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This study re-analyzes an online homework RCT by combining randomized and nonrandomized subjects without introducing confounding. A random forest model trained on observational covariates predicts student test scores, and predicted outcomes are added to a hierarchical linear model. The approach reduces the standard error by 15%, comparable to increasing sample size by over one third, and adapts wherever auxiliary observational datasets exist.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/improved-power-in-a-reanalysis-of-an-assistments-efficacy-trial-leveraging-auxiliary-data/585375/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/improved-power-in-a-reanalysis-of-an-assistments-efficacy-trial-leveraging-auxiliary-data/585375.png","ImageObject",300,407,{"name":92,"@type":93},"Aria Callaghan","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-31","2026-10-15",true,{"@type":102,"interactionType":103,"userInteractionCount":19},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"Why do standard analyses of randomized trials usually discard nonrandomized auxiliary data?","Question",{"text":112,"@type":113},"Because auxiliary data can contain subjects that are not guaranteed to be comparable to the randomized participants, creating confounding and undermining the RCT’s purpose.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does the proposed reanalysis incorporate auxiliary data without introducing confounding?",{"text":117,"@type":113},"It trains a random forest on observational covariates to predict test scores, then adds these predicted outcomes as an additional regressor in a hierarchical linear model.",{"name":119,"@type":110,"acceptedAnswer":120},"What power or precision improvement does the method achieve?",{"text":121,"@type":113},"The standard error is reduced by 15%, which corresponds to the improvement expected from increasing the sample size by more than one third.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},585375,1792471789,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":19,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":34,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":143,"read_time":144,"preview_page_count":4},962084926284,"https://ap-avatar.wpscdn.com/davatar_29158cc5080c5b710cf443261637dec0","Improved Power in a Reanalysis of an ASSISTments Efficacy Trial by Leveraging Auxiliary Data  \nAdam C. Sales Worcester Polytechnic Institute  \n[asales@wpi.edu](asales@wpi.edu)  \nChun-Wei Huang  \nWestEd  \n[chuang@wested.org](chuang@wested.org)  \nMingyu Feng  \nWestEd  \n[mfeng@wested.org](mfeng@wested.org)  \nJohann A. Gagnon-Bartsch  \nUniversity of Michigan  \n[johanngb@umich.edu](johanngb@umich.edu)  \nABSTRACT  \nRandomized controlled trials (RCTs) in social or biomedical science often rely on covariate and outcome data drawn from a larger administrative database. For instance, a recent paired, clustered RCT of an online homework platform used covariates (demographics and prior achievement measures) and outcomes (standardized test scores) from the state’s educational database. To avoid confounding, typical analyses use only data from randomized subjects, discarding the remainder of the database.  \nIn this study, we re-analyze data from the online homework study, substantially improving the precision of the effect estimates by using data from both randomized and nonrandomized subjects. Our estimator does not introduce confounding and relies largely on standard modeling techniques. Specifically, we use observational data to train a random forest model predicting student test scores from student- and school-level covariates, and use it to generate predicted outcomes for students in the randomized schools. Then, we modify the hierarchical linear model from the original analysis by adding the predicted outcomes as an additional regressor, reducing the standard error by 15%—the improvement expected from increasing the sample size by over a third. Since it requires few additional modeling skills and no additional assumptions, this method can be easily adapted wherever auxiliary observational data are available.  \nKeywords  \nCausal Inference, Randomized Experiments, Supervised Learning, Hierarchical Linear Models  \n1. INTRODUCTION  \nIn 2018, WestEd, an educational research agency, began a large-scale randomized field trial of the online mathematics application ASSISTments in 63 schools in North CarAdam Sales, Kevin Huang, Mingyu Feng, and Johann GagnonBartsch. Improved Power in a Reanalysis of an ASSISTments Efficacy Trial by Leveraging Auxiliary Data. In Anthony Botelho, Maria Mercedes T. Rodrigo, Adish Singla, Hiroaki Ogata, Hyojeong So, and Young Hoan Cho (eds.) Proceedings of the 19th International Conference on Educational Data Mining, Seoul, Republic of Korea, June, 2026, pp. 487–493. International Educational Data Mining Society (2026) .  \n© 2026 Copyright is held by the author(s) . This work is distributed under the Creative Commons Attribution NonCommercial NoDerivatives 4.0 International (CC BY-NC-ND 4.0) license. [https://doi.org/10.5281/zenodo.21039716](https://doi.org/10.5281/zenodo.21039716)  \nolina [3] . The researchers were granted access to the North Carolina student longitudinal data system, from which they drew most of the data used for the evaluation, including demographic and student achievement data from the students in the study—seventh-grade math students in the 63 randomized schools. However, the researchers had access to even more data: demographic, prior achievement, and outcome data from over 65 thousand additional 7th-grade students who attended North Carolina middle schools other than those 63 .  \nThe WestEd ASSISTments study is one example of a common phenomenon: covariate and outcome data for a randomized controlled trial (RCT) are drawn from a larger database that also includes data from similar subjects who were not randomized as part of the experiment. Other examples include A/B tests, which draw baseline covariatesand outcomes from log data, and clinical trials, which draw baseline and outcome data from patients’ medical records. In these examples, researchers have access to big auxiliary observational datasets that are typically discarded or left unused. Granted, pooling data from randomized and nonran","cbCais5zoiHanJkq","https://ap.wps.com/l/cbCais5zoiHanJkq","pdf",652975,"English","# Abstract\n# 1. Introduction\n## Background: auxiliary data in RCTs and other trials\n## Prior work: auxiliary-data prediction and power gains\n## Gaps addressed by the current study","[{\"question\":\"Why do standard analyses of randomized trials usually discard nonrandomized auxiliary data?\",\"answer\":\"Because auxiliary data can contain subjects that are not guaranteed to be comparable to the randomized participants, creating confounding and undermining the RCT’s purpose.\"},{\"question\":\"How does the proposed reanalysis incorporate auxiliary data without introducing confounding?\",\"answer\":\"It trains a random forest on observational covariates to predict test scores, then adds these predicted outcomes as an additional regressor in a hierarchical linear model.\"},{\"question\":\"What power or precision improvement does the method achieve?\",\"answer\":\"The standard error is reduced by 15%, which corresponds to the improvement expected from increasing the sample size by more than one third.\"}]","Improved Power in a Reanalysis of an ASSISTments Efficacy Trial - Leveraging Auxiliary Data | PDF",1792054552,18]