{"id":163,"date":"2018-12-31T07:13:19","date_gmt":"2018-12-31T07:13:19","guid":{"rendered":"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/?post_type=chapter&#038;p=163"},"modified":"2018-12-31T07:24:34","modified_gmt":"2018-12-31T07:24:34","slug":"hotelling-t2-test-and-manova-using-r","status":"publish","type":"chapter","link":"https:\/\/ebooks.inflibnet.ac.in\/statp11\/chapter\/hotelling-t2-test-and-manova-using-r\/","title":{"rendered":"Hotelling T2 Test and MANOVA using R"},"content":{"raw":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/o5o9NentGuA\" target=\"_blank\" rel=\"noopener\"><img src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a>\r\n<\/span><\/div>\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n&nbsp;\r\n\r\n<img class=\"aligncenter size-full wp-image-166\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-02.jpg\" alt=\"\" width=\"1133\" height=\"1609\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-167\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-03.jpg\" alt=\"\" width=\"1041\" height=\"1429\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-168\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-04.jpg\" alt=\"\" width=\"1117\" height=\"1309\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-169\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-05.jpg\" alt=\"\" width=\"1249\" height=\"1245\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-170\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-06.jpg\" alt=\"\" width=\"1093\" height=\"721\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-171\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-07.jpg\" alt=\"\" width=\"1081\" height=\"1281\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-172\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-08.jpg\" alt=\"\" width=\"1037\" height=\"1537\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-173\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-09.jpg\" alt=\"\" width=\"1073\" height=\"1053\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-174\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-10.jpg\" alt=\"\" width=\"1217\" height=\"1133\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-175\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-11.jpg\" alt=\"\" width=\"1065\" height=\"1153\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-176\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-12.jpg\" alt=\"\" width=\"1101\" height=\"1401\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-177\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-13.jpg\" alt=\"\" width=\"1157\" height=\"1473\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-178\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-14.jpg\" alt=\"\" width=\"1153\" height=\"1573\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-179\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-15.jpg\" alt=\"\" width=\"1093\" height=\"1441\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-180\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-16.jpg\" alt=\"\" width=\"1061\" height=\"1377\" \/>\r\n\r\n<img class=\"aligncenter size-full wp-image-181\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-17.jpg\" alt=\"\" width=\"1097\" height=\"1133\" \/>\r\n<table>\r\n<tbody>\r\n<tr>\r\n<td><strong>you can view video on Hotelling T<sup>2<\/sup> Test and MANOVA using R<\/strong><\/td>\r\n<td><a href=\"https:\/\/youtu.be\/o5o9NentGuA\" target=\"_blank\" rel=\"noopener\"><img class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n\r\n<img class=\"aligncenter size-full wp-image-182\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691254HotellingT2TestandMANOVAUsingR_Ref-1.jpg\" alt=\"\" width=\"1053\" height=\"385\" \/>","rendered":"<div><span style=\"float: right\"><a href=\"https:\/\/youtu.be\/o5o9NentGuA\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"epgp books\" width=\"75px\" height=\"75px;\" \/><\/a><br \/>\n<\/span><\/div>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-166\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-02.jpg\" alt=\"\" width=\"1133\" height=\"1609\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-02.jpg 1133w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-02-211x300.jpg 211w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-02-768x1091.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-02-721x1024.jpg 721w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-02-65x92.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-02-225x320.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-02-350x497.jpg 350w\" sizes=\"auto, (max-width: 1133px) 100vw, 1133px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-167\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-03.jpg\" alt=\"\" width=\"1041\" height=\"1429\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-03.jpg 1041w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-03-219x300.jpg 219w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-03-768x1054.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-03-746x1024.jpg 746w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-03-65x89.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-03-225x309.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-03-350x480.jpg 350w\" sizes=\"auto, (max-width: 1041px) 100vw, 1041px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-168\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-04.jpg\" alt=\"\" width=\"1117\" height=\"1309\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-04.jpg 1117w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-04-256x300.jpg 256w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-04-768x900.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-04-874x1024.jpg 874w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-04-65x76.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-04-225x264.