[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"detail-sidebar-cat-0-en-105":3,"doc-seo-397959-105":59,"doc-detail-397959-en":122},{"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":115,"head_meta":117,"extra_data":119,"updated_unix":121},105,"en","chi-square-distribution-table-lookup-critical-values","Chi-Square Distribution Table - lookup critical values","","Chi-square distribution table providing critical values for a chi-square test across degrees of freedom (df) and multiple significance levels (e.g., 0.995, 0.990, 0.975, 0.950, 0.900, 0.100, 0.050, 0.025, 0.010, 0.005). Use the table to identify threshold statistics corresponding to chosen alpha levels. The layout organizes df values in rows and chi-square quantiles by columns for direct comparison with computed test statistics.",{"@graph":69,"@context":114},[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/chi-square-distribution-table-lookup-critical-values/397959/",{"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/chi-square-distribution-table-lookup-critical-values/397959.png","ImageObject",300,407,{"name":92,"@type":93},"dhado","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-11-09","2026-09-27",true,{"@type":102,"interactionType":103,"userInteractionCount":44},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108],{"name":109,"@type":110,"acceptedAnswer":111},"Why are the table values organized by degrees of freedom (df)?","Question",{"text":112,"@type":113},"The chi-square distribution changes shape with df, so critical values depend on df. Using the correct df ensures the threshold is appropriate for the specific test setup.","Answer","https://schema.org",{"og:url":83,"og:type":116,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":118,"canonical":83},"index,follow",{"doc_id":120,"site_id":62},397959,1791378846,{"code":4,"msg":5,"data":123},{"doc_id":120,"user_id":124,"nickname":92,"user_avatar":125,"doc_module":4,"category_id":19,"category_name":20,"doc_title":65,"doc_description":67,"doc_content":126,"file_id":127,"file_url":128,"file_type":129,"file_size":130,"view_count":44,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":8,"language":131,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":132,"faqs":133,"seo_title":134,"seo_description":67,"update_tm":135,"read_time":81,"preview_page_count":4},5909893218464,"https://ap-avatar.wpscdn.com/davatar_085a072bc5b1113ac321206ff7593b45","Chi-Square Distribution Table  \nThe shaded area is equal to ® for Â2 = Â2 .  \n®  \n\n| df | Â2:995 | Â2:990 | Â2:975 | Â2:950 | Â2:900 | Â2: 100 | Â2:050 | Â2:025 | Â2:010 | Â2:005 |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n\n\n| 1 2\u003Cbr>3 4\u003Cbr>5 | 0.000\u003Cbr>0.010\u003Cbr>0.072\u003Cbr>0.207\u003Cbr>0.412 | 0.000\u003Cbr>0.020\u003Cbr>0.115\u003Cbr>0.297\u003Cbr>0.554 | 0.001\u003Cbr>0.051\u003Cbr>0.216\u003Cbr>0.484\u003Cbr>0.831 | 0.004\u003Cbr>0.103\u003Cbr>0.352\u003Cbr>0.711\u003Cbr>1.145 | 0.016\u003Cbr>0.211\u003Cbr>0.584\u003Cbr>1.064\u003Cbr>1.610 | 2.706\u003Cbr>4.605\u003Cbr>6.251\u003Cbr>7.779\u003Cbr>9.236 | 3.841\u003Cbr>5.991\u003Cbr>7.815\u003Cbr>9.488\u003Cbr>11.070 | 5.024\u003Cbr>7.378\u003Cbr>9.348\u003Cbr>11.143\u003Cbr>12.833 | 6.635\u003Cbr>9.210\u003Cbr>11.345\u003Cbr>13.277\u003Cbr>15.086 | 7.879\u003Cbr>10.597\u003Cbr>12.838\u003Cbr>14.860\u003Cbr>16.750 |\n| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |\n| 6 7\u003Cbr>8 9\u003Cbr>10 | 0.676\u003Cbr>0.989\u003Cbr>1.344\u003Cbr>1.735\u003Cbr>2.156 | 0.872\u003Cbr>1.239\u003Cbr>1.646\u003Cbr>2.088\u003Cbr>2.558 | 1.237\u003Cbr>1.690\u003Cbr>2.180\u003Cbr>2.700\u003Cbr>3.247 | 1.635\u003Cbr>2.167\u003Cbr>2.733\u003Cbr>3.325\u003Cbr>3.940 | 2.204\u003Cbr>2.833\u003Cbr>3.490\u003Cbr>4.168\u003Cbr>4.865 | 10.645\u003Cbr>12.017\u003Cbr>13.362\u003Cbr>14.684\u003Cbr>15.987 | 12.592\u003Cbr>14.067\u003Cbr>15.507\u003Cbr>16.919\u003Cbr>18.307 | 14.449\u003Cbr>16.013\u003Cbr>17.535\u003Cbr>19.023\u003Cbr>20.483 | 16.812\u003Cbr>18.475\u003Cbr>20.090\u003Cbr>21.666\u003Cbr>23.209 | 18.548\u003Cbr>20.278\u003Cbr>21.955\u003Cbr>23.589\u003Cbr>25.188 |\n| 11\u003Cbr>12\u003Cbr>13\u003Cbr>14\u003Cbr>15 | 2.603\u003Cbr>3.074\u003Cbr>3.565\u003Cbr>4.075\u003Cbr>4.601 | 3.053\u003Cbr>3.571\u003Cbr>4.107\u003Cbr>4.660\u003Cbr>5.229 | 3.816\u003Cbr>4.404\u003Cbr>5.009\u003Cbr>5.629\u003Cbr>6.262 | 4.575\u003Cbr>5.226\u003Cbr>5.892\u003Cbr>6.571\u003Cbr>7.261 | 5.578\u003Cbr>6.304\u003Cbr>7.042\u003Cbr>7.790\u003Cbr>8.547 | 17.275\u003Cbr>18.549\u003Cbr>19.812\u003Cbr>21.064\u003Cbr>22.307 | 19.675\u003Cbr>21.026\u003Cbr>22.362\u003Cbr>23.685\u003Cbr>24.996 | 21.920\u003Cbr>23.337\u003Cbr>24.736\u003Cbr>26.119\u003Cbr>27.488 | 24.725\u003Cbr>26.217\u003Cbr>27.688\u003Cbr>29.141\u003Cbr>30.578 | 26.757\u003Cbr>28.300\u003Cbr>29.819\u003Cbr>31.319\u003Cbr>32.801 |\n| 16\u003Cbr>17\u003Cbr>18\u003Cbr>19\u003Cbr>20 | 5.142\u003Cbr>5.697\u003Cbr>6.265\u003Cbr>6.844\u003Cbr>7.434 | 5.812\u003Cbr>6.408\u003Cbr>7.015\u003Cbr>7.633\u003Cbr>8.260 | 6.908\u003Cbr>7.564\u003Cbr>8.231\u003Cbr>8.907\u003Cbr>9.591 | 7.962\u003Cbr>8.672\u003Cbr>9.390\u003Cbr>10.117\u003Cbr>10.851 | 9.312\u003Cbr>10.085\u003Cbr>10.865\u003Cbr>11.651\u003Cbr>12.443 | 23.542\u003Cbr>24.769\u003Cbr>25.989\u003Cbr>27.204\u003Cbr>28.412 | 26.296\u003Cbr>27.587\u003Cbr>28.869\u003Cbr>30.144\u003Cbr>31.410 | 28.845\u003Cbr>30.191\u003Cbr>31.526\u003Cbr>32.852\u003Cbr>34.170 | 32.000\u003Cbr>33.409\u003Cbr>34.805\u003Cbr>36.191\u003Cbr>37.566 | 34.267\u003Cbr>35.718\u003Cbr>37.156\u003Cbr>38.582\u003Cbr>39.997 |\n| 21\u003Cbr>22\u003Cbr>23\u003Cbr>24\u003Cbr>25 | 8.034\u003Cbr>8.643\u003Cbr>9.260\u003Cbr>9.886\u003Cbr>10.520 | 