Properties of hypothesis testing techniques and (Bayesian) model selection for exploration‐based and theory‐based (order‐restricted) hypotheses

In this paper, the performance of six types of techniques for comparisons of means is examined. These six emerge from the distinction between the method employed (hypothesis testing, model selection using information criteria, or Bayesian model selection) and the set of hypotheses that is investigated (a classical, exploration‐based set of hypotheses containing equality constraints on the means, or a theory‐based limited set of hypotheses with equality and/or order restrictions). A simulation study is conducted to examine the performance of these techniques. We demonstrate that, if one has specific, a priori specified hypotheses, confirmation (i.e., investigating theory‐based hypotheses) has advantages over exploration (i.e., examining all possible equality‐constrained hypotheses). Furthermore, examining reasonable order‐restricted hypotheses has more power to detect the true effect/non‐null hypothesis than evaluating only equality restrictions. Additionally, when investigating more than one theory‐based hypothesis, model selection is preferred over hypothesis testing. Because of the first two results, we further examine the techniques that are able to evaluate order restrictions in a confirmatory fashion by examining their performance when the homogeneity of variance assumption is violated. Results show that the techniques are robust to heterogeneity when the sample sizes are equal. When the sample sizes are unequal, the performance is affected by heterogeneity. The size and direction of the deviations from the baseline, where there is no heterogeneity, depend on the effect size (of the means) and on the trend in the group variances with respect to the ordering of the group sizes. Importantly, the deviations are less pronounced when the group variances and sizes exhibit the same trend (e.g., are both increasing with group number).     

A Test of Order-Constrained Hypotheses for Circular Data With Applications to Human Movement Science

Researchers studying the movements of the human body often encounter data measured in angles (e.g., angular displacements of joints). The evaluation of these circular data requires special statistical methods. The authors introduce a new test for the analysis of order-constrained hypotheses for circular data. Through this test, researchers can evaluate their expectations regarding the outcome of an experiment directly by representing their ideas in the form of a hypothesis containing inequality constraints. The resulting data analysis is generally more powerful than one using standard null hypothesis testing. Two examples of circular data from human movement science are presented to illustrate the use of the test. Results from a simulation study show that the test performs well.     

Bayes factor approaches for testing interval null hypotheses

Psychological theories are statements of constraint. The role of hypothesis testing in psychology is to test whether specific theoretical constraints hold in data. Bayesian statistics is well suited to the task of finding supporting evidence for constraint, because it allows for comparing evidence for 2 hypotheses against each another. One issue in hypothesis testing is that constraints may hold only approximately rather than exactly, and the reason for small deviations may be trivial or uninteresting. In the large-sample limit, these uninteresting, small deviations lead to the rejection of a useful constraint. In this article, we develop several Bayes factor 1-sample tests for the assessment of approximate equality and ordinal constraints. In these tests, the null hypothesis covers a small interval of non-0 but negligible effect sizes around 0. These Bayes factors are alternatives to previously developed Bayes factors, which do not allow for interval null hypotheses, and may especially prove useful to researchers who use statistical equivalence testing. To facilitate adoption of these Bayes factor tests, we provide easy-to-use software.     

Bayesian model selection of informative hypotheses for repeated measurements

When analyzing repeated measurements data, researchers often have expectations about the relations between the measurement means. The expectations can often be formalized using equality and inequality constraints between (i) the measurement means over time, (ii) the measurement means between groups, (iii) the means adjusted for time-invariant covariates, and (iv) the means adjusted for time-varying covariates. The result is a set of informative hypotheses. In this paper, the Bayes factor is used to determine which hypothesis receives most support from the data. A pivotal element in the Bayesian framework is the specification of the prior. To avoid subjective prior specification, training data in combination with restrictions on the measurement means are used to obtain so-called constrained posterior priors. A simulation study and an empirical example from developmental psychology show that this prior results in Bayes factors with desirable properties.     

Gender differences in depression in children as a function of motivational orientation

Based on previous theoretical and empirical analyses, the present study examined two hypotheses. First, we hypothesized that children who have an extrinsic motivational orientation, i.e., children who perform schoolwork for approval or fear of evaluation, would be more depressed than intrinsics, who are generally more interested in learning and exhibit the desire to obtain mastery over challenge. Second, based on data showing that girls are more likely to be extrinsic than boys, we hypothesized that girls would also be more depressed than their male counterparts. The data proved strong support for the hypotheses. In our discussion, we highlight the need for further research to examine the causal relation among motivational orientation, gender, and depression to develop social-developmental theories and clinical interventions for depressed, extrinsic girls and boys.     