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-04-350x410.jpg 350w\" sizes=\"auto, (max-width: 1117px) 100vw, 1117px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-169\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-05.jpg\" alt=\"\" width=\"1249\" height=\"1245\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-05.jpg 1249w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-05-150x150.jpg 150w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-05-300x300.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-05-768x766.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-05-1024x1021.jpg 1024w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-05-65x65.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-05-225x224.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-05-350x349.jpg 350w\" sizes=\"auto, (max-width: 1249px) 100vw, 1249px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-170\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-06.jpg\" alt=\"\" width=\"1093\" height=\"721\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-06.jpg 1093w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-06-300x198.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-06-768x507.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-06-1024x675.jpg 1024w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-06-65x43.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-06-225x148.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-06-350x231.jpg 350w\" sizes=\"auto, (max-width: 1093px) 100vw, 1093px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-171\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-07.jpg\" alt=\"\" width=\"1081\" height=\"1281\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-07.jpg 1081w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-07-253x300.jpg 253w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-07-768x910.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-07-864x1024.jpg 864w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-07-65x77.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-07-225x267.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-07-350x415.jpg 350w\" sizes=\"auto, (max-width: 1081px) 100vw, 1081px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-172\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-08.jpg\" alt=\"\" width=\"1037\" height=\"1537\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-08.jpg 1037w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-08-202x300.jpg 202w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-08-768x1138.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-08-691x1024.jpg 691w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-08-65x96.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-08-225x333.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-08-350x519.jpg 350w\" sizes=\"auto, (max-width: 1037px) 100vw, 1037px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-173\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-09.jpg\" alt=\"\" width=\"1073\" height=\"1053\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-09.jpg 1073w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-09-300x294.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-09-768x754.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-09-1024x1005.jpg 1024w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-09-65x64.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-09-225x221.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-09-350x343.jpg 350w\" sizes=\"auto, (max-width: 1073px) 100vw, 1073px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-174\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-10.jpg\" alt=\"\" width=\"1217\" height=\"1133\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-10.jpg 1217w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-10-300x279.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-10-768x715.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-10-1024x953.jpg 1024w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-10-65x61.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-10-225x209.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-10-350x326.jpg 350w\" sizes=\"auto, (max-width: 1217px) 100vw, 1217px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-175\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-11.jpg\" alt=\"\" width=\"1065\" height=\"1153\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-11.jpg 1065w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-11-277x300.jpg 277w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-11-768x831.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-11-946x1024.jpg 946w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-11-65x70.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-11-225x244.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-11-350x379.jpg 350w\" sizes=\"auto, (max-width: 1065px) 100vw, 1065px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-176\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-12.jpg\" alt=\"\" width=\"1101\" height=\"1401\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-12.jpg 1101w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-12-236x300.jpg 236w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-12-768x977.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-12-805x1024.jpg 805w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-12-65x83.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-12-225x286.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-12-350x445.jpg 350w\" sizes=\"auto, (max-width: 1101px) 100vw, 1101px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-177\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-13.jpg\" alt=\"\" width=\"1157\" height=\"1473\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-13.jpg 1157w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-13-236x300.jpg 236w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-13-768x978.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-13-804x1024.jpg 804w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-13-65x83.