Unequal Sample Sizes Research Articles

Introduction to Bayesian methods

The concepts of Bayesian analysis are introduced by discussing a 2 × 2 confusion matrix with unequal sample sizes for each class.

Common and distinct neural connectivity in attention-deficit/hyperactivity disorder and alcohol use disorder studied using resting-state functional magnetic resonance imaging.

A link between attention-deficit/hyperactivity disorder (ADHD) and alcohol use disorder (AUD) has been widely demonstrated. In this study, we used neuroimaging to investigate the connectivity traits that may contribute to the comorbidity of these disorders. The study included an AUD group (N=18), an ADHD group (N=17), a group with AUD+ADHD comorbidity (N=12) and a control group (N=18). We used resting-state functional connectivity in a seed-based approach in the default mode networks, the dorsal attention network, and the salience network. Within the default mode networks, all affected groups shared greater connectivity toward the temporal gyrus when compared to the control group. Regarding the dorsal attention network, the Brodmann area 6 presented greater connectivity for each affected group in comparison with the control group, displaying the strongest aberrations in the AUD+ADHD group. In the salience network, the prefrontal cortex showed decreased connectivity in each affected group compared to the control group. Despite the small and unequal sample sizes, our findings show evidence of common neurobiological alterations in AUD and ADHD, supporting the hypothesis that ADHD could be a risk factor for the development of AUD. The results highlight the importance of an early ADHD diagnosis and treatment to reduce the risk of a subsequent AUD.

High-Low Level Support Vector Regression Prediction Approach (HL-SVR) for Data Modeling with Input Parameters of Unequal Sample Sizes

Support vector regression (SVR) has been widely used to reduce the high computational cost of computer simulation. SVR assumes the input parameters have equal sample sizes, but unequal sample sizes are often encountered in engineering practices. To solve this issue, a new prediction approach based on SVR, namely as high-low level SVR approach (HL-SVR) is proposed for data modeling of input parameters of unequal sample sizes in this paper. The proposed approach consists of low-level SVR models for the input parameters of larger sample sizes and high-level SVR model for the input parameters of smaller sample sizes. For each training point of the input parameters of smaller sample sizes, one low-level SVR model is built based on its corresponding input parameters of larger sample sizes and their responses of interest. The high-level SVR model is built based on the obtained responses from the low-level SVR models and the input parameters of smaller sample sizes. A number of numerical examples are used to validate the performance of HL-SVR. The experimental results indicate that HL-SVR can produce more accurate prediction results than SVR. The proposed approach is applied to the stress analysis of dental implant, in which the structural parameters have massive samples but the material of implant can only be selected from Ti and its alloys. The obtained prediction results of the HL-SVR approach are much better than SVR. The proposed approach can be used for the design, optimization, and analysis of engineering systems with input parameters of unequal sample sizes.

Quality control using S2 or S charts for subgroups of varying sample sizes and their exact average run lengths

AbstractThis article generalizes the historical chart (of equal sample sizes) to subgroups of differing sample sizes. As a sequel to a previous article, Section 2 compares all estimators of process standard deviation for more than 1 subgroups of equal sample sizes from a normal universe. Section 3 provides the general probability control limits (CONLs) for the chart of unequal sample sizes. Section 4 uses the chi‐square distribution to obtain the exact ‐level CONLs for the S chart. Section 5 proves that the average run length (ARL) of and charts are identical and tabulates the ARL for the most common sample sizes = 2, 3, , and 12. Further, as expected, the ARL of charts always perform better than those of the corresponding charts.

Power formulas for mixed effects models with random slope and intercept comparing rate of change across groups.

