Normality Assumption Research Articles

Supplemental Material for Normality Assumption in Latent Interaction Models

Supplemental Material for Normality Assumption in Latent Interaction Models

A redescending M-estimator approach for outlier-resilient modeling

The OLS model is built on the assumption of normality in the distribution of error terms. However, this assumption can be easily violated, especially when there are outliers in the data. A single outlier can disrupt the normality assumption of error terms, making the OLS model less effective. In such situations, M-estimators (MEs) come into play to obtain reliable estimates. We introduce a redescending M-estimators (RME) for robust regression to handle datasets with outliers. The proposed RME produces more robust estimates by effectively managing the influence of outliers, even at lower values of the tuning constant. We compared the performance of this estimator with existing RMEs using real-life data examples and an extensive simulation study. The results show that our suggested RME is more efficient than the compared ME in various situations.

Application of Six Sigma methodology in the analysis of variance: process shift versus inflation coefficient

Purpose The purpose of this article is to study the link between mean shift and inflation coefficient when the underlying null hypothesis is rejected in the analysis of variance (ANOVA) application after the preliminary test on the model specification.Design/methodology/approach A new approach is proposed to study the link between mean shift and inflation coefficient when the underlying null hypothesis is rejected in the ANOVA application. First, we determine this relationship from the general perspective of Six Sigma methodology under the normality assumption. Then, the approach is extended to a balanced two-stage nested design with a random effects model in which a preliminary test is used to fix the main test statistic.Findings The features of mean-shifted and inflated (but centred) processes with the same specification limits from the perspective of Six Sigma are studied. The shift and inflation coefficients are derived for the two-stage balanced ANOVA model. We obtained good predictions for the process shift, given the inflation coefficient, which has been demonstrated using numerical results and applied to case studies. It is understood that the proposed method may be used as a tool to obtain an efficient variance estimator under mean shift.Research limitations/implications In this work, as a new research approach, we studied the link between mean shift and inflation coefficients when the underlying null hypothesis is rejected in the ANOVA. Derivations for these coefficients are presented. The results when the null hypothesis is accepted are also studied. This needs the help of preliminary tests to decide on the model assumptions, and hence the researchers are expected to be familiar with the application of preliminary tests.Practical implications After studying the proposed approach with extensive numerical results, we have provided two practical examples that demonstrate the significance of the approach for real-time practitioners. The practitioners are expected to take additional care before deciding on the model assumptions by applying preliminary tests.Originality/value The proposed approach is original in the sense that there have been no similar approaches existing in the literature that combine Six Sigma and preliminary tests in ANOVA applications.

Abstract 2140: Untargeted lipidomics reveals racial differences in lipid species among women

