[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-206559-105":59,"doc-detail-206559-en":124},{"code":4,"msg":5,"data":6},0,"success",[7,13,18,23,28,33,38,43,48,51,55],{"id":8,"doc_module":4,"doc_module_name":9,"category_name":10,"show_sort_weight":11,"slug":12},1,"Document","Story & Novel",90,"story-novel",{"id":14,"doc_module":4,"doc_module_name":9,"category_name":15,"show_sort_weight":16,"slug":17},2,"Literature",80,"literature",{"id":19,"doc_module":4,"doc_module_name":9,"category_name":20,"show_sort_weight":21,"slug":22},4,"Exam",70,"exam",{"id":24,"doc_module":4,"doc_module_name":9,"category_name":25,"show_sort_weight":26,"slug":27},5,"Comic",60,"comic",{"id":29,"doc_module":4,"doc_module_name":9,"category_name":30,"show_sort_weight":31,"slug":32},6,"Technology",50,"technology",{"id":34,"doc_module":4,"doc_module_name":9,"category_name":35,"show_sort_weight":36,"slug":37},7,"Healthcare",40,"healthcare",{"id":39,"doc_module":4,"doc_module_name":9,"category_name":40,"show_sort_weight":41,"slug":42},8,"Research & Report",30,"research-report",{"id":44,"doc_module":4,"doc_module_name":9,"category_name":45,"show_sort_weight":46,"slug":47},9,"Religion & Spirituality",20,"religion-spirituality",{"id":46,"doc_module":4,"doc_module_name":9,"category_name":49,"show_sort_weight":46,"slug":50},"World Cup","world-cup",{"id":52,"doc_module":4,"doc_module_name":9,"category_name":53,"show_sort_weight":52,"slug":54},10,"Lifestyle","lifestyle",{"id":56,"doc_module":4,"doc_module_name":9,"category_name":57,"show_sort_weight":24,"slug":58},19,"General","general",{"code":4,"msg":60,"data":61},"ok",{"site_id":62,"language":63,"slug":64,"title":65,"keywords":66,"description":67,"schema_data":68,"social_meta":117,"head_meta":119,"extra_data":121,"updated_unix":123},105,"en","a-multilevel-analysis-of-school-examination-results","A Multilevel Analysis of School Examination Results","","Examination outcome data from inner London schools are analyzed with multilevel models to account for intake achievement, pupil gender, and school type. Total examination performance is assessed alongside subject-specific achievement in mathematics and English. School-level variation is quantified using school residuals/effects, showing wide confidence intervals that limit reliable school separation. A bivariate model links mathematics and English outcomes, indicating increasing student-level variance across intake groups and a moderately high cross-subject correlation. Implications are discussed for publishing league tables of school exam results.",{"@graph":69,"@context":116},[70,84,99],{"@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":20,"@type":76,"position":81},"https://docshare.wps.com/document/exam/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/a-multilevel-analysis-of-school-examination-results/206559/",{"url":83,"name":65,"@type":85,"author":86,"headline":65,"publisher":89,"fileFormat":92,"inLanguage":63,"description":67,"dateModified":93,"datePublished":93,"encodingFormat":92,"isAccessibleForFree":94,"interactionStatistic":95},"DigitalDocument",{"name":87,"@type":88},"Skyler","Person",{"url":74,"name":90,"@type":91},"DocShare","Organization","application/pdf","2026-09-05",true,{"@type":96,"interactionType":97,"userInteractionCount":4},"InteractionCounter",{"@type":98},"ViewAction",{"@type":100,"mainEntity":101},"FAQPage",[102,108,112],{"name":103,"@type":104,"acceptedAnswer":105},"What data and student grouping variables are used in the analysis?","Question",{"text":106,"@type":107},"The study uses GCSE mathematics and English grades and a total score from 5748 students across 66 schools. It also includes intake measures, pupil gender, and school type characteristics, including a reading test and verbal reasoning categories.","Answer",{"name":109,"@type":104,"acceptedAnswer":110},"Why can’t schools be reliably ranked using the results?",{"text":111,"@type":107},"The fitted models show wide confidence intervals for school residuals/effects, meaning only few schools can be separated reliably. As a result, fine rank ordering of schools is not supported by the analysis.",{"name":113,"@type":104,"acceptedAnswer":114},"How are mathematics and English achievement modeled together?",{"text":115,"@type":107},"A bivariate multilevel model is fitted for mathematics and English examination scores. The analysis finds student-level variance increases from the lowest to the highest intake achievement group, with a moderately high correlation between subject outcomes.","https://schema.org",{"og:url":83,"og:type":118,"og:title":65,"og:site_name":90,"og:description":67},"article",{"robots":120,"canonical":83},"index,follow",{"doc_id":122,"site_id":62},206559,1788594835,{"code":4,"msg":5,"data":125},{"doc_id":122,"user_id":126,"nickname":87,"user_avatar":127,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":128,"file_id":129,"file_url":130,"file_type":131,"file_size":132,"view_count":4,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":44,"language":133,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":134,"faqs":135,"seo_title":136,"seo_description":67,"update_tm":123,"read_time":137},2336464648746,"https://ap-avatar.wpscdn.com/davatar_276721f389ce27ea32af1340a28f341c","# A Multilevel Analysis of School