[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-268835-105":59,"doc-detail-268835-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","t-table-statistical-critical-values","t Table - statistical critical values","","t Table provides statistical t critical values for different degrees of freedom (df) and cumulative probabilities (cum. prob), covering one-tail and two-tails thresholds such as 0.50, 0.75, 0.80, 0.85, 0.90, 0.95, 0.975, 0.99, 0.995, 0.999, and 0.9995. The table includes rows for multiple df values (e.g., 1 through 30, plus 40, 60, 80, 100, 1000) and also lists z-related entries. It supports confidence level selection and hypothesis testing decision making.",{"@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/t-table-statistical-critical-values/268835/",{"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/t-table-statistical-critical-values/268835.png","ImageObject",300,407,{"name":92,"@type":93},"Ava Thompson","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-12","2026-09-15",true,{"@type":102,"interactionType":103,"userInteractionCount":81},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"What does the t table provide for hypothesis testing?","Question",{"text":112,"@type":113},"It provides t critical values matched to cumulative probabilities and degrees of freedom. These values help set rejection thresholds for one-tail and two-tail tests.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"How do you use the one-tail vs two-tails columns?",{"text":117,"@type":113},"Choose the column corresponding to the test type: one-tail for one-sided tests and two-tails for two-sided tests. Then match the value to the chosen cum. prob level and df row.",{"name":119,"@type":110,"acceptedAnswer":120},"What is the role of degrees of freedom (df) in this table?",{"text":121,"@type":113},"Each df row corresponds to a specific sampling distribution shape, and the critical values change with df. Select the df that matches the test or model used, then read the critical t for the desired cum. prob.","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},268835,1791496037,{"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":81,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":8,"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":81},1649267921044,"https://us-avatar.wpscdn.com/avatar/1800007509477c92dfb?_k=1786009248482753345","t Table  \n\n| cum. prob | t .50 | t .75 | t .80 | t .85 | t .90 t .95 t .975 | t .99 | t .995 | t .999 | t .9995 |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| one-tail | 0.50 | 0.25 | 0.20 | 0.15 | 0.10 0.05 0.025 | 0.01 | 0.005 | 0.001 | 0.0005 |\n| two-tails | 1.00 | 0.50 | 0.40 | 0.30 | 0.20 0.10 0.05 | 0.02 | 0.01 | 0.002 | 0.001 |\n| df |  |  |  |  |  |  |  |  |  |\n| 1 | 0.000 | 1.000 | 1.376 | 1.963 | 3.078 6.314 12.71 | 31.82 | 63.66 | 318.31 | 636.62 |\n| 2 | 0.000 | 0.816 | 1.061 | 1.386 | 1.886 2.920 4.303 | 6.965 | 9.925 | 22.327 | 31.599 |\n| 3 | 0.000 | 0.765 | 0.978 | 1.250 | 1.638 2.353 3.182 | 4.541 | 5.841 | 10.215 | 12.924 |\n| 4 | 0.000 | 0.741 | 0.941 | 1.190 | 1.533 2.132 2.776 | 3.747 | 4.604 | 7.173 | 8.610 |\n| 5 | 0.000 | 0.727 | 0.920 | 1.156 | 1.476 2.015 2.571 | 3.365 | 4.032 | 5.893 | 6.869 |\n| 6 | 0.000 | 0.718 | 0.906 | 1.134 | 1.440 1.943 2.447 | 3.143 | 3.707 | 5.208 | 5.959 |\n| 7 | 0.000 | 0.711 | 0.896 | 1.119 | 1.415 1.895 2.365 | 2.998 | 3.499 | 4.785 | 5.408 |\n| 8 | 0.000 | 0.706 | 0.889 | 1.108 | 1.397 1.860 2.306 | 2.896 | 3.355 | 4.501 | 5.041 |\n| 9 | 0.000 | 0.703 | 0.883 | 1.100 | 1.383 1.833 2.262 | 2.821 | 3.250 | 4.297 | 4.781 |\n| 10 | 0.000 | 0.700 | 0.879 | 1.093 | 