Unequal Sample Sizes Research Articles

Readers' Comprehension of New Text Formats. Part I. Empirical Evidence from Russian and Research Methodology Behind It

In this article, we review a range of Russian-language studies investigating readers’ interaction with new text formats. We identify the key problems preventing proper generalization of such research data. These include: (1) the absence of agreed terminology for describing texts of new formats shared by most researchers, and (2) the lack of consistency in theoretical approaches for describing cognitive mechanisms underpinning processing of these types of texts by readers. The following factors further complicate comparison and systematization of the data obtained by different research groups: (1) the lack of explicitly described theoretical bases of the hypotheses formulated by researchers, (2) the lack of consistency in describing the putative connections between such theoretical backgrounds and empirically tested hypotheses, (3) heterogeneity of methodological approaches, (4) insufficient, unequal or unbalanced sample sizes, (5) low reliability of statistical approaches and tools used for data analysis, as well as (6) research artefacts confounding the results.

Intentional learning establishes multiple attentional sets that simultaneously guide attention.

One of the key human cognitive capabilities is to extract regularities from the environment to guide behavior. An attentional set for a target feature can be established through statistical learning of probabilistic target associations; however, whether an array of attentional sets of predictive target features can be established during intentional learning, and how they might guide attention, is not known yet. To address these questions, we had human observers perform a visual search task where we instructed them to try to use color to find their target shape. We structured the task with a fine-grained statistical regularity such that the target shapes appeared in different colors with five unique probabilities (i.e., 33%, 26%, 19%, 12%, and 5%) while we recorded their electroencephalogram. Observers rapidly learned these regularities, evidenced by being faster to report targets that appeared in higher probability colors. These effects were not due to unequal sample sizes or simple feature priming. More importantly, equivalent speeding across a set of high-probability colors suggests that the brain was driving attention to multiple targets simultaneously. Our electrophysiological results showed larger amplitude N2 posterior contralateral component, indexing perceptual attention, and late positive complex (LPC) component, indexing postperceptual processes, for targets paired with high-probability colors. These electrophysiological data suggest that the learned attentional sets change both perceptual selection and how postperceptual decisions are made. In sum, we show that multiple attentional sets can be established during intentional learning that accompanies general task acquisition and that these attentional sets can simultaneously guide attention by enhancing both perceptual attention and postperceptual processes. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

General weighted extropy of minimum and maximum ranked set sampling with unequal samples

. In industrial, environmental, and ecological investigations, ranked set sampling is a sample method that enables the experimenter to use the whole range of population values. The ranked set sampling process can be modified in two extremely helpful ways: maximum ranked set sampling with unequal samples and minimum ranked set sampling with unequal samples. They permit an increase in set size without too many ranking errors being introduced. In this article, we are defining general weighted extropy (GWJ) of minimum and maximum ranked set samples when samples are of unequal size (minRSSU and maxRSSU, respectively). Stochastic comparison and monotone properties have been studied under different situations. Additionally, we compare the extropy of these two sampling data with that of ranked set sampling data and simple random sampling data. Bounds of GWJ of minRSSU and maxRSSU have been obtained. Finally, we investigate the weighted discrimination information between simple random sampling, ranked set sampling, and minimum and maximum ranked set sampling with unequal sample sizes. Some results for equality of GWJ of minRSSU and maxRSSU under symmetric assumption are also obtained.

A class of nonparametric tests for the two-sample problem based on order statistics

In this paper, a new class of distribution-free statistics based on order statistics from two independent samples is introduced to test the equality of two continuous distributions. The null distributions are obtained, and the symmetry property of the proposed test statistics is studied. The exact power functions of the new class of tests under the Lehmann alternative family are derived. Extensions of the proposed class of test statistics to situations with unequal sample sizes are discussed. We also study the power performance of the proposed test under the location-shift and scale-shift alternatives using Monte Carlo simulations. We observe that the power performance of the new class of test procedures is comparable to some commonly used nonparametric tests under various scenarios, which indicates that the new class of test procedures can be a good alternative to those classic nonparametric tests for the two-sample problem.

Diversity on the American Academy of Orthopaedic Surgeons National Meeting Podium: Changes Over Two Decades.