Abstract Introduction: Lipids are important for many cellular processes and have been implicated in cancer development. Adopting a lipidomic approach has revealed sex-specific differences in lipid species but whether there are racial differences in lipid profiles remain unexplored. As a result, we investigated differences in lipid species between Non-Hispanic Black (NHB) vs Non-Hispanic White (NHW) women. Methods: We performed lipidomic profiling on 705 premenopausal women who were recruited during their annual screening mammogram at Washington University School of Medicine, St. Louis, MO. A total of 982 lipid species were profiled at Metabolon (Durham, NC®). 125 lipid species missing in 300 or more women were excluded from the analysis. For the remaining missing values, we employed the nearest neighbor method for imputation. We investigated the race-differentiating lipid species concentrations using linear regression models, adjusting for age and body mass index (BMI). To satisfy the assumptions of normality and homoscedasticity, we log-transformed the lipid concentrations before performing regression analyses. The linear regression coefficients were then back-transformed as percentage differences. We accounted for multiple testings by applying the Bonferroni correction. Statistical significance was defined as a Bonferroni-adjusted p-value < 10−5. Pathway enrichment analyses was conducted for differential lipid species for each sub pathway. Results: Of the 705 women, 506 were NHW and 163 were NHB. In analysis adjusted for age and BMI, 278 lipid species were significantly lower in NHB, and one lipid specie (TAG58:10-FA20:4) was higher in NHB. These species belonged to triacylglycerols (TAG, n=213), phosphatidylcholines (PC, n=25), diacylglycerols (DAG, n=22), cholesteryl esters (CE, n=4), phosphatidylethanolamines (PE, n=4), lysophosphatidylcholines (LPC, n=3), lysophosphatidylethanolamines (LPE, n=3), sphingomyelins (SM, n=2), ceramides (CER, n=1), lactosylceramides (LCER, n=1) and phosphatidylinositols (PI, n=1) sub-pathways. The TAG sub-pathway was enriched with differential lipid species (213 significant out of 518 species, p = 1.26 × 10−11). Forty-three lipid species (42 TAGs and one DAG) exhibited an absolute percentage difference > 50% between NHB and NHW women. The top 3 TAG species with the largest absolute percentage differences were TAG44:0-FA14:0 (60.6% lower in NHB women, p = 6.25 × 10−8), TAG46:2-FA16:1 (59.8% lower in NHB women, p = 1.11 × 10−14) and TAG47:2-FA16:1 (59.4% lower in NHB women, p = 8.66 × 10−20). Conversely, TAG58:10-FA20:4 was 47.1% (p = 5.79 × 10−8) higher in NHB women. Conclusions: Our study reveals novel substantial racial differences in lipid species among women, mostly in the TAG sub-pathway, highlighting the influence of race on the lipidome. Validation in a different study population is needed. Citation Format: ang Li, Ghazaleh Pourali, Kayla R. Getz, Myung Sik Jeon, Jingqin Luo, Chongliang Luo, Adetunji T. Toriola. Untargeted lipidomics reveals racial differences in lipid species among women [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2024; Part 1 (Regular Abstracts); 2024 Apr 5-10; San Diego, CA. Philadelphia (PA): AACR; Cancer Res 2024;84(6_Suppl):Abstract nr 2140.

Mixed Traffic Behaviour in Heavy Flow: Two-Lane Road Insights

The current paper outlines a comprehensive methodology for modeling speed data on two-lane roads during periods of heavy traffic characterized by heterogeneous vehicle types. In such scenarios, the presence of diverse vehicle types causes a significant departure from the normal speed distribution model. This deviation becomes particularly pronounced during heavy traffic flows due to the frequent interactions among vehicles within the traffic stream. Consequently, there arises a necessity to develop a modeling approach specifically tailored to such flow conditions. Drawing upon empirical data collected from a major intercity road in India, this study uncovers a notable skewness in speed data under heavy traffic conditions. This skewness primarily stems from the formation of vehicle platoons within the traffic stream, exerting a substantial influence on their speed characteristics. By scrutinizing the distribution of this data, the study concludes that a logarithmic transformation effectively aligns with the assumption of normality. This assertion is supported by various goodness-of-fit metrics, affirming the suitability of the proposed modeling approach for capturing the intricacies of speed behavior in heterogeneous traffic environments.

Rivalry of celebrity and influencer endorsement for advertising effectiveness

<p>Using the theoretical framework of the elaboration likelihood model, this study attempts to analyze the level of difference in effectiveness between celebrity and influencer endorsement in social media advertising to influence consumer purchase intention. This study highlights the phenomenon of Pantene Indonesia's social media advertising, which is endorsed by Maudy Ayunda as a celebrity endorsement and Keanu Angelo as an influencer endorsement, by comparing these two categories of endorsers. This study uses a positivist paradigm, a quantitative approach, and a survey to collect data. Questionnaires were distributed online to 400 respondents for a month in December 2023. The study used a non-parametric test because the data did not meet the normality assumption. Comparative hypotheses were tested using the Wilcoxon Signed Rank Test with the assistance of SPSS 25. The study results indicate a significant difference between the use of influencer and celebrity endorsements in social media advertising to drive consumer purchase intention. This is demonstrated through the significance values of all variables: the quality of arguments (X1), source credibility (X2), attractiveness (X3), and purchase intention (Y), which are less than 0.005. Furthermore, the study reveals that celebrity endorsements have a higher effectiveness level than influencer endorsements. The comparative mean scores for all variables show that the average for celebrity endorsement is 37.85 compared to influencer endorsement at 36.29, which is proof of this. Through the most important route of the elaboration likelihood model that is, the quality of the endorser's arguments—consumers evaluate social media advertising messages, resulting in more persistent increases in attitudes such purchase intention.</p>

