A parametric bootstrap approach for ANOVA with unequal variances: Fixed and random models

Multiple comparisons of treatment against control under unequal variances using parametric bootstrap

In one-way analysis of variance models, performing simultaneous multiple comparisons of treatment groups with a control group may be of interest. Dunnett's test is used to test such differences and assumes equal variances of the response variable for each group. This assumption is not always met even after transformation. A parametric bootstrap (PB) method is developed here for comparing multiple treatment group means against the control group with unequal variances and unbalanced data. In simulation studies, the proposed method outperformed Dunnett's test in controlling the type I error under various settings, particularly when data have heteroscedastic variance and unbalanced design. Simulations show that power is often lower for the PB method than for Dunnett's test under equal variance, balanced data, or smaller sample size, but similar to or higher than for Dunnett's test with unequal variance, unbalanced data and larger sample size. The method is applied to a dataset concerning isotope levels found in elephant tusks from various geographical areas. These data have very unbalanced group sizes and unequal variances. This example illustrates that the PB method is easy to implement and avoids the need for transforming data to meet the equal variance assumption, simplifying interpretation of results.

Proximate Composition, Predictive Analysis and Allometric Relationships, of the Edible Water Frog (Pelophylax epeiroticus) in Lake Pamvotida (Northwest Greece)

The edible water frog Pelophylax epeiroticus, distributed mainly in Northwest Greece and utilized commercially as food, was investigated in lake Pamvotida (Ioannina). The objective was to assess aspects of population structure (sex ratio, morphometric characteristics, allometric relationships) and proximate composition of the Epirus water frog (Pelophylax epeiroticus). Commercial samples (31 females and 54 males) were obtained and sex ratio, morphometric characteristics, allometric relationships and proximate composition were assessed. A significantly lower abundance of females was indicated (31 females and 54 males). Body length range was higher in females (females 3.4 mm, males 2.6 mm), whereas total weight range was higher in males (females 45.08 gr, males 48.35 gr). Differences in allometric relationships were indicated between sexes. The high protein (15.93 ± 3.32) and low lipid (0.25 ± 0.13) contents indicated that P. epeiroticus is an excellent food source of high nutritional value. A tree classification algorithm indicated that the principal contributing component for sex classification was dry matter, followed by a proportion of edible flesh and protein content. A predicted future increase in demand for wild-caught individuals requires the use of a suitable management plan, coupled with the development of farming practices aiming to assure the sustainable exploitation of this important resource and alleviate the pressure on its populations.

Social Emotional Learning (sel) Program Among Fifth graders, Three and Six Months Later

This study carried out a follow-up three and six months after the application of a Social Emotional Learning (SEL) program, aiming to verify the maintenance of social skills in Elementary Education students in situations of social vulnerability from Rio de Janeiro, Brazil. A sample of the intervention and control groups composed of 20 students aged 10 to 13 (M = 10.3, SD = 0.8), boys and girls were selected. The SSRS (Social Skill Rating System) and the TDE (School Achievement Test) used in the intervention for teachers and students were reapplied. The results showed that the decrease in psychopathological symptoms and the improvements in academic performance were maintained after the intervention. These findings highlight the relevance of developing social emotional learning programs with elementary school students.   How to cite this article: Souza, M.S., Soares, A.B., & Freitas, C.P.P. (2021). Social emotional learning (sel) program among fifth graders, three and six months later. Revista Colombiana de Psicologia, 31 (1), 35-48. https://doi.org/10.15446/rcp.v31n1.83042

Autistic Traits and Empathy in Children With Attention Deficit Hyperactivity Disorder, Autism Spectrum Disorder and Co-occurring Attention Deficit Hyperactivity Disorder/Autism Spectrum Disorder