There has been an increase in diversity initiatives regarding selecting speakers for the American Academy of Orthopaedic Surgeons (AAOS) annual meeting and courses. The purpose of this study was to determine the percentage of female or underrepresented minority (URM) speakers for instructional course lectures (ICLs) and AAOS courses over the past 2 decades including a surrogate for expertise. For 2002, 2012, and 2022, the academic and demographic information of speakers and the number of publications at the time of their speaking role were obtained and compared by sex and URM status. Owing to the unequal sample sizes between male versus female cohorts and URM versus non-URM cohorts, the Welch t -test was used. The percentage of ICL and AAOS course speakers who were female increased over time (ICL, AAOS courses): 2002 (2.6%, 3.3%), 2012 (3.9%, 6.3%), and 2022 (11.8%, 15.5%) ( P < 0.001, P < 0.001). The percentage of female AAOS fellows in these years was 2.9%, 4.7%, and 7.4%, respectively. For ICLs and AAOS course speakers, female presenters had fewer publications than male counterparts (ICL, AAOS courses): 2002 ( P < 0.001, P = 0.048), 2012 ( P = 0.003, P < 0.001), and 2022 ( P < 0.001, P < 0.001). For ICLs in 2022, URM speakers had a similar number of publications compared with non-URM speakers. In 2022, URMs comprised 6.9% of ICL speakers and 4% of AAOS fellows. For 2022 ICLs, there were no significant differences in academic institution, position, or region when compared by sex or URM status. For AAOS courses, the percentage of URM speakers increased over time: 2002 (1.1%), 2012 (4.5%), and 2022 (8.6%). For AAOS courses, URM presenters had similar publications compared with non-URM presenters in 2002 and 2022 but less in 2012 ( P = 0.027). The percentage of women and URMs presenting ICLs and AAOS courses has increased over the past 2 decades and exceeded the percentage they represent in the AAOS by over 50%. The female cohort has fewer publications, on average, than the male cohort for all years evaluated, indicating no institutional bias against female speakers.

Family Relationship and Attitude towards Children with Disability among Households with Children living with Disability in Southeast Nigeria: Implication to Sustainable Development

Disability has come to stay with humanity and now placing demand on our technological, scientific, spirituality and humanitarian management prowess and capability in adapting and managing it as global community. However, there are different levels and contexts at which people living with disability are highlighted and practically require our cooperation and assistance, which included family setting. In sub-Saharan Africa and other developing nations, families with children living with disability have found it a difficult task to meet the needs of these ones especially the children. This study investigated the relationship challenges faced by children living with disability among their siblings in southeast Nigeria among households with children living with disability. The study applied cross-sectional survey design; one hundred and eighteen (118) adolescent participants that have at least one sibling with any form of physical disability took part in the study, while attitude towards disabled sibling scale developed by the researchers using some adaptations from the Attitude Scale of Parents towards their mentally retarded children (Govender, 2002). A 2 x 3 x 2 Analysis of Variance (Three-way ANOVA) technique from unequal sample size was used to analyze the data. According to the major findings, there is significant interaction of birth order and Parental level of Education (PLoE) on attitude of siblings towards their physically disabled brother/sister, F(1,108)=7.568, p

The safety effect of increased pedestrian protection, autonomous emergency braking for pedestrians and bicyclists on passenger cars, and speed management