ANALYSIS FOR MULTIPLE RESPONSES IN A COMPLETELY RANDOMIZED EXPERIMENTAL DESIGN

Multiple responses are often generated in agricultural and forestry research. For example, the moisture content, fatty acids, carbohydrates, size, diameter, length, shape and hardness, among other characteristics are measured to cottonseed. Of course, multiple responses are observed in many other areas of research. Multivariate analysis of variance (MANOVA) can be useful for multiple response analysis when differences in treatment effects are to be determined. However, the performance of current post hoc tests in this context is not satisfactory due to the limitations of the available methods, or because they are difficult to use for non-statistician researchers. Furthermore, this methodology requires the assumptions of multivariate normality and homogeneity of variance and covariance matrices, assumptions that are difficult to verify if the sample size is small. This research proposes an alternative analysis to test the hypothesis of equality of effects between treatments and post hoc tests in the case of multiple responses. An asymptotic result is demonstrated for the random variable generated in the proposal for the case of uncorrelated normal variables and the case for correlated normal random variables is left open. A simulation study shows that the performance of the proposal with small samples is satisfactory in terms of power and that it has advantages compared to MANOVA. Furthermore, the methodological approach allows for post hoc testing in the case of multiple responses in the completely randomized experimental design.

Influence of Grazing on the Gestation Phase of Sows and the Birth of the Piglet

The present investigation was carried out in the “Rancho Rubén” pig farm, located in the Panecillo site of the Casacay Parish of the Pasaje Canton, Province of El Oro, Coastal Region of Ecuador. The aim of this work was to determine the possible benefits of grazing in pregnant breeders and newborn piglets. For the field experiment, the regulations of the Guide to Good Swine Practices (Agrocalidad-Ecuador) were taken into account. The variables evaluated were: initial weight of the sow, prepartum sow’s weight, postpartum sow’s weight, weight of the sow at weaning, number of piglets at birth, weight of the piglet at birth, mortality on the first day and feed consumption during gestation. A completely randomized design was used, with 2 treatments, each with a replica of 5 females, for a total of 20 animals; treatment 1 (balanced feeding and management in individual pens); and treatment 2 (feeding with balanced, and grazing). The statistical analysis was based on the book by Blasco [1], applying an ANOVA, prior to assumptions of normality and homogeneity, establishing the differences through the Bonferroni multiple comparison procedure (95% confidence). The statistical program used was Statgraphics Centurión XVI. The results show that there is no difference between the treatments with respect to the variables evaluated, except for the consumption of concentrate feed, which is observed to be reduced in grazing animals, assuming that the grazing system is beneficial by facilitating a more natural behavior and greater animal welfare.

Mixtures of regressions using matrix-variate heavy-tailed distributions

AbstractFinite mixtures of regressions (FMRs) are powerful clustering devices used in many regression-type analyses. Unfortunately, real data often present atypical observations that make the commonly adopted normality assumption of the mixture components inadequate. Thus, to robustify the FMR approach in a matrix-variate framework, we introduce ten FMRs based on the matrix-variate t and contaminated normal distributions. Furthermore, once one of our models is estimated and the observations are assigned to the groups, different procedures can be used for the detection of the atypical points in the data. An ECM algorithm is outlined for maximum likelihood parameter estimation. By using simulated data, we show the negative consequences (in terms of parameter estimates and inferred classification) of the wrong normality assumption in the presence of heavy-tailed clusters or noisy matrices. Such issues are properly addressed by our models instead. Additionally, over the same data, the atypical points detection procedures are also investigated. A real-data analysis concerning the relationship between greenhouse gas emissions and their determinants is conducted, and the behavior of our models in the presence of heterogeneity and atypical observations is discussed.