Attention Deficit Hyperactivity Disorder (ADHD) and Autism Spectrum Disorders (ASD) are two of the most represented neurodevelopmental conditions in childhood. The diagnostic shift introduced by the DSM-5, allowing a combined diagnosis of ADHD and ASD, poses different clinical challenges related to diagnostic overshadowing, accuracy of clinical judgment and potential delay in an ASD diagnosis in children presenting with ADHD. Here we tried to disentangle the clinical phenotype and specificity of the two co-occurring conditions in relation to autism traits and empathy, by comparing children with ASD with and without comorbid ADHD with children presenting ADHD only and children with typical development. The child versions of the Autism Quotient (C-AQ) and Empathy Quotient (C-EQ) were administered to a total sample of 198 male children between 6 and 14 years old with age appropriate language skills and normal intelligence. Univariate analysis demonstrated no significant differences in the C-AQ total and subscale scores as well as the C-EQ between children with ASD and children with ASD + ADHD, while children with ADHD alone presented an intermediate phenotype between ASD and TD. Furthermore, a receiver operating characteristic (ROC) analysis was applied to discriminate among the different phenotypes. We found that the C-AQ and C-EQ were accurate at distinguishing with satisfactory reliability between: (a) ASD vs. non- ASD (N-ASD) groups comprising both ADHD and TD children (Area Under the Curve AUC 88% for C-AQ and 81% for C-EQ); (b) ASD and TD (AUC 92% for C-AQ and 95% for C-EQ); (c) ASD and ADHD (AUC 80% for C-AQ and 68% for C-EQ). Our data confirm the reliability of the C-AQ and C-EQ as behavioral markers to differentiate ASD (regardless of comorbid ADHD) from an ADHD condition and TD. Interestingly, in our sample an ADHD condition does not increase the severity of the clinical phenotype in terms of autism traits distribution and empathy, suggesting that the psychological measures detected by the two quantitative instruments are independent of ADHD traits. This evidence will contribute to the translational efforts in developing better tailored treatments and preventive strategies.

Validating the regional estimates of changes in soil organic carbon by using the data from paired-sites: the case study of Mediterranean arable lands

BACKGROUND

Legacy data are unique occasions for estimating soil organic carbon (SOC) concentration changes and spatial variability, but their use showed limitations due to the sampling schemes adopted and improvements may be needed in the analysis methodologies. When SOC changes is estimated with legacy data, the use of soil samples collected in different plots (i.e., non-paired data) may lead to biased results. In the present work, N = 302 georeferenced soil samples were selected from a regional (Sicily, south of Italy) soil database. An operational sampling approach was developed to spot SOC concentration changes from 1994 to 2017 in the same plots at the 0-30 cm soil depth and tested.

RESULTS

The measurements were conducted after computing the minimum number of samples needed to have a reliable estimate of SOC variation after 23 years. By applying an effect size based methodology, 30 out of 302 sites were resampled in 2017 to achieve a power of 80%, and an α = 0.05. A Wilcoxon test applied to the variation of SOC from 1994 to 2017 suggested that there was not a statistical difference in SOC concentration after 23 years (Z = - 0.556; 2-tailed asymptotic significance = 0.578). In particular, only 40% of resampled sites showed a higher SOC concentration than in 2017.

CONCLUSIONS

This finding contrasts with a previous SOC concentration increase that was found in 2008 (75.8% increase when estimated as differences of 2 models built with non-paired data), when compared to 1994 observed data (Z = - 9.119; 2-tailed asymptotic significance < 0.001). This suggests that the use of legacy data to estimate SOC concentration dynamics requires soil resampling in the same locations to overcome the stochastic model errors. Further experiment is needed to identify the percentage of the sites to resample in order to align two legacy datasets in the same area.

