the number of subjects under investigation and is often represented in the significance test by the df associated with the denominator of the ratio of variances; (2) the size of the effect, which refers to the magnitude of the relationship between the IV and DV, a quantity that represents the amount of variability in the DV that is due to variation in each IV; (3) the Type I error; and (4) the power and Type II errors.
The Alpha Level or Type I Error Rate
The Type I error rate is the probability of falsely rejecting the null hypothesis, that is, the chance of concluding that a systematic relationship exists in the population when in fact it does not. This possibility tends to dominate the consciousness of investigators, so many post-hoc techniques (e.g., the Bonferoni inequality, the Newman-Keuls test) have been developed to control it. By convention, the level of alpha is usually set at 0.05, but this figure is arbitrary.

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The Power and Type II Error Rate (Beta)
Power refers to the probability that a relationship in the population will be detected when one in fact exists. Power and its related Type II error rate (failure to reject a false null hypothesis) are probably the most neglected aspects of a statistical test. Power might reflect what Fisher (1966) called the “sensitivity” of an experiment. Importantly, the power of an obtained statistical test reflects the probability that such a result can be replicated (Goodman, 1992). The effects of low statistical power on the reproducibility of research findings have been well documented (Abelson, 1997; Goodman, 1992; Harris, 1997; Hunter, 1997; Scarr, 1997; Shrout, 1997). The Type II error occurs when one fails to reject a false null hypothesis. This error is inversely related to the power of a test:
Power=1−beta
One factor that leads to low power or inflated Type II error risk is an inadequate sample size.
As a convention, Type I error rates of 0.05 and implicit Type II error rates of 0.20 (power of 0.80) are adopted. However, in practice in many areas of investigation, one rarely has adequate power (that is, power≥0.80), and therefore the Type II error rate is much higher (Cohen, 1992).
The following equation reveals the relationship between the statistical test value on the one hand, and the effect size and size of the study on the other:
Statistical (i.e., significance) test=effect size×size of the study
or more concretely for a two-group test:
F=mean square error of interest÷mean square error of noninterest ×dfdenominator
with the appropriate F distribution based on the numerator and denominator dfs and the mean squares representing the variability per df. Thus the numerator is an estimate of the variability of interest and the denominator is an estimate of the variability of noninterest (Rosenthal and Rosnow, 1984).
What is clear from the equation of the experiment is that statistical significance is a function not only of the magnitude of the relationship (the effect size), but also of the size of the study. Thus one way to achieve a statistically significant result is to increase the size of the study. A consequence of this fact is that any nonzero association between IVs and DVs can be statistically significant if one runs enough subjects (Meehl, 1978). In fact, the probability that the so-called “null” hypothesis, if taken literally, is truly false is essentially zero. Perhaps the best information derived from a significant statistical test result is that a lot of subjects were run, which one knows without having do to any mathematical calculations.

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Moreover, all other things being equal, the probability of a Type I error is inversely related to the probability of a Type II error. Thus as the risk of a Type I error is decreased, for example by decreasing the alpha level considered acceptable, the risk of a Type II error increases. The appropriate balancing of Type I and Type II errors is very much content-area specific (Rosenthal and Rosnow, 1984). However, using the conventional values for Type I and Type II errors (0.05 and 0.20, respectively), a Type I error is deemed to be four times more egregious than a Type II error. In areas such as those involving monitoring metabolic status of combat service members, where the cost per datum tends to be relatively high, this level of balance in which we are more apt to accept a Type II error and thus conclude that no relationship exists when in fact one does, may not be cost effective.
Though an extended discussion of the relative merits of statistical hypothesis testing is beyond the scope of this chapter (for a recent debate, see Ableson, 1997; Harris, 1997; Hunter, 1997; Scarr, 1997; Shrout, 1997), knowledge of the nature of these tests is crucial for the design of the experiment. At the very least, this awareness can help to determine the number of subjects necessary to have a good chance of detecting an effect of a certain size while balancing the risk of Type I and Type II errors. Moreover, reasoned consideration of the effect size can greatly enhance the ability to determine the practical significance—and not just the statistical significance—of the results of an experiment.
Choosing What to Measure
On the IV side, Cattell (1988) presented a system of relationships based on three dimensions (persons, occasions, and variables [or tests]), termed the data box. Common to both data theory and the data box is the notion that the researcher, explicitly or more often, implicitly, selects from a broad range of possible dimensions or modes of interest. This critical decision involves selection from a universe of possible scores those that will be the subject of investigation. That this choice often occurs without full knowledge of the various selection effects threatens not only the validity of the inferences drawn from such experiments, but also ultimately the quality of research that serves as the collective database of the field.
Nesselroade and Jones (1991) have provided a cogent exposition on the nature of these selection effects. They noted that a single datum can be characterized as a “…‘draw’ of one piece of information from a universe of information” (P. 21). Minimally, this hypothesized universe represents the scores for every conceivable person and variable on all possible measurement occasions. Thus the three dimensions of persons, variables, and occasions represent a minimum universe from which data are selected. Since each possible score is not likely to be available due to constraints such as time, money, and population base rates, most of the data will remain unrealized. Therefore, in attempting to make gener-