Single-Index Mixed-Effects Model for Asymmetric Bivariate Clustered Data

Studies/trials assessing status and progression of periodontal disease (PD) usually focus on quantifying the relationship between the clustered (tooth within subjects) bivariate endpoints, such as probed pocket depth (PPD), and clinical attachment level (CAL) with the covariates. Although assumptions of multivariate normality can be invoked for the random terms (random effects and errors) under a linear mixed model (LMM) framework, violations of those assumptions may lead to imprecise inference. Furthermore, the response-covariate relationship may not be linear, as assumed under a LMM fit, and the regression estimates obtained therein do not provide an overall summary of the risk of PD, as obtained from the covariates. Motivated by a PD study on Gullah-speaking African-American Type-2 diabetics, we cast the asymmetric clustered bivariate (PPD and CAL) responses into a non-linear mixed model framework, where both random terms follow the multivariate asymmetric Laplace distribution (ALD). In order to provide a one-number risk summary, the possible non-linearity in the relationship is modeled via a single-index model, powered by polynomial spline approximations for index functions, and the normal mixture expression for ALD. To proceed with a maximum-likelihood inferential setup, we devise an elegant EM-type algorithm. Moreover, the large sample theoretical properties are established under some mild conditions. Simulation studies using synthetic data generated under a variety of scenarios were used to study the finite-sample properties of our estimators, and demonstrate that our proposed model and estimation algorithm can efficiently handle asymmetric, heavy-tailed data, with outliers. Finally, we illustrate our proposed methodology via application to the motivating PD study.

Penggunaan Biopot dan Media Tanam dalam Gerakan Go Green: Perspektif Seminar Eco-Harmony

This research investigates the impact of the Eco Harmony Seminar: Exploring the Potential of Bioporeen, Biopot, and Growing Media on participants' knowledge of the Go Green movement and environmentally friendly practices. Utilizing a one-group pretest-posttest experimental design, the study involved 39 high school students from SMA Negeri 8 Kota Serang. The data analysis revealed a significant improvement in participants' understanding after the seminar, despite the data not meeting the normality assumption. Participants acknowledged the importance of using Go Green-based biopot and growing media, although implementation challenges such as the availability of supplementary materials were noted. In conclusion, the Eco Harmony Seminar not only enhanced participants' knowledge but also motivated them to support environmentally friendly practices. This study highlights the urgency of education and training in advancing the environmental movement and creating higher environmental awareness among the public.

태블릿PC와 노트필기 사용 집단 간 학습효과 분석

Objectives This study analyzes the learning effects between groups using Tablet PCs and handwritten notes methods among early childhood education freshmen. The focus is on examining learning engagement, enthusiasm, satisfaction with university life, and academic achievement.
 Methods The study participants consisted of 45 freshmen majoring in early childhood education at A university in Chungcheong province, all of whom had completed courses in early childhood music education. I conducted frequency(%) distributions and performed trend, normality, and reliability coefficient analyses of the research variables using SPSS 25.0. Since the normality assumptions were not met, I utilized the Mann-Whitney U test to assess the differences between the group using tablet PCs and the group employing handwritten notes. The statistical significance of the mean difference in pre-post scores between two groups was analyzed at the p<.001, p<.01, and p<.05 levels.
 Results The main results are as follows: First, the preliminary homogeneity test between the groups using tablet PCs and handwritten notes revealed no statistically significant differences, indicatingthat homogeneity was established between the two groups. Second, the tablet PC group scored higher than the handwritten notes group on variables related to learning engagement and its sub-domains(cognitive, behavioral, and emotional engagement), academic enthusiasm and its sub-domains(energetic, committed, and engaged), and university life satisfaction and its sub-domain(administrative and welfare services), and these differences were statistically significant. On the other hand, there were no statistically significant differences in the variables related to overall university life satisfaction and the quality of university education, which are sub-domains of university life satisfaction. Academic achievement was higher in the tablet PC user group compared to the handwritten note user group, and this difference was statistically significant.
 Conclusions The research results suggest the need for contemplation on teaching and learning methods in response to the changes in the digital educational environment in higher education. I aim to propose a way to operate courses by applying AI-based innovative teaching methods, focusing on both theoretical and practical courses inthe field of early childhood education.