Multiplicity,directional (type III) errors,and the null hypothesis

L. V. Jones and J. W. Tukey (2000) pointed out that the usual 2-sided, equal-tails null hypothesis test at level alpha can be reinterpreted as simultaneous tests of 2 directional inequality hypotheses, each at level alpha/2, and that the maximum probability of a Type I error is alpha/2 if the truth of the null hypothesis is considered impossible. This article points out that in multiple testing with familywise error rate controlled at alpha, the directional error rate (assuming all null hypotheses are false) is greater than alpha/2 and can be arbitrarily close to alpha. Single-step, step-down, and step-up procedures are analyzed, and other error rates, including the false discovery rate, are discussed. Implications for confidence interval estimation and hypothesis testing practices are considered.     

A prior predictive loss function for the evaluation of inequality constrained hypotheses

In many types of statistical modeling, inequality constraints are imposed between the parameters of interest. As we will show in this paper, the DIC (i.e., posterior Deviance Information Criterium as proposed as a Bayesian model selection tool by Spiegelhalter, Best, Carlin, & Van Der Linde, 2002) fails when comparing inequality constrained hypotheses. In this paper, we will derive the prior DIC and show that it also fails when comparing inequality constrained hypotheses. However, it will be shown that a modification of the prior predictive loss function that is minimized by the prior DIC renders a criterion that does have the properties needed in order to be able to compare inequality constrained hypotheses. This new criterion will be called the Prior Information Criterion (PIC) and will be illustrated and evaluated using simulated data and examples. The PIC has a close connection with the marginal likelihood in combination with the encompassing prior approach and both methods will be compared. All in all, the main message of the current paper is: (1) do not use the classical DIC when evaluating inequality constrained hypotheses, better use the PIC; and (2) the PIC is considered a proper model selection tool in the context of evaluating inequality constrained hypotheses.     

Self-reported assertiveness in Swedish and Turkish adolescents: a cross-cultural comparison

The present cross-cultural study compared self-reported assertiveness in 652 Swedish and 654 Turkish high school students by using a multi-dimensional measure called the Scale for Interpersonal Behavior (SIB). Four hypotheses were tested in the study. First, the hypothesis that Swedish adolescents would be more assertive than their Turkish counterparts was supported by the data. Second, the expectation that Turkish boys would be more assertive than Turkish girls, while there would be no differences between Swedish girls and boys, was not confirmed. In general, girls were found to be more skilled than boys in expressing and dealing with personal limitations. Third, as expected, more assertive adolescents in both Sweden and Turkey reported having more friends and receiving more social support than their less assertive peers. Finally, the data supported the expectation that older adolescents would be more assertive than younger ones. The results are discussed in terms of cultural and gender differences.     

Bayes factors for testing inequality constrained hypotheses: Issues with prior specification

Several issues are discussed when testing inequality constrained hypotheses using a Bayesian approach. First, the complexity (or size) of the inequality constrained parameter spaces can be ignored. This is the case when using the posterior probability that the inequality constraints of a hypothesis hold, Bayes factors based on non‐informative improper priors, and partial Bayes factors based on posterior priors. Second, the Bayes factor may not be invariant for linear one‐to‐one transformations of the data. This can be observed when using balanced priors which are centred on the boundary of the constrained parameter space with a diagonal covariance structure. Third, the information paradox can be observed. When testing inequality constrained hypotheses, the information paradox occurs when the Bayes factor of an inequality constrained hypothesis against its complement converges to a constant as the evidence for the first hypothesis accumulates while keeping the sample size fixed. This paradox occurs when using Zellner's g prior as a result of too much prior shrinkage. Therefore, two new methods are proposed that avoid these issues. First, partial Bayes factors are proposed based on transformed minimal training samples. These training samples result in posterior priors that are centred on the boundary of the constrained parameter space with the same covariance structure as in the sample. Second, a g prior approach is proposed by letting g go to infinity. This is possible because the Jeffreys–Lindley paradox is not an issue when testing inequality constrained hypotheses. A simulation study indicated that the Bayes factor based on this g prior approach converges fastest to the true inequality constrained hypothesis.     