Brain connectivity analysis in fathers of children with autism

Autism Spectrum Disorder (ASD) is a neurodevelopmental disorder in which changes in brain connectivity, associated with autistic-like traits in some individuals. First-degree relatives of children with autism may show mild deficits in social interaction. The present study investigates electroencephalography (EEG) brain connectivity patterns of the fathers who have children with autism while performing facial emotion labeling task. Fifteen biological fathers of children with the diagnosis of autism (Test Group) and fifteen fathers of neurotypical children with no personal or family history of autism (Control Group) participated in this study. Facial emotion labeling task was evaluated using a set of photos consisting of six categories (mild and extreme: anger, happiness, and sadness). Group Independent Component Analysis method was applied to EEG data to extract neural sources. Dynamic causal connectivity of neural sources signals was estimated using the multivariate autoregressive model and quantified by using the Granger causality-based methods. Statistical analysis showed significant differences (p value < 0.01) in the connectivity of neural sources in recognition of some emotions in two groups, which the most differences observed in the mild anger and mild sadness emotions. Short-range connectivity appeared in Test Group and conversely, long-range and interhemispheric connections are observed in Control Group. Finally, it can be concluded that the Test Group showed abnormal activity and connectivity in the brain network for the processing of emotional faces compared to the Control Group. We conclude that neural source connectivity analysis in fathers may be considered as a potential and promising biomarker of ASD.

Confidence intervals for the ratio of two independent Poisson rates: Parametric bootstrap, modified asymptotic, and approximate-estimate approaches

We propose four confidence intervals for the ratio of two independent Poisson rates. We apply a parametric bootstrap approach, two modified asymptotic results, and we propose an ad-hoc approximate-estimate method to construct confidence intervals. We justify the correctness of the proposed methods asymptotically in the case of non-rare events (when the Poisson rates are large). We also compare the proposed confidence intervals with some recommended ones in the case of rare events (when the Poisson rates are small) via an extensive simulation study. The results show that the proposed modified asymptotic and the approximate-estimate confidence intervals perform reasonably well in terms of coverage probability and average length.

Nature and specificity of altered cognitive functioning in IBS

BACKGROUND

It is unknown whether cognitive dysfunction found in patients with irritable bowel syndrome (IBS) was attributable to the different subtypes, ongoing pathophysiological processes, trait characteristics, or psychiatric comorbidity.

METHODS

Forty Rome-III patients with IBS (20 diarrhea-predominant [IBS-D] and 20 constipation-predominant [IBS-C]) and 40 age-, sex-, education-matched healthy controls were systematically recruited and compared on their cognitive function with continuous performance test (CPT), Wisconsin Card Sorting Test (WCST) and emotional Stroop test. Beck Anxiety Inventory (BAI), Beck Depression Inventory-II (BDI-II), Patient Health Questionnaire-15 (PHQ-15) and a structured bowel symptom questionnaire were performed to measure anxiety, depressive, somatization, and bowel symptoms, respectively. Psychiatric diagnoses were ascertained with SCID-I (Structured Clinical Interview for DSM-IV Axis I Disorders).

KEY RESULTS

Patients with IBS showed significantly increased standard deviation of reaction time (SDRT) (P = .003) on CPT, increased failure to maintain set (FMS) (P=.002), and percentage of perseverative errors (P = .003) on WCST. SDRT did not correlate with illness chronicity or bowel symptoms. FMS correlated with bowel symptom severity. In logistic regression models controlled for BAI, BDI-II, and PHQ-15, SDRT (AOR = 1.08, P = .025), but not FMS (P = .25) or percentage of perseverative errors (P = .24), significantly differentiated IBS from controls. Cognitive function was not significantly different between IBS-C and IBS-D (P > .05), or between pure IBS (n = 22) and IBS with generalized anxiety disorder (GAD) (n = 17) (P > .05).

CONCLUSIONS & INFERENCES

Patients with IBS showed attentional and executive function impairment irrespective of subtypes but otherwise heterogeneous in terms of its state-trait correlations and overlap with anxiety comorbidity.