ESG 인식과 소비성향, 환경문제 및 환경친화적 행동 간의 구조적 관계

Objectives The purpose of this study is to examine the structural relationship between ESG awareness, consumer behavior, environmental issues, and environmentally friendly actions of pre-service early childhood teachers.
 Methods For this study, a total of 255 pre-service early childhood teachers from the Seoul, Gyeonggi-do, and Chungcheong-do regions were surveyed. The tendencies, normality, and reliability coefficients of the research variables were examined using SPSS 23.0 and AMOS 25.0 software. Pearson's correlation analysis and structural equation modeling were conducted. The structural model was validated using various fit indices such as X2, NFI, IFI, TLI, CFI, RMSEA(LO-HI) and SRMR.
 Results These are the main findings. First, regarding the research variables, ESG awareness and environmental issues scored above 4.0 points, while consumer behavior and environmentally friendly actions averaged above 3.0 points. This indicates relatively high levels, and the data also met the assumption of normality. Second, regarding environmental issues and environmentally friendly actions, statistically significant positive correlations were found between ESG awareness and its sub-factors (Environmental, Social, Governance), as well as consumer behavior. Additionally, statistically significant positive correlations were observed between environmental issues and environmentally friendly actions. Third, based on the path coefficients of the structural model, it was found that ESG awareness had a statistically significant influence on consumer behavior, environmental issues, and environmentally friendly actions. Consumer behavior also had a statistically significant influence on environmental issues and environmentally friendly actions. Fourth, The results of the mediation analysis indicated that consumer behavior partially mediated the effects of ESG awareness on both environmentally friendly actions and environmental issues.
 Conclusions These research findings indicate the need for education on ESG awareness to address environmental issues and promote environmentally friendly behaviors. It emphasizes the utmost importance of cultivating habits related to consumer preferences through education. Based on these research results, I aim to propose strategies for enhancing ESG awareness among pre-service early childhood teachers.

Non-linear regression models in the management of accumulated production of parchment coffee in Peru

Parchment coffee results from washing the coffee cherry, and its production has achieved a significant increase in the coffee-growing regions of Peru. Knowing the production pattern of this grain is essential to help coffee producers make decisions in the economic and social sector. As growth curves generally have sigmoidal behavior, which is well fit by non-linear models, this study aimed to model the cumulative production pattern of parchment coffee as a function of time (in months) in the year 2022, comparing the fit of the non-linear Logistic, Gompertz and von Bertalanffy models. The cumulative national production, and production of the departments of Huánuco and San Martín, in Peru, were analyzed. Data used to fit the models were obtained from the Ministry of Development and Irrigation (MIDAGRI) of Peru. To check the assumptions of normality, homoscedasticity, and independence of residuals, the Shapiro-Wilk, Breusch-Pagan, and Durbin-Watson tests were used, respectively. The model parameters were estimated using the least squares method using the Gauss-Newton algorithm in the R software. The goodness-of-fit of the models was tested using goodness-of-fit measures such as Coefficient of Determination (R2), Residual Standard Deviation (RSD), Akaike Information Criterion (AIC), and nonlinearity measures. Based on the models’ goodness-of-fit measures, the Gompertz model with a first-order autoregressive error term (AR1) fit best to national production data, and the Logistic model was the most suitable for describing the production of the departments of Huánuco, and San Martín.