This was the first retrospective study to estimate the effect of increased pedestrian protection, autonomous emergency braking, and speed management to reduce serious injuries among pedestrians and bicyclists. More specifically, the aim was to estimate the injury mitigating effects of the following interventions: AEB with pedestrian and bicyclist detection, Euro NCAP pedestrian test score, active bonnet, traffic calming at pedestrian and bicycle crossings, and additionally, the combined effect of the above-mentioned treatments. The main source of data was the Swedish traffic data acquisition system (Strada), where information of road traffic crashes between passenger cars and pedestrians or bicyclists for the period 1 January 2003–31 December 2022 was obtained. Cars with optional fitment of AEB systems were identified, and the license registration number was used to access individual car equipment lists to identify whether the vehicle was equipped with AEB with pedestrian and/or cyclist detection. Information about traffic calming at pedestrian and bicycle crossings was obtained from the Swedish Transport Administration. The injury metric used was risk of permanent medical impairment (RPMI) of at least one percent and ten percent. RPMI captures the risk of long-term medical impairment based on a diagnosed injury location and Abbreviated Injury Severity (AIS) score. The relative difference between the mean values of RPMI (mRPMI1%+ and mRPMI10%+) was calculated and tested using an independent two sample t-test which was conducted for unequal sample sizes and variance. Although many results were found to be statistically non-significant, the following results were found to be significant at least at 90% level. Pedestrian mRPMI10%+ was reduced by 44% in speed zones ≤ 50 km/h comparing the group struck by cars equipped with AEB with pedestrian detection compared to the group struck by cars without the system. For cyclists, the mRPMI10%+ was reduced by 35% in speed zones ≤ 50 km/h. For crashes within ± 20 meters from a pedestrian or bicycle crossing, the AEB system reduced 60% of pedestrians mRPMI10%+ at crossings with good safety standard compared to crossings of poor safety standard. The comparison of cars with poor performance (1–9 points) in the NCAP pedestrian test and cars with a high score (28–36 points) showed that pedestrian mRPMI10%+ was reduced by 48% across all speed limits, and by 64% including only those aged ≤ 64 years. For bicyclists, a significant reduction of cyclist mRPMI10%+ was found comparing low scoring cars to high scoring cars in ≤ 30 km/h speed limit (-73%) and across all speed limits (-36%). Including only those aged ≤ 64 years, the reduction was 49%. For the active bonnet, a significant reduction of mRPMI1%+ by 24% was observed but given that the rate of helmet wearing was higher in the group struck by cars with active bonnet, this difference cannot be attributed to an effect of an active bonnet. The STA safety rating of pedestrian and bicycle crossings showed that overall pedestrian mRPMI1%+ was reduced by 15%, while cyclists mRPMI10%+ was reduced by 32% comparing crossings of high safety level to crossings of poor safety level. The analysis of combined interventions showed that the total reduction of pedestrians and cyclists mRPMI10%+ together was 69%, from 6.4% to 2%. This paper demonstrates that a road environment with adapted infrastructure and speed, combined with passenger car technologies that improve the safety for vulnerable road users, can create significant reductions of serious (long-term) injuries among pedestrians and bicyclists.

Evaluation of 278 New Bluephase Style Light Curing Units Purchased Over Six Years.

This study measured 278 new curing lights (LCUs) to determine if they met the manufacturer's specifications. Over a 6-year period, the light output from 278 Bluephase Style LCUs was measured before the LCUs were given to students (41 in 2017, 44 in 2018, 46 in 2019, 48 in 2020, 50 in 2021, and 49 in 2022). The radiant exitance (mW/cm²) from each year was compared using ANOVA and Tukey- Kramer multiple comparisons test with adjustment for the unequal sample sizes (α=0.05). The results were also compared against the manufacturer's stated radiant exitance of 1200 mW/cm². The 278 LCUs delivered an average (± standard deviation) radiant exitance of 1203 ± 16.7 mW/cm². The lowest radiant exitance was 1149 mW/cm² and the highest was 1257 mW/cm². Although there were statistically significant differences in the LCUs from each year, these values were within the manufacturer's tolerance of values of ± 10%. Approximately 13% of the emitted light was below 420 nm, and 87% was above 420 nm. These new LCUs were all multiple peak LCUs that emitted an average radiant exitance of 1,203 mW/cm² (range 1149 to 1257 mW/cm². Purchasers of the Style LCU can be confident that their new LCU will meet the manufacturer's specifications.

An Evaluation of Racial and Ethnic Representation in Research Conducted with Young Adults Diagnosed with Cancer: Challenges and Considerations for Building More Equitable and Inclusive Research Practices.