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alizations from the results, the necessity of selecting a representative subset of scores to comprise the data cannot be overestimated.
A thornier situation exists in biobehavioral research, in which there are a myriad of possible dimensions to select from. Cattell (1988) mentioned ten such dimensions, and innumerable others are possible. Thus this decision is a complex, multimodal selection operation (Nesselroade and Jones, 1991). For example, if an investigator attends exclusively to the persons mode, which is often the case, even appropriate sampling methods do not protect against selection effects on the variables or occasions modes.
Known Systematic Sources of Variability
The three sources of variance (persons, occasions, and variables) are present in nearly all experimental designs. Their relationship with a set of scores should be explicitly investigated and the systematic variance associated with each accounted for before valid inferences can be drawn (Cattell, 1988). The most familiar source is that of persons; the effects of inadequate selection on this dimension are widely known. However, the exclusive emphasis on this mode has tended to distract investigators from selection effects on the variables and occasions dimensions, inadvertently providing a false sense of security to experimenters who have accounted for bias on person selection while neglecting these other equally important dimensions.
Multivariate techniques are required to assess multiple sources of variance. Yet there has generally been a paucity of multivariate studies in experimental psychology and in experimental research in general (Harris, 1992). In addition, the occasions dimension holds particular significance for biobehavioral research since most studies involve repeated measurements to some degree (Vasey and Thayer, 1987).
The dynamics of a system cannot be investigated unless the organism is observed repeatedly over time. Organismic theory views the human being as a unified entity whose component parts function according to laws that direct the whole organism (Goldstein, 1939). These principles guide which aspects of the environment the organism attends and reacts to. Goldstein asserted that in-depth investigations of single individuals, over a wide range of observation conditions, are necessary to comprehend the operation of these superordinate functions in naturalistic environments.
Indeed, a full description of human responses requires an observation on some measure in a certain individual at a particular time and place (occasion) (Nesselroade and Ford, 1987). Thus three known sources of variability must be taken into account in the design and analysis of studies involving combat service members. First, experiments should be designed to highlight the particular variability of interest. For example, if one is interested in individual differences, persons should be observed over many different occasions to estimate the variance in scores that is relatively unchanging. Moreover, one may want to use “raw” rather than “change” scores, since partial ipsatization (from subtraction of

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base values; see Cattell, 1988) tends to minimize the variance due to persons. Second, the focus should be on indices of the magnitude of the association; less reliance should be placed on tests of statistical significance. Third, a program of research studies should be examined in aggregate, that is, the results of several studies should be combined to produce estimates of the magnitude of associations. Meta-analytical procedures for this purpose can produce more stable estimates of the importance of various factors and can aid in the accumulation of knowledge that lies at the heart of any scientific enterprise (Guzzo et al., 1987). However, for meta-analysis to be meaningful, scientific and explicit protocols that ensure comparability of randomized, controlled clinical trials should be followed. Furthermore, a significant p value found in any one study yields essentially no useful information regarding the probability of replicating that finding (Goodman, 1992; Guttman, 1985).
Inter- Versus Intraindividual Variability
An important and often overlooked distinction that has led to confusion in the literature is the difference between inter- and intraindividual variability. Relationships that exist among individuals may not be the same as those relationships that exist within individuals. From a research design perspective, it is important to be clear which of these associations is being investigated. A common mistake is to formulate a hypothesis concerning an intraindividual association, say, on the effects of different treatments on an individual’s blood pressure, but to then conduct an experiment in which each person receives a different treatment or manipulation.
Another relevant example is that few studies have truly tested the James (1884) model of emotion, which suggests that the physiological responses and the subjective experience of a given emotion are highly related (an intraindividual hypothesis). Instead, most studies have involved an emotional response elicited from a group of individuals exposed to several manipulations, such as viewing pictures of facial expressions (for a review, see Ellsworth, 1994). Subjects may have various physiological measures taken, such as the facial electromyogram (EMG) from the brow and the cheek, and then are asked to rate their subjective emotional state after viewing each picture. The data are then analyzed by correlating physiological and self-reported responses aggregated across all individuals. In this case, inter- and intraindividual differences are confounded. A more appropriate test of the Jamesian hypothesis (James, 1884) would be to correlate the physiological and subjective responses within individuals and then combine the results of these within-person correlations. Using this within-person approach with a multivariate measure of association (redundancy analysis; Lambert et al., 1988), responses aggregated across subjects revealed little relationship (shared variance on the order of magnitude of 10 percent) between EMG and subjective responses (Uijtdehaage and Thayer, 1988). When the same