Unveiling the Dynamics of Women's Self-Help Groups: Exploring Socio-Economic and Socio-Psychological Factors in Debre Birhan, Ethiopia

The study aimed to address the critical research gap in understanding the effectiveness of Group Dynamics (GD) within Self-Help Groups (SHGs) in the Ethiopian context. Specifically, it sought to examine the extent to which socioeconomic and sociopsychological variables predicted group dynamics and how well these dynamics predicted attitudes among SHG members. A correlational design was employed to investigate the relationships between various variables. A sample of 372 SHG members was selected using simple random sampling. Data analysis included correlation and multiple regression techniques. Assumptions of normality, outliers, and multicollinearity were assessed and met. The results revealed several significant findings. Firstly, attitude, extension contact, socioeconomic profile, and social participation of SHG members were found to have statistically significant positive relationships with Group Dynamics Effectiveness (GDE). Secondly, the regression model including these predictors significantly explained 59.3% of the variance in GDE. Attitude emerged as the strongest predictor, contributing 18.5% uniquely to explaining GDE. Lastly, the socioeconomic profile of SHG members was identified as the weakest predictor, explaining only 0.5% of the unique variance in GDE. The study concluded that there is a significant relationship between various factors such as attitude, extension contact, socioeconomic status, and social participation with the effectiveness of group dynamics within SHGs in Ethiopia. Attitude was highlighted as the most influential factor contributing to GDE, while socioeconomic status had a relatively minimal impact. These findings have important implications for the design and implementation of SHG programs in Ethiopia. Specifically, efforts to enhance attitude and extension contact among SHG members may lead to more effective group dynamics, ultimately improving the overall success and impact of SHG initiatives on socioeconomic development in the region.

Small area estimation with partially linear mixed-t model with measurement error

In small area estimation (SAE), using direct conventional methods will not lead to reliable estimates because the sample size is small compared to the population. Small Area Estimation under Fay Herriot Model is used to borrow strength from auxiliary variables to improve the effectiveness of a sample size. However, the normality assumption is a limiting assumption for heavy-tailed data and outlying observations. Also, it is usually assumed that the predictors are measured without errors, which can be easily violated in SAE. In this study, we provide a more flexible model beyond these limitations, which is more accurate than the existing models. Specifically, we study SAE in the partially linear mixed-effects model where measurement error is present for the predictors and the vectors of random components and error jointly follow a multivariate t-distribution. Numerical studies are carried out to illustrate the superior performance of the proposed model in the prediction accuracy sense.

A robust test approach for equality of mean vectors of two independent groups under the multivariate Behrens-Fisher problem

In multivariate statistical inference, the Hotelling T 2 statistic is used to test the equality of mean vectors for two independent groups. This statistic needs the multivariate normality and homogeneous covariance matrices assumptions. However, homogeneous covariance matrices assumption may not be provided in real applications. This case is called the multivariate Behrens-Fisher problem. There are several studies to test the equality of two mean vectors for the independent groups under the multivariate Behrens-fisher problem. But these studies do not interest in outliers at data sets. In this study, we propose solving problems caused by multivariate Behrens-Fisher and outliers in the dataset. We compare our proposed approach with other approaches regarding empirical size and power at simulated data that are both uncontaminated and contaminated. Thus we show that our proposed approach can be used to test the equality of mean vectors for two independent groups under multivariate Behrens-Fisher problem without being affected by outliers in the data. Moreover, we construct an R function in the MVTests package to use our proposed approach for real data applications.

Forecasting weekly dengue incidence in Sri Lanka: Modified Autoregressive Integrated Moving Average modeling approach.

