Nonnormality of univariate data has been extensively examined previously (Blanca et al., Methodology Behavioral and Social Sciences, 9(2), 78-84, 2013; Miceeri, Psychological Bulletin, 105(1), 156, 1989). However, less is known of the potential nonnormality of multivariate data although multivariate analysis is commonly used in psychological and educational research. Using univariate and multivariate skewness and kurtosis as measures of nonnormality, this study examined 1,567 univariate distriubtions and 254 multivariate distributions collected from authors of articles published in Psychological Science and the American Education Research Journal. We found that 74 % of univariate distributions and 68 % multivariate distributions deviated from normal distributions. In a simulation study using typical values of skewness and kurtosis that we collected, we found that the resulting type I error rates were 17 % in a t-test and 30 % in a factor analysis under some conditions. Hence, we argue that it is time to routinely report skewness and kurtosis along with other summary statistics such as means and variances. To facilitate future report of skewness and kurtosis, we provide a tutorial on how to compute univariate and multivariate skewness and kurtosis by SAS, SPSS, R and a newly developed Web application. Almost all commonly used statistical methods in psychology and other social sciences are based on the assumption that the collected data are normally distributed. For example, t-and F-distributions for mean comparison, Fisher Ztransformation for inferring correlation, and standard errors and confidence intervals in multivariate statistics are all based on the normality assumption (Tabachnick & Fidell, 2012). Researchers rely on these methods to accurately portray the effects under investigation, but may not be aware that their data do not meet the normality assumption behind these tests or what repercussions they face when the assumption is violated. From a methodological perspective, if quantitative researchers know the type and severity of nonnormality that researchers are facing, they can examine the robustness of normal-based methods as well as develop new methods that are better suited for the analysis of nonnormal data. It is thus critical to understand whether practical data satisfy the normality assumption and if not, how severe the nonnormality is, what type of nonnormality it is, what the consequences are, and what can be done about it. : European Journal of Research Methods for theTo understand normality or nonnormality, we need to first define a measure of it. Micceri (1989) evaluated deviations from normality based on arbitrary cut-offs of various measures of nonnormality, including asymmetry, tail weight, outliers, and modality. He found that all 440 large-sample achievement and psychometric measures distributions were nonnormal, 90 % of which had sample sizes larger than 450. More recently, Blanca et al. (2013) evaluated nonnormality using the skewness and kurtosis 1 of 693 1 Without specifi...

Score limitation at the top of a scale is commonly termed "ceiling effect." Ceiling effects can lead to serious artifactual parameter estimates in most data analysis. This study examines the consequences of ceiling effects in longitudinal data analysis and investigates several methods of dealing with ceiling effects through Monte Carlo simulations and empirical data analyses. Data were simulated based on a latent growth curve model with T = 5 occasions. The proportion of the ceiling data [10%-40%] was manipulated by using different thresholds, and estimated parameters were examined for R = 500 replications. The results showed that ceiling effects led to incorrect model selection and biased parameter estimation (shape of the curve and magnitude of the changes) when regular growth curve models were applied. The Tobit growth curve model, instead, performed very well in dealing with ceiling effects in longitudinal data analysis. The Tobit growth curve model was then applied in an empirical cognitive aging study and the results were discussed.Many tests and scales have been developed in psychological and educational research to measure participants' abilities, well-being, and other constructs. However, if a test is relatively easy, high-scoring participants may answer every item correctly and reach the highest possible score, or ceiling, on the test. When this happens, the true extent of the high-scoring participants cannot be correctly measured, and this phenomenon is usually termed "ceiling effects." Uttl (2005) defined the ceiling effects as occurring when the tests or scales are relatively easy such that substantial proportions of individuals obtain either maximum or near-maximum scores and the true extent of their abilities cannot be determined.Ceiling effects are related to, but different from, performance asymptotes. Asymptotes occur when participants' scores cannot exceed a specific value with more information, additional practice, or retests (Miller, 1956). The asymptotic values are the greatest true values that participants can actually demonstrate. In this study, we assume ceiling effects happen before participants reach asymptotic values. The concept of ceiling effects is also distinct from the concept of semicontinuous variables (Olsen & Schafer, 2001). A semicontinuous variable combines a continuous distribution with point masses at one or more locations. For example, in alcohol usage research, the alcohol usage variable is a mixture of 0s and continuously distributed positive values, which is one of the typical semicontinuous variables. The difference between semicontinuous variables and ceiling effects is that the 0s are valid data values, not

Purpose An estimated 30% of cancer patients are expected to experience clinically significant psychological distress during the treatment phase of their disease. Despite significant attention being directed to the mental health needs of individuals undergoing and completing treatment, there is less known about the mental health needs of survivors and the role of potential protective factors in survivorship, such as coping self-efficacy and social support. Method One hundred and twenty-four post-treatment cancer survivors (mean age = 62.23 years, female = 70%, average 9.3 years post-treatment) were asked to complete measures of physical symptoms, coping self-efficacy, social support, and depression as part of a national convenience sample of cancer patients and survivors. Results About 20% of participants possessed scores on the CES-D indicative of clinically-relevant depression. Coping self-efficacy was not only a significant predictor of depression (43% VAC); it also partially mediated the relationship between symptoms and depression. Social support accounted for limited variance and was not a significant predictor of depression in a model containing both social support and coping self-efficacy as predictors. Conclusion A substantial minority of post-treatment survivors reported depression symptomatology. Coping self-efficacy may be an important component of patients’ adjustment and possible target for intervention. These results highlight the ongoing mental health and support needs of cancer survivors.

Cronbach's coefficient alpha is a widely used reliability measure in social, behavioral, and education sciences. It is reported in nearly every study that involves measuring a construct through multiple items. With non-tau-equivalent items, McDonald's omega has been used as a popular alternative to alpha in the literature. Traditional estimation methods for alpha and omega often implicitly assume that data are complete and normally distributed. This study proposes robust procedures to estimate both alpha and omega as well as corresponding standard errors and confidence intervals from samples that may contain potential outlying observations and missing values. The influence of outlying observations and missing data on the estimates of alpha and omega is investigated through two simulation studies. Results show that the newly developed robust method yields substantially improved alpha and omega estimates as well as better coverage rates of confidence intervals than the conventional nonrobust method. An R package coefficientalpha is developed and demonstrated to obtain robust estimates of alpha and omega.

This study examined parenting style dimensions as moderators of relations between family religiousness and individual religiousness and spirituality. Participants were 122 emerging adults ages 17-31 (M ϭ 20.90, SD ϭ 2.75). Cross-sectional data were obtained through an online survey. Participants rated the frequency with which they engaged in various religious activities with their families when they were younger, the frequency with which they personally do those behaviors currently, their current spirituality, and the parenting styles used by their parents when they were younger. Family religiousness positively predicted individual religiousness and spirituality. Rejection and autonomy-support moderated the association between family religiousness and individual religiousness, while warmth, rejection, structure, chaos, and autonomy-support moderated the relationship between family religiousness and individual spirituality. Thus, religious beliefs and practices, at whatever level, may be more readily appropriated by the next generation in families characterized by authoritative parenting.