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data were analyzed using within-subject measures of association, the shared variance increased to approximately 80 percent.
Clearly, different data aggregation procedures lead to vastly different inferences about the Jamesian hypothesis (James, 1884). In a related study, it was reported that the physiological measures that best discriminated the group emotion profiles were not those that best discriminated among any individual’s emotion profiles (Thayer and Faith, 1994). These findings suggest that the effects of confounding inter- and intraindividual variability can have enormous consequences for the generalizations and conclusions reached in any particular study.
Multivariate, Replicated, Repeated-Measures, Single-Subject Designs
In any one study, it is generally not feasible to represent all possible modes of data classification in a completely satisfactory manner. Therefore, it behooves investigators to make informed choices on these dimensions rather than let chance and expediency dictate research design. Preparation for conducting large group studies may involve prior intensive study of individuals with multiple measures on numerous occasions in order to discern information on sampling of variables and occasions (Nesselroade and Jones, 1991). Indeed, the history of biobehavioral research is replete with prominent examples in which principles of broad applicability emerged from the intensive study of individuals (for a review, see Barlow and Hersen, 1984). Importantly, it is only through intensive studies of individuals that behavior patterns can be examined as they unfold over time, a critical feature in the study of nonlinear dynamics. Finally, the individual has long been recognized as the ultimate entity in biobehavioral research, for it is there that processes occur and applications are made (Rosenzweig, 1958). This point is especially salient to research on combat service members.
In summary, multivariate, replicated, repeated-measures, single-subject designs are highly compatible with the aims of research on combat service members. Central to these aims is the desire to develop applications that are relevant to specific individuals as they carry out complex, multivariate behaviors that evolve over time. Repeated-measures designs and the collection of multiple interrelated measures are common in biobehavioral research, and so the considered application of this research paradigm can enhance the quality of research that is already being conducted. Thus no radical change in experimental procedures is required; only a more reasoned data extraction from the rich corpus of already available information is necessary.
Furthermore, recent statistical advances have expanded the repertoire of tools with which to analyze data from these designs. For example, hierarchical linear models (Schwartz et al., 1994), random regression models (Jacob et al., 1999), and pooled cross-sectional time series (Dielman, 1983) allow for the partitioning of inter- and intraindividual variability from a number of different sources. Complemented by set analytical techniques that allow for the examina-

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tion of multiple DVs (Cohen, 1982), these methods offer many data analytical strategies for multivariate, replicated, repeated-measures, single-subject designs.
An Example Using Multilevel Models
Recent advances in statistical software have brought the use of hierarchical linear models and stochastic regression models into easy reach. PROC MIXED in the SAS software package (SAS Institute Inc.) and BMDP 5V in the Biomedical software package (SPSS Inc.) can be used to estimate these types of models. There are numerous advantages to these approaches compared with previous methods. First, inter- and intraindividual variability can be simultaneously estimated. Second, the use of random coefficients allows for the generalizability of these estimates beyond the particular data sample. Third, differing numbers of observations per participant can be accommodated. Finally, missing data can be easily handled in these models.
Ambulatory monitoring of physiological responses has the potential to greatly impact research on combat service members. Researchers are no longer confined to the laboratory; subjects can now be monitored during actual work situations. Several versions of these multilevel models have been applied to study the effects of various factors, such as mood, location, and postural effects on ambulatory heart rate and blood pressure (Jacob et al., 1999; Schwartz et al., 1994). Schwartz and colleagues (1994) present a simple illustration of the model; for a single, within-person factor, such as location (work versus home), the model is:
Yij(k)=(μ+αi)+(βk+δik)+εij(k)
where Yij(k) is the jth blood pressure reading for person i, taken in the kth location; μ is the weighted grand mean of an individual’s average awake blood pressures, weighted by the number of readings per person; αi is the deviation of person i’s average awake blood pressure (from the grand mean μ); βk is the average intraindividual (main) effect of being in location k (the weighted average of the βs equals zero); δik is the deviation of the effect for person i of being in location k from βk, the person by location interaction effect (the weighted average of the δs equals zero for each person); εij(k) is the deviation of person i’s jth observation from its predicted value, based upon the preceding parameters (the mean of these deviations for all observations of person i taken in the kth location equals zero); the first term on the right side of the equation (μ+αi) is the interindividual variance; and the second term on the right side (βk+δik) is the intraindividual variance. (Full details for estimation of the model are given in Schwartz et al., 1994.)
Application of this model to multiple-parameter estimation is illustrated by Schwartz and colleagues (1994); a similar model and estimation procedure has been applied to longitudinal regression (Jacob et al., 1999). These models allow