The psychosocial outcomes of adolescents and young adults (AYAs) diagnosed with cancer are poorer compared to their peers without cancer. However, AYAs with cancer from diverse racial and ethnic groups have been under-represented in research, which contributes to an incomplete understanding of the psychosocial outcomes of all AYAs with cancer. This paper evaluated the racial and ethnic representation in research on AYAs diagnosed with cancer using observational, cross-sectional data from the large Young Adults with Cancer in Their Prime (YACPRIME) study. The purpose was to better understand the psychosocial outcomes for those from diverse racial and ethnic groups. A total of 622 participants with a mean age of 34.15 years completed an online survey, including measures of post-traumatic growth, quality of life, psychological distress, and social support. Of this sample, 2% (n = 13) of the participants self-identified as Indigenous, 3% (n = 21) as Asian, 3% (n = 20) as "other," 4% (n = 25) as multi-racial, and 87% (n = 543) as White. A one-way ANOVA indicated a statistically significant difference between racial and ethnic groups in relation to spiritual change, a subscale of post-traumatic growth, F(4,548) = 6.02, p < 0.001. Post hoc analyses showed that those under the "other" category endorsed greater levels of spiritual change than those who identified as multi-racial (p < 0.001, 95% CI = [2.49,7.09]) and those who identified as White (p < 0.001, 95% CI = [1.60,5.04]). Similarly, participants that identified as Indigenous endorsed greater levels of spiritual change than those that identified as White (p = 0.03, 95% CI = [1.16,4.08]) and those that identified as multi-racial (p = 0.005, 95% CI = [1.10,6.07]). We provided an extensive discussion on the challenges and limitations of interpreting these findings, given the unequal and small sample sizes across groups. We concluded by outlining key recommendations for researchers to move towards greater equity, inclusivity, and culturally responsiveness in future work.

Towards improving online learning in physical education: Gender differences and determinants of motivation, psychological needs satisfaction, and academic achievement in Saudi students.

Studies on students' perceptions and expectations during physical education (PE) online learning remain scarce. Centered on self-determination theory, the present cross-sectional study aims to identify gender differences and predictors affecting motivation, psychological needs satisfaction (PNS), and academic achievement during PE online learning. Data were collected from Saudi students' (N = 308, 161 females and 147 males) responses to the PE autonomy, relatedness, competence, and motivation questionnaires. Welch's t-test for unequal sample sizes, multiple linear regression, and binary logistic regression were used to compare means and to predict the relationships between the independent and dependent variables. The results showed higher autonomy and competence perceptions in female than in male students, but no differences were observed in relatedness. Female students presented higher intrinsic motivations, lower amotivation perceptions than males. However, no gender differences were recorded in extrinsic motivation. Students with less experience in online learning and weak grade point averages (GPAs) are more susceptible to having a high level of amotivation. Gender, GPA, and prior experience with online learning are the common predictors for all PNS and amotivation, while GPA and prior experience with online learning are the determinants of intrinsic motivation. GPA is affected by prior experience with online learning, autonomy, competence, intrinsic motivation, and amotivation. Therefore, teachers are encouraged to adapt their didactic-pedagogical behaviors during PE online learning according to students' motivation and autonomy perceptions. Structuring teaching activities with more individualized support for autonomy, competence, intrinsic motivation, and students' online skills/competencies ensures better learning efficiency and academic achievements.

Mixed Bootstrap-Marascuilo test for testing equality of means under unequal variances in a completely randomized design

This study introduces a pioneering statistical methodology, the Mixed Bootstrap-Marascuilo test, which emerges from the fusion of the Bootstrap method and the Marascuilo test. The test examines the means of three or more populations with unequal variances in a completely randomized design. The research compares the Mixed Bootstrap-Marascuilo test's ability to control the probability of type I error using Cochran's criteria and its test power using penalized power with those of One-Way ANOVA and the Marascuilo test. The research design thoughtfully encompasses three populations: small, medium, and large, each exhibiting variations in size and equality. It systematically manipulates variances, encompassing a range from equal to slightly different, moderately different, and significantly different. Furthermore, the error distribution is specified to be normal with a designated mean. The research methodology embraces the utilization of R ver.4.2.2 and the Monte Carlo technique, leveraging 5,000 simulations per case to ensure the robustness and reliability of the study's findings. The outcomes of the comprehensive analysis yield intriguing insights. The results indicate that the Mixed Bootstrap-Marascuilo test exhibits superior testing ability in scenarios involving equal small sample sizes with equal and moderate variances, as well as medium sample sizes with equal and small variances. Furthermore, it demonstrates effectiveness even when dealing with large, unequal sample sizes with equal and large variances. In essence, this research advances the realm of statistical hypothesis testing through the introduction and meticulous evaluation of the Mixed Bootstrap-Marascuilo test. Its demonstrated ability to navigate complexities in mean examination across diverse populations, coupled with its versatile applicability to scenarios of unequal variances and varying sample sizes, underscores its potential as a valuable tool for researchers across disciplines.

