{"id":482,"date":"2023-07-29T18:24:50","date_gmt":"2023-07-29T18:24:50","guid":{"rendered":"https:\/\/statorials.org\/my\/manova-%e1%80%99%e1%80%be-r\/"},"modified":"2023-07-29T18:24:50","modified_gmt":"2023-07-29T18:24:50","slug":"manova-%e1%80%99%e1%80%be-r","status":"publish","type":"post","link":"https:\/\/statorials.org\/my\/manova-%e1%80%99%e1%80%be-r\/","title":{"rendered":"R \u1016\u103c\u1004\u1037\u103a manova \u1000\u102d\u102f\u1019\u100a\u103a\u101e\u102d\u102f\u1037\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1019\u100a\u103a\u1014\u100a\u103a\u1038\u104b"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">MANOVA \u1000\u102d\u102f \u1014\u102c\u1038\u101c\u100a\u103a\u101b\u1014\u103a\u104a ANOVA \u1000\u102d\u102f \u1014\u102c\u1038\u101c\u100a\u103a\u101b\u1014\u103a \u1026\u1038\u1005\u103d\u102c \u1021\u1000\u1030\u1021\u100a\u102e\u1016\u103c\u1005\u103a \u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/my\/one-way-anova\/\" target=\"_blank\" rel=\"noopener\">ANOVA<\/a> (\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1000\u102d\u102f \u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u1001\u103c\u1004\u103a\u1038) \u1000\u102d\u102f \u101e\u102f\u1036\u1038\u101e\u1031\u102c \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1011\u102d\u102f\u1037\u1011\u1000\u103a\u1015\u102d\u102f\u101e\u1031\u102c \u101e\u102e\u1038\u1001\u103c\u102c\u1038\u1021\u102f\u1015\u103a\u1005\u102f\u1019\u103b\u102c\u1038\u104f \u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1019\u103b\u102c\u1038\u1000\u103c\u102c\u1038\u1010\u103d\u1004\u103a \u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1021\u101b \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u101e\u1031\u102c \u1001\u103c\u102c\u1038\u1014\u102c\u1038\u1019\u103e\u102f \u101b\u103e\u102d\u104a \u1019\u101b\u103e\u102d \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1025\u1015\u1019\u102c\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a\u104a \u101c\u1031\u1037\u101c\u102c\u1001\u103c\u1004\u103a\u1038\u1014\u100a\u103a\u1038\u1015\u100a\u102c\u101e\u100a\u103a \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u1019\u103b\u102c\u1038\u104f \u1021\u1010\u1014\u103a\u1038\u1010\u1005\u103a\u1010\u1014\u103a\u1038\u104f \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u101b\u1019\u103e\u1010\u103a\u1019\u103b\u102c\u1038\u1021\u1015\u1031\u102b\u103a \u101e\u1000\u103a\u101b\u1031\u102c\u1000\u103a\u1019\u103e\u102f\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u101e\u102d\u1001\u103b\u1004\u103a\u101e\u100a\u103a\u1006\u102d\u102f\u1000\u103c\u1015\u102b\u1005\u102d\u102f\u1037\u104b \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1021\u1010\u1014\u103a\u1038\u1000\u102d\u102f \u1021\u102f\u1015\u103a\u1005\u102f\u101e\u102f\u1036\u1038\u1005\u102f\u1001\u103d\u1032\u104d \u1000\u103b\u1015\u1014\u103a\u1038\u1001\u103d\u1032\u101e\u100a\u103a\u104b \u1021\u102f\u1015\u103a\u1005\u102f\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u101e\u100a\u103a \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u1021\u1010\u103d\u1000\u103a \u1015\u103c\u1004\u103a\u1006\u1004\u103a\u101b\u1014\u103a \u1010\u1005\u103a\u101c\u1021\u1010\u103d\u1000\u103a \u1019\u1010\u1030\u100a\u102e\u101e\u1031\u102c \u101c\u1031\u1037\u101c\u102c\u1019\u103e\u102f\u1014\u100a\u103a\u1038\u1005\u1014\u1005\u103a\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a\u104b \u101c\u1000\u102f\u1014\u103a\u1010\u103d\u1004\u103a \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u1021\u102c\u1038\u101c\u102f\u1036\u1038 \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u1000\u102d\u102f \u1021\u1010\u1030\u1010\u1030\u1016\u103c\u1031\u1006\u102d\u102f\u1000\u103c\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1014\u100a\u103a\u1038\u1005\u1014\u1005\u103a\u101c\u1031\u1037\u101c\u102c\u1001\u103c\u1004\u103a\u1038\u101e\u100a\u103a \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u101b\u1019\u103e\u1010\u103a\u1019\u103b\u102c\u1038\u1021\u1015\u1031\u102b\u103a \u101e\u1000\u103a\u101b\u1031\u102c\u1000\u103a\u1019\u103e\u102f\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u101e\u102d\u101b\u103e\u102d\u101b\u1014\u103a\u104a \u1021\u102f\u1015\u103a\u1005\u102f\u101e\u102f\u1036\u1038\u1005\u102f\u104f \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u101b\u1019\u103e\u1010\u103a\u1019\u103b\u102c\u1038\u1021\u1000\u103c\u102c\u1038 \u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1006\u102d\u102f\u1004\u103a\u101b\u102c \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u101e\u1031\u102c \u1000\u103d\u102c\u1001\u103c\u102c\u1038\u1001\u103b\u1000\u103a\u101b\u103e\u102d\u1019\u101b\u103e\u102d\u1000\u102d\u102f \u1015\u103c\u1031\u102c\u1015\u103c\u1019\u100a\u1037\u103a one-way ANOVA \u1000\u102d\u102f \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">ANOVA \u1010\u103d\u1004\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1010\u103d\u1004\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f \u1015\u103c\u1031\u102c\u1004\u103a\u1038\u101c\u1032\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c \u1010\u1005\u103a\u1001\u102f\u101b\u103e\u102d\u101e\u100a\u103a\u104b \u101e\u102d\u102f\u1037\u101e\u1031\u102c\u103a\u104a <strong>MANOVA<\/strong> (\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u104f \u1000\u103d\u1032\u1015\u103c\u102c\u1038\u1019\u103e\u102f \u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u1019\u103e\u102f) \u1010\u103d\u1004\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1010\u103d\u1004\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\u1005\u103d\u102c\u101b\u103e\u102d\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1025\u1015\u1019\u102c\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a\u104a \u1015\u100a\u102c\u101b\u1031\u1038\u1021\u1006\u1004\u1037\u103a (\u1025\u1015\u1019\u102c \u1021\u1011\u1000\u103a\u1010\u1014\u103a\u1038\u1000\u103b\u1031\u102c\u1004\u103a\u1038\u104a \u1010\u103d\u1032\u1018\u1000\u103a\u1018\u103d\u1032\u1037\u104a \u1018\u103d\u1032\u1037\u104a \u1019\u101f\u102c\u1018\u103d\u1032\u1037\u1005\u101e\u100a\u103a\u1016\u103c\u1004\u1037\u103a) \u101e\u100a\u103a \u1014\u103e\u1005\u103a\u1005\u1009\u103a\u101d\u1004\u103a\u1004\u103d\u1031\u1014\u103e\u1004\u1037\u103a \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u1000\u103c\u103d\u1031\u1038\u1019\u103c\u102e\u1015\u1019\u102c\u100f\u1021\u1015\u1031\u102b\u103a \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u1021\u1000\u103b\u102d\u102f\u1038\u101e\u1000\u103a\u101b\u1031\u102c\u1000\u103a\u101e\u100a\u103a\u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u101e\u102d\u101c\u102d\u102f\u101e\u100a\u103a\u1006\u102d\u102f\u1015\u102b\u1005\u102d\u102f\u1037\u104b \u1024\u1000\u102d\u1005\u1039\u1005\u1010\u103d\u1004\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1010\u103d\u1004\u103a \u1021\u1001\u103b\u1000\u103a\u1010\u1005\u103a\u1001\u103b\u1000\u103a (\u1015\u100a\u102c\u101b\u1031\u1038\u1021\u1006\u1004\u1037\u103a) \u1014\u103e\u1004\u1037\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1015\u103c\u1031\u102c\u1004\u103a\u1038\u101c\u1032\u1019\u103e\u102f\u1014\u103e\u1005\u103a\u1001\u102f (\u1014\u103e\u1005\u103a\u1005\u1009\u103a\u101d\u1004\u103a\u1004\u103d\u1031\u1014\u103e\u1004\u1037\u103a \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u1000\u103c\u103d\u1031\u1038\u1019\u103c\u102e) \u101b\u103e\u102d\u101e\u100a\u103a\u104a \u1011\u102d\u102f\u1037\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1010\u1005\u103a\u101c\u1019\u103a\u1038\u1010\u100a\u103a\u1038 MANOVA \u1000\u102d\u102f \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u1006\u1000\u103a\u1005\u1015\u103a-<\/strong><\/span> <a href=\"https:\/\/statorials.org\" target=\"_blank\" rel=\"noopener\">ANOVA\u104a ANCOVA\u104a MANOVA \u1014\u103e\u1004\u1037\u103a MANCOVA \u1021\u1000\u103c\u102c\u1038 \u1000\u103d\u102c\u1001\u103c\u102c\u1038\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1014\u102c\u1038\u101c\u100a\u103a\u1001\u103c\u1004\u103a\u1038<\/a><\/p>\n<h2> <span style=\"color: #000000;\"><strong>R \u1016\u103c\u1004\u1037\u103a MANOVA \u1000\u102d\u102f\u1019\u100a\u103a\u101e\u102d\u102f\u1037\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1019\u100a\u103a\u1014\u100a\u103a\u1038\u104b<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">\u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1025\u1015\u1019\u102c\u1010\u103d\u1004\u103a\u104a \u1019\u1010\u1030\u100a\u102e\u101e\u1031\u102c\u1019\u103b\u102d\u102f\u1038\u1005\u102d\u1010\u103a\u101e\u102f\u1036\u1038\u1019\u103b\u102d\u102f\u1038\u1021\u1010\u103d\u1000\u103a \u1019\u1010\u1030\u100a\u102e\u101e\u1031\u102c\u1015\u1014\u103a\u1038\u1015\u103d\u1004\u1037\u103a\u1019\u103b\u102c\u1038\u104f\u1021\u101c\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a\u1021\u1014\u1036\u1006\u102d\u102f\u1004\u103a\u101b\u102c\u1021\u1001\u103b\u1000\u103a\u1021\u101c\u1000\u103a\u1019\u103b\u102c\u1038\u1015\u102b\u101b\u103e\u102d\u101e\u1031\u102c built-in <strong>iris<\/strong> dataset \u1000\u102d\u102f\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d R \u1010\u103d\u1004\u103a MNOVA \u1000\u102d\u102f \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1019\u100a\u103a\u1000\u102d\u102f \u1025\u1015\u1019\u102c\u1015\u103c\u1015\u102b\u1019\u100a\u103a\u104b , &#8220; versicolor&#8221; ):<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#view first six rows of <em>iris<\/em> dataset<\/span>\nhead(iris)\n\n# Sepal.Length Sepal.Width Petal.Length Petal.Width Species\n#1 5.1 3.5 1.4 0.2 setosa\n#2 4.9 3.0 1.4 0.2 setosa\n#3 4.7 3.2 1.3 0.2 setosa\n#4 4.6 3.1 1.5 0.2 setosa\n#5 5.0 3.6 1.4 0.2 setosa\n#6 5.4 3.9 1.7 0.4 setosa\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u1019\u103b\u102d\u102f\u1038\u1005\u102d\u1010\u103a\u1019\u103b\u102c\u1038\u101e\u100a\u103a sepal \u1021\u101b\u103e\u100a\u103a\u1014\u103e\u1004\u1037\u103a \u1021\u1014\u1036\u1021\u1015\u1031\u102b\u103a \u101e\u1000\u103a\u101b\u1031\u102c\u1000\u103a\u1019\u103e\u102f\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u101e\u102d\u101c\u102d\u102f\u101e\u100a\u103a\u1006\u102d\u102f\u1015\u102b\u1005\u102d\u102f\u1037\u104b \u1021\u1019\u103e\u102e\u1021\u1001\u102d\u102f\u1000\u1004\u103a\u1038\u101e\u1031\u102c \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1021\u1016\u103c\u1005\u103a <em>\u1019\u103b\u102d\u102f\u1038\u1005\u102d\u1010\u103a\u1019\u103b\u102c\u1038<\/em> \u1014\u103e\u1004\u1037\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\u1021\u1016\u103c\u1005\u103a sepal <em>\u1021\u101c\u103b\u102c\u1038<\/em> \u1014\u103e\u1004\u1037\u103a <em>\u1021\u1000\u103b\u101a\u103a\u1000\u102d\u102f<\/em> \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d R \u1010\u103d\u1004\u103a <strong>manova()<\/strong> \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u103b\u1000\u103a\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d \u1010\u1005\u103a\u101c\u1019\u103a\u1038\u101e\u103d\u102c\u1038 MANOVA \u1000\u102d\u102f \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>manova()<\/strong> \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u103b\u1000\u103a\u101e\u100a\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b syntax \u1000\u102d\u102f\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a-<\/span><\/p>\n<p style=\"text-align: left;\"> <strong><span style=\"color: #000000;\">manova (cbind (rv1\u104a rv2\u104a \u2026) ~ iv\u104a \u1012\u1031\u1010\u102c)<\/span><\/strong><\/p>\n<p> <span style=\"color: #000000;\">\u101b\u103d\u103e\u1031-<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>rv1\u104a rv2<\/strong> : \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a 1\u104a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a 2 \u1005\u101e\u100a\u103a\u1010\u102d\u102f\u1037\u104b<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>iv<\/strong> : \u101e\u102e\u1038\u1001\u103c\u102c\u1038 \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>data<\/strong> : \u1012\u1031\u1010\u102c\u1018\u1031\u102c\u1004\u103a\u1021\u1019\u100a\u103a<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">iris dataset \u1014\u103e\u1004\u1037\u103a\u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f\u1014\u1019\u1030\u1014\u102c\u1010\u103d\u1004\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a MANOVA \u1014\u103e\u1004\u1037\u103a \u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1015\u103c\u102e\u1038 \u1021\u1031\u102c\u1000\u103a\u1015\u102b syntax \u1000\u102d\u102f\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d \u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f\u1015\u103c\u101e\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a-<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#fit the MANOVA model<\/span>\nmodel &lt;- manova(cbind(Sepal.Length, Sepal.Width) ~ Species, data = iris)\n\n<span style=\"color: #008080;\">#view the results\n<\/span>summary(model)\n# Df Pillai approx F num Df den Df Pr(&gt;F)    \n#Species 2 0.94531 65.878 4,294 &lt; 2.2e-16 ***\n#Residuals 147                                             \n#---\n#Significant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u101b\u101c\u1012\u103a\u1019\u103e\u104a F \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u101e\u100a\u103a 65.878 \u1016\u103c\u1005\u103a\u1015\u103c\u102e\u1038 \u101e\u1000\u103a\u1006\u102d\u102f\u1004\u103a\u101b\u102c p-value \u101e\u100a\u103a \u1021\u101c\u103d\u1014\u103a\u101e\u1031\u1038\u1004\u101a\u103a\u101e\u100a\u103a\u1000\u102d\u102f \u1010\u103d\u1031\u1037\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b \u104e\u1004\u103a\u1038\u101e\u100a\u103a \u1019\u103b\u102d\u102f\u1038\u1005\u102d\u1010\u103a\u1015\u1031\u102b\u103a\u1019\u1030\u1010\u100a\u103a\u104d sepal \u1010\u102d\u102f\u1004\u103a\u1038\u1010\u102c\u1019\u103e\u102f\u1010\u103d\u1004\u103a \u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1021\u101b \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u101e\u1031\u102c \u1000\u103d\u102c\u1001\u103c\u102c\u1038\u1019\u103e\u102f\u101b\u103e\u102d\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u100a\u103d\u103e\u1014\u103a\u1015\u103c\u101e\u100a\u103a\u104b<\/span><\/p>\n<blockquote>\n<p> <span style=\"color: #000000;\"><strong>\u1014\u100a\u103a\u1038\u1015\u100a\u102c\u1019\u103e\u1010\u103a\u1005\u102f-<\/strong> \u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a\u104a