Confidence Interval Estimation Research Articles

Expert insights into future trajectories: assessing cost reductions and scalability of carbon dioxide removal technologies

IntroductionTo achieve net-zero targets, it is essential to evaluate and model the costs and scalability of emerging carbon dioxide removal technologies like direct air capture with CO2 storage (DACCS) and bioenergy with carbon capture and storage (BECCS). Yet such efforts are often impeded by varying assessments of the climate impact and potential contributions of these technologies. This study explores the future costs and scalability of DACCS and BECCS to advance net-zero goals.MethodsWe analyze expert opinions on these technologies’ potential costs and deployment scales for 2030, 2040, and 2050. Data was collected from 34 experts, comprising 21 DACCS and 13 BECCS specialists. They provided 90% confidence interval estimates and ‘best estimates’ for future costs and deployment under two International Energy Agency (IEA) policy scenarios—Stated Policies (STEPS) and Net Zero Emissions by 2050 (NZE).ResultsWe find that BECCS costs start at a lower level but decrease more slowly, whereas DACCS costs decline more steeply from a higher initial cost. However, DACCS estimates varied significantly among experts, showing no convergence over time. Regarding potential scalability, both technologies are associated with substantially higher deployment under the NZE scenario. Yet the combined estimated capacity of DACCS and BECCS by 2050 is only about a quarter of the CO2 removals projected by the IEA for its NZE scenario (1.9 GtCO2).DiscussionThis study provides valuable insights into the future of DACCS and BECCS technologies in Europe, especially since our experts expect that DACCS and BECCS costs will be even higher (and deployment scales lower) than those predicted by recent IEA tracking, opening future research directions.

Reliability evaluation in the zero‐failure Weibull case based on double‐modified hierarchical Bayes

AbstractHierarchical Bayes, or E‐Bayes, is frequently used to estimate the failure probability when solving a zero‐failure reliability evaluation model; however, the accuracy of the reliability estimation using these methods is not very good in practice. Due to this, a novel double‐modified hierarchical Bayes (DMH‐Bayes) is proposed for Weibull characteristic data in this study to enhance failure probability estimation and improve reliability point estimation accuracy. Meanwhile, in order to guarantee the preservation of the assessment findings' consistency and confidence level, the parametric Bootstrap method (P‐Bootstrap) and the L‐moment estimation method based on point estimation are introduced to obtain reliability confidence interval estimates. Based on Monte–Carlo simulation testing and analysis of a gyroscope bearing, the new model is confirmed to have better applicability and robustness while improving the accuracy of reliability assessment.

Binomial Confidence Intervals for Rare Events: Importance of Defining Margin of Error Relative to Magnitude of Proportion

ABSTRACT Confidence interval performance is typically assessed in terms of two criteria: coverage probability and interval width (or margin of error). In this paper, we assess the performance of four common proportion interval estimators: the Wald, Clopper-Pearson (exact), Wilson and Agresti-Coull, in the context of rare-event probabilities. We define the interval precision in terms of a relative margin of error which ensures consistency with the magnitude of the proportion. Thus, confidence interval estimators are assessed in terms of achieving a desired coverage probability whilst simultaneously satisfying the specified relative margin of error. We illustrate the importance of considering both coverage probability and relative margin of error when estimating rare-event proportions, and show that within this framework, all four interval estimators perform somewhat similarly for a given sample size and confidence level. We identify relative margin of error values that result in satisfactory coverage whilst being conservative in terms of sample size requirements, and hence suggest a range of values that can be adopted in practice. The proposed relative margin of error scheme is evaluated analytically, by simulation, and by application to a number of recent studies from the literature.

Estimation and comparison of Weibull-Normal distribution with some other probability models using Bayesian method of estimation

In statistical applications the Normal distribution is adjudged to be the best. Recent studies Terna (2017) using classical method indicated that Weibull-Normal distribution outperformed the Normal distribution. In this study we used the non-classical Bayesian method of estimation to estimate and compare the Weibull-Normal distribution with some other distributions including Normal and Gamma-Normal distributions. This study derived explicit expressions for basic statistical properties such as moments, moment generating function, the characteristic function, reliability analysis and the distribution of order statistics. It looks at estimation of confidence intervals for the parameters of the Weibull-Normal distribution and estimated the parameters of the new distribution using a non-classical approach for the purpose of theoretical comparisons. The two other distributions whose parameters were also estimated by using Bayesian estimation are the normal distribution and gamma distribution as well as the combination Gamma-Normal distribution. Based on the analyses and interpretations of the results obtained it was found that the parameters and other general properties of Normal distribution gives a better fit than other distributions. R-software was used; the models were written as an R code in R program using the rjags library, the distribution parameters were obtained from a Gibbs sampling of a Bayesian Fit for data set I and data set II. The criteria used in R for comparisons were the negative log-likelihood, AIC (Akaike information criterion), CAIC (Consistent Akaike Information Criterion) and BIC (Bayesian information Criterion).