Sample sizes and statistical methods in interventional studies on individuals with spinal cord injury: A systematic review

AIM

Prevalence and incidence of spinal cord injury (SCI) are low. However, sample sizes have not been systematically examined yet, although this might represent useful information for study planning and power considerations. Therefore, our objective was to determine the median sample size in clinical trials on SCI individuals. Moreover, within small-sample size studies, statistical methods and awareness of potential problems regarding small samples were examined.

METHODS

We systematically reviewed all studies on human SCI individuals published between 2014 and 2015, where the effect of an intervention on one or more health-related outcomes was assessed by means of a hypothesis test. If at least one group had a size <20, the study was classified as a small sample size study. PubMed was searched for eligible studies; subsequently, data on sample sizes and statistical methods were extracted and summarized descriptively.

RESULTS

Out of 8897 studies 207 were included. Median total sample size was 18 (range 4-582). Small sample sizes were found in 167/207 (81%) studies, resulting limitations and implications for statistical analyses were mentioned in 109/167 (65%) studies.

CONCLUSIONS

Although most recent SCI trials have been conducted with small samples, the consequences on statistical analysis methods and the validity of the results are rarely acknowledged.

Study of the ambient air metallic elements Cr, Cu, Zn, Cd and Pb at HAF sampling sites

This study characterized diurnal variations in the compositions of total suspended particulates (TSP) and dry deposits of particulates from ambient air, and the metallic elements that are contained in them at harbor, airport and farmland (HAF) sampling sites from August, 2013 to July, 2014. Two-way ANOVA of the amounts of metallic elements in the TSP and dry deposits was carried out in all four seasons at the HAF sampling sites. The metallic elements Cr and Cu originated in local emission sources at the airport. Metallic elements Zn and Pb originated in local emission sources at the harbor. Finally, metallic element Cd originated in local emissions form farmland. The following results were also obtained. (1) The metallic composition of the TSP differed significantly from that of the dry deposits in all four seasons at the harbor and farmland sampling sites, but not at the airport sampling site. (2) High correlations coefficients were found between the amounts of metallic elements Cr and Cu in the TSP and those in the dry deposits at the airport sampling site. (3) Pb was present in the TSP and the dry deposits at the harbor sampling site.

Seasonal variations and sources study by way of back trajectories and ANOVA for ambient air pollutants (particulates and metallic elements) within a mixed area at Longjing, central Taiwan: 1-year observation

This study measured the concentrations of particulates and metallic elements in ambient air by using PS-1 sampler (TSP) at Longjing area. And this study focuses on the collection of ambient air particulates, metallic elements, particulate-bound mercury Hg(p), concentrations. In addition, the sources of ambient pollutants by way of back trajectory analysis are found. Moreover, test mean concentration variance differences for metallic elements (PM, Hg(p), Mn, Fe, Zn, Cr, Cu, and Pb) among the four seasons (spring, summer, autumn and winter) through ANOVA are calculated. The result indicates that the average highest particulate concentration occurred in winter season, and the order was winter > spring > autumn > summer, and the mostly highest average metallic element (Mn, Fe, Zn, Cr, Cu, Pb) concentrations occurred in autumn. Moreover, the mostly average lowest metallic element concentrations occurred in summer. In addition, the above results of backward trajectories that the major particulate pollutants parcel mainly come from northeastern Taiwan. Moreover, when comparing the results of the first half year to that of the second half year, the they indicated that all metallic elements displayed significant differences in concentrations except those of Hg(p), Mn, Fe, Zn. Finally, metallic element Hg(p) is the only one which showed no significant concentration difference from either seasonal variations or half-year observations.