The electroencephalogram and childhood aggression

Available evidence reveals that, although the incidence of abnormal electroencephalograms (EEGs) varies between 10% and 15% in the general adult population, abnormal EEGs occur in 48–70% of aggressive psychopaths. The fact that the EEGs of aggressive, adult psychopaths show a high degree of similarity to the EEGs of normal young children has suggested that aggression may somehow result from a failure in the normal development of the central nervous system. This “maturational-retardation” hypothesis of aggression was investigated in the present study, the purpose of which was to discover whether behavior-problem children who are severely aggressive have immature EEGs, or EEGs characteristic of chronologically younger children. Six severely aggressive boys, aged 8.7–13.6 years, had their EEGs recorded while performing a simple reaction task. For each subject, an interval histogram consisting of measurements of the duration of 780 half wavelengths in the EEG was generated by the computer using the tracing from the left parietal-occipital (P₃ -0₂ ) derivation. The resulting histograms were subjected to a central moments analysis and age of each subject was estimated from the moments by means of a multiple regression equation. This equation, which relates an individual's age to the 2nd, 3rd, and 4th central moments of his EEG interval histogram, had been derived by Surwillo [1975a] on a group of normal boys. In every case, age predicted from the EEG of a severely aggressive subject was less than the subjecťs actual age. This finding was statistically significant, as the probability of the outcome occurring by chance was only 0.016. The results of the experiment supported the maturational-retardation hypothesis of aggressive behavior.     

Trait emotional intelligence profiles of students from different university faculties

This study investigated the trait emotional intelligence (trait EI or trait emotional self‐efficacy) profiles of 512 students from five university faculties: technical studies, natural sciences, social sciences, arts, and humanities. Using the Trait Emotional Intelligence Questionnaire, it was hypothesised that (a) social sciences would score higher than technical studies in Emotionality, (b) arts would score higher than technical studies in Emotionality, (c) arts would score lower than technical studies in Self‐control, and (d) there would be an interaction between gender and faculty, whereby female students would score higher than male students within the social sciences only. Several other exploratory comparisons were also performed. Results supported hypotheses (a), (b), and (d), but not hypothesis (c), although the differences were in the predicted direction.     

Proactive and reactive aggression among school bullies,victims, and bully‐victims

Bullies, victims, bully‐victims, and control children were identified from a sample of 1062 children (530 girls and 532 boys), aged 10 to 12 years, participating in the study. Their reactive and proactive aggression was measured by means of peer and teacher reports. Peer and teacher reports were more concordant with respect to reactive than proactive aggression. Comparing the children in different bullying roles in terms of their reactive and proactive aggression, bully‐victims were found to be the most aggressive group of all. For this group, it was typical to be highly aggressive both reactively and proactively. Although bullies were significantly less aggressive than bully‐victims, they scored higher than victims and controls on both reactive and proactive aggression. However, observations at the person level, i.e., cross‐tabulational analyses, indicated that bullies were not only overrepresented among children who were both reactively and procatively aggressive but also among the only reactively aggressive as well as the only proactively aggressive groups. Victims scored higher than control children on reactive aggression, but they were not proactively aggressive. Furthermore, even their reactive aggression was at a significantly lower level than that of bullies and bully‐victims. Aggr. Behav. 28:30–44, 2002. © 2002 Wiley‐Liss, Inc.     

A comparison of 8- and 11-year-old girls' and boys' participation in specific types of rough-and-tumble play and aggressive fighting: Implications for functional hypotheses

Study 1 compared the extent to which 8- and 11-year-old girls and boys (N = 86) participated in specific types of rough-and-tumble play. It used an observational methodology. The data were used to test two prominent hypotheses about the evolutionary function of this general category of play behaviour that have been applied to children, especially boys, of this age. One is that rough-and-tumble play provides practice for the development of real fighting skills and the other that it serves as a safe way to establish/display social dominance. Both hypotheses predict that boys will engage in more rough-and-tumble play than girls, especially those types that are used in fighting/dominance contests. Boys were found to engage in significantly more chase initiation activities, more bouts of brief rough-and-tumble play, more bouts of restraining and more bouts of boxing/hitting than girls. These data provide some support for the two hypotheses, although significant sex differences were not found for all types of rough-and-tumble play observed. No significant age differences were obtained, suggesting that the two hypotheses may be applicable throughout the 8- to 11-year-old period and not just at the end of it as previous research had suggested. Study 2 presented observational data concerning the motor patterns used in aggressive fighting. In all but one case, there were no significant differences in the extent to which 8/9- and 10/11-year-old girls and boys employed wrestling, hitting and restraining, supporting the view that the practice fighting hypothesis is relevant throughout the 8-11-year-old period. It was argued that age and sex differences provide a useful means of scrutinising functional hypotheses, and that splitting behavioural categories that contain disparate action patterns facilitates more refined tests of those hypotheses. © 1996 Wiley-Liss, Inc.     