LINEAR REGRESSION WITH DATA MISSING NOT AT RANDOM: BOOTSTRAP APPROACH

OLS regressions have a set of assumption in order to have its point and interval estimates to be unbiased and efficient. Data missing not at random (MNAR) can pose serious estimations issues in the linear regression. In this study we evaluate the performance of OLS confidence interval estimates with MNAR data. We also suggest bootstrapping as a remedy for such data cases and compare the traditional confidence intervals against bootstrap ones. As we need to know the true parameters, we carry out a simulations study. Research results indicate that both approaches show similar results having similar intervals size. Given that bootstrap required a lot of computations, traditional methods is still recommended to be used even in case of MNAR

Statistical inference of reliability for a K-out-of-N: G system with switching failure under Poisson shocks

Based on the stochastic uncertainty of the system's operating environment, this research presents statistical inferences on the mean time to failure (MTTF) of a K-out-of-N: G non-repairable system model with switching failure under Poisson shocks. The standby component is switched to the operating component when an operating component fails, with a switching failure probability of p. The MTTF of the system is derived by using the Markov process theory and the Laplace transform for two cases where the shock threshold is a constant value or a random variable. The maximum likelihood estimator (MLE) of the MTTF is obtained, and based on this estimator, asymptotic confidence interval estimation and hypothesis testing are performed. Based on the setting of the basic parameter values, the MTTF under two different cases of the shock threshold is compared. The effect of each parameter on the MTTF is analyzed in numerical simulation. The effectiveness of the above statistical inference methods is also verified by numerical simulation.

Computationally Efficient Demographic History Inference from Allele Frequencies with Supervised Machine Learning.

Inferring past demographic history of natural populations from genomic data is of central concern in many studies across research fields. Previously, our group had developed dadi, a widely used demographic history inference method based on the allele frequency spectrum (AFS) and maximum composite-likelihood optimization. However, dadi's optimization procedure can be computationally expensive. Here, we present donni (demography optimization via neural network inference), a new inference method based on dadi that is more efficient while maintaining comparable inference accuracy. For each dadi-supported demographic model, donni simulates the expected AFS for a range of model parameters then trains a set of Mean Variance Estimation neural networks using the simulated AFS. Trained networks can then be used to instantaneously infer the model parameters from future genomic data summarized by an AFS. We demonstrate that for many demographic models, donni can infer some parameters, such as population size changes, very well and other parameters, such as migration rates and times of demographic events, fairly well. Importantly, donni provides both parameter and confidence interval estimates from input AFS with accuracy comparable to parameters inferred by dadi's likelihood optimization while bypassing its long and computationally intensive evaluation process. donni's performance demonstrates that supervised machine learning algorithms may be a promising avenue for developing more sustainable and computationally efficient demographic history inference methods.

Fixed width confidence interval estimation for general continuous responses under a response adaptive design

. A fixed width confidence interval for the treatment difference is obtained under heteroscedastic normal responses following a response adaptive allocation targeting Neyman optimum allocation. The developed procedure is further extended for general location-scale model based responses under a compound response adaptive allocation. The developed procedures are studied theoretically and are supported empirically assuming various response models. A real data study is also provided following the proposed procedure for the purpose of illustration.

