Complex analyses of variance: General problems

Problems in applying the analysis of variance are discussed. Emphasis is placed on using the technique to understand the data. The scale of the dependent variable is important for the analysis. Crossed and nested categories must be recognized. The error terms in the analysis depend on whether the classes of each independent variable are (1) all out of a few or (2) a few out of many. To simplify the analysis, mean squares should be aggregated with their error term when they are less than twice its size. An illustrative example is discussed in detail.Prepared in connection with research sponsored in part by the Office of Naval Research, in part by the Educational Testing Service, and in part by Lincoln Laboratory, a center for research operated by Massachusetts Institute of Technology with the joint support of the U. S. Army, Navy, and Air Force.     

The relation between information and variance analyses

Analysis of variance and uncertainty analysis are analogous techniques for partitioning variability. In both analyses negative interaction terms due to negative covariance terms that appear when non-orthogonal predictor variables are allowed may occur. Uncertainties can be estimated directly from variances if the form of distribution is assumed. The decision as to which of the techniques to use depends partly on the properties of the criterion variable. Only uncertainty analysis may be used with a non-metric criterion. Since uncertainties are dimensionless (using no metric), however, uncertainty analysis has a generality which may make it useful even when variances can be computed.The work of the senior author was supported by Contract N5ori-166, Task Order 1, between the U.S. Office of Naval Research and The Johns Hopkins University. This is Report No. 166-I-192, Project Designation No. NR 145-089, under that contract.     

Robust principal components: A generalized variance perspective

This article compares several methods for performing robust principal component analysis, two of which have not been considered in previous articles. The criterion here, unlike that of extant articles aimed at comparing methods, is how well a method maximizes a robust version of the generalized variance of the projected data. This is in contrast to maximizing some measure of scatter associated with the marginal distributions of the projected scores, which does not take into account the overall structure of the projected data. Included are comparisons in which distributions are not elliptically symmetric. One of the new methods simply removes outliers using a projection-type multivariate outlier detection method that has been found to perform well relative to other outlier detection methods that have been proposed. The other new method belongs to the class of projection pursuit techniques and differs from other projection pursuit methods in terms of the function it tries to maximize. The comparisons include the method derived by Maronna (2005), the spherical method derived by Locantore et al. (1999), as well as a method proposed by Hubert, Rousseeuw, and Vanden Branden (2005). From the perspective used, the method by Hubert et al. (2005), the spherical method, and one of the new methods dominate the method derived by Maronna.     

Exploring attributions in natural settings: Gender and self-esteem effects

Two studies investigated the attributions of undergraduates for the outcomes of satisfying and dissatisfying achievement events that occurred naturally over the course of a 3-week period. In both studies, women with low performance self-esteem gave less ego-enhancing attributions than high self-esteem women, high self-esteem men, or low self-esteem men. Also, in Study 2 high self-esteem subjects attributed greater stability to causes of satisfying events than to causes of dissatisfying events, whereas low self-esteem subjects gave both types of events equivalent stability ratings. Both studies provide evidence of consistent individual differences in attributional style across occasions and situations. The gender differences were interpreted in the context of sex-role socialization factors and Anderson and Slusher's (1986) two-stage model of the attribution process.     

Assessing coping flexibility in real-life and laboratory settings: a multimethod approach

This research sought to formulate a theoretically based conceptualization of coping flexibility and to adopt a multimethod approach in assessing this construct. A self-report daily measure and an experiment were designed geared to theoretical and empirical grounds. The new daily measure was used in Study 1 to examine coping flexibility in a life transition. Findings showed individual differences in patterns of coping flexibility across different real-life stressful events. In Study 2, coping flexibility was examined in both real-life and laboratory settings. Results replicated those of Study 1 and further revealed consistency between the self-report and the experiment data. Study 3 extended previous studies by adopting a longitudinal design over a 3-month time span. Participants' flexibility in coping with laboratory tasks was found to predict how flexible they would be in handling real-life stressful events.     

Verbal contingent stimulation of stuttering in laboratory and home settings

The effect of verbal contingent stimulation for stuttering behaviors was examined during changes of stimulus delivery mode and experimental setting. In Experiment I, contingent stimuli were delivered in the laboratory setting with the experimenter and subject in a face-to-face arrangement versus presentations by the experimenter from a control room via a headset arrangement. In Experiment II, contingent stimulation of stuttering was examined in the laboratory and home setting. Findings revealed that stuttering frequency was reduced in all conditions of both experiments. However, the only significant reductions occurred under the headset delivery conditions in the laboratory setting.     