Examination Results[1]\n\nHARVEY GOLDSTEIN,JON RASBASH,MIN YANG,GEOFFREYWOODHOUSE,HUIQI PAN,DESMOND NUTTALL &SALLY THOMAS  \nABSTRACT Data on examination results from inner London schools are analysed inrelation to intake achievement,pupil gender and school type.The examination achieve-ment,averaged over subjects,is studied as is achievement in the separate subjects ofmathematics and English.Multilevel models are fitted,so that the variation betzweenschools can be studied.It is shown that confidence intervals for school ‘residuals'oreffects'are wide,so that few schools can be separated reliably.In particular,no fine rankordering of schools legitimately can be produced.A bivariate model for mathematics andEnglish examination achievement scores is fitted.The student level variance for bothsubjects is shown to increase from the lowest to the highest intake achievement group,withmoderately high correlation betveen the subjects.The paper discusses the implications ofthese findings for the publication of league tables’of school examination and test scores.  \n## INTRODUCTION\n\nThere is now a considerable literature on methods for comparing schools and otherinstitutions on the basis of the achievement of their students.The important paper ofAitkin and Longford(1986)established that the minimal requirement for valid institu-tional comparisons was an analysis based upon individual level data which adjusted forintake differences and used efficient techniques of multilevel modelling.In that paperand the discussion on it,several outstanding problems were raised.The purely techni-cal problems of carrying out the estimation for large data sets have been solved fairlyeffectively by the development of computer programs,summarised in Kreft et al.(1990).The remaining problems are concerned with the existence of suitable measure-ments which can be used to adjust for intake,and any other relevant differences,themultivariate nature of school outcomes,and the kinds of interpretations which can bemade of results.The present paper addresses these latter issues.Specifically it looks attwo measures of intake achievement for each school in the study,and examines theinterpretational issue by studying the dimensionality of school differences.  \n## DATA\n\nThe data are examination results from 5748 students in 66 schools in six Inner LondonEducation Authorities.These students had data on their General Certificate of Sec-ondary Examination(GCSE)grades in mathematics and English,together with a totalscore for all the subjects taken in that examination.A description of the types of data  \nTABLE I.Mean scores by intake categories  \n\n|  | Mathematics   | English   | Total   | %   |\n| --- | --- | --- | --- | --- |\n| VR group 1   | 0.75   | 0.80   | 0.81   | 24   |\n| VR group 2   | -0.07   | -0.07   | -0.07   | 56   |\n| VR group 3   | -0.75   | -0.80   | -0.81   | 20   |\n| Total   | 0.00   | 0.00   | 0.00   | 100   |\n| Corrn with LRT   | 0.51   | 0.58   | 0.58   |  |\n\nand the scoring system used is given in Nuttall et al.(1989).For mathematics andEnglish,a scale ranging from 0(no grade awarded)to 7(grade A)was used in theanalysis and,for the total score,the scale ranged from 0 to 70.These students also hadscores on a common reading test taken when they were 11 years old—the LondonReading Test(LRT)(Levy &Goldstein,1984)and were graded also into threecategories on the basis of a verbal reasoning(VR)test at 11 years(Nuttall et al.,1989).Table I shows the standardised mean scores on the three outcome measures by verbalreasoning group and the correlations with the standardised reading test score.All threescores are scaled to have mean zero and standard deviation 1.The pattern is similar forall three response variables.  \nThe original number of students on whom some examination data had been obtainedwas 8857 in 74 schools.Students were omitted from the analysis if they did not haveboth intake measures.Where students did not take an examinatio","cbCaigfg0Q8qWuq8","https://ap.wps.com/l/cbCaigfg0Q8qWuq8","pdf",396620,"English","# INTRODUCTION\n# DATA\n## TABLE I. Mean scores by intake categories\n# TOTAL EXAMINATION SCORE\n## TABLE II. Analysis of total examination score","[{\"question\":\"What data and student grouping variables are used in the analysis?\",\"answer\":\"The study uses GCSE mathematics and English grades and a total score from 5748 students across 66 schools. It also includes intake measures, pupil gender, and school type characteristics, including a reading test and verbal reasoning categories.\"},{\"question\":\"Why can’t schools be reliably ranked using the results?\",\"answer\":\"The fitted models show wide confidence intervals for school residuals/effects, meaning only few schools can be separated reliably. As a result, fine rank ordering of schools is not supported by the analysis.\"},{\"question\":\"How are mathematics and English achievement modeled together?\",\"answer\":\"A bivariate multilevel model is fitted for mathematics and English examination scores. The analysis finds student-level variance increases from the lowest to the highest intake achievement group, with a moderately high correlation between subject outcomes.\"}]","A Multilevel Analysis of School Examination Results | PDF",23]