A Note on the Assumption of Identical Distributions for Nonparametric Tests of Location

Often, when testing for shift in location, researchers will utilize nonparametric statistical tests in place of their parametric counterparts when there is evidence or belief that the assumptions of the parametric test are not met (i.e., normally distributed dependent variables). An underlying and often unattended to assumption of nonparametric tests of location is that of identical distributions. The assumption of identical distributions requires that distributions conform to one another in terms of variability and shape (i.e., variance, skew and kurtosis). The purpose of the current study is to demonstrate, via the use of Monte Carlo simulation, the assumption of identical distribution using the Wilcoxon-Mann-Whitney (WMW) test and the Student t-test for comparison. For each of the conditions, there are several levels of sample size, variance ratio, group sample size ratio, and degree of skew in the parent distribution. Empirical Type I error rates are compared to nominal Type I error rates to determine the validity of the result for each run of the simulation. Violation of the assumption of identical distributions lead to bias in the result of the WMW test and the Student t-test. Practical implications are also discussed. Accessed 1,139 times on https://pareonline.net from April 05, 2018 to December 31, 2019. For downloads from January 1, 2020 forward, please click on the PlumX Metrics link to the right

Who Is the Successful University Student? An Analysis of Personal Resources

A number of factors have been identified in the research literature as being important for student success in university. However, the rather large body of literature contains few studies that have given students the opportunity to directly report what they believe contributes to their success as an undergraduate student. The primary purpose of this study is to explore students’ descriptions of the personal resources that they use to succeed while attempting to reach their goals as well as those personal characteristics or obstacles that keep them from reaching their goals. Prominent themes supportive of student success included having a future orientation, persistence, and executive functioning skills such as time management and organization. Results also demonstrate that stress, inadequate academic skills, and distractions are detrimental to student success in university. This study is unique in that it gathers the content data directly from the population of interest; it is one of the few qualitative studies of undergraduate students’ self-generated perceptions. Implications for university administrators and academic counsellors and directions for future research are discussed.  Des travaux de recherche ont déjà relevé certains facteurs comme étant importants pour la réussite des étudiants de niveau universitaire. Mais bien qu’abondante, la recherche n’a cependant pas donné aux étudiants de premier cycle la possibilité de communiquer directement leur avis quant aux raisons de leur réussite. Le but principal de cette étude est d’explorer les descriptions que les étudiants font des ressources personnelles qu’ils utilisent pour atteindre leurs objectifs et, subsidiairement, les caractéristiques personnelles ou les obstacles qui les empêchent d’atteindre leurs objectifs. Parmi les thèmes importants menant à la réussite des élèves on trouve l’orientation vers l’avenir, la persévérance et des compétences exécutives telles que la gestion du temps et l’organisation. Les résultats démontrent également que le stress, des compétences académiques inadéquates et les distractions représentent des obstacles à la réussite des études universitaires. Cette étude est unique car elle collige les données directement de la population concernée. Elle est aussi l’une des rares études qualitatives portant sur la perception des étudiants de premier cycle. On y examine les conséquences pour les administrateurs universitaires et les conseillers scolaires, de même que les orientations possibles de futures recherches

A Note on Using the Nonparametric Levene Test When Population Means Are Unequal

This computer simulation study evaluates the robustness of the nonparametric Levene test of equal variances (Nordstokke & Zumbo, 2010) when sampling from populations with unequal (and unknown) means. Testing for population mean differences when population variances are unknown and possibly unequal is often referred to as the Behrens-Fisher problem when the populations are normally distributed, and the generalized Behrens-Fisher problem when the populations are non-normal. The nonparametric Levene test was developed to overcome reductions in power of the original Levene test of equal variances in the case of the generalized Behrens-Fisher problem. We use a Monte Carlo computer simulation to demonstrate that sampling from populations with unequal and unknown means can lead to incorrect (either inflated or decreased) Type I error rates of the nonparametric Levene test. Centering samples using either sample means or medians does not correct the Type I error rates. This note is intended to make applied researchers aware of this problem when testing for the equality of population variances with the NPL test and in general. Accessed 1,444 times on https://pareonline.net from September 17, 2018 to December 31, 2019. For downloads from January 1, 2020 forward, please click on the PlumX Metrics link to the right

The operating characteristics of the nonparametric Levene test for equal variances with assessment and evaluation data