Somatic mutation effects diffused over microRNA dysregulation.

As an important player in transcriptome regulation, microRNAs may effectively diffuse somatic mutation impacts to broad cellular processes and ultimately manifest disease and dictate prognosis. Previous studies that tried to correlate mutation with gene expression dysregulation neglected to adjust for the disparate multitudes of false positives associated with unequal sample sizes and uneven class balancing scenarios. To properly address this issue, we developed a statistical framework to rigorously assess the extent of mutation impact on microRNAs in relation to a permutation-based null distribution of a matching sample structure. Carrying out the framework in a pan-cancer study, we ascertained 9008 protein-coding genes with statistically significant mutation impacts on miRNAs. Of these, the collective miRNA expression for 83 genes showed significant prognostic power in nine cancer types. For example, in lower-grade glioma, 10 genes' mutations broadly impacted miRNAs, all of which showed prognostic value with the corresponding miRNA expression. Our framework was further validated with functional analysis and augmented with rich features including the ability to analyze miRNA isoforms; aggregative prognostic analysis; advanced annotations such as mutation type, regulator alteration, somatic motif, and disease association; and instructive visualization such as mutation OncoPrint, Ideogram, and interactive mRNA-miRNA network. The data underlying this article are available in MutMix, at http://innovebioinfo.com/Database/TmiEx/MutMix.php.

Development of robust X‐bar charts with unequal sample sizes

AbstractThe traditional variable control charts, such as the chart, are widely used to monitor variation in a process. They have been shown to perform well for monitoring processes under the general assumptions that the observations are normally distributed without data contamination and that the sample sizes from the process are all equal. However, these two assumptions may not be met and satisfied in many practical applications and thus make them potentially limited for widespread application especially in production processes. In this paper, we alleviate this limitation by providing a novel method for constructing the robust control charts, which can simultaneously deal with both data contamination and unequal sample sizes. The proposed method for the process parameters is optimal in a sense of the best linear unbiased estimation. Numerical results from extensive Monte Carlo simulations and a real data analysis reveal that traditional control charts seriously underperform for monitoring process in the presence of data contamination and are extremely sensitive to even a single contaminated value, while the proposed robust control charts outperform in a manner that is comparable with the traditional ones, whereas they are far superior when the data are contaminated by outliers.

P-151 In women with recurrent implantation failures, can hyaluronan enriched media optimize reproductive outcomes?

Abstract Study question To evaluate the efficacy of Hyaluronan Enriched Media (HEM) to optimize Reproductive Outcomes in women with Recurrent Implantation Failures (RIF)? Summary answer In women with RIF, HEM seems to offer beneficial and safer reproductive outcomes. What is known already HEM has shown to enhance the implantation process of an embryo in-utero. Efficacy of HEM to optimize reproductive outcomes is still not proven. Study design, size, duration This retrospective study comprises data of 430 women with two failed IVF cycles or had RIF undergoing infertility treatment between 2016 to 2021. Study group included Young women (&amp;lt;37yrs) with RIF who opted elective-single blastocyst transfer (eSET) with HEM (n = 228). Control group had young women with RIF and eSET without use HEM (n = 202). Only self-gamete cycles with No PGT-A screening were included in this study. Women with known uterine pathologies were excluded from the study. Participants/materials, setting, methods All women had ICSI - freeze all culture strategy. In a FET, blastocyst showing 100% survival post warming was considered transfer. In study group, embryos were incubated in pre-equilibrated HEM for 10minutes before the intended embryo transfer. In control group embryo was transferred in single step media. ET procedure done as per the clinic’s SOP. Outcomes measured: Clinical Pregnancy Rates (CPR), Implantation rates (IR), Miscarriage Rates(MR), Live Birth rates(LBR) and Neonatal outcomes. Main results and the role of chance Following were the outcomes measured in HEM group Vs Control group: CPR- 66.22% Vs 61.38% (p = 0.2938) IR – 49.56% Vs 31.68% (p = 0.0002; Significant) MR – 11.4% Vs 16.33% (p = 0.1359) LBR – 54.82% Vs 45.05% (p = 0.0418; Significant) There was no significant adverse events with neonatal outcomes between the groups and data looked comparable. Use of HEM at embryo transfer for women with RIF seemed to be a beneficial intervention. It showed significant improvement with embryo implantation and live birth. Data in this study has also looked at Neonatal outcomes. Since HEM group had no reported adverse neonatal outcomes, it not only aids in improving reproductive outcomes but also is a safe intervention and can be considered for routine clinical use for indicated cases. Limitations, reasons for caution Retrospective data with small and unequal sample size. Wider implications of the findings Efficacy of various therapies is still unknown for women who had RIF. PGT-A and ERA (invasive therapies) have been tried for such cases, but its effectiveness is still up in question. Development for newer &amp; safer therapies to improve embryo implantation and live birth for these patients is still awaited. Trial registration number Not applicable

