Unbalanced 2 x 2 factorial designs and the interaction effect: a troublesome combination.

In this power study, ANOVAs of unbalanced and balanced 2 x 2 datasets are compared (N = 120). Datasets are created under the assumption that H1 of the effects is true. The effects are constructed in two ways, assuming: 1. contributions to the effects solely in the treatment groups; 2. contrasting contributions in treatment and control groups. The main question is whether the two ANOVA correction methods for imbalance (applying Sums of Squares Type II or III; SS II or SS III) offer satisfactory power in the presence of an interaction. Overall, SS II showed higher power, but results varied strongly. When compared to a balanced dataset, for some unbalanced datasets the rejection rate of H0 of main effects was undesirably higher. SS III showed consistently somewhat lower power. When the effects were constructed with equal contributions from control and treatment groups, the interaction could be re-estimated satisfactorily. When an interaction was present, SS III led consistently to somewhat lower rejection rates of H0 of main effects, compared to the rejection rates found in equivalent balanced datasets, while SS II produced strongly varying results. In data constructed with only effects in the treatment groups and no effects in the control groups, the H0 of moderate and strong interaction effects was often not rejected and SS II seemed applicable. Even then, SS III provided slightly better results when a true interaction was present. ANOVA allowed not always for a satisfactory re-estimation of the unique interaction effect. Yet, SS II worked better only when an interaction effect could be excluded, whereas SS III results were just marginally worse in that case. Overall, SS III provided consistently 1 to 5% lower rejection rates of H0 in comparison with analyses of balanced datasets, while results of SS II varied too widely for general application.

Parenting style as a mediator between children's negative emotionality and problematic behavior in early childhood.

Negative emotionality is considered to be the core of the difficult temperament concept (J. E. Bates, 1989; R. L. Shiner, 1998). In this correlational study, the authors examined whether the relations between children's negative emotionality and problematic behavior (internalizing and externalizing) were partially mediated by parenting style (authoritative and authoritarian) in a community sample of 196 3-year-old children and their mothers. The authors assessed maternal perception of child negative emotionality using the Children's Behavior Questionnaire (M. K. Rothbart, S. A. Ahadi, K. L. Hershey, & P. Fisher, 2001) and assessed problematic child behavior by means of maternal report using the Child Behavior Checklist (T. M. Achenbach, 1992). The results showed that the relations between child negative emotionality and internalizing and externalizing behaviors were partially mediated by mothers' authoritative parenting style. Moreover, when the authors used confirmatory factor analysis to decontaminate possible overlap in item content between measures assessing temperament and problematic behavior, the association between negative emotionality and internalizing behavior was fully mediated by authoritative parenting.

Contribution of infants' sleep and crying to marital relationship of first-time parent couples in the 1st year after childbirth.

This study investigated the influence of infants' sleep and crying on marital relationship in first-time parent couples (N = 107) during the 1st year after birth. Control variables are parents' insomnia and parental self-efficacy in handling the baby. Questionnaires were administered to both parents before birth, at 2 and 7 weeks after birth, and at 1 year after birth. Results show that marital problem-solving ability did not change but that marital satisfaction diminished significantly over time. Crying was the main child variable that affected marital satisfaction. Fathers' self-efficacy contributed positively to marital problem solving and negatively to paternal insomnia. Both maternal and paternal insomnia affected spouses' insomnia. As infant sleep problems may worsen preexisting parental insomnia, it is recommended that first-time parents be informed about treatments of insomnia.

On the likelihood ratio test in structural equation modeling when parameters are subject to boundary constraints.

The authors show how the use of inequality constraints on parameters in structural equation models may affect the distribution of the likelihood ratio test. Inequality constraints are implicitly used in the testing of commonly applied structural equation models, such as the common factor model, the autoregressive model, and the latent growth curve model, although this is not commonly acknowledged. Such constraints are the result of the null hypothesis in which the parameter value or values are placed on the boundary of the parameter space. For instance, this occurs in testing whether the variance of a growth parameter is significantly different from 0. It is shown that in these cases, the asymptotic distribution of the chi-square difference cannot be treated as that of a central chi-square-distributed random variable with degrees of freedom equal to the number of constraints. The correct distribution for testing 1 or a few parameters at a time is inferred for the 3 structural equation models mentioned above. Subsequently, the authors describe and illustrate the steps that one should take to obtain this distribution. An important message is that using the correct distribution may lead to appreciably greater statistical power.

Respiratory variability and psychological well-being in schoolchildren.

Among the relations between respiration and psychological state, associations with respiratory variability have been contradictory. In this study, respiration was measured noninvasively in 162 children with a mean age of 11 years (from 9 to 13). They completed a battery of psychological tests. Structural Equation Modeling (SEM or LISREL) revealed a model that fit the data well (chi 2 = 88.201, df = 79, p = .224). In this model, respiratory variability was positively related to anger-in and negatively to negative fear of failure and neurotic complaints. Respiration rate was positively related to positive fear of failure, and duty cycle was positively related to the latent variable of negative affect. Variability in resting time components of respiration was higher among children with less fear of failure and fewer complaints. Therefore, respiratory variability need not necessarily be a sign of psychological dysfunctions, and interventions should not always impose a fixed breathing pattern.