8.897\u003Cbr>9.542\u003Cbr>10.196\u003Cbr>10.856\u003Cbr>11.524 | 10.283\u003Cbr>10.982\u003Cbr>11.689\u003Cbr>12.401\u003Cbr>13.120 | 11.591\u003Cbr>12.338\u003Cbr>13.091\u003Cbr>13.848\u003Cbr>14.611 | 13.240\u003Cbr>14.041\u003Cbr>14.848\u003Cbr>15.659\u003Cbr>16.473 | 29.615\u003Cbr>30.813\u003Cbr>32.007\u003Cbr>33.196\u003Cbr>34.382 | 32.671\u003Cbr>33.924\u003Cbr>35.172\u003Cbr>36.415\u003Cbr>37.652 | 35.479\u003Cbr>36.781\u003Cbr>38.076\u003Cbr>39.364\u003Cbr>40.646 | 38.932\u003Cbr>40.289\u003Cbr>41.638\u003Cbr>42.980\u003Cbr>44.314 | 41.401\u003Cbr>42.796\u003Cbr>44.181\u003Cbr>45.559\u003Cbr>46.928 |\n| 26\u003Cbr>27\u003Cbr>28\u003Cbr>29\u003Cbr>30 | 11.160\u003Cbr>11.808\u003Cbr>12.461\u003Cbr>13.121\u003Cbr>13.787 | 12.198\u003Cbr>12.879\u003Cbr>13.565\u003Cbr>14.256\u003Cbr>14.953 | 13.844\u003Cbr>14.573\u003Cbr>15.308\u003Cbr>16.047\u003Cbr>16.791 | 15.379\u003Cbr>16.151\u003Cbr>16.928\u003Cbr>17.708\u003Cbr>18.493 | 17.292\u003Cbr>18.114\u003Cbr>18.939\u003Cbr>19.768\u003Cbr>20.599 | 35.563\u003Cbr>36.741\u003Cbr>37.916\u003Cbr>39.087\u003Cbr>40.256 | 38.885\u003Cbr>40.113\u003Cbr>41.337\u003Cbr>42.557\u003Cbr>43.773 | 41.923\u003Cbr>43.195\u003Cbr>44.461\u003Cbr>45.722\u003Cbr>46.979 | 45.642\u003Cbr>46.963\u003Cbr>48.278\u003Cbr>49.588\u003Cbr>50.892 | 48.290\u003Cbr>49.645\u003Cbr>50.993\u003Cbr>52.336\u003Cbr>53.672 |\n| 40\u003Cbr>50\u003Cbr>60\u003Cbr>70 | 20.707\u003Cbr>27.991\u003Cbr>35.534\u003Cbr>43.275 | 22.164\u003Cbr>29.707\u003Cbr>37.485\u003Cbr>45.442 | 24.433\u003Cbr>32.357\u003Cbr>40.482\u003Cbr>48.758 | 26.509\u003Cbr>34.764\u003Cbr>43.188\u003Cbr>51.739 | 29.051\u003Cbr>37.689\u003Cbr>46.459\u003Cbr>55.329 | 51.805\u003Cbr>63.167\u003Cbr>74.397\u003Cbr>85.527 | 55.758\u003Cbr>67.505\u003Cbr>79.082\u003Cbr>90.531 | 59.342\u003Cbr>71.420\u003Cbr>83.298\u003Cbr>95.023 | 63.691\u003Cbr>76.154\u003Cbr>88.379\u003Cbr>100.425 | 66.766\u003Cbr>79.490\u003Cbr>91.952\u003Cbr>104.215 |\n| 80\u003Cbr>90\u003Cbr>100 | 51.172\u003Cbr>59.196\u003Cbr>67.328 | 53.540\u003Cbr>61.754\u003Cbr>70.065 | 57.153\u003Cbr>65.647\u003Cbr>74.222 | 60.391\u003Cbr>69.126\u003Cbr>77.929 | 64.278\u003Cbr>73.291\u003Cbr>82.358 | 96.578\u003Cbr>107.565\u003Cbr>118.498 | 101.879\u003Cbr>113.145\u003Cbr>124.342 | 106.629\u003Cbr>118.136\u003Cbr>129.561 | 112.329\u003Cbr>124","cbCaig0liCyEPenm","https://ap.wps.com/l/cbCaig0liCyEPenm","pdf",35966,"English","# Chi-square distribution table\n## Degrees of freedom (df)\n## Chi-square quantiles by significance level","[{\"question\":\"Why are the table values organized by degrees of freedom (df)?\",\"answer\":\"The chi-square distribution changes shape with df, so critical values depend on df. Using the correct df ensures the threshold is appropriate for the specific test setup.\"}]","Chi-Square Distribution Table - lookup critical values | PDF",1790468839]