[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-35928":3,"doc-seo-35928":29},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":13,"seo_description":14,"update_tm":27,"read_time":28},35928,1099513958607,"Jiven","https://ap-avatar.wpscdn.com/avatar/100002390cf8733938c?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778829742770036399",8,"Research & Report","Corrected Item-Test Correlations","Corrected item-test correlations are derived to address the spurious inflation found in ordinary item–test correlations when an item is part of the test whose reliability varies with the omitted remainder. The proposal replaces an item with a rationally equivalent item so the test’s variance and reliability remain unchanged. For factorially homogeneous tests, the corrected formulas are modified for dichotomous items, yielding corrected point-biserial, biserial, and Brogden biserial correlations based on item reliability.","","cbCaisNgXoeb5ZLQ","https://ap.wps.com/l/cbCaisNgXoeb5ZLQ","pdf",214530,1,4,"English","en",105,"# Corrected correlations and motivation\n# Rationally equivalent item substitution\n# Product-moment item-test correlation transformation\n# Factorial homogeneity assumption\n# Reliability via Kuder–Richardson formula\n# Dichotomous-item special cases","[{\"question\":\"Why are ordinary point-biserial and biserial item–test correlations considered spurious?\",\"answer\":\"Because the correlation uses a test that includes the item, while the reliability of the remainder (test scores excluding the item) varies inversely with the reliability of the omitted item, inflating the correlation.\"},{\"question\":\"What does it mean to replace an item with a rationally equivalent item?\",\"answer\":\"An item i' is rationally equivalent to the real item i when it preserves key variance and reliability relationships across all other items (for j≠i), so the replacement leaves the test variance and reliability unchanged.\"},{\"question\":\"Under what condition do the corrected formulas apply?\",\"answer\":\"They apply strictly to factorially homogeneous tests, where every item measures the same trait (or combination of traits), apart from measurement error.\"}]",1782766832,10,null]