Field-independent carbon mapping and quantification in forest plantation through remote sensing

ABSTRACT Quantifying the carbon-stocking contribution of forest plantations is a crucial but challenging and expensive process, usually performed through field analysis. For this reason, plantations’ carbon storage is often calculated and reported using generic and inaccurate functions relying exclusively on tree species and plantation age. This study introduces a new field-independent (FI) method for forest plantations’ carbon quantification and mapping through automatic analysis of Sentinel-2 data. The study area is a Guatemalan forest plantation of 20 hectares, for which we constructed a reference dataset measuring in the field the diameter and the height of all trees within 20 randomly selected plots (10-meter radius). The CO2 equivalent absorbed by the plantation was first estimated using ground data and a design-based (DB) approach. Then, to obtain CO2 equivalent estimates but also maps, we used both ground and Sentinel-2 data to compare a standard model-assisted (MA) approach relying on Random Forests with the FI approach. Our results demonstrate that the FI method provides carbon stock statistics comparable to those obtained using DB and MA methods and more accurate maps. Accordingly, the RMSE obtained using the FI method was 34% while that obtained by the MA method – exploiting random forest algorithm – was greater (RMSE = 39%). The 95% confidence interval estimates of the CO2 stored in the plantation were 100 ± 18 MgC ha−1 and 102 ± 8 MgC ha−1, for DB and MA respectively. Using the FI method, the CO2 ranged between 89 and 117 Mg C ha−1, all values within the DB confidence interval. In addition, the FI map was surprisingly consistent with the MA-derived map, making our approach a valid alternative for monitoring plantation status and carbon storage when ground data are not available.

Abstract 7530: Harmonization radiomics models to predict tumor response in non-small cell lung cancer (NSCLC) patients treated with immunotherapy

Abstract Background: Precise prediction of immunotherapy response in non-small cell lung cancer (NSCLC) is crucial for personalized treatment. This study investigates the application of pretreatment CT-based radiomics and use of harmonization model in predicting these outcomes in NSCLC patients receiving immunotherapy. Methods: This retrospective study examined data from 152 stage III-IV NSCLC patients undergoing immunotherapy. Patient responses were categorized using immune-related RECIST (irRECIST) criteria into durable responders (complete response [CR], partial response [PR], or stable disease [SD]) for at least 24 weeks and non-responders. Tumor segmentation was performed using LIFEx software (IMIV/CEA, Orsay, France). 3D-radiomic features were extracted from both the tumor and surrounding 1 cm thick peritumoral regions. The Random Forest (RF) algorithm was employed to develop a classification model to differentiate between responders and non-responders. A harmonization model was deployed to account for the scanner-related differences by using spleen and normal lung signals. The dataset was divided into a training set (75%) and a test set (25%). Bootstrapping with 1,000 iterations was performed to estimate the model's performance by calculating the median and 95% confidence interval (CI) estimate. The accuracy of the model's predictions was evaluated by creating a confusion matrix. The model's performance was assessed by calculating the sensitivity, specificity, positive predictive values (PPV), negative predictive values (NPV), and area under the ROC curve (AUC) for response prediction. Results: A total of 152 patients were analyzed. 87 (57.23%) were female and 65 (42.76%) were male. The median age was 59 years. Histology types included were: 111 Adenocarcinoma (73%), 27 Squamous cell carcinoma (17.8%), and 14 other types (9.2%). The model achieved a sensitivity of 0.63, a specificity of 0.59, a PPV of 0.51, and NPV of 0.7 for response prediction of NSCLC patients receiving immunotherapy. The AUC of 0.61 indicates that the model may discriminate between responders and non-responders with an accuracy of 61%. Conclusion: This study demonstrates the potential of radiomics and the use of harmonization models to predict immunotherapy responses in NSCLC patients, offering insights into personalized treatment approaches. Larger studies are needed to validate our findings and the utility of harmonization models in predicting a tumor response. Citation Format: Monica Yadav, Jeeyeon Lee, Peter Haseok Kim, Seyoung Lee, Taegyu Um, Salie Lee, Maria Jose Chuchuca, Trie Arni Djunadi, Liam Il-Young Chung, Jisang Yu, Darren Rodrigues, Nicolo Gennaro, Leeseul Kim, Myungwoo Nam, Youjin Oh, Sungmi Yoon, Zunairah Shah, Yuchan Kim, Ilene Hong, Jessica Jang, Grace Kang, Amy Cho, Soowon Lee, Timothy Hong, Cecilia Nam, Yury S Velichko, Young Kwang Chae. Harmonization radiomics models to predict tumor response in non-small cell lung cancer (NSCLC) patients treated with immunotherapy [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 7530.