We have previously derived power calculation formulas for cohort studies and clinical trials using the longitudinal mixed effects model with random slopes and intercepts to compare rate of change across groups [Ard & Edland, Power calculations for clinical trials in Alzheimer’s disease. J Alzheim Dis 2011;21:369–77]. We here generalize these power formulas to accommodate 1) missing data due to study subject attrition common to longitudinal studies, 2) unequal sample size across groups, and 3) unequal variance parameters across groups. We demonstrate how these formulas can be used to power a future study even when the design of available pilot study data (i.e., number and interval between longitudinal observations) does not match the design of the planned future study. We demonstrate how differences in variance parameters across groups, typically overlooked in power calculations, can have a dramatic effect on statistical power. This is especially relevant to clinical trials, where changes over time in the treatment arm reflect background variability in progression observed in the placebo control arm plus variability in response to treatment, meaning that power calculations based only on the placebo arm covariance structure may be anticonservative. These more general power formulas are a useful resource for understanding the relative influence of these multiple factors on the efficiency of cohort studies and clinical trials, and for designing future trials under the random slopes and intercepts model.

Two-sample multivariate tests for high-dimensional data when one covariance matrix is unknown

In this study, the test statistics for one-sided and two-sided multivariate hypotheses to the high-dimensional two-sample problem with one unknown covariance matrix were proposed. The tests were developed based on the idea of keeping as much information as possible from the pooled sample covariance matrix by arranging the blocks along its diagonal. The asymptotic distributions of the test statistics were derived under the null hypothesis. The performance of the proposed tests were evaluated on both equal and unequal sample sizes via a simulation study. The simulated results showed that the proposed tests performed well for both equal and unequal sample sizes. An illustration of the proposed tests was carried out using a dataset of prostate cancer microarray.

Two-sample nonparametric test for comparing mean time to failure functions in age replacement

A two-sample nonparametric test based on two independent samples is proposed for comparing mean time to failure (MTTF) functions of two life distributions. The proposed test has the flexibility of handling unequal sample sizes and crossings of mean time to failure functions. The test is shown to be consistent and a bound on asymptotic size has been derived. A computational technique is devised for evaluating the proposed test statistic. A simulation study is carried out for assessing the merit of the proposed test procedure. Finally, the test is applied to real-life data sets for illustration.

Ranks and Pseudo‐ranks—Surprising Results of Certain Rank Tests in Unbalanced Designs

SummaryRank‐based inference methods are applied in various disciplines, typically when procedures relying on standard normal theory are not justifiable. Various specific rank‐based methods have been developed for two and more samples and also for general factorial designs (e.g. Kruskal–Wallis test or Akritas–Arnold–Brunner test). It is the aim of the present paper (1) to demonstrate that traditional rank procedures for several samples or general factorial designs may lead to surprising results in case of unequal sample sizes as compared with equal sample sizes, (2) to explain why this is the case and (3) to provide a way to overcome these disadvantages. Theoretical investigations show that the surprising results can be explained by considering the non‐centralities of the test statistics, which may be non‐zero for the usual rank‐based procedures in case of unequal sample sizes, while they may be equal to 0 in case of equal sample sizes. A simple solution is to consider unweighted relative effects instead of weighted relative effects. The former effects are estimated by means of the so‐called pseudo‐ranks, while the usual ranks naturally lead to the latter effects. A real data example illustrates the practical meaning of the theoretical discussions.

Picturing pre-service and in-service teachers’ views about scientists and science teaching

ABSTRACT Courses in teacher training programmes, especially science method courses, play a major role in the development of beliefs. Because children’s science learning starts in preschool years, it is critical to investigate early childhood teachers’ beliefs about scientists and science teaching. The purpose of this study was to describe, document, and then compare the pre-service and in-service early childhood teachers’ beliefs about scientists and science teaching. A causal-comparative design with unequal sample sizes was used. The independent variables were the type of service, pre-service or in-service. The dependent variable was the score obtained on the ‘Draw a Scientist Test’ and the ‘Draw a Science Teacher Test'. The sample consisted of 139 pre-service and in-service early childhood teachers. Pre-service teachers were studying in a teacher-training programme at a major research university and in-service teachers were working in public schools in the south part of Turkey. The results indicate that inservice teachers held more stereotypical images than pre-service teachers about scientists. In addition, pre-service teachers had positive belief of scientists while in the training programme, but in-service teachers lacked this positive belief. A key implication of the study is that more professional training for in-service teachers should be offered within professional development programmes.

