{"id":420,"date":"2023-07-30T01:30:00","date_gmt":"2023-07-30T01:30:00","guid":{"rendered":"https:\/\/statorials.org\/my\/mann-whitney-u-%e1%80%85%e1%80%99%e1%80%ba%e1%80%b8\/"},"modified":"2023-07-30T01:30:00","modified_gmt":"2023-07-30T01:30:00","slug":"mann-whitney-u-%e1%80%85%e1%80%99%e1%80%ba%e1%80%b8","status":"publish","type":"post","link":"https:\/\/statorials.org\/my\/mann-whitney-u-%e1%80%85%e1%80%99%e1%80%ba%e1%80%b8\/","title":{"rendered":"Mann-whitney u \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>Mann-Whitney U \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f<\/strong> (\u1010\u1005\u103a\u1001\u102b\u1010\u1005\u103a\u101b\u1036 Wilcoxon rank sum test \u101f\u102f\u1001\u1031\u102b\u103a\u101e\u100a\u103a) \u1000\u102d\u102f\u1014\u1019\u1030\u1014\u102c\u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1019\u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1018\u1032\u1014\u103e\u1004\u1037\u103a \u1014\u1019\u1030\u1014\u102c\u1021\u101b\u103d\u101a\u103a\u1021\u1005\u102c\u1038\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u101e\u1031\u1038\u1004\u101a\u103a\u101e\u100a\u103a (n &lt;30) \u1010\u103d\u1004\u103a \u101e\u102e\u1038\u1001\u103c\u102c\u1038\u1014\u1019\u1030\u1014\u102c\u1014\u103e\u1005\u103a\u1001\u102f\u1000\u103c\u102c\u1038 \u1000\u103d\u102c\u1001\u103c\u102c\u1038\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1014\u103e\u102d\u102f\u1004\u103a\u1038\u101a\u103e\u1009\u103a\u101b\u1014\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\" target=\"_blank\" rel=\"noopener\">\u101c\u103d\u1010\u103a\u101c\u1015\u103a\u101e\u1031\u102c\u1014\u1019\u1030\u1014\u102c\u1014\u103e\u1005\u103a\u1001\u102f t \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f<\/a> \u104f parametric \u100a\u102e\u1019\u103b\u103e\u1001\u103c\u1004\u103a\u1038\u101f\u102f \u101a\u1030\u1006\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1024\u101e\u100a\u103a\u1019\u103e\u102c Mann-Whitney U \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u101e\u1004\u103a\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u1037\u103a\u1021\u1001\u102b \u1025\u1015\u1019\u102c\u1021\u1001\u103b\u102d\u102f\u1037\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u1010\u1000\u1039\u1000\u101e\u102d\u102f\u101c\u103a A \u1019\u103e \u1018\u103d\u1032\u1037\u101b\u1004\u102b\u1038\u1026\u1038\u104f \u101c\u1005\u102c\u1014\u103e\u1004\u1037\u103a \u1010\u1000\u1039\u1000\u101e\u102d\u102f\u101c\u103a B \u1018\u103d\u1032\u1037\u101b\u1004\u102b\u1038\u1026\u1038\u104f \u101c\u1005\u102c\u1010\u102d\u102f\u1037\u1000\u102d\u102f \u1014\u103e\u102d\u102f\u1004\u103a\u1038\u101a\u103e\u1009\u103a\u101c\u102d\u102f\u101e\u100a\u103a\u104b \u101c\u1005\u102c\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1001\u103d\u1032\u101d\u1031\u1015\u1031\u1038\u1019\u100a\u103a\u1019\u101f\u102f\u1010\u103a\u1015\u102b\u104b<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u1000\u102d\u102f\u101a\u103a\u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a\u1000\u103b\u1001\u103c\u1004\u103a\u1038\u1021\u1010\u103d\u1000\u103a \u1021\u102f\u1015\u103a\u1005\u102f\u1014\u103e\u1005\u103a\u1005\u102f\u1000\u103d\u1032\u1015\u103c\u102c\u1038\u1019\u103e\u102f\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u101e\u102d\u101c\u102d\u102f\u1015\u102b\u101e\u100a\u103a- \u1021\u1005\u102c\u1038\u1021\u101e\u1031\u102c\u1000\u103a A \u1000\u102d\u102f\u101e\u102f\u1036\u1038\u101e\u1031\u102c \u101c\u1030 \u1041\u1042 \u1026\u1038\u1014\u103e\u1004\u1037\u103a \u1021\u1005\u102c\u1038\u1021\u101e\u1031\u102c\u1000\u103a B \u101e\u102f\u1036\u1038\u1005\u103d\u1032\u101e\u1030 \u1041\u1040 \u1026\u1038\u1010\u102d\u102f\u1037\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b \u1021\u1006\u102d\u102f\u1015\u102b\u1000\u102d\u102f\u101a\u103a\u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a\u1000\u102d\u102f \u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1019\u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1015\u102b\u104b<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u1021\u1010\u1014\u103a\u1038 A \u101b\u103e\u102d \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038 \u1048 \u1026\u1038\u104f \u101b\u1019\u103e\u1010\u103a\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1021\u1010\u1014\u103a\u1038 B \u101b\u103e\u102d \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038 \u1047 \u1026\u1038\u1014\u103e\u1004\u1037\u103a \u1000\u103d\u102c\u1001\u103c\u102c\u1038\u1019\u103e\u102f\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u101e\u102d\u101c\u102d\u102f\u1015\u102b\u101e\u100a\u103a\u104b \u101b\u1019\u103e\u1010\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1021\u1010\u102d\u102f\u1004\u103a\u1038 \u1001\u103d\u1032\u101d\u1031\u1015\u1031\u1038\u1019\u100a\u103a\u1019\u101f\u102f\u1010\u103a\u1015\u102b\u104b<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u1025\u1015\u1019\u102c\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1010\u103d\u1004\u103a \u1021\u102f\u1015\u103a\u1005\u102f\u1014\u103e\u1005\u103a\u1001\u102f\u1000\u102d\u102f \u1014\u103e\u102d\u102f\u1004\u103a\u1038\u101a\u103e\u1009\u103a\u101c\u102d\u102f\u101e\u100a\u103a\u104a \u1014\u1019\u1030\u1014\u102c\u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1019\u101f\u102f\u1010\u103a\u1015\u102b\u104a \u1014\u1019\u1030\u1014\u102c\u1021\u101b\u103d\u101a\u103a\u1021\u1005\u102c\u1038\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u101e\u1031\u1038\u1004\u101a\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1011\u102d\u102f\u1037\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b \u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a \u1015\u103c\u100a\u1037\u103a\u1019\u102e\u101e\u101b\u103d\u1031\u1037 Mann-Whitney U \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u101e\u100a\u103a \u101e\u1004\u1037\u103a\u101c\u103b\u1031\u102c\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<h2> <strong><span style=\"color: #000000;\">Mann-Whitney U \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f \u101a\u1030\u1006\u1001\u103b\u1000\u103a<\/span><\/strong><\/h2>\n<p> <span style=\"color: #000000;\">Mann-Whitney U \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f \u1019\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1019\u102e\u104a \u1021\u1031\u102c\u1000\u103a\u1015\u102b \u101a\u1030\u1006\u1001\u103b\u1000\u103a\u101c\u1031\u1038\u1001\u102f\u1014\u103e\u1004\u1037\u103a \u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u101e\u1031\u1001\u103b\u102c\u1005\u1031\u101b\u1019\u100a\u103a\u104b<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u101e\u102c\u1019\u102c\u1014\u103a \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1005\u1009\u103a\u1006\u1000\u103a\u1019\u1015\u103c\u1010\u103a-<\/strong> \u101e\u1004\u103a\u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u101e\u1031\u102c \u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u101e\u100a\u103a \u1015\u102f\u1036\u1019\u103e\u1014\u103a \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1006\u1000\u103a\u1010\u102d\u102f\u1000\u103a\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b \u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1019\u1015\u103c\u1031\u102c\u1004\u103a\u1038\u101c\u1032\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c \u1025\u1015\u1019\u102c\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a Likert \u1015\u1005\u1039\u1005\u100a\u103a\u1038\u1019\u103b\u102c\u1038\u1015\u102b\u101d\u1004\u103a\u101e\u100a\u103a (\u1025\u1015\u1019\u102c\u104a \u201c\u1015\u103c\u1004\u103a\u1038\u1011\u1014\u103a\u1005\u103d\u102c\u101e\u1018\u1031\u102c\u1019\u1010\u1030\u201d \u1019\u103e \u201c\u1015\u103c\u1004\u103a\u1038\u1011\u1014\u103a\u1005\u103d\u102c\u101e\u1018\u1031\u102c\u1010\u1030\u101e\u100a\u103a\u201d \u1021\u1011\u102d 5-\u1019\u103e\u1010\u103a\u1005\u1000\u1031\u1038\u1010\u1005\u103a\u1001\u102f)\u104b \u1005\u1009\u103a\u1006\u1000\u103a\u1019\u1015\u103c\u1010\u103a\u1015\u103c\u1031\u102c\u1004\u103a\u1038\u101c\u1032\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c\u1014\u1019\u1030\u1014\u102c\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a \u1021\u101b\u1015\u103a (\u101c\u1000\u103a\u1019\u1016\u103c\u1004\u1037\u103a\u1010\u102d\u102f\u1004\u103a\u1038\u1010\u102c\u1001\u103c\u1004\u103a\u1038)\u104a \u1000\u102d\u102f\u101a\u103a\u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a (\u1015\u1031\u102b\u1004\u103a\u1016\u103c\u1004\u1037\u103a\u1010\u102d\u102f\u1004\u103a\u1038\u1010\u102c\u1001\u103c\u1004\u103a\u1038) \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u101b\u1019\u103e\u1010\u103a\u1019\u103b\u102c\u1038 (0 \u1019\u103e 100 \u1021\u1011\u102d\u1010\u102d\u102f\u1004\u103a\u1038\u1010\u102c\u101e\u100a\u103a) \u1015\u102b\u101d\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u101c\u103d\u1010\u103a\u101c\u1015\u103a\u101b\u1031\u1038-<\/strong> \u1021\u1016\u103d\u1032\u1037\u1014\u103e\u1005\u103a\u1016\u103d\u1032\u1037\u101c\u102f\u1036\u1038\u1019\u103e \u101b\u103e\u102f\u1019\u103c\u1004\u103a\u1001\u103b\u1000\u103a\u1021\u102c\u1038\u101c\u102f\u1036\u1038\u101e\u100a\u103a \u1010\u1005\u103a\u1001\u102f\u1014\u103e\u1004\u1037\u103a\u1010\u1005\u103a\u1001\u102f \u101e\u102e\u1038\u1001\u103c\u102c\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u1015\u102f\u1036\u101e\u100f\u1039\u100d\u102c\u1014\u103a-<\/strong> \u1021\u102f\u1015\u103a\u1005\u102f\u1014\u103e\u1005\u103a\u1001\u102f\u1021\u1010\u103d\u1000\u103a \u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1019\u103e\u102f\u1015\u102f\u1036\u1005\u1036\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103c\u1031\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a \u1010\u1030\u100a\u102e\u101e\u100a\u103a\u104b<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u1021\u1006\u102d\u102f\u1015\u102b\u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a\u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1015\u102b\u1000 Mann-Whitney U \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1015\u103c\u102f\u101c\u102f\u1015\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<h2> <strong><span style=\"color: #000000;\">Mann-Whitney U Test \u1000\u102d\u102f \u1018\u101a\u103a\u101c\u102d\u102f\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1019\u101c\u1032\u104b<\/span><\/strong><\/h2>\n<p> <span style=\"color: #000000;\">Mann-Whitney U \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1015\u103c\u102f\u101c\u102f\u1015\u103a\u101b\u1014\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a <a href=\"https:\/\/statorials.org\" target=\"_blank\" rel=\"noopener\">\u1005\u1036\u1004\u102b\u1038\u1006\u1004\u1037\u103a\u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1001\u103c\u1004\u103a\u1038\u101c\u102f\u1015\u103a\u1004\u1014\u103a\u1038\u1005\u1009\u103a\u1000\u102d\u102f<\/a> \u101c\u102d\u102f\u1000\u103a\u1014\u102c\u101e\u100a\u103a-<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. \u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b\u104b<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1000\u102d\u1005\u1039\u1005\u1021\u1019\u103b\u102c\u1038\u1005\u102f\u1010\u103d\u1004\u103a\u104a