Abstract 7529: Harmonization radiomics model to predict immune checkpoint inhibitor-related pneumonitis (CIP) in non small cell lung cancer (NSCLC) in patients treated with immunotherapy

Abstract Background: With the increasing use of immunotherapy in advanced non-small cell lung cancer (NSCLC), managing adverse events, particularly checkpoint inhibitor-associated pneumonitis (CIP), poses a significant challenge. CIP often necessitates discontinuation of immunotherapy, even in cases of tumor response. Currently there are no effective models in predicting CIP. This study leverages artificial intelligence (AI) algorithms and the use of harmonization models to analyze radiomic features from chest CT scans, aiming to predict the occurrence of CIP in patients with NSCLC. Methods: This retrospective study examined data from 152 stage III-IV NSCLC patients undergoing immunotherapy. Tumor segmentation was performed using LIFEx software (IMIV/CEA, Orsay, France). 3D-radiomic features were extracted from both the tumor and the surrounding 1 cm thick peritumoral regions. The Random Forest (RF) algorithm was employed to develop a classification model to differentiate between CIP and non-CIP. A harmonization model was deployed to account for the scanner-related differences by using spleen and normal lung signals. The dataset was divided into a training set (75%) and a test set (25%). Bootstrapping with 1,000 iterations was performed to estimate the model's performance by calculating the median and 95% confidence interval (CI) estimate. The accuracy of the model's predictions was evaluated by creating a confusion matrix. The model's performance was assessed by calculating the sensitivity, specificity, positive predictive values (PPV), negative predictive values (NPV), and area under the ROC curve (AUC) for CIP prediction. Results: Among 152 patients, 87 (57.23%) are female and 65 (42.76%) are male. The median age was 59 years. Histology types included were Adenocarcinoma 111 (73%), Squamous cell carcinoma 27 (17.8%), and others 14 (9.2%). CIP was seen in 30 (19.73%) patients. Among the 30 patients with CIP, 17 (56.7%) patients had grade 1 pneumonitis, 11 (36.7%) patients had grade 2 pneumonitis, 2 (6.6%) patients had grade 3 pneumonitis, and none had grade 4 or grade 5 pneumonitis. The model achieved a sensitivity of 0.57, a specificity of 0.67, a PPV of 0.48, and NPV of 0.38 for predicting CIP. The AUC of 0.59 indicates that the model may predict checkpoint inhibitor-associated pneumonitis with an accuracy of 59%. Conclusions: The study provides insights into the potential of radiomic analysis coupled with AI algorithms and the use of harmonization model in predicting CIP among NSCLC patients treated with immunotherapy. Larger studies are needed to validate our findings and the utility of harmonization models in predicting CIP. Citation Format: Monica Yadav, Jeeyeon Lee, Peter Haseok Kim, Seyoung Lee, Taegyu Um, Salie Lee, Maria Jose Chuchuca, Trie Arni Djunadi, Liam Il-Young Chung, Jisang Yu, Darren Rodrigues, Nicolo Gennaro, Leeseul Kim, Myungwoo Nam, Youjin Oh, Sungmi Yoon, Zunairah Shah, Yuchan Kim, Ilene Hong, Jessica Jang, Grace Kang, Amy Cho, Soowon Lee, Timothy Hong, Cecilia Nam, Yury S Velichko, Young Kwang Chae. Harmonization radiomics model to predict immune checkpoint inhibitor-related pneumonitis (CIP) in non small cell lung cancer (NSCLC) in patients treated with immunotherapy [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 7529.

Inputs-Oriented VRS DEA in dairy farms

Background This paper aims to examine the efficiency of Mexico’s dairy farms within its four regions of Tlaxcala Stated. Methods The Envelopment Data Analysis (DEA) applied to the variable returns to a scale model (VRS) for the year 2020. Also, Examine the statistical accuracy of efficiency estimation using bootstrap resampling techniques. The results reveal that Tlaxcala’s dairy farm efficiency, on the other hand, was adversely influenced by three inputs (costs): cost of investment in livestock, the total annual cost for feeding, reproduction, diseases and treatments, preventive medicine, sanitation, milking, fuel, and total labor. Results The efficiency distribution among farms using VRS, CRS, and FDH technologies reveals varying patterns. Under VRS and CRS, the majority of farms exhibit high efficiency within the 0 to less than 0.2 range, while FDH displays a broader distribution, with notable efficiency at 1 and across various ranges. These findings highlight the diverse landscape of efficiency levels across different technological approaches within the agricultural sector, offering valuable insights for optimization strategies and resource allocation. Conclusions The utilization of Bootstrap methodology enhances the reliability of efficiency assessments by providing robust statistical techniques that accommodate non-normal data distributions. By incorporating Bootstrap, decision-makers can obtain more accurate estimates of efficiency levels and confidence intervals, thereby making informed decisions regarding resource allocation and optimization strategies within the agricultural sector. As part of the study, provided The Policy suggestions.