The Development of Aggression in 18 to 48 Month Old Children of Alcoholic Parents

This study examined the development of aggressive and oppositional behavior among alcoholic and nonalcoholic families using latent growth modeling. The sample consisted of 226 families assessed at 18, 24, 36, and 48 months of child age. Results indicated that children in families with nonalcoholic parents had the lowest levels of aggressive behavior at all time points compared to children with one or more alcoholic parents. Children in families with two alcoholic parents did not exhibit normative decreases in aggressive behavior from 3 to 4 years of age compared to nonalcoholic families. However, this association was no longer significant once a cumulative family risk score was added to the model. Children in families with high cumulative risk scores, reflective of high parental depression, antisocial behavior, negative affect during play, difficult child temperament, marital conflict, fathers’ education, and hours spent in child care, had higher levels of aggression at 18 months than children in low risk families. These associations were moderated by child gender. Boys had higher levels of aggressive behavior at all ages than girls, regardless of group status. Cumulative risk was predictive of higher levels of initial aggressive behavior in both girls and boys. However, boys with two alcoholic parents had significantly less of a decline in aggression from 36 to 48 months compared to boys in the nonalcoholic group.     

Parental Influences on the Prevalence and Development of Child Aggressiveness

The development of aggressiveness between 5 and 17 years and some parental influences on this development were analyzed using data from Germany. International studies have shown a “camel humps” curve, i.e., a peak of aggression of children (primarily boys) between 2 and 4 years and a second peak of antisocial or aggressive behavior of boys between 15 and 20 years, but small groups of children and adolescents were persistently aggressive. A representative longitudinal study (2,190 children and their parents) and an additional study (1,372 children and adolescents) were conducted in Germany. The hypotheses of this article are that in the data can be found (a) an U-shaped course of aggressiveness for boys and girls, but on different levels, (b) a minority of persistently aggressive children and youth, (c) influences of parental temperaments, behavioral tendencies, parenting styles and the family status on the children’s aggressiveness. The results replicate roughly the “valley” of the U-shaped course of aggressiveness. Small groups of chronically aggressive children were found as well. Influences of parental temperaments and corresponding behavioral tendencies (internalizing and externalizing behavior), parenting styles (child-centered communication, use of violence) and the social status of the families on child aggressiveness confirmed the hypotheses. These processes were moderated by gender effects between mothers, fathers, daughters, and sons. In regard to the group of persistently aggressive young people prevention of aggression should start early in childhood and over the long term. Parent education should consider more the individual personalities of the parents, not only parenting styles.     

Do They Get What They Want or Are They Stuck With What They Can Get? Testing Homophily Against Default Selection for Friendships of Highly Aggressive Boys. The TRAILS Study

In this study a homophily selection hypothesis was tested against a default selection hypothesis, to answer whether preferred and realized friendships of highly aggressive boys differed. In a large peer-nomination sample, we assessed who highly overt aggressive, low prosocial boys (n = 181) nominated as friends (preferred friendships) and who among the nominated friends reciprocated the friendship (realized friendships). These preferred and realized friendships were compared with those of less aggressive (n = 1,268) and highly aggressive but also prosocial boys (bi-strategics; n = 55). Results showed that less aggressive boys preferred peers low on aggression, whereas highly aggressive and bi-strategic boys preferred peers not particular high or low on aggression. In line with default selection, highly aggressive boys ended up with aggressive peers even though that was not their preference. In general, received support proved an important determinant of highly aggressive, bi-strategic, and less aggressive boys’ preferred and realized friendships. Especially highly aggressive boys preferred emotionally supportive friends, but ended up with the least supportive peers. In sum, for friendships of highly overt aggressive boys, the evidence favors default selection over homophily selection.     