A-080 Prediction Model for Verbal Memory Decline in Different Epilepsy Surgery Procedures: Temporal Lobectomy vs. Amygdalohippocampectomy

Abstract Objective Mathematical models predicting risk of verbal memory decline after resective epilepsy surgery have been developed for patients undergoing temporal lobectomies. This study was undertaken to determine if application of the Stroup memory loss prediction model was as accurate in foreseeing verbal memory decline after temporal lobectomy as in the less invasive selective amygdalohippocampectomy procedure. Method This retrospective study examined the verbal memory performances of 40 left temporal lobectomy (ATL), and 16 left subtemporal approach selective amygdalohippocampectomy (SA-H), patients before and after epilepsy surgery using word list learning (Rey Auditory-Verbal Learning Test, Buschke Selective Reminding Test) and story memory (WMS Logical Memory) tests. Patients were assigned to one of four groups using the Stroup multiple regression equation: Minimal Risk (61% risk). To classify memory decline in individual patients, a pre-to-post surgery decrease of > 1 SD on at least one memory test constituted memory decline. Results The prediction model accurately classified 82% (9/11) of ATL, and 75% (3/4) of SA-H, High Risk patients. Verbal memory loss was higher among ATLs than SA-Hs in the Moderate Risk (87% vs. 18%) and Low Risk (71% vs. 0%) groups. Conclusion The Stroup verbal memory loss risk model under-predicted memory loss among temporal lobectomy patients (71% of Low Risk patients showed memory decline) and over-predicted memory loss among selective amygdalohippocampectomy patients (only 18% of Moderate Risk patients showed memory decline). Results should be considered preliminary due to methodological limitation including small Ns and unequal sample sizes.

Detecting changes in the second moment structure of high-dimensional sensor-type data in a K-sample setting

The K sample problem for high-dimensional vector time series is studied, especially focusing on sensor data streams, in order to analyze the second moment structure and detect changes across samples and/or across variables cumulated sum (CUSUM) statistics of bilinear forms of the sample covariance matrix. In this model, K independent vector time series are observed over a time span which may correspond to K sensors (locations) yielding d-dimensional data as well as K locations where d sensors emit univariate data. Unequal sample sizes are considered as arising when the sampling rate of the sensors differs. We provide large-sample approximations and two related change point statistics, a sum of squares and a pooled variance statistic. The resulting procedures are investigated by simulations and illustrated by analyzing a real data set.

Energy Expenditure And Body Composition In Mexican Female Recreational Dancers Of Latin, Zumba, And Twerk

Caloric surplus has been associated with issues in body composition and weight management. In Mexico, 36% of women over 18 years of age reported performing some type of physical activity (PA). This troubling data are related to the overweight/obesity prevalence among female Mexican adults. Dance like, Latin, Zumba, and Twerk appears as an attractive form of PA for women. However, the effect they may have on energy expenditure and body composition remains unknown. PURPOSE: To investigate energy expenditure and body composition in Mexican female recreational dancers of Latin, Zumba, and Twerk. METHOD: 77 women agreed to participate: Latin, 36, age 32.64 ± 13.16, BMI 24.41 ± 6.53, Zumba, 18, age 42.78 ± 16.55, BMI 26.63 ± 4.92, and Twerk, 23, age, 24.39 ± 5.38, BMI, 22.57 ± 1.45. Inclusion criteria included participation for more than 4 weeks and at least four times per week. Body fat percentage and fat-free mass were calculated bio impedance (BIA). Total Kcal spent during the session were measured with a pedometer. The BMI was calculated using weight and height. The analysis consisted of ANOVA. Results Based on BMI standards, all (but the Zumba participants) were classified as normal. Body fat percentage: Latin 22.62 ± 7.65, Zumba 27.68 ± 7.86 and Twerk 23.59 ± 4.53 (p = 0.043). Fat-free mass: Latin 23.62 ± 7.65, Zumba 23.23 ± 3.92, and Twerk 28.63 ± 9.58 (p = 0.031). Total Kcal spent: Latin 62.84 ± 15.47, Zumba 67.22 ± 16.91, and Twerk 32.18 ± 7.90 (p = 0.000). CONCLUSION: The overweight/obesity prevalence in Mexican women and its health implications have precipitated an increased awareness in the value of exercise prescription and adherence. These preliminary results show that Zumba generates greater energy expenditure. They also reveal that Zumba is more popular among older participants with higher BMI and fat percentage. Future studies should be longitudinal, investigate the effects of intensity of exercise and dietary habits on weight loss, and include participants of other weight classifications and dance fitness classes. Possible limitations include small sample size and unequal sample sizes.