1.372 1.812 2.228 | 2.764 | 3.169 | 4.144 | 4.587 |\n| 11 | 0.000 | 0.697 | 0.876 | 1.088 | 1.363 1.796 2.201 | 2.718 | 3.106 | 4.025 | 4.437 |\n| 12 | 0.000 | 0.695 | 0.873 | 1.083 | 1.356 1.782 2.179 | 2.681 | 3.055 | 3.930 | 4.318 |\n| 13 | 0.000 | 0.694 | 0.870 | 1.079 | 1.350 1.771 2.160 | 2.650 | 3.012 | 3.852 | 4.221 |\n| 14 | 0.000 | 0.692 | 0.868 | 1.076 | 1.345 1.761 2.145 | 2.624 | 2.977 | 3.787 | 4.140 |\n| 15 | 0.000 | 0.691 | 0.866 | 1.074 | 1.341 1.753 2.131 | 2.602 | 2.947 | 3.733 | 4.073 |\n| 16 | 0.000 | 0.690 | 0.865 | 1.071 | 1.337 1.746 2.120 | 2.583 | 2.921 | 3.686 | 4.015 |\n| 17 | 0.000 | 0.689 | 0.863 | 1.069 | 1.333 1.740 2.110 | 2.567 | 2.898 | 3.646 | 3.965 |\n| 18 | 0.000 | 0.688 | 0.862 | 1.067 | 1.330 1.734 2.101 | 2.552 | 2.878 | 3.610 | 3.922 |\n| 19 | 0.000 | 0.688 | 0.861 | 1.066 | 1.328 1.729 2.093 | 2.539 | 2.861 | 3.579 | 3.883 |\n| 20 | 0.000 | 0.687 | 0.860 | 1.064 | 1.325 1.725 2.086 | 2.528 | 2.845 | 3.552 | 3.850 |\n| 21 | 0.000 | 0.686 | 0.859 | 1.063 | 1.323 1.721 2.080 | 2.518 | 2.831 | 3.527 | 3.819 |\n| 22 | 0.000 | 0.686 | 0.858 | 1.061 | 1.321 1.717 2.074 | 2.508 | 2.819 | 3.505 | 3.792 |\n| 23 | 0.000 | 0.685 | 0.858 | 1.060 | 1.319 1.714 2.069 | 2.500 | 2.807 | 3.485 | 3.768 |\n| 24 | 0.000 | 0.685 | 0.857 | 1.059 | 1.318 1.711 2.064 | 2.492 | 2.797 | 3.467 | 3.745 |\n| 25 | 0.000 | 0.684 | 0.856 | 1.058 | 1.316 1.708 2.060 | 2.485 | 2.787 | 3.450 | 3.725 |\n| 26 | 0.000 | 0.684 | 0.856 | 1.058 | 1.315 1.706 2.056 | 2.479 | 2.779 | 3.435 | 3.707 |\n| 27 | 0.000 | 0.684 | 0.855 | 1.057 | 1.314 1.703 2.052 | 2.473 | 2.771 | 3.421 | 3.690 |\n| 28 | 0.000 | 0.683 | 0.855 | 1.056 | 1.313 1.701 2.048 | 2.467 | 2.763 | 3.408 | 3.674 |\n| 29 | 0.000 | 0.683 | 0.854 | 1.055 | 1.311 1.699 2.045 | 2.462 | 2.756 | 3.396 | 3.659 |\n| 30 | 0.000 | 0.683 | 0.854 | 1.055 | 1.310 1.697 2.042 | 2.457 | 2.750 | 3.385 | 3.646 |\n| 40 | 0.000 | 0.681 | 0.851 | 1.050 | 1.303 1.684 2.021 | 2.423 | 2.704 | 3.307 | 3.551 |\n| 60 | 0.000 | 0.679 | 0.848 | 1.045 | 1.296 1.671 2.000 | 2.390 | 2.660 | 3.232 | 3.460 |\n| 80 | 0.000 | 0.678 | 0.846 | 1.043 | 1.292 1.664 1.990 | 2.374 | 2.639 | 3.195 | 3.416 |\n| 100 | 0.000 | 0.677 | 0.845 | 1.042 | 1.290 1.660 1.984 | 2.364 | 2.626 | 3.174 | 3.390 |\n| 1000 | 0.000 | 0.675 | 0.842 | 1.037 | 1.282 1.646 1.962 | 2.330 | 2.581 | 3.098 | 3.300 |\n| z | 0.000 | 0.674 | 0.842 | 1.036 | 1.282 1.645 1.960 | 2.326 | 2.576 | 3.090 | 3.291 |\n|  | 0% | 50% | 60% | 70% | 80% 90% 95% | 98% | 99% | 99.8% | 99.9% |\n|  |  |  |  |  | Confidence Level |  |  |  |  |\n\nt-table.xls 7/14/2007","cbCairdN8SP1XC1P","https://ap.wps.com/l/cbCairdN8SP1XC1P","pdf",12671,"English","# t critical values\n## One-tail and two-tail probabilities\n## Degrees of freedom (df) and z entries","[{\"question\":\"What does the t table provide for hypothesis testing?\",\"answer\":\"It provides t critical values matched to cumulative probabilities and degrees of freedom. These values help set rejection thresholds for one-tail and two-tail tests.\"},{\"question\":\"How do you use the one-tail vs two-tails columns?\",\"answer\":\"Choose the column corresponding to the test type: one-tail for one-sided tests and two-tails for two-sided tests. Then match the value to the chosen cum. prob level and df row.\"},{\"question\":\"What is the role of degrees of freedom (df) in this table?\",\"answer\":\"Each df row corresponds to a specific sampling distribution shape, and the critical values change with df. Select the df that matches the test or model used, then read the critical t for the desired cum. prob.\"}]","t Table - statistical critical values | PDF",1789437719]