Dengue poses a significant and multifaceted public health challenge in Sri Lanka, encompassing both preventive and curative aspects. Accurate dengue incidence forecasting is pivotal for effective surveillance and disease control. To address this, we developed an Autoregressive Integrated Moving Average (ARIMA) model tailored for predicting weekly dengue cases in the Colombo district. The modeling process drew on comprehensive weekly dengue fever data from the Weekly Epidemiological Reports (WER), spanning January 2015 to August 2020. Following rigorous model selection, the ARIMA (2,1,0) model, augmented with an autoregressive component (AR) of order 16, emerged as the best-fitted model. It underwent initial calibration and fine-tuning using data from January 2015 to August 2020, and was validated against independent 2000 data. Selection criteria included parameter significance, the Akaike Information Criterion (AIC), and Schwarz Bayesian Information Criterion (SBIC). Importantly, the residuals of the ARIMA model conformed to the assumptions of randomness, constant variance, and normality affirming its suitability. The forecasts closely matched observed dengue incidence, offering a valuable tool for public health decision-makers. However, an increased percentage error was noted in late 2020, likely attributed to factors including potential underreporting due to COVID-19-related disruptions amid rising dengue cases. This research contributes to the critical task of managing dengue outbreaks and underscores the dynamic challenges posed by external influences on disease surveillance.

Bayesian model updating of super high‐rise building for construction simulation

SummaryA finite element model was established using SAP2000 software for the C1 tower, a super high‐rise building in the second phase of the Nanjing Financial City project, and the construction process of the tower was simulated. The C1 tower adopts a frame core tube extension arm and ring truss structure system, with 87 floors above ground and five floors underground. The roof structure has an elevation of 416.6 m. Precise measurements of inter‐story compression deformation were conducted using advanced surveying equipment. Sensitivity analysis, based on the finite difference method, identified the shear wall elastic modulus, frame column elastic modulus, steel beam elastic modulus, and shear wall unit weight as four highly influential parameters. Employing the Bayesian principle, the Markov Chain Monte Carlo (MCMC) method was applied to determine the posterior density probability function of the parameters targeted for modification. Subsequently, the Metropolis–Hastings (MH) sampling algorithm was employed to refine the C1 Tower model. This refinement significantly reduced the root mean square error between the measured and simulated vertical displacements, achieving an error reduction of approximately 10% from 6.082 to around 2.160. The modified material parameters, for the most part, adhered to a normal distribution assumption and exhibited mean values in the posterior probability density functions for the elastic modulus of Q345 steel beams, C70 frame columns, and C60 shear walls. Compared to the initial finite element parameters, the variation range was approximately 13% to 17%. These results serve as a validation of the effectiveness of the proposed method.

Comparisons of the mean differences and standardized mean differences for continuous outcome measures on the same scale.

When conducting systematic reviews and meta-analyses of continuous outcomes, the mean differences (MDs) and standardized mean differences (SMDs) are 2 commonly used choices for effect measures. The SMDs are motivated by scenarios where studies collected in a systematic review do not report the continuous measures on the same scale. The standardization process transfers the MDs to be unit-free measures that can be synthesized across studies. As such, some evidence synthesis researchers tend to prefer the SMD over the MD. However, other researchers have concerns about the interpretability of the SMD. The standardization process could also yield additional heterogeneity between studies. In this paper, we use simulation studies to illustrate that, in a scenario where the continuous measures are on the same scale, the SMD could have considerably poorer performance compared with the MD in some cases. The simulations compare the MD and SMD in various settings, including cases where the normality assumption of continuous measures does not hold. We conclude that although the SMD remains useful for evidence synthesis of continuous measures on different scales, the SMD could have substantially greater biases, greater mean squared errors, and lower coverage probabilities of CIs than the MD. The MD is generally more robust to the violation of the normality assumption for continuous measures. In scenarios where continuous measures are inherently comparable or can be transformed to a common scale, the MD is the preferred choice for an effect measure.