The Reliability Inference for Multicomponent Stress–Strength Model under the Burr X Distribution

The reliability of the multicomponent stress–strength system was investigated under the two-parameter Burr X distribution model. Based on the structure of the system, the type II censored sample of strength and random sample of stress were obtained for the study. The maximum likelihood estimators were established by utilizing the type II censored Burr X distributed strength and complete random stress data sets collected from the multicomponent system. Two related approximate confidence intervals were achieved by utilizing the delta method under the asymptotic normal distribution theory and parametric bootstrap procedure. Meanwhile, point and confidence interval estimators based on alternative generalized pivotal quantities were derived. Furthermore, a likelihood ratio test to infer the equality of both scalar parameters is provided. Finally, a practical example is provided for illustration.

Statistical inference for a two-parameter Rayleigh distribution under generalized progressive hybrid censoring scheme

The two-parameter Rayleigh distribution, as an extended distribution of the Rayleigh distribution, has been widely applied in reliability analysis. With the introduction of the location parameter, two-parameter Rayleigh distribution becomes more flexible in fitting real-data. In this paper, based on generalized progressively hybrid censored(GPHC) sample from the two-parameter Rayleigh distribution, Classical and Bayesian inferences are discussed. The Newton-Raphson(NR) and Expectation-Maximization(EM) algorithms are used to compute the maximum likelihood estimates(MLEs). As well as the asymptotic confidence interval(ACI) estimation is obtained through the asymptotic distribution theory of maximum likelihood estimation(MLE) and computation of the observed Fisher information matrix. In Bayesian frame, the estimation of unknown parameters and prediction of future observable are taken into consideration. Due to Bayesian estimation is challenging to compute precisely and for the purpose of comparison, the Lindley's approximation, the Tierney-Kadane(TK) approximation and Markov chain Monte Carlo(MCMC) method are employed to obtain Bayesian estimates. Then, combining the MCMC algorithm mentioned in the article, the one- and two- samples Bayesian prediction are obtained. Finally, the simulation results are provided and a real-life data set is used for illustration purpose.

Stress Prediction Model of Super-High Arch Dams during Their Initial Operation Stages

It is of great significance to identify the spatiotemporal stress distribution characteristics to ensure the safety of a super-high arch dam during the initial operation stage. Taking the 285.5 m-high Xiluodu Dam as an example, the spatiotemporal distribution characteristics were analyzed based on the five-year observation data after impoundment. Statistical and boosted-regression-tree-based prediction models for the dam stress were established. The boosted-regression-tree-based prediction model is more accurate than the statistical model. The monitoring indicators for the measuring points of focused locations were determined using the confidence interval estimation method. The results show that the dam was in a compression state, and the arching effect was obvious. The arch direction compressive stress gradually increased and stabilized, and the maximum appeared in the middle of the upstream face of the crown cantilever monolith. For the crown cantilever, the cantilever direction stress at the dam heel was significantly affected by the interior temperature recovery, and the arch direction stress in the middle of the upstream face was significantly affected by the reservoir water level. The measuring points of the focused locations with reliable observation data can be selected as a monitoring index to guide the initial operation.

BOOTSTRAP CONFIDENCE INTERVALS IN LINEAR MODELS: CASE OF OUTLIERS

Confidence interval estimations in linear models have been of large interest in social science. However, traditional approach of building confidence intervals has a set of assumption including dataset having no extreme outliers. In this study, we discuss presence of severe outliers in linear models and suggest bootstrap approach as an alternative way to construct confidence intervals. We conclude that bootstrap confidence intervals can outperform traditional confidence intervals in presence of outliers when sample size is small or population distribution is not normal. Lastly, we encourage researchers to run a computer simulation to evaluate conclusions of this study.