Does Mindfulness Underpin The Mental Toughness - Self-compassion Relationship In Collegiate Athletes?

Self-compassion (SC) and mental toughness (MT) are two psychological constructs that protect athletes against the stressors of sports, despite their seemingly contradictory conceptualizations. In the first exploration of their compatibility towards athletic performance at the elite level, Wilson, Bennett, Mosewich, Faulkner, and Crocker (2019) concluded that the connection between SC and MT is underpinned by mindfulness. This relationship however has not yet been explored at other levels. National Association of Intercollegiate Athletics (NAIA) programs can be compared with Division II (DII) and Division III (DIII) National Collegiate Athletic Association (NCAA) programs given their similar financial, competitive, and enrollment philosophies. PURPOSE: To investigate if mindfulness underpins the MT - SC relationship in DII, DIII, and NAIA student-athletes. Hypothesis: MT and SC are compatible via mindfulness in all three collegiate environments. METHODS: Two inventories were administered via Qualtrics: the Mental Toughness Index and the Self-Compassion Scale, which includes a mindfulness subscale. The total sample was 396 student athletes: 313 DII or DIII; 86 NAIA. Statistical analyses consisted of zero-order correlations and regression analysis in SPSS. RESULTS: The estimated zero-order correlation between MT and SC was .46, but dropped to .31 after controlling for mindfulness. To further explore this relationship, the percentage of variability attributable to mindfulness was examined in a regression model. Mindfulness explained 32% of the variability beyond the 21% explained by MT for a total of 53%. CONCLUSIONS: This is the first study to explore the compatibility of MT and SC via mindfulness in the collegiate environment. Results suggest considerable overlap between MT and SC via mindfulness, supporting the hypothesis. Preliminary findings are in accordance with Wilson et al. (2019): mindfulness may be crucial to increasing and conserving both constructs in the sporting environment. Results may also support the notion that mindfulness be investigated as a possible component of MT, too. Suggestions for future research include larger-scale studies and triangulation through multi-rating. Possible limitations include convenience samples, unequal sample sizes, and self-reported data.

Growth from adversity in trans and gender diverse people of color

Background Trans-negativity and gender-based discrimination negatively impact on the wellbeing and mental health in transgender (trans) and gender diverse people (TGD). There is limited research on TGD people thriving under adversity, and no research to date has considered TGD people of color in this context. Method We used the Post-Traumatic Growth Inventory (PTGI-X) to survey 125 TGD people of color and 625 white TGD adults (18 to 68 years old, M = 26.0, SD = 9.2) about their experiences of growth from adversity. Confirmatory factor analysis (CFA), using sub-sampling to compensate for our unequal sample sizes, supported a five-factor structure of the PTGI-X consisting of growth in relating to others, finding new possibilities, personal strength, greater appreciation of life, and spiritual/existential change. Measurement invariance tests confirmed configural, metric, and scalar invariance of this structure across the two TGD subgroups. Results A MANOVA revealed that growth from adversity in TGD participants was generally greater than that reported by people who have recently been exposed to a traumatic event. T-tests revealed that TGD people of color experienced more growth in terms of relating to others and more personal strength than white TGD participants. Subsequent hierarchical regressions revealed that race moderated associations between PTGI-X scores and personal well-being, with TGD people of color reporting more benefits (more well-being) at high levels of growth but also more deficits (less well-being) at low levels of growth than the white TGD subgroup. Conclusion The results support the use of the PTGI-X with TGD populations and across racial TGD subgroups and indicate that growth from adversity is not only prevalent in TGD people but also relevant to positive outcomes, particularly in TGD people of color.