A microcomputer-based laboratory for psychopathology research in rural settings

An Apple-based computer system for research use in rural mental health settings is described. Hardware and software modifications are detailed. Techniques to aid in the acceptance of psychopathology research programs in these rural settings are discussed.     

Distance perception in photographic displays of natural settings

Distance perception of depicted objects was examined as a function of photographic perspective. 24 subjects viewed slides of outdoor scenes and directly estimated the distances to specified objects. Perspective was manipulated by photographing each scene with lenses of four different focal lengths: 48 mm, 28 mm, 24 mm, and 17 mm. Distance perception along the pictorial depth plane (z-axis) was systematically transformed by changing the photographic perspective: the shorter the focal length of the camera lens, the greater the perceived distance. Perceived distance between objects along the lateral plane (x-axis) was unaffected by changes in lens focal length.     

Parental assessment and treatment of food selectivity in natural settings

This study evaluated the effects of a parent-conducted functional analysis and treatment consisting of differential reinforcement of an alternative behavior, escape extinction, and demand fading on food selectivity in a young child with autism. Increases in food acceptance at home and in a restaurant were obtained.     

Exploratory second-order analyses for components and factors

Abstract: Exploratory methods using second‐order components and second‐order common factors were proposed. The second‐order components were obtained from the resolution of the correlation matrix of obliquely rotated first‐order principal components. The standard errors of the estimates of the second‐order component loadings were derived from an augmented information matrix with restrictions for the loadings and associated parameters. The second‐order factor analysis proposed was similar to the classical method in that the factor correlations among the first‐order factors were further resolved by the exploratory method of factor analysis. However, in this paper the second‐order factor loadings were estimated by the generalized least squares using the asymptotic variance‐covariance matrix for the first‐order factor correlations. The asymptotic standard errors for the estimates of the second‐order factor loadings were also derived. A numerical example was presented with simulated results.     

Trait aggression is primarily a facet of antagonism: Evidence from dominance,latent correlational,and item-level analyses

Trait aggression has been studied for decades and yet remains adrift from broader frameworks of personality such as the Five Factor Model. Across two datasets from undergraduate participants (Study 1: N = 359; Study 2; N = 620), we observed strong manifest and latent correlations between trait aggression and lower agreeableness (i.e., greater antagonism). Trait aggression was also linked to greater neuroticism and lower conscientiousness, but their effect sizes fell beneath our preregistered threshold. Subsequent item-level analyses were unable to articulate trait aggression and agreeableness items into separate factors using the IPIP-NEO, but not the Big Five Inventory. Our findings suggest that trait aggression is accurately characterized as primarily a facet of antagonism, while also reflecting other personality dimensions.     

Personality research: components of variance attributable to the person and the situation.

Studies involving personality and situational variables were surveyed. Studies permitting determination of main effects and interactions involving these variables have increased since 1950. In one comparison, situational main effects were significant in 65.5% of the cases, whereas the figure was 31% for individual difference variables and 59.9% for interactions. In another comparison, 35% of situational main effects accounted for more than 10% of the variance, compared with 29% for personality indexes; 19% of the situational variable effects accounted for more than 20% of the variance, compared with 14% of the personality main effects. Low percentages of variance were accounted for by all variables investigated: situational, personality, demographic, and interactions among these variables.     

Mothers' speech to their 1-year-old infants in home and laboratory settings

The speech of mothers and their 1-year-old infants was compared in the home and in the laboratory playroom. The home and laboratory settings were similar for measuring the number of actual words that infants spoke and were similar for measuring the complexity of the mother's speech, including the number of different words, the type-token ratio, and the length of the utterances. Infants vocalized at similar rates in the two settings, but mothers spoke at a faster rate in the laboratory playroom. The usefulness of a preliminary warm-up period was supported by the finding that for the second half of the sessions, mothers slowed their rate of speech and increased the complexity of their speech.     

A technique for controlling behavior in natural life settings

A behavior control technique is presented, consisting primarily of having a patient give up some portion of his reinforcers (usually money) with the understanding that he must behave in therapeutically prescribed ways in his natural environment to re-earn the reinforcers. The critical features and requirements of the technique are discussed, various applications are suggested, and implications for research are drawn.