manova() \u101e\u100a\u103a <em>Pillai<\/em> \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a\u104b \u1024\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1021\u102c\u1038 \u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1019\u103e\u102f\u101e\u100a\u103a \u101b\u103e\u102f\u1015\u103a\u1011\u103d\u1031\u1038\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a\u104a \u1015\u102d\u102f\u1019\u102d\u102f\u101c\u103d\u101a\u103a\u1000\u1030\u1005\u103d\u102c \u1021\u1014\u1000\u103a\u1015\u103c\u1014\u103a\u1006\u102d\u102f\u101b\u1014\u103a\u1021\u1010\u103d\u1000\u103a \u1021\u1014\u102e\u1038\u1005\u1015\u103a\u1006\u102f\u1036\u1038 F \u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1000\u102d\u102f\u101c\u100a\u103a\u1038 \u1015\u1031\u1038\u1011\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1011\u102d\u102f\u1037\u1021\u1015\u103c\u1004\u103a\u104a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1021\u1011\u102c\u1038\u1021\u101e\u102d\u102f\u1000\u102d\u102f\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101b\u1014\u103a \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1021\u1016\u103c\u1005\u103a &#8216;Roy&#8217;\u104a &#8216;Hotelling-Lawley&#8217; \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a &#8216;Wilks&#8217; \u1000\u102d\u102f \u101e\u1010\u103a\u1019\u103e\u1010\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a- \u1021\u1000\u103b\u1009\u103a\u1038\u1001\u103b\u102f\u1015\u103a(\u1019\u1031\u102c\u103a\u1012\u101a\u103a\u104a \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f = &#8216;Wilks&#8217;)<\/span><\/p>\n<\/blockquote>\n<p> <span style=\"color: #000000;\"><em>\u1019\u103b\u102d\u102f\u1038\u1005\u102d\u1010\u103a\u1019\u103b\u102c\u1038<\/em> \u1019\u103e sepal <em>\u1021\u101b\u103e\u100a\u103a<\/em> \u1014\u103e\u1004\u1037\u103a <em>\u1021\u1000\u103b\u101a\u103a\u1000\u102d\u102f<\/em> \u1019\u100a\u103a\u1000\u1032\u1037\u101e\u102d\u102f\u1037 \u1011\u102d\u1001\u102d\u102f\u1000\u103a\u101e\u100a\u103a\u1000\u102d\u102f \u1021\u1010\u102d\u1021\u1000\u103b \u101e\u102d\u101b\u103e\u102d\u101b\u1014\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1000\u102f\u1012\u103a\u1010\u103d\u1004\u103a \u1015\u103c\u1011\u102c\u1038\u101e\u100a\u1037\u103a\u1021\u1010\u102d\u102f\u1004\u103a\u1038 <strong>summary.aov()<\/strong> \u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d univariate ANOVA \u1019\u103b\u102c\u1038\u1000\u102d\u102f \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a-<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong>summary.aov(model)\n\n\n# Response Sepal.Length:\n# Df Sum Sq Mean Sq F value Pr(&gt;F)    \n#Species 2 63.212 31.606 119.26 &lt; 2.2e-16 ***\n#Residuals 147 38.956 0.265                      \n#---\n#Significant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n\n# Response Sepal.Width:\n# Df Sum Sq Mean Sq F value Pr(&gt;F)    \n#Species 2 11.345 5.6725 49.16 &lt; 2.2e-16 ***\n#Residuals 147 16.962 0.1154                      \n#---\n#Significant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">univariate ANOVA \u1014\u103e\u1005\u103a\u1001\u102f\u101c\u102f\u1036\u1038\u1021\u1010\u103d\u1000\u103a p-values \u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1021\u101c\u103d\u1014\u103a\u1014\u102d\u1019\u1037\u103a\u1000\u103b\u1014\u1031\u101e\u100a\u103a (&lt;2.2e-16) \u101e\u100a\u103a <em>\u1019\u103b\u102d\u102f\u1038\u1005\u102d\u1010\u103a\u1019\u103b\u102c\u1038\u101e\u100a\u103a<\/em> <em>sepal<\/em> <em>width<\/em> \u1014\u103e\u1004\u1037\u103a