Posturography measures in specific ballet stance position discriminate ballet dancers with different occurrences of musculoskeletal injuries

BackgroundThis study aimed to identify the postural sway variables that can distinguish between ballet dancers with high and low occurrences of musculoskeletal injuries. MethodsFourteen professional ballet dancers were assigned to a high-occurrence group (N = 5, reports >2 injuries in the previous 6-months) or a low-occurrence group (N = 9, reports ≤1 injury). Center-of-pressure (COP) data were acquired using a force platform during the following tasks: single-leg stance with eyes open, single-leg stance with eyes closed, and demi-pointe stance with eyes open. The COP standard deviation (SD) and range (RA) in both the medial-lateral (ML) and anterior-posterior (AP) directions were estimated. Between-group comparisons were made through Welch's t-tests for unequal sample size along the effect size measure (Cohen's d). Spearman's rho was used to estimate the association between the number of injuries and the COP variables. The statistical threshold was set at 1%. ResultsA between-group effect was found only for the demi-pointe stance, with large effects for SDML (P = 0.006, d = 1.7), RAAP (P = 0.006, d = 1.7), and RAML (P = 0.005, d = 1.7). An inverse relationship was found between the number of injuries and the demi-pointe's COP range in both directions (Spearman's rho from −0.681 to −0.726, P = 0.007). ConclusionsCOP measures taken in ballet-specific positions can distinguish between dancers with a high and low occurrence of musculoskeletal injuries. Suggestions are made to include ballet-specific tasks in the functional assessments of professional dancers.

Differentiated processing of emotional cues in adolescents and young adults with ICD-11 PTSD and complex PTSD after child abuse.

The recent update of the International Classification of Diseases 11th revision (ICD-11) introduced the diagnosis of complex posttraumatic stress disorder (CPTSD) as a distinct entity from posttraumatic stress disorder (PTSD). Because psychophysiological alterations are a core diagnostic feature of PTSD and CPTSD, the aim of the current study was to examine potential distinctive patterns in cortical and cardiac responses to emotional words in adolescent and young adult patients with PTSD and CPTSD. Event-related potentials and heart rate responses were studied in 81 adolescent and young adult participants, of which 17 individuals were diagnosed with ICD-11 PTSD and 32 individuals with CPTSD, each after childhood sexual and/or physical abuse. Thirty-two individuals served as healthy controls. The paradigm consisted of a passive reading task with neutral, positive, physically threatening, and socially threatening words. Differentiated early processing of emotional words was indicated by differences on P1 and left EPN components. Additionally, PTSD and CPTSD patients presented with specific patterns of heart rate responses to emotional words. In CPTSD patients, heart rate reactions to emotional words were more variable than in PTSD patients. These findings provide early evidence of differentiated cortical and cardiac response patterns in adolescent and young adult patients with CPTSD and PTSD, supporting a nosological distinction between PTSD and complex PTSD. However, due to small and unequal sample sizes, findings presented in the current study are preliminary and require future research.