Prospective Mathematics Teachers’ Professional Noticing of Students’ Reasoning about Mean and Variability

This study examined prospective secondary mathematics teachers’ professional noticing of students’ reasoning about mean and variability as described in a current statistics curriculum in the USA. Six prospective mathematics teachers were asked to analyse students’ written solutions to statistics problems, constructed at the two levels described in the statistics curriculum. Findings indicated that prospective teachers had difficulties noticing students’ reasoning about variability. None of the prospective teachers explicitly interpreted the student’s limited understanding of variability when comparing data sets with unequal sample sizes. There was a gradation in their noticing skill, ranging from those who showed no evidence of differentiating between students’ different levels of reasoning and made general pedagogical decisions to those who differentiated between students’ developmental levels and decided how to respond based on students’ existing understanding as well as identifying the intrinsic statistical properties in students’ solutions. Implications for research and mathematics teacher education are discussed.

A Study on the X ¯ and S Control Charts with Unequal Sample Sizes

The control charts based on X ¯ and S are widely used to monitor the mean and variability of variables and can help quality engineers identify and investigate causes of the process variation. The usual requirement behind these control charts is that the sample sizes from the process are all equal, whereas this requirement may not be satisfied in practice due to missing observations, cost constraints, etc. To deal with this situation, several conventional methods were proposed. However, some methods based on weighted average approaches and an average sample size often result in degraded performance of the control charts because the adopted estimators are biased towards underestimating the true population parameters. These observations motivate us to investigate the existing methods with rigorous proofs and we provide a guideline to practitioners for the best selection to construct the X ¯ and S control charts when the sample sizes are not equal.

8 ROLE OF THE HOST IMMUNE RESPONSE TO ENTERIC PROKARYOTIC VIRUSES IN INFLAMMATORY BOWEL DISEASE

Abstract Background Gut microbiota comprise important environmental exposures that influence human immune systems and may alter the clinical course of inflammatory bowel disease (IBD). Little is known about the role of gut bacteriophages (viral components that infect prokaryotic bacteria) and their interactions with the host’s immune responses. We tested the hypotheses that (1) immune responses of individuals with IBD to phages differ from those without IBD and (2) immune responses to phages are associated with disease type (i.e. those with Crohn’s disease have different responses than those with ulcerative colitis). Methods We have constructed the first bacteriophage peptidome library (“phageome”), based on sequencing of environmental phages and large-scale metagenomic sequencing of virus-like particles isolated from stool samples from IBD patients and their non-IBD household contacts. Using Phage ImmunoPrecipitation Sequencing (PhIP-Seq) technology, we generated complete serum antibody binding profiles of 48 IBD patients (16 ulcerative colitis, 11 Crohn’s, and 11 indeterminate), 9 of their non-IBD household contacts, and an independent non-IBD cohort of 674 volunteers collected by the Vaccine Research Center (VRC) at the National Institutes of Health. Antibody binding profiles were compared among groups using nonparametric statistics. Results IBD patients as a group had lower antibody responses to specific phages compared to both non-IBD household contacts and the non-IBD VRC controls; this difference was significant and remained after control for unequal sample sizes [Figure 1]. Patients with Crohn’s disease compared to those with ulcerative colitis had similar antibody responses. Particularly for phages of the genera Phifelvirus, the immune responses of Crohn’s patients were significantly reduced compared to their non-IBD household contacts, while the immune responses of patients with ulcerative colitis did not significantly differ from non-IBD household contacts [Figure 2]. IBD disease type comparisons to the VRC controls yielded similar results. Conclusion PhIP-Seq with a phageome library can be used to study the relationship between immune responses and gut bacteriophages in IBD. Our results suggest that IBD patients may have lower antibody responses to specific phages compared to non-IBD individuals. Differential antibody reactivities in Crohn’s disease vs. ulcerative colitis compared to their household contacts and VRC controls suggest disease-specific response to the gut phageome that warrant further study.