Many assessment and evaluation studies use statistical hypothesis tests, such as the independent samples t test or analysis of variance, to test the equality of two or more means for gender, age groups, cultures or language group comparisons. In addition, some, but far fewer, studies compare variability across these same groups or research conditions. Tests of the equality of variances can therefore be used on their own for this purpose but they are most often used alongside other methods to support assumptions made about variances. This is often done so that variances can be pooled across groups to yield an estimate of variance that is used in the standard error of the statistic in question. The purposes of this paper are twofold. The first purpose is to describe a new nonparametric Levene test for equal variances that can be used with widely available statistical software such as SPSS or SAS, and the second purpose is to investigate this test’s operating characteristics, Type I error and statistical power, with real assessment and evaluation data. To date, the operating characteristics of the nonparametric Levene test have been studied with mathematical distributions in computer experiments and, although that information is valuable, this study will be an important next step in documenting both the level of non-normality (skewness and kurtosis) of real assessment and evaluation data, and how this new statistical test operates in these conditions. Accessed 15,120 times on https://pareonline.net from February 26, 2011 to December 31, 2019. For downloads from January 1, 2020 forward, please click on the PlumX Metrics link to the right

Investigating tests for equal variances

One of the central messages of this dissertation is that (a) unequal variances may be more prevalent than typically recognized in educational and policy research, and (b) when considering tests of equal variances, one needs to be cautious about what is being referred to as “Levene’s test” because Levene’s test is actually a family of techniques. Depending on which of the Levene tests that are being implemented, and particularly the Levene’s test based on means which is found in widely used software like SPSS, one may be using a statistical technique that is as bad (if not worse) than the F test which the Levene test was intended to replace. The primary goals of this dissertation are to (a) demonstrate that the current statistical practice of testing for equality of variances in hypothesis testing (as prescribed by textbooks and statistical software programs) is insufficient, (b) introduce a new non-parametric statistical test for homogeneity of variances, and (c) investigate the Type I error rate and power of the non-parametric Levene test with that of the median version of the Levene test. Under all conditions investigated, both tests maintained their nominal Type I error rates. As population distributions become more skewed, the non-parametric Levene test becomes more powerful than the median version of the Levene test. These results promise to impact applied statistical practice by informing researchers about the relative efficiencies of the two tests. This dissertation concludes with remarks about the implications of the findings, and the future work that has arisen from the results.Education, Faculty ofEducational and Counselling Psychology, and Special Education (ECPS), Department ofGraduat

A New Nonparametric Levene Test for Equal Variances

Tests of the equality of variances are sometimes used on their own to compare variability across groups of experimental or non-experimental conditions but they are most often used alongside other methods to support assumptions made about variances. A new nonparametric test of equality of variances is described and compared to current 'gold standard' method, the median-based Levene test, in a computer simulation study. The simulation results show that when sampling from either symmetric or skewed population distributions both the median based and nonparametric Levene tests maintain their nominal Type I error rate; however, when one is sampling from skewed population distributions the nonparametric test has more statistical power

The symphonic structure of childhood stress reactivity: patterns of sympathetic, parasympathetic, and adrenocortical responses to psychological challenge.

Despite widespread recognition that the physiological systems underlying stress reactivity are well coordinated at a neurobiological level, surprisingly little empirical attention has been given to delineating precisely how the systems actually interact with one another when confronted with stress. We examined cross-system response proclivities in anticipation of and following standardized laboratory challenges in 664 4- to 14-year-olds from four independent studies. In each study, measures of stress reactivity within both the locus coeruleus-norepinephrine system (i.e., the sympathetic and parasympathetic branches of the autonomic nervous system) and the corticotrophin releasing hormone system (i.e., the hypothalamic-pituitary-adrenal axis) were collected. Latent profile analyses revealed six distinctive patterns that recurred across the samples: moderate reactivity (average cross-system activation; 52%-80% of children across samples), parasympathetic-specific reactivity (2%-36%), anticipatory arousal (4%-9%), multisystem reactivity (7%-14%), hypothalamic-pituitary-adrenal axis specific reactivity (6%-7%), and underarousal (0%-2%). Groups meaningfully differed in socioeconomic status, family adversity, and age. Results highlight the sample-level reliability of children's neuroendocrine responses to stress and suggest important cross-system regularities that are linked to development and prior experiences and may have implications for subsequent physical and mental morbidity