Clinical Psychology Quantitative sophistication is increasingly central to research in clinical psychology. Both our theories and the statistical techniques available to test our hypotheses have grown in complexity over the last few decades, such that the novice clinical researcher now faces a bewildering array of analytic options. The purpose of this article is to provide a conceptual overview of the use of statistics in clinical science. The first portion of this article describes five major research questions that clinical psychology researchers commonly address and provides a brief overview of the statistical methods that frequently are employed to address each class of questions. These questions are neither exhaustive nor mutually exclusive, but rather are intended to serve as a heuristic for organizing and thinking about classes of research questions in clinical psychology and the techniques most closely associated with them. The second portion of the article articulates guiding principles that underlie the responsible use of statistics in clinical psychology. Five Classes of Research Questions in Clinical Psychology Defining and Measuring Constructs Careful attention to the definition and measurement of constructs is the bread and butter of clinical research. Constructs refer to abstract psychological entities and phenomena such as depression, marital violence, genetic influences, attention to negative information, acculturation, and cognitive-behavioral therapy (CBT). We specify these unobserved variables (see Latent Variable), as well as their interrelationships, in a theoretical model (e.g., CBT might be assumed to decrease depression in one’s partner, which then decreases the likelihood of marital violence in the relationship). Our measurement model (see Measurement: Overview) specifies the way in which we operationally define the constructs of interest (e.g., our ‘measurement variable’, or ‘indicator variable’, for the construct of depression might Reproduced from the Encyclopedia of Statistics in Behavioral Science.  John Wiley & Sons, Ltd. ISBN: 0-470-86080-4. be patient scores on the Beck Depression Inventory (BDI) [4]). Finally, our analytical model refers to the way in which we statistically evaluate the hypothesized relationships between our measured variables (e.g., we might use structural-equation modeling (SEM), analysis of variance (ANOVA), or logistic regression). Later in this article, we discuss the importance of the consistency between these three models for making valid inferences about a theoretical model, as well as the importance of ‘starting at the top’ (i.e., the importance of theory for the rapid advancement of clinical research). Readers are urged to consult McFall and Townsend [36] for a more comprehensive overview of the specification and evaluation of the multiple _layer_s of scientific models in clinical research. Deciding how best to measure our constructs – that is, specifying the measurement model for the theoretical model of interest – is a critical first step in every clinical research project. Sometimes this step entails a challenging process of thinking logically and theoretically about how best to assess a particular construct. Consider, for example, the difficulty in defining what ‘counts’ as a suicide attempt. Is any dangerous personal action ‘suicidal’ (e.g., driving recklessly, jumping from high places, mixing barbiturates and alcohol)? Does the person have to report intending to kill herself, or are others’ perceptions of her intention enough? How should intention be assessed in the very young or the developmentally delayed? Does the exhibited behavior have to be immediately life-threatening? What about lifethreatening parasuicidal behaviors? Similar difficulties arise in attempting to decide how to assess physical child abuse, cognitive therapy, or an episode of overeating. These examples are intended to highlight the importance of recognizing that all phenomena of interest to clinical researchers are constructs. As a result, theoretical models of a construct and the chosen measurement models always should be distinguished – not collapsed and treated as one and the same thing – and the fit between theoretical and measurement models should be maximized. More commonly, defining and measuring constructs entails scale development, in which researchers (a) create a set of items that are believed to assess the phenomenon or construct; (b) obtain many participants’ responses to these items; and (c) use factor-analytic techniques (see History of Factor Analysis: Statistical Perspective) to reduce the 2 Clinical Psychology complexity of the numerous items to a much smaller subset of theoretically interpretable constructs, which commonly are referred to as ‘factors’ or ‘latent variables’. For example, Walden, Harris, and Catron [53] used factor analysis when developing ‘How I Feel’, a measure on which children report the frequency and intensity of five emotions (happy, sad, mad, excited, and scared), as well as how well they can control these emotions. The authors generated 30 relevant items (e.g., the extent to which children were ‘scared almost all the time’ during the past three months) and then asked a large number of children to respond to them. Exploratory factor analyses of the data indicated that three underlying factors, or constructs, accounted for much of the variability in children’s responses: Positive Emotion, Negative Emotion, and Control. For example, the unobserved Negative Emotion factor accounted particularly well for variability in children’s responses to the sample item above (i.e., this item showed a large factor loading on the Negative Emotion factor, and small factor loadings on the remaining two factors). One particularly useful upshot of conducting a factor analysis is that it produces factor scores, which index a participant’s score on each of the underlying latent variables (e.g., a child who experiences chronic sadness over which she feels little control presumably would obtain a high score on the Negative Emotion factor and a lot score on the Control factor). Quantifying factor scores remains a controversial enterprise, however, and researchers who use this technique should understand the relevant issues [20]. Both Reise,Waller, and Comrey [44] and Fabrigar, Wegener, MacCallum, and Strahan [19] provide excellent overviews of the major decisions that clinical researchers must make when using exploratory factor-analytic techniques. Increasingly, clinical researchers are making use of confirmatory factor-analytic techniques when defining and measuring constructs. Confirmatory approaches require researchers to specify both the number of factors and which items load on which factors prior to inspection and analysis of the data. Exploratory factor-analytic techniques, on the other hand, allow researchers to _base_ these decisions in large part on what the data indicate are the best answers. Although it may seem preferable to let the data speak for themselves, the exploratory approach capitalizes on sampling variability in the data, and the resulting factor structures may be less likely to cross-validate (i.e., to hold up well in new samples of data). Thus, when your theoretical expectations are sufficiently strong to place a priori constraints on the analysis, it typically is preferable to use the confirmatory approach to evaluate the fit of your theoretical model to the data. Walden et al. [53] followed up the exploratory factor analysis described above by using confirmatory factor analysis to demonstrate the validity and temporal stability of the factor structure for ‘How I Feel’. Clinical researchers also use item response theory, often in conjunction with factor-analytic approaches, to assist in the definition and measurement of constructs [17]. A detailed de_script_ion of this approach is beyond the scope of this article, but it is helpful to note that this technique highlights the importance of inspecting item-specific measurement properties, such as their difficulty level and their differential functioning as indicators of the construct of interest. For clinical examples of the application of this technique, see [27] and [30]. Cluster analysis is an approach to construct definition and measurement that is closely allied to factor analysis but exhibits one key difference. Whereas factor analysis uncovers unobserved ‘factors’ on the basis of the similarity of variables, cluster analysis uncovers unobserved ‘typologies’ on the basis of the similarity of people. Cluster analysis entails (a) selecting a set of variables that are assumed to be relevant for distinguishing members of the different typologies; (b) obtaining many participants’ responses to these variables; and (c) using clusteranalytic techniques to reduce the complexity among the numerous participants to a much smaller subset of theoretically interpretable typologies, which commonly are referred to as ‘clusters’. Representative recent examples of the use of this technique can be found in [21] and [24]. Increasingly, clinical researchers also are using latent class analysis and taxometric approaches to define typologies of clinical interest, because these methods are less de_script_ive and more model-_base_d than most cluster-analytic techniques. See [40] and [6], respectively, for application of these techniques to defining and measuring clinical typologies. Evaluating Differences between Either Experimentally Created or Naturally Occurring Groups After establishing a valid measurement model for the particular theoretical constructs of interest, clinical Clinical Psychology 3 researchers frequently evaluate
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