A Robust Test for Checking the Homogeneity of Variability Measures and Its Application to the Analysis of Implicit Attitudes

A new two-sample test for comparing variability measures is proposed. To make the test robust and powerful, a new modified structural zero removal method is applied to the Brown–Forsythe transformation. The t-test-based statistic allows results to be expressed as the ratio of mean absolute deviations from median. Extensive simulation study demonstrates that the proposed test is robust to small or unequal sample sizes across many distributions. Moreover, careful exploratory analysis provides a new method for calculating the implicit association test scores for reaction time data with multiplicative treatment effects. Using this, a possible difference between variability of men and women’s implicit attitudes toward gay men is analyzed.

An international cross-cultural study of nursing students' perceptions of caring

BackgroundSingle studies suggest that nursing students perceive caring as more an instrumental than expressive behaviour and indicate some differences between caring perceptions in junior and senior nursing students. However, there are limited studies investigating caring perceptions in nursing students across multiple cultures. ObjectiveTo determine perceptions of caring in Slovene, Croatian, Chinese and Russian nursing students and explore whether there are statistically significant differences in perceptions of caring between countries and between first and third-year nursing students. DesignA cross-sectional descriptive study design was used. Settings and participantsThe study included 604 nursing students enrolled in first and third year in seven different nursing faculties in four countries: Slovenia; China; Croatia; and the Russian Federation. MethodsThe 25-item Caring Dimension Inventory (CDI-25) was used to measure caring perceptions. We also included demographic questions regarding age, gender, country, year of study and type of study. Demographic data were analysed using descriptive analysis while a two-way analysis of variance (ANOVA) adjusted for unequal sample sizes was performed together with a post hoc analysis of the results. ResultsThe results of two-way ANOVA showed that both main effects (country and year of study) were statistically significant, as well as their interaction at the 0.05 significance level. The main effect for country was F(3, 596) = 3.591, p < 0.0136 indicating a significant difference in CDI-25 between Slovenia (M = 108.9, SD = 9.2), Russian Federation (M = 107.1, SD = 8.2), China (M = 102.8, SD = 9.7) and Croatia (M = 110.0, SD = 8.6). ConclusionsPerceptions of caring in nursing students differ across countries, probably due to different educational systems, curricula, cultural differences and societal values. Implementing caring theories in nursing curricula could help students to cultivate caring during their education.

Computing the exact distribution of the Bartlett's test statistic by numerical inversion of its characteristic function

Application of the exact statistical inference frequently leads to non-standard probability distributions of the considered estimators or test statistics. The exact distributions of many estimators and test statistics can be specified by their characteristic functions, as is the case for the null distribution of the Bartlett's test statistic. However, analytical inversion of the characteristic function, if possible, frequently leads to complicated expressions for computing the distribution function and the corresponding quantiles. An efficient alternative is the well-known method based on numerical inversion of the characteristic functions, which is, however, ignored in popular statistical software packages. In this paper, we present the explicit characteristic function of the corrected Bartlett's test statistic together with the computationally fast and efficient implementation of the approach based on numerical inversion of this characteristic function, suggested for evaluating the exact null distribution used for testing homogeneity of variances in several normal populations, with possibly unequal sample sizes.