length \u1015\u1031\u102b\u103a\u1010\u103d\u1004\u103a \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1021\u101b \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u101e\u1031\u102c \u101e\u1000\u103a\u101b\u1031\u102c\u1000\u103a\u1019\u103e\u102f\u101b\u103e\u102d\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u100a\u103d\u103e\u1014\u103a\u1015\u103c\u1014\u1031\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<h2> <strong><span style=\"color: #000000;\">\u1021\u1016\u103d\u1032\u1037\u104f\u1021\u101b\u1004\u103a\u1038\u1021\u1019\u103c\u1005\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1019\u103c\u1004\u103a\u101a\u1031\u102c\u1004\u103a\u1000\u103c\u100a\u1037\u103a\u1015\u102b\u104b<\/span><\/strong><\/h2>\n<p> <span style=\"color: #000000;\">\u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f\u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1015\u102d\u102f\u1019\u102d\u102f\u1000\u1031\u102c\u1004\u103a\u1038\u1019\u103d\u1014\u103a\u1005\u103d\u102c\u1014\u102c\u1038\u101c\u100a\u103a\u1014\u102d\u102f\u1004\u103a\u1005\u1031\u101b\u1014\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f \u101e\u102e\u1038\u1001\u103c\u102c\u1038\u1000\u103d\u1032\u1015\u103c\u102c\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c <em>\u1019\u103b\u102d\u102f\u1038\u1005\u102d\u1010\u103a<\/em> \u1021\u1006\u1004\u1037\u103a\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1021\u1010\u103d\u1000\u103a \u1021\u102f\u1015\u103a\u1005\u102f\u104f\u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1019\u103c\u1004\u103a\u101a\u1031\u102c\u1004\u103a\u1000\u103c\u100a\u1037\u103a\u101b\u1014\u103a\u101c\u100a\u103a\u1038 \u1021\u101e\u102f\u1036\u1038\u101d\u1004\u103a\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1025\u1015\u1019\u102c\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a\u104a <em>\u1019\u103b\u102d\u102f\u1038\u1005\u102d\u1010\u103a\u1021\u101c\u102d\u102f\u1000\u103a<\/em> <em>sepals \u1019\u103b\u102c\u1038\u104f\u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1021\u101b\u103e\u100a\u103a\u1000\u102d\u102f<\/em> \u1019\u103c\u1004\u103a\u101a\u1031\u102c\u1004\u103a\u101b\u1014\u103a <strong>gplots<\/strong> library \u1014\u103e\u1004\u1037\u103a <strong>plotmeans()<\/strong> function \u1000\u102d\u102f\u101e\u102f\u1036\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#load <em>gplots<\/em> library<\/span>\nlibrary(gplots)\n\n<span style=\"color: #008080;\">#visualize mean <em>sepal length<\/em> by <em>species<\/em>\n<\/span>plotmeans(iris$Sepal.Length ~ iris$Species)<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u1002\u101b\u1015\u103a\u1016\u103a\u1019\u103e \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1019\u103b\u102d\u102f\u1038\u1005\u102d\u1010\u103a\u1019\u103b\u102c\u1038\u1000\u103c\u102c\u1038\u1010\u103d\u1004\u103a \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e sepal \u1021\u101b\u103e\u100a\u103a \u1000\u103d\u1032\u1015\u103c\u102c\u1038\u101e\u100a\u103a\u1000\u102d\u102f \u1010\u103d\u1031\u1037\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b \u104e\u1004\u103a\u1038\u101e\u100a\u103a \u1019\u103b\u102d\u102f\u1038\u1005\u102d\u1010\u103a\u1019\u103b\u102c\u1038\u1010\u1005\u103a\u101c\u103b\u103e\u1031\u102c\u1000\u103a \u1006\u102e\u1038\u1001\u102f\u1036\u1038\u1010\u102d\u102f\u1004\u103a\u1038\u1010\u102c\u1019\u103e\u102f\u1010\u103d\u1004\u103a \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u101e\u102d\u101e\u102d\u101e\u102c\u101e\u102c \u1000\u103d\u102c\u1001\u103c\u102c\u1038\u1019\u103e\u102f\u101b\u103e\u102d\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1000\u102d\u102f\u1015\u103c\u1031\u102c\u1015\u103c\u101e\u1031\u102c \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f MANOVA \u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a \u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><em>\u1019\u103b\u102d\u102f\u1038\u1005\u102d\u1010\u103a<\/em> \u1021\u101c\u102d\u102f\u1000\u103a <em>sepals \u1019\u103b\u102c\u1038\u104f \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1021\u1000\u103b\u101a\u103a\u1000\u102d\u102f<\/em> \u1019\u103c\u1004\u103a\u101a\u1031\u102c\u1004\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a \u104b<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong>plotmeans(iris$Sepal.Width ~ iris$Species)<\/strong><\/pre>\n<p> <span style=\"color: #000000;\"><strong>manova()<\/strong> \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u103b\u1000\u103a\u1021\u1010\u103d\u1000\u103a \u1005\u102c\u101b\u103d\u1000\u103a\u1005\u102c\u1010\u1019\u103a\u1038\u1021\u1015\u103c\u100a\u1037\u103a\u1021\u1005\u102f\u1036\u1000\u102d\u102f <a href=\"https:\/\/www.rdocumentation.org\/packages\/stats\/versions\/3.5.2\/topics\/manova\" target=\"_blank\" rel=\"noopener\">\u1024\u1014\u1031\u101b\u102c\u1010\u103d\u1004\u103a<\/a> \u1000\u103c\u100a\u1037\u103a\u1015\u102b\u104b<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>MANOVA \u1000\u102d\u102f \u1014\u102c\u1038\u101c\u100a\u103a\u101b\u1014\u103a\u104a ANOVA \u1000\u102d\u102f \u1014\u102c\u1038\u101c\u100a\u103a\u101b\u1014\u103a \u1026\u1038\u1005\u103d\u102c \u1021\u1000\u1030\u1021\u100a\u102e\u1016\u103c\u1005\u103a \u101e\u100a\u103a\u104b ANOVA (\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1000\u102d\u102f \u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u1001\u103c\u1004\u103a\u1038) \u1000\u102d\u102f \u101e\u102f\u1036\u1038\u101e\u1031\u102c \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1011\u102d\u102f\u1037\u1011\u1000\u103a\u1015\u102d\u102f\u101e\u1031\u102c \u101e\u102e\u1038\u1001\u103c\u102c\u1038\u1021\u102f\u1015\u103a\u1005\u102f\u1019\u103b\u102c\u1038\u104f \u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1019\u103b\u102c\u1038\u1000\u103c\u102c\u1038\u1010\u103d\u1004\u103a \u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1021\u101b \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u101e\u1031\u102c \u1001\u103c\u102c\u1038\u1014\u102c\u1038\u1019\u103e\u102f \u101b\u103e\u102d\u104a \u1019\u101b\u103e\u102d \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a\u104b \u1025\u1015\u1019\u102c\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a\u104a \u101c\u1031\u1037\u101c\u102c\u1001\u103c\u1004\u103a\u1038\u1014\u100a\u103a\u1038\u1015\u100a\u102c\u101e\u100a\u103a \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u1019\u103b\u102c\u1038\u104f \u1021\u1010\u1014\u103a\u1038\u1010\u1005\u103a\u1010\u1014\u103a\u1038\u104f \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u101b\u1019\u103e\u1010\u103a\u1019\u103b\u102c\u1038\u1021\u1015\u1031\u102b\u103a \u101e\u1000\u103a\u101b\u1031\u102c\u1000\u103a\u1019\u103e\u102f\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u101e\u102d\u1001\u103b\u1004\u103a\u101e\u100a\u103a\u1006\u102d\u102f\u1000\u103c\u1015\u102b\u1005\u102d\u102f\u1037\u104b \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1021\u1010\u1014\u103a\u1038\u1000\u102d\u102f \u1021\u102f\u1015\u103a\u1005\u102f\u101e\u102f\u1036\u1038\u1005\u102f\u1001\u103d\u1032\u104d \u1000\u103b\u1015\u1014\u103a\u1038\u1001\u103d\u1032\u101e\u100a\u103a\u104b \u1021\u102f\u1015\u103a\u1005\u102f\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u101e\u100a\u103a \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u1021\u1010\u103d\u1000\u103a \u1015\u103c\u1004\u103a\u1006\u1004\u103a\u101b\u1014\u103a \u1010\u1005\u103a\u101c\u1021\u1010\u103d\u1000\u103a \u1019\u1010\u1030\u100a\u102e\u101e\u1031\u102c \u101c\u1031\u1037\u101c\u102c\u1019\u103e\u102f\u1014\u100a\u103a\u1038\u1005\u1014\u1005\u103a\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a\u104b \u101c\u1000\u102f\u1014\u103a\u1010\u103d\u1004\u103a \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u1021\u102c\u1038\u101c\u102f\u1036\u1038 \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u1000\u102d\u102f \u1021\u1010\u1030\u1010\u1030\u1016\u103c\u1031\u1006\u102d\u102f\u1000\u103c\u101e\u100a\u103a\u104b \u1014\u100a\u103a\u1038\u1005\u1014\u1005\u103a\u101c\u1031\u1037\u101c\u102c\u1001\u103c\u1004\u103a\u1038\u101e\u100a\u103a \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u101b\u1019\u103e\u1010\u103a\u1019\u103b\u102c\u1038\u1021\u1015\u1031\u102b\u103a \u101e\u1000\u103a\u101b\u1031\u102c\u1000\u103a\u1019\u103e\u102f\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u101e\u102d\u101b\u103e\u102d\u101b\u1014\u103a\u104a \u1021\u102f\u1015\u103a\u1005\u102f\u101e\u102f\u1036\u1038\u1005\u102f\u104f \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u101b\u1019\u103e\u1010\u103a\u1019\u103b\u102c\u1038\u1021\u1000\u103c\u102c\u1038 \u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1006\u102d\u102f\u1004\u103a\u101b\u102c \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u101e\u1031\u102c [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>R - Statology \u1010\u103d\u1004\u103a MANOVA \u1000\u102d\u102f\u1019\u100a\u103a\u101e\u102d\u102f\u1037\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1019\u100a\u103a\u1014\u100a\u103a\u1038\u104b<\/title>\n<meta name=\"description\" content=\"\u1024\u1000\u103b\u1030\u1010\u102d\u102f\u101b\u102e\u101b\u101a\u103a\u1010\u103d\u1004\u103a R \u1010\u103d\u1004\u103a MANOVA (\u1000\u103d\u1032\u1015\u103c\u102c\u1038\u1019\u103e\u102f\u1000\u103d\u1032\u1015\u103c\u102c\u1038\u1019\u103e\u102f \u1000\u103d\u1032\u1015\u103c\u102c\u1038\u1019\u103e\u102f\u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u1019\u103e\u102f) \u1000\u102d\u102f \u101c\u103d\u101a\u103a\u1000\u1030\u1005\u103d\u102c\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1014\u100a\u103a\u1038\u1000\u102d\u102f \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1011\u102c\u1038\u101e\u100a\u103a\u104b\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/my\/manova-\u1019\u103e-r\/\" \/>\n<meta property=\"og:locale\" content=\"my_MM\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"R - Statology \u1010\u103d\u1004\u103a MANOVA \u1000\u102d\u102f\u1019\u100a\u103a\u101e\u102d\u102f\u1037\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1019\u100a\u103a\u1014\u100a\u103a\u1038\u104b\" \/>\n<meta property=\"og:description\" content=\"\u1024\u1000\u103b\u1030\u1010\u102d\u102f\u101b\u102e\u101b\u101a\u103a\u1010\u103d\u1004\u103a R \u1010\u103d\u1004\u103a MANOVA (\u1000\u103d\u1032\u1015\u103c\u102c\u1038\u1019\u103e\u102f\u1000\u103d\u1032\u1015\u103c\u102c\u1038\u1019\u103e\u102f \u1000\u103d\u1032\u1015\u103c\u102c\u1038\u1019\u103e\u102f\u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u1019\u103e\u102f) \u1000\u102d\u102f \u101c\u103d\u101a\u103a\u1000\u1030\u1005\u103d\u102c\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1014\u100a\u103a\u1038\u1000\u102d\u102f 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