[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-621079-105":59,"doc-detail-621079-en":130},{"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":123,"head_meta":125,"extra_data":127,"updated_unix":129},105,"en","difficulty-plots-dif-analysis-without-the-partial-credit-model","Difficulty plots: DIF analysis without the partial credit model","","The report compares two approaches for assessing differential item functioning (DIF) when vertically scaling tiered exams, focusing on a difficulty-plot method that avoids fitting the partial credit model (PCM). It explains how DIF should be evaluated on common items between foundation and higher tiers, discusses orthogonal regression residuals for difficulty plots, and uses calibrated PCM difficulty parameters and item facilities to interpret results. Evidence is drawn from 12 tiered GCSE papers from summer 2016, identifying items with large DIF for potential removal to preserve fairness.",{"@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":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/difficulty-plots-dif-analysis-without-the-partial-credit-model/621079/",{"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/difficulty-plots-dif-analysis-without-the-partial-credit-model/621079.png","ImageObject",300,407,{"name":92,"@type":93},"Sarah ","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-21","2026-10-20",true,{"@type":102,"interactionType":103,"userInteractionCount":8},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"Why is DIF assessment important for vertically scaling tiered exams?","Question",{"text":112,"@type":113},"DIF must be assessed among common items to ensure a fair link between foundation and higher tiers. Items that behave very differently across tiers may need to be dropped from the common item pool.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How does the report assess DIF without fitting the partial credit model?",{"text":117,"@type":113},"It uses difficulty plots based on relative item difficulties and orthogonal regression, defining residuals as orthogonal distances to the regression line. These residuals help flag items that may require investigation.",{"name":119,"@type":110,"acceptedAnswer":120},"What evidence in the paper indicates that certain items show DIF?",{"text":121,"@type":113},"Items with large differences in calibrated PCM difficulty estimates (β) across tiers and/or large orthogonal residuals are treated as evidence of DIF. Table 1 and Figure 2 highlight specific items with high PCM DIF.","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},621079,1792547074,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":8,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":24,"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},962085320529,"https://ap-avatar.wpscdn.com/davatar_9964176cb1d06d4a9deccf72a44ae3dc","Centre for Education Research and Practice  \nDifficulty plots: DIF analysis without the partial credit model  \nElizabeth Harrison  \nIntroduction  \nFrom summer 2017, the preferred method for vertical scaling of tiered exams will be chained equipercentile equating (JCQ, 2015; Kolen & Brenan, 2004) . AQA has previously used the partial credit model (PCM) to perform vertical scaling (see Kolen & Brennan, 2004; Harrison & Pointer, 2016) . For either method, differential item functioning (DIF) should be assessed among the common items, ideally at the time of the award (JCQ, 2015) . Any items that perform very differently on the foundation and the higher tier might need to be dropped from the common item pool to ensure a fair link between the two tiers. DIF is fairly straightforward to assess when using the PCM; this report illustrates a simple method, using difficulty plots, to assess DIF without fitting the PCM. The two approaches are compared over 12 tiered GCSE papers from the summer 2016 series.  \nIllustration comparing PCM DIF and difficulty plots  \nTable 1 shows some summary statistics for the common items for GCSE Gardening.1 The itemlevel parameters βF and βH are from the fitted PCMs (after calibration2) and describe the difficulty of each item. The facility is the mean mark divided by the tariff; it is also a measure of the item difficulty.  \nTable 1 Common item statistics for GCSE Gardening  \n\n| F item | H item | tariff | βF | βH | F facility | H facility | Orthogonal\u003Cbr>residual | PCM DIF\u003Cbr>(βF-βH) |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| 8a | 1a | 1 | 0.32 | 0.75 | 0.28 | 0.49 | -0.020 | -0.43 |\n| 8bi | 1bi | 1 | -0.17 | 0.80 | 0.39 | 0.48 | -0.103 | -0.97 |\n| 8bii | 1bii | 1 | 0.31 | 0.48 | 0.30 | 0.56 | 0.019 | -0.17 |\n| 8biii | 1biii | 1 | 5.20 | 3.19 | 0.01 | 0.10 | -0.106 | 2.01 |\n| 8biv | 1biv | 2 | 1.63 | 1.13 | 0.10 | 0.42 | 0.051 | 0.49 |\n| 8c | 1c | 3 | 0.61 | 0.98 | 0.36 | 0.53 | -0.043 | -0.36 |\n| 9a | 2a | 1 | 2.29 | 1.05 | 0.06 | 0.43 | 0.092 | \u003Cbr>1.24 |\n| 9bi | 2bi | 1 | -0.24 | 0.21 | 0.40 | 0.61 | -0.019 | -0.44 |\n| 9bii | 2bii | 1 | 1.88 | 1.25 | 0.08 | 0.38 | 0.041 | 0.63 |\n| 9c | 2c | 1 | -1.00 | -0.97 | 0.58 | 0.81 | 0.002 | -0.03 |\n| 9d | 2d | 6 | 0.28 | 0.57 | 0.20 | 0.56 | 0.085 | -0.29 |\n|  |  |  |  |  |  |  |  |  |\n\n1 The data is from a real GCSE qualification but a fictional subject name has been used.  \n2 Calibration is the process of aligning the scales of the PCMs fitted to the foundation and higher tiers.  \n[cerp.org.uk](cerp.org.uk)  \nCopyright © 2017 AQA Education and its licensors. All rights reserved.  \nAQA Education (AQA) is a registered charity (registered charity number 1073334) and a company limited by guarantee registered in England and Wales (company number 3644723) . Registered address: AQA, Devas Street, Manchester M15 6EX.  \nThere is a strong, negative correlation between the β estimates and the item facilities over the 12 papers analysed here: ranging from-0.85 to-0.99 (high β values are equivalent to low item facilities) . The final two columns of Table 1 are measures of DIF and will be explained later in this report.  \nThe relative difficulty of each common item on each of the two tiers can be summarised graphically using a difficulty plot (Livingstone, 2004, p. 32) . Figure 1 shows the relative difficulties of the common items from GCSE Gardening. The line shown is the orthogonal regression line.3 Orthogonal regression assumes that there is error in the measurement in the observations on both the x- and y-axis. It is also symmetric; hence the same items would be flagged if y were regressed on x or x regressed on y. It assumes that the error variances are equal. (Simple linear regression assumes there is only error in observations on the y-axis) . A residual can then be defined as the orthogonal distance to the regression line; this distance is given in Table 1. Figure 1 shows item 8biii as an outlier, together with a few others (8bi, 9a and 9d) that mig","cbCaiklACkcqqGLH","https://ap.wps.com/l/cbCaiklACkcqqGLH","pdf",304094,"English","# Introduction\n## DIF assessment in vertical scaling\n## Common item statistics and PCM DIF\n## Difficulty plots and orthogonal regression\n## Interpreting residuals and flagging DIF","[{\"question\":\"Why is DIF assessment important for vertically scaling tiered exams?\",\"answer\":\"DIF must be assessed among common items to ensure a fair link between foundation and higher tiers. Items that behave very differently across tiers may need to be dropped from the common item pool.\"},{\"question\":\"How does the report assess DIF without fitting the partial credit model?\",\"answer\":\"It uses difficulty plots based on relative item difficulties and orthogonal regression, defining residuals as orthogonal distances to the regression line. These residuals help flag items that may require investigation.\"},{\"question\":\"What evidence in the paper indicates that certain items show DIF?\",\"answer\":\"Items with large differences in calibrated PCM difficulty estimates (β) across tiers and/or large orthogonal residuals are treated as evidence of DIF. Table 1 and Figure 2 highlight specific items with high PCM DIF.\"}]","Difficulty plots: DIF analysis without the partial credit model | PDF",1792464932,13]