An improved statistical approach to compare means

&lt;abstract&gt;&lt;p&gt;In many experiments, our interest lies in testing the significance of means from the grand mean of the study variable. Sometimes, an additional linearly related uncontrollable factor is also observed along with the main study variable, known as a covariate. For example, in Electrical Discharge Machining (EDM) problem, the effect of pulse current on the surface roughness (study variable) is affected by the machining time (covariate). Hence, covariate plays a vital role in testing means, and if ignored, it may lead to false decisions. Therefore, we have proposed a covariate-based approach to analyze the means in this study. This new approach capitalizes on the covariate effect to refine the traditional structure and rectify misleading decisions, especially when covariates are present. Moreover, we have investigated the impact of assumptions on the new approach, including normality, linearity, and homogeneity, by considering equal or unequal sample sizes. This study uses percentage type Ⅰ error and power as our performance indicators. The findings reveal that our proposal outperforms the traditional one and is more useful in reaching correct decisions. Finally, for practical considerations, we have covered two real applications based on experimental data related to the engineering and health sectors and illustrated the implementation of the study proposal.&lt;/p&gt;&lt;/abstract&gt;

Comparison of profile-likelihood-based confidence intervals with other rank-based methods for the two-sample problem in ordered categorical data

ABSTRACT For ordered categorical data from randomized clinical trials, the relative effect, the probability that observations in one group tend to be larger, has been considered appropriate for a measure of an effect size. Although the Wilcoxon–Mann–Whitney test is widely used to compare two groups, the null hypothesis is not just the relative effect of 50%, but the identical distribution between groups. The null hypothesis of the Brunner–Munzel test, another rank-based method used for arbitrary types of data, is just the relative effect of 50%. In this study, we compared actual type I error rates (or 1 – coverage probability) of the profile-likelihood-based confidence intervals for the relative effect and other rank-based methods in simulation studies at the relative effect of 50%. The profile-likelihood method, as with the Brunner– Munzel test, does not require any assumptions on distributions. Actual type I error rates of the profile-likelihood method and the Brunner–Munzel test were close to the nominal level in large or medium samples, even under unequal distributions. Those of the Wilcoxon–Mann–Whitney test largely differed from the nominal level under unequal distributions, especially under unequal sample sizes. In small samples, the actual type I error rates of Brunner–Munzel test were slightly larger than the nominal level and those of the profile-likelihood method were even larger. We provide a paradoxical numerical example: only the Wilcoxon–Mann–Whitney test was significant under equal sample sizes, but by changing only the allocation ratio, it was not significant but the profile-likelihood method and the Brunner–Munzel test were significant. This phenomenon might reflect the nature of the Wilcoxon–Mann–Whitney test in the simulation study, that is, the actual type I error rates become over and under the nominal level depending on the allocation ratio.

A nonparametric test for the two-sample problem based on order statistics

We study a nonparametric test procedure based on order statistics for testing the null hypothesis of equality of two continuous distributions. The exact null distribution of the proposed test statistic is obtained using an enumeration method and a novel combinatorial argument. A recurrence relation for the probability generating function and a sequential approach for computing the mean and variance of the distribution are given. Critical values and characteristics of the distribution for selected small sample sizes are presented. For the Lehmann alternative family, the exact power function of the new test is derived, and its power performance is examined. We also study the power performance of the proposed test under the location-shift and scale-shift alternatives using Monte Carlo simulations and observe its superior performance when compared to commonly used nonparametric tests under various scenarios. A generalization of the proposed procedure for unequal sample sizes is discussed. An illustrative example and some concluding remarks are provided.

Statistical Comparison of the Performance of Alternative Contracting Methods in Florida

This study empirically examines the performance of alternative contracting methods using data from 2,721 highway projects gathered from a Florida Department of Transportation database. Contracting methods can significantly influence the cost and time of highway projects, so it is essential to use appropriate contracting methods in highway projects, especially considering the huge current volume of work and great need for more lane miles and new bridges. The most widely used alternative contracting methods in horizontal construction include Design–Build Major, Design–Build Minor, Cost Plus Time, Incentive/Disincentive, Lump Sum, and No Excuse Bonus. These have been devised to overcome shortcomings of the conventional Design–Bid–Build (DBB) method; however, their actual performance in practice has not previously been rigorously studied. To fill this gap, we statistically analyze our sample of highway projects using the Shapiro–Wilk test, Levene’s test, Kruskal–Wallis test, Wilcoxon–Mann–Whitney test, and Dunn’s test for unequal sample sizes. Another unique contribution of this research is the analytical techniques employed, which led to more reliable results based on the large quantity of data gathered. We find that some contracting methods performed better than others in each cost category for cost and time, and based on average cost and time savings, but not all were confirmed statistically. All seven contracting methods performed better in achieving time reductions than cost reductions, and all methods were more effective in reducing the cost and time of projects worth less $20 million than those worth over $20 million.