A hybrid deep learning model for lithium-ion batteries state of charge estimation based on quantile regression and attention

Accurate estimation of the state of charge (SOC) is essential to ensure the safe and efficient utilization of lithium-ion batteries. However, external factors can affect the SOC, making it challenging to achieve precise estimations. To address this issue, we propose a deep learning model that integrates the parallel computing capabilities of temporal convolutional networks with the robust learning abilities of gated recurrent units. This model incorporates an attention mechanism to dynamically assign weights and focus on salient features based on correlations in historical information. Furthermore, we employ the quantile regression loss function during network training, thereby equipping the neural network model with the capability to directly generate interval estimates. The results show that the MAE and RMSE of the lithium iron phosphate battery, lithium cobalt oxide battery and ternary lithium battery dataset are below 1.45 and 1.98, 1.12 and 1.25, 0.61 and 0.75 respectively. The comparison analysis with other SOC estimation methods demonstrates its exceptional accuracy in point estimation and high reliability in confidence interval estimation. Furthermore, it showcases remarkable generalization ability across diverse temperatures, operating conditions, battery lifetimes, and battery types.

A simulated ‘sandbox’ for exploring the modifiable areal unit problem in aggregation and disaggregation

We present a spatial testbed of simulated boundary data based on a set of very high-resolution census-based areal units surrounding Guadalajara, Mexico. From these input areal units, we simulated 10 levels of spatial resolutions, ranging from levels with 5,515–52,388 units and 100 simulated zonal configurations for each level – totalling 1,000 simulated sets of areal units. These data facilitate interrogating various realizations of the data and the effects of the spatial coarseness and zonal configurations, the Modifiable Areal Unit Problem (MAUP), on applications such as model training, model prediction, disaggregation, and aggregation processes. Further, these data can facilitate the production of spatially explicit, non-parametric estimates of confidence intervals via bootstrapping. We provide a pre-processed version of these 1,000 simulated sets of areal units, meta- and summary data to assist in their use, and a code notebook with the means to alter and/or reproduce these data.

LIMBARE: An Advanced Linear Mixed-Effects Breakpoint Analysis With Robust Estimation Method With Applications to Longitudinal Ophthalmic Studies.

Broken stick analysis is a widely used approach for detecting unknown breakpoints where the association between measurements is nonlinear. We propose LIMBARE, an advanced linear mixed-effects breakpoint analysis with robust estimation, especially designed for longitudinal ophthalmic studies. LIMBARE accommodates repeated measurements from both eyes and over time, and it effectively addresses the presence of outliers. The model setup of LIMBARE and the computing algorithm for point and confidence interval estimates of the breakpoint were introduced. The performance of LIMBARE and other competing methods was assessed via comprehensive simulation studies and application to a longitudinal ophthalmic study with 216 eyes (145 subjects) followed for an average of 3.7 ± 1.3years to examine the longitudinal association between structural and functional measurements. In simulation studies, LIMBARE showed the smallest bias and mean squared error for estimating the breakpoint, with an empirical coverage probability of corresponding confidence interval estimates closest to the nominal level for scenarios with and without outlier data points. In the application to the longitudinal ophthalmic study, LIMBARE detected two breakpoints between visual field mean deviation (MD) and retinal nerve fiber layer thickness and one breakpoint between MD and cup-to-disc ratio, whereas the cross-sectional analysis approach detected only one and none, respectively. LIMBARE enhances breakpoint estimation accuracy in longitudinal ophthalmic studies, and the cross-sectional analysis approach is not recommended for future studies. Our proposed method and companion R package provide a valuable computational tool for advancing longitudinal ophthalmology research and exploring the association relationships among ophthalmic variables.

Some additional remarks on statistical properties of Cohen’s d in the presence of covariates

AbstractThe size of the effect of the difference in two groups with respect to a variable of interest may be estimated by the classical Cohen’s d. A recently proposed generalized estimator allows conditioning on further independent variables within the framework of a linear regression model. In this note, it is demonstrated how unbiased estimation of the effect size parameter together with a corresponding standard error may be obtained based on the non-central t distribution. The portrayed estimator may be considered as a natural generalization of the unbiased Hedges’ g. In addition, confidence interval estimation for the unknown parameter is demonstrated by applying the so-called inversion confidence interval principle. The regarded properties collapse to already known ones in case of absence of any additional independent variables. The stated remarks are illustrated with a publicly available data set.