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-13-225x286.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-13-350x446.jpg 350w\" sizes=\"auto, (max-width: 1157px) 100vw, 1157px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-178\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-14.jpg\" alt=\"\" width=\"1153\" height=\"1573\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-14.jpg 1153w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-14-220x300.jpg 220w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-14-768x1048.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-14-751x1024.jpg 751w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-14-65x89.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-14-225x307.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-14-350x477.jpg 350w\" sizes=\"auto, (max-width: 1153px) 100vw, 1153px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-179\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-15.jpg\" alt=\"\" width=\"1093\" height=\"1441\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-15.jpg 1093w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-15-228x300.jpg 228w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-15-768x1013.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-15-777x1024.jpg 777w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-15-65x86.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-15-225x297.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-15-350x461.jpg 350w\" sizes=\"auto, (max-width: 1093px) 100vw, 1093px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-180\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-16.jpg\" alt=\"\" width=\"1061\" height=\"1377\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-16.jpg 1061w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-16-231x300.jpg 231w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-16-768x997.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-16-789x1024.jpg 789w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-16-65x84.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-16-225x292.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-16-350x454.jpg 350w\" sizes=\"auto, (max-width: 1061px) 100vw, 1061px\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-181\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-17.jpg\" alt=\"\" width=\"1097\" height=\"1133\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-17.jpg 1097w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-17-290x300.jpg 290w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-17-768x793.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-17-991x1024.jpg 991w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-17-65x67.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-17-225x232.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691246HotellingT2TestandMANOVAUsingR-17-350x361.jpg 350w\" sizes=\"auto, (max-width: 1097px) 100vw, 1097px\" \/><\/p>\n<table>\n<tbody>\n<tr>\n<td><strong>you can view video on Hotelling T<sup>2<\/sup> Test and MANOVA using R<\/strong><\/td>\n<td><a href=\"https:\/\/youtu.be\/o5o9NentGuA\" target=\"_blank\" rel=\"noopener\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-120\" src=\"http:\/\/epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/2018\/11\/download.png\" alt=\"\" width=\"36\" height=\"36\" \/><\/a><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-182\" src=\"http:\/\/statp11.epgpbooks.inflibnet.ac.in\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691254HotellingT2TestandMANOVAUsingR_Ref-1.jpg\" alt=\"\" width=\"1053\" height=\"385\" srcset=\"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691254HotellingT2TestandMANOVAUsingR_Ref-1.jpg 1053w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691254HotellingT2TestandMANOVAUsingR_Ref-1-300x110.jpg 300w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691254HotellingT2TestandMANOVAUsingR_Ref-1-768x281.jpg 768w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691254HotellingT2TestandMANOVAUsingR_Ref-1-1024x374.jpg 1024w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691254HotellingT2TestandMANOVAUsingR_Ref-1-65x24.jpg 65w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691254HotellingT2TestandMANOVAUsingR_Ref-1-225x82.jpg 225w, https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-content\/uploads\/sites\/139\/2018\/12\/1525691254HotellingT2TestandMANOVAUsingR_Ref-1-350x128.jpg 350w\" sizes=\"auto, (max-width: 1053px) 100vw, 1053px\" \/><\/p>\n","protected":false},"author":3,"menu_order":14,"template":"","meta":{"_acf_changed":false,"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":["prof-sumitra-purkayastha"],"pb_section_license":""},"chapter-type":[],"contributor":[59],"license":[],"class_list":["post-163","chapter","type-chapter","status-publish","hentry","contributor-prof-sumitra-purkayastha"],"part":3,"_links":{"self":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-json\/pressbooks\/v2\/chapters\/163","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-json\/wp\/v2\/users\/3"}],"version-history":[{"count":3,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-json\/pressbooks\/v2\/chapters\/163\/revisions"}],"predecessor-version":[{"id":183,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-json\/pressbooks\/v2\/chapters\/163\/revisions\/183"}],"part":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-json\/pressbooks\/v2\/parts\/3"}],"metadata":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-json\/pressbooks\/v2\/chapters\/163\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-json\/wp\/v2\/media?parent=163"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-json\/pressbooks\/v2\/chapter-type?post=163"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-json\/wp\/v2\/contributor?post=163"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/ebooks.inflibnet.ac.in\/statp11\/wp-json\/wp\/v2\/license?post=163"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}