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for the estimation of multiple influences on a DV in a nonarbitrary metric. For example, Schwartz and colleagues (1994) found that the average intraindividual effect of being at work versus at home on systolic blood pressure was 2 to 4 mm Hg. Thus the implications of this result are easy to comprehend, whereas traditional ANOVA-type models may state results in standard deviation units or other derived indices, the practical significance of which is often difficult to gauge.
SYSTEMS THEORY AND THE STUDY OF INDIVIDUALS
Systems theory seeks principles that are widely applicable across diverse complex systems (Miller, 1978; Schwartz, 1982). The ideal venue for modeling such organismic systems may be the single-subject paradigm (Denenberg, 1982; Goldstein, 1939; Nesselroade and Ford, 1987). A basic advantage of such designs is their sensitivity to temporal patterns in biobehavioral processes. Multivariate, multioccasion, single-subject paradigms have the resolving power necessary to portray patterns of stability and change that characterize organism-environment interactions (Nesselroade, 1991). The replication of these patterns across individuals in turn can bridge specific and general applicability. This spiraling process is therefore congruent with the quest for principles that are relevant at multiple levels of analysis.
It is fundamental to systems theory that basic processes operating at the level of the individual will also be manifested at both lower and higher levels of analysis (Schwartz, 1982). In nonlinear dynamics terminology, these similarities are referred to as fractals and occur frequently in nature (Barton, 1994; Bassingthwaighte, 1988; Goldberger, 1992; Nonnenmacher et al, 1994; West, 1990). In general, systems approaches have revealed the utility of seeking correspondences across multiple layers of biobehavioral inquiry (Friedman and Thayer, 1998a, 1998b; Kandel, 1983; Mandell et al., 1981). For example, perception of the relationship between individual and population disease-prevention strategies has been underscored in epidemiological research (Rose, 1992). Clearly, studies of individuals are integral components in the scientific quest for general laws of behavior; they are complementary parts of a whole (Rosenzweig, 1958).
Another aspect of this area that is of great concern to research on combat service members is the study of individual differences. Biological organisms display wide-ranging individual differences in physiology (Fahrenberg, 1986; Sargent and Weinman, 1966; Woodhead et al., 1985). The importance of individual differences for research on combat service members can be illustrated by the effects of differences in visual acuity on cardiovascular responses to a computer display (Tyrrell et al., 2000).
A thorough exploration of biobehavioral responding requires the extensive study of individuals over time, a highly problematic enterprise in large N designs. Beyond pragmatic concerns, these designs constrain individual response patterns into group molds. To take advantage of the emerging field of dynamic systems, experiments must be designed in such a way as to mine the rich inter-

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and intraindividual variability inherent in living systems. In this context, time-series analysis is a useful adjunct to traditional data analysis strategies. Time-series analysis has been used extensively in many fields, from econometrics to physiology, and it allows for the examination of the temporal structure of a set of sequentially collected data points. Time series from individual subjects can be examined and parameters extracted that can be used in data aggregation procedures. For example, the time series of heart periods (the time between successive heart beats) has been used to extract indices of autonomic nervous system control that can be used to characterize the physiological, emotional, and cognitive state of an individual (Friedman et al., 1996; Thayer and Lane, 2000).
Moreover, the parameters extracted from time-series analyses can be combined and the pattern of these parameters examined using pattern classification and neural network techniques. These techniques allow for the investigation of nonlinear patterns in data that might usefully distinguish subjects or conditions into meaningful classes or categories at the level of the individual (see Tyrrell et al., 1995).
SUMMARY
In this chapter we have attempted to expose assumptions that are often deceptively implicit in the design and analysis of experiments. Research on combat service members, with its focus on person-environment interactions, has a pressing need to elucidate those factors that contribute to interindividual differences and distinguish them from sources of intraindividual variability. The search for associations among IVs and DVs can be expressed as the partitioning of system variability into factors that contribute to this observed variation. Furthermore, although the assumption of linearity has been useful in promoting well-controlled studies of biobehavioral variables, it also represents a limiting influence on the burgeoning study of complexity and dynamic systems. However, designs that can be used to partition data into linear estimates of variance can also be used to investigate the dynamics of person-environment transactions. It is hoped that researchers will not only take advantage of contemporary analytical techniques for the study of dynamic systems, but also pursue research that will aid in the understanding and appropriate use of extant data analytical tools.
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