Multiple Comparison of Age Groups in Bone Mineral Density under Heteroscedasticity

Osteoporosis is a silent disease because individuals may not know that they have osteoporosis until their bones become so fragile. Bone mineral density (BMD) test helps to detect osteoporosis and determine the risk fractures. This study covers bone measurement data from total body dual energy X-ray absorptiometry scans for 28,454 persons who participated in the 1996–2006 National Health and Nutrition Examination Survey in USA Dual energy X-ray absorptiometry (DXA) method is known as the primary method for detecting osteoporosis because of its high precision and accuracy. Testing the equality of the means of normal populations when the variances are unknown and unequal is a fundamental problem in clinical trials and biomedical research. In this study we compare age groups based upon BMD in case of unequal variance being present among the groups. First we test equality of variances among the age groups by the Hartley test. And then Scott-Smith test is used to test equality of BMD means for the age groups. Finally, Tukey-Cramer confidence intervals are constructed to detect which groups start to differ from the reference group in which BMD reaches the peak level.

Statistical analysis of the influence of major tributaries to the eco-chemical status of the Danube River

We have assembled and assessed the statistical procedure which is capable to objectively explore influence of the Danube's major tributaries (the Rivers Tisa, Sava, and Velika Morava) to its eco-chemical status. Procedure contains several tests for measurement of central tendencies: one-way analysis of variance (ANOVA), repeated measures ANOVA, and nonparametric Kruskal-Wallis and Mann-Whitney tests. Various nuisance factors, (outliers, departures from normality, seasonality, and heteroscedasticity) which are present in large data bases, affect the objectivity of central tendency tests; therefore, it was important not only to estimate their robustness, but also to apply proper procedures for detection of the nuisance factors (Grubbs', generalized ESD-extreme Studentized deviate, Kolmogorov-Smirnov, Shapiro-Wilk, turning point, Wald-Wolfowitz runs, Kendall rank, and Levene's tests) and to mitigate their influence (outlier exclusion, Box-Cox, and logarithmic transformations). The analysis of selected eco-chemical parameters: biological oxygen demand-5, chemical oxygen demand, UV extinction at 254 nm, dissolved oxygen, oxygen saturation, total dissolved solids, electrical conductivity, suspended matter, total phosphorus, phosphates, nitrates, ammonia, pH, total alkalinity, m-2p alkalinity, CO2, and temperature, was performed for 15 years period. The Tisa was the most polluted tributary, but its pollution load was not substantial enough to exceed the Danube self-purification potential. The City of Belgrade was also identified as serious pollution source. Assessment of assembled statistical procedure, which was based on the real environmental data, indicates that proposed tests are sufficiently robust to the observed level of nuisance factors with the exception of pronounced seasonality.

High self-control protects the link between social support and positivity ratio for Israeli students exposed to contextual risk

This study examined how Israeli students, despite exposure to contextual risk factors, may experience a high ratio of self-reported positive to negative emotions (i.e., positivity ratio). Self-control skills and perceived social support were tested as protective factors, where each was posited to moderate the relation between risk status and positivity ratio. The participants were 460 Israeli students (51% girls) in grades 8-10. Contrary to expectations, students attending a school with high contextual risks did not differ from students attending a school with low contextual risks in their scores on self-control skills, perceived social support, or positivity ratio. However, an exploratory follow-up moderation analysis revealed a significant three-way interaction, indicating that while low self-control skills eliminate the link between social support and positivity ratio for students attending the school defined as at-risk, high self-control protects this link. These results suggest that neither contextual risk in itself nor initial differences in self-control or social support account for differences in students' positivity ratio. Rather, it is the way these factors interact with each other that matters. Study limitations and implications are discussed.

Inference for one-way ANOVA with equicorrelation error structure

We consider inferences in a one-way ANOVA model with equicorrelation error structures. Hypotheses of the equality of the means are discussed. A generalized F-test has been proposed by in the literature to compare the means of all populations. However, they did not discuss the performance of that test. We propose two methods, a generalized pivotal quantities-based method and a parametric bootstrap method, to test the hypotheses of equality of the means. We compare the empirical performance of the proposed tests with the generalized F-test. It can be seen from the simulation results that the generalized F-test does not perform well in terms of Type I error rate, and the proposed tests perform much better. We also provide corresponding simultaneous confidence intervals for all pair-wise differences of the means, whose coverage probabilities are close to the confidence level.