The role of proactive and reactive aggression in the formation and development of boys' friendships

This study tested the hypothesis that friends are more similar in proactive aggression than in reactive aggression. Interpersonal processes that may account for this similarity (i.e., selection and mutual influence) were also examined. In the fall and spring of the school year, the friendships of 185 4th-, 5th-, and 6th-grade boys were identified. Proactive and reactive aggressive behavior were assessed with a teacher-rating instrument for each boy. The results support the general hypothesis and suggest that proactively aggressive boys tend to select proactively aggressive peers as friends; however, mutual influence between stable friends does not appear to account for similarity. These findings are discussed within the framework of G. R. Patterson, J. B. Reid, and T. J. Dishion's (1992) theory of antisocial behavior.     

Social-information-processing factors in reactive and proactive aggression in children's peer groups

We examined social-information-processing mechanisms (e.g., hostile attributional biases and intention-cue detection deficits) in chronic reactive and proactive aggressive behavior in children's peer groups. In Study 1, a teacher-rating instrument was developed to assess these behaviors in elementary school children (N = 259). Reactive and proactive scales were found to be internally consistent, and factor analyses partially supported convergent and discriminant validities. In Study 2, behavioral correlates of these forms of aggression were examined through assessments by peers (N = 339). Both types of aggression related to social rejection, but only proactively aggressive boys were also viewed as leaders and as having a sense of humor. In Study 3, we hypothesized that reactive aggression (but not proactive aggression) would occur as a function of hostile attributional biases and intention-cue detection deficits. Four groups of socially rejected boys (reactive aggressive, proactive aggressive, reactive-proactive aggressive, and nonaggressive) and a group of average boys were presented with a series of hypothetical videorecorded vignettes depicting provocations by peers and were asked to interpret the intentions of the provocateur (N = 117). Only the two reactive-aggressive groups displayed biases and deficits in interpretations. In Study 4, attributional biases and deficits were found to be positively correlated with the rate of reactive aggression (but not proactive aggression) displayed in free play with peers (N = 127). These studies supported the hypothesis that attributional biases and deficits are related to reactive aggression but not to proactive aggression.     

A study of the greater male variability hypothesis in creative thinking in Mainland China: Male superiority exists

This study tested the greater male variability hypothesis in creative thinking with a Chinese student sample in Mainland China. The Test for Creative Thinking-Drawing Production (TCT-DP) was administered to 627 Chinese adolescent boys (n = 332) and girls (n = 295). Results using the boy/girl variance ratio (VR) generally supported the hypothesis that boys have greater variability than girls in creativity test performance. However, results using the boy/girl ratios from different regions of the creativity score distribution revealed a pattern of male superiority. While boys significantly outnumbered girls in the higher extremes, girls tended to outnumber boys in the central region and the lower extremes. Results from an analysis of the means lent further support to the findings of male superiority. Plausible explanations for greater male variability and male superiority in Mainland China are proposed. The theoretical and practical implications of the findings are discussed.     

Depression and Self-Esteem in Boys with Attention-Deficit/Hyperactivity Disorder: Associations with Comorbid Aggression and Explanatory Attributional Mechanisms

It was tested whether boys with attention-deficit/hyperactivity disorder (ADHD), subgrouped by aggressive status, would show higher rates of depressive symptomatology and lower levels of self-esteem than would comparison boys and, in a subsample, explored attributional mechanisms that may be related to such internalizing features. Study 1 utilized 114 boys with ADHD (all prior recipients of stimulant medication) and 87 comparison boys, aged 7–12 years. Aggressive boys with ADHD reported more symptoms of depression than did nonaggressive boys with ADHD, who, in turn, reported more depression than did comparison boys. Effect sizes were moderate to large and did not vary with a depression rating scale uncontaminated by ADHD-related items. For self-esteem, the most pronounced effect was that aggressive boys with ADHD showed lower levels than did nonaggressive ADHD or comparison boys; effects were again moderate to large. Study 2 participants were a subsample of boys with ADHD from Study 1 (N = 27). We probed causal attributions in ADHD-related domains through responses to hypothetical vignettes, in which the protagonist's medication status (medicated, not medicated) was crossed with type of outcome (good, bad). Medication-related attributions were frequent. In describing the protagonist's success in relation to medication treatment, the sample showed significant associations between (a) medication-related attributions and (b) increased depressive symptomatology as well as decreased self-esteem. We discuss attributional processes that may help to explain the variation in internalizing symptoms among children with ADHD.