[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-36538-en":3,"doc-seo-36538-105":29,"detail-sidebar-cat-0-en-105":89},{"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":20,"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},36538,1099513958607,"Jiven","https://ap-avatar.wpscdn.com/avatar/100002390cf8733938c?x-image-process=image/resize,m_fixed,w_180,h_180&k=1778829742770036399",8,"Research & Report","An Analytic Approximation to the Distribution of Lilliefors's Test Statistic for Normality","The article presents an analytic approximation for the upper-tail probabilities of Lilliefors’s Dmax test statistic used for testing normality when population mean and variance are unknown. It corrects critical values reported in Lilliefors (1967) via extensive simulation, addressing inaccuracies and anti-conservative behavior in the original table. A practical exponential-based formula is provided for p\u003C0.100 and sample sizes between 5 and 100, with an adjusted version for n>100.","","cbCaijhJN1x6kU3T","https://ap.wps.com/l/cbCaijhJN1x6kU3T","pdf",338702,1,4,"English","en",105,"# 1. Introduction\n# 2. Analytic Approximation","[{\"question\":\"What problem does the article address about Lilliefors’s normality test?\",\"answer\":\"The article addresses inaccuracies in the critical values from Lilliefors (1967), including differences caused by too few simulation replications and cases where the original values are anti-conservative.\"},{\"question\":\"How is the Dmax statistic defined in the paper?\",\"answer\":\"Dmax is defined as the maximum absolute difference between the sample distribution function S(x) and the estimated cumulative normal distribution F*(x), with parameters estimated from the sample.\"},{\"question\":\"What analytic approximation does the paper provide for the upper-tail probability of Dmax?\",\"answer\":\"For p\\u003c0.100 and sample sizes n between 5 and 100, the paper gives an exponential-based approximation in terms of Dmax and n. For n\\u003e100, it uses the same form with Dmax and n modified by the provided scaling rules.\"}]",1782939809,10,{"code":4,"msg":30,"data":31},"ok",{"site_id":24,"language":23,"slug":32,"title":13,"keywords":15,"description":14,"schema_data":33,"social_meta":84,"head_meta":86,"extra_data":88,"updated_unix":27},"an-analytic-approximation-to-the-distribution-of-lillieforss-test-statistic-for-normality",{"@graph":34,"@context":83},[35,51,66],{"@type":36,"itemListElement":37},"BreadcrumbList",[38,42,46,49],{"item":39,"name":40,"@type":41,"position":20},"https://docshare.wps.com","Home","ListItem",{"item":43,"name":44,"@type":41,"position":45},"https://docshare.wps.com/document/","Document",2,{"item":47,"name":12,"@type":41,"position":48},"https://docshare.wps.com/document/research-report/",3,{"item":50,"name":13,"@type":41,"position":21},"https://docshare.wps.com/document/an-analytic-approximation-to-the-distribution-of-lillieforss-test-statistic-for-normality/36538/",{"url":50,"name":13,"@type":52,"author":53,"headline":13,"publisher":55,"fileFormat":58,"inLanguage":23,"description":14,"dateModified":59,"datePublished":60,"encodingFormat":58,"isAccessibleForFree":61,"interactionStatistic":62},"DigitalDocument",{"name":9,"@type":54},"Person",{"url":39,"name":56,"@type":57},"DocShare","Organization","application/pdf","2026-07-07","2026-07-01",true,{"@type":63,"interactionType":64,"userInteractionCount":20},"InteractionCounter",{"@type":65},"ViewAction",{"@type":67,"mainEntity":68},"FAQPage",[69,75,79],{"name":70,"@type":71,"acceptedAnswer":72},"What problem does the article address about Lilliefors’s normality test?","Question",{"text":73,"@type":74},"The article addresses inaccuracies in the critical values from Lilliefors (1967), including differences caused by too few simulation replications and cases where the original values are anti-conservative.","Answer",{"name":76,"@type":71,"acceptedAnswer":77},"How is the Dmax statistic defined in the paper?",{"text":78,"@type":74},"Dmax is defined as the maximum absolute difference between the sample distribution function S(x) and the estimated cumulative normal distribution F*(x), with parameters estimated from the sample.",{"name":80,"@type":71,"acceptedAnswer":81},"What analytic approximation does the paper provide for the upper-tail probability of Dmax?",{"text":82,"@type":74},"For p\u003C0.100 and sample sizes n between 5 and 100, the paper gives an exponential-based approximation in terms of Dmax and n. For n>100, it uses the same form with Dmax and n modified by the provided scaling rules.","https://schema.org",{"og:url":50,"og:type":85,"og:title":13,"og:site_name":56,"og:description":14},"article",{"robots":87,"canonical":50},"index,follow",{"doc_id":7,"site_id":24},{"code":4,"msg":5,"data":90},[91,95,99,103,108,113,118,121,126,129,132],{"id":20,"doc_module":4,"doc_module_name":44,"category_name":92,"show_sort_weight":93,"slug":94},"Story & Novel",90,"story-novel",{"id":45,"doc_module":4,"doc_module_name":44,"category_name":96,"show_sort_weight":97,"slug":98},"Literature",80,"literature",{"id":21,"doc_module":4,"doc_module_name":44,"category_name":100,"show_sort_weight":101,"slug":102},"Exam",70,"exam",{"id":104,"doc_module":4,"doc_module_name":44,"category_name":105,"show_sort_weight":106,"slug":107},5,"Comic",60,"comic",{"id":109,"doc_module":4,"doc_module_name":44,"category_name":110,"show_sort_weight":111,"slug":112},6,"Technology",50,"technology",{"id":114,"doc_module":4,"doc_module_name":44,"category_name":115,"show_sort_weight":116,"slug":117},7,"Healthcare",40,"healthcare",{"id":11,"doc_module":4,"doc_module_name":44,"category_name":12,"show_sort_weight":119,"slug":120},30,"research-report",{"id":122,"doc_module":4,"doc_module_name":44,"category_name":123,"show_sort_weight":124,"slug":125},9,"Religion & Spirituality",20,"religion-spirituality",{"id":124,"doc_module":4,"doc_module_name":44,"category_name":127,"show_sort_weight":124,"slug":128},"World Cup","world-cup",{"id":28,"doc_module":4,"doc_module_name":44,"category_name":130,"show_sort_weight":28,"slug":131},"Lifestyle","lifestyle",{"id":133,"doc_module":4,"doc_module_name":44,"category_name":134,"show_sort_weight":104,"slug":135},19,"General","general"]