Mann-Whitney U \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1021\u1019\u103c\u102e\u1038\u1014\u103e\u1005\u103a\u1015\u102d\u102f\u1004\u103a\u1038\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1021\u1016\u103c\u1005\u103a \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101e\u100a\u103a\u104b null \u1014\u103e\u1004\u1037\u103a \u1021\u1001\u103c\u102c\u1038\u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1021\u102c\u1038 \u1015\u102f\u1036\u1005\u1036\u1016\u103c\u1004\u1037\u103a \u101b\u1031\u1038\u101e\u102c\u1038\u1011\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub> :<\/strong> \u101c\u1030\u1026\u1038\u101b\u1031 \u1014\u103e\u1005\u103a\u1001\u102f\u101e\u100a\u103a \u100a\u102e\u1019\u103b\u103e\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>H <sub>a<\/sub> :<\/strong> \u101c\u1030\u1026\u1038\u101b\u1031\u1014\u103e\u1005\u103a\u1001\u102f\u1000 \u1019\u100a\u102e\u1018\u1030\u1038\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. \u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1021\u1010\u103d\u1000\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101b\u1014\u103a \u1021\u101b\u1031\u1038\u1015\u102b\u1019\u103e\u102f\u1021\u1006\u1004\u1037\u103a\u1000\u102d\u102f \u101e\u1010\u103a\u1019\u103e\u1010\u103a\u1015\u102b\u104b<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u101b\u1031\u1038\u1015\u102b\u1019\u103e\u102f\u1021\u1006\u1004\u1037\u103a\u1000\u102d\u102f \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u1015\u102b\u104b \u1018\u102f\u1036\u101b\u103d\u1031\u1038\u1001\u103b\u101a\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u1019\u103e\u102c .01\u104a .05\u104a \u1014\u103e\u1004\u1037\u103a .1 \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>3. \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1000\u102d\u102f\u101b\u103e\u102c\u1015\u102b\u104b<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1021\u102c\u1038 U \u1016\u103c\u1004\u1037\u103a\u101b\u100a\u103a\u100a\u103d\u103e\u1014\u103a\u1038\u1015\u103c\u102e\u1038 \u1021\u1031\u102c\u1000\u103a\u1010\u103d\u1004\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1011\u102c\u1038\u101e\u100a\u1037\u103a\u1021\u1010\u102d\u102f\u1004\u103a\u1038 U <sub>1<\/sub> \u1014\u103e\u1004\u1037\u103a U <sub>2<\/sub> \u104f\u101e\u1031\u1038\u1004\u101a\u103a\u101e\u100a\u103a-<\/span><\/p>\n<p> <span style=\"color: #000000;\">U <sub>1<\/sub> = n <sub>1<\/sub> n <sub>2<\/sub> + n <sub>1<\/sub> (n <sub>1<\/sub> +1)\/2 \u2013 R <sub>1<\/sub><\/span><\/p>\n<p> <span style=\"color: #000000;\">U <sub>2<\/sub> = n <sub>1<\/sub> n <sub>2<\/sub> + n <sub>2<\/sub> (n <sub>2<\/sub> +1)\/2 \u2013 R <sub>2<\/sub><\/span><\/p>\n<p> <span style=\"color: #000000;\">n <sub>1<\/sub> \u1014\u103e\u1004\u1037\u103a n <sub>2<\/sub> \u101e\u100a\u103a \u1014\u1019\u1030\u1014\u102c\u1021\u101b\u103d\u101a\u103a\u1021\u1005\u102c\u1038 1 \u1014\u103e\u1004\u1037\u103a 2 \u1021\u101e\u102e\u1038\u101e\u102e\u1038\u1016\u103c\u1005\u103a\u1015\u103c\u102e\u1038 R <sub>1<\/sub> \u1014\u103e\u1004\u1037\u103a R <sub>2<\/sub> \u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1014\u1019\u1030\u1014\u102c 1 \u1014\u103e\u1004\u1037\u103a 2 \u1021\u1010\u103d\u1000\u103a \u1021\u1006\u1004\u1037\u103a\u1019\u103b\u102c\u1038\u104f \u1015\u1031\u102b\u1004\u103a\u1038\u101c\u1012\u103a\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <em><span style=\"color: #000000;\">\u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1014\u1019\u1030\u1014\u102c\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1024\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1021\u102c\u1038 \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u101b\u103e\u102c\u1016\u103d\u1031\u101b\u1019\u100a\u103a\u1000\u102d\u102f \u1021\u101e\u1031\u1038\u1005\u102d\u1010\u103a\u1015\u103c\u101e\u1015\u102b\u1019\u100a\u103a\u104b<\/span><\/em><\/p>\n<p> <span style=\"color: #000000;\"><strong>4. null hypothesis \u1000\u102d\u102f \u1004\u103c\u1004\u103a\u1038\u1015\u101a\u103a\u1001\u103c\u1004\u103a\u1038 \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1004\u103c\u1004\u103a\u1038\u1015\u101a\u103a\u1001\u103c\u1004\u103a\u1038\u1019\u1015\u103c\u102f\u1015\u102b\u1014\u103e\u1004\u1037\u103a\u104b<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1005\u102c\u101b\u1004\u103a\u1038\u1007\u101a\u102c\u1038\u1000\u102d\u102f\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d Mann-Whitney U \u1007\u101a\u102c\u1038\u1010\u103d\u1004\u103a\u1010\u103d\u1031\u1037\u101b\u103e\u102d\u101b\u101e\u1031\u102c \u1021\u101b\u1031\u1038\u1015\u102b\u1019\u103e\u102f\u1021\u1006\u1004\u1037\u103a\u1014\u103e\u1004\u1037\u103a \u1021\u101b\u1031\u1038\u1015\u102b\u101e\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1021\u1015\u1031\u102b\u103a\u1021\u1001\u103c\u1031\u1001\u1036\u104d null hypothesis \u1000\u102d\u102f \u1004\u103c\u1004\u103a\u1038\u1015\u101a\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u1016\u103c\u1005\u103a\u1005\u1031 \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u1015\u102b\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>5. \u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1018\u102c\u101e\u102c\u1015\u103c\u1014\u103a\u1015\u102b\u104b<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1019\u1031\u1038\u101e\u100a\u1037\u103a\u1019\u1031\u1038\u1001\u103d\u1014\u103a\u1038\u104f \u1006\u1000\u103a\u1005\u1015\u103a\u1019\u103e\u102f\u1010\u103d\u1004\u103a \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u101b\u101c\u1012\u103a\u1000\u102d\u102f \u1015\u103c\u1014\u103a\u1006\u102d\u102f\u1015\u102b\u104b<\/span><\/p>\n<h2> <strong><span style=\"color: #000000;\">Mann-Whitney U \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f \u1015\u103c\u102f\u101c\u102f\u1015\u103a\u1001\u103c\u1004\u103a\u1038\u104f \u1014\u1019\u1030\u1014\u102c\u1019\u103b\u102c\u1038<\/span><\/strong><\/h2>\n<p> <span style=\"color: #000000;\">\u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b \u1025\u1015\u1019\u102c\u1019\u103b\u102c\u1038\u101e\u100a\u103a Mann-Whitney U \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\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 \u1015\u103c\u101e\u1011\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u1025\u1015\u1019\u102c \u1041<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u1006\u1031\u1038\u101d\u102b\u1038\u1021\u101e\u1005\u103a\u101e\u100a\u103a \u1021\u1011\u102d\u1010\u103a\u1010\u101c\u1014\u1037\u103a\u1010\u102d\u102f\u1000\u103a\u1001\u102d\u102f\u1000\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1000\u102c\u1000\u103d\u101a\u103a\u101b\u1014\u103a \u1011\u102d\u101b\u1031\u102c\u1000\u103a\u1019\u103e\u102f \u101b\u103e\u102d\u104a \u1019\u101b\u103e\u102d \u101e\u102d\u101c\u102d\u102f\u1015\u102b\u101e\u100a\u103a\u104b \u1005\u102f\u1005\u102f\u1015\u1031\u102b\u1004\u103a\u1038\u101c\u1030\u1014\u102c 12 \u1026\u1038\u1000\u102d\u102f 6 \u1021\u102f\u1015\u103a\u1005\u102f\u1014\u103e\u1005\u103a\u1005\u102f\u1001\u103d\u1032\u104d \u1006\u1031\u1038\u101d\u102b\u1038\u1021\u101e\u1005\u103a \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a placebo \u1000\u102d\u102f\u101c\u1000\u103a\u1001\u1036\u101b\u101b\u103e\u102d\u101b\u1014\u103a\u1010\u102c\u101d\u1014\u103a\u1015\u1031\u1038\u1021\u1015\u103a\u101e\u100a\u103a\u104b \u1011\u102d\u102f\u1037\u1014\u1031\u102c\u1000\u103a \u101c\u1030\u1014\u102c\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1010\u1005\u103a\u101c\u1010\u102c\u1021\u1010\u103d\u1004\u103a\u1038 \u101e\u1030\u1010\u102d\u102f\u1037\u1000\u103c\u102f\u1036\u1010\u103d\u1031\u1037\u1001\u1032\u1037\u101b\u101e\u100a\u1037\u103a \u1011\u102d\u1010\u103a\u101c\u1014\u1037\u103a\u1010\u102d\u102f\u1000\u103a\u1001\u102d\u102f\u1000\u103a\u1019\u103e\u102f\u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a\u1000\u102d\u102f \u1019\u103e\u1010\u103a\u1010\u1019\u103a\u1038\u1010\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1021\u1031\u102c\u1000\u103a\u1010\u103d\u1004\u103a \u1015\u103c\u1011\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/p>\n<div style=\"width: 50%;\">\n<table>\n<thead>\n<tr>\n<th style=\"text-align: center;\"> <span style=\"color: #000000;\">\u1006\u1031\u1038\u1021\u101e\u1005\u103a<\/span><\/th>\n<th style=\"text-align: center;\"> <span style=\"color: #000000;\">PLACEBO<\/span><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">\u1043<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">\u1044<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">\u1045<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">\u1048<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">\u1041<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">\u1046<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">\u1044<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">\u1042<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">\u1043<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">\u1041<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">\u1045<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">\u1049<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p> <span style=\"color: #000000;\"><em><strong>\u1006\u1031\u1038\u1021\u102f\u1015\u103a\u1005\u102f\u1021\u101e\u1005\u103a\u1014\u103e\u1004\u1037\u103a \u1014\u103e\u102d\u102f\u1004\u103a\u1038\u101a\u103e\u1009\u103a\u1015\u102b\u1000 placebo \u1021\u102f\u1015\u103a\u1005\u102f\u101b\u103e\u102d \u101c\u1030\u1014\u102c\u1019\u103b\u102c\u1038\u1021\u1000\u103c\u102c\u1038 \u1011\u102d\u1010\u103a\u101c\u1014\u1037\u103a\u1010\u102d\u102f\u1000\u103a\u1001\u102d\u102f\u1000\u103a\u1019\u103e\u102f \u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a \u1000\u103d\u102c\u1001\u103c\u102c\u1038\u1019\u103e\u102f\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u101e\u102d\u101b\u1014\u103a Mann-Whitney U \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f \u1015\u103c\u102f\u101c\u102f\u1015\u103a\u1015\u102b\u104b \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u1019\u103e\u102f\u1021\u1006\u1004\u1037\u103a 0.05 \u1000\u102d\u102f\u101e\u102f\u1036\u1038\u1015\u102b\u104b<\/strong><\/em><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. \u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b\u104b<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub> :<\/strong> \u101c\u1030\u1026\u1038\u101b\u1031 \u1014\u103e\u1005\u103a\u1001\u102f\u101e\u100a\u103a \u100a\u102e\u1019\u103b\u103e\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>H <sub>a<\/sub> :<\/strong> \u101c\u1030\u1026\u1038\u101b\u1031\u1014\u103e\u1005\u103a\u1001\u102f\u1000 \u1019\u100a\u102e\u1018\u1030\u1038\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. \u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1021\u1010\u103d\u1000\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101b\u1014\u103a \u1021\u101b\u1031\u1038\u1015\u102b\u1019\u103e\u102f\u1021\u1006\u1004\u1037\u103a\u1000\u102d\u102f \u101e\u1010\u103a\u1019\u103e\u1010\u103a\u1015\u102b\u104b<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1015\u103c\u103f\u1014\u102c\u1000 \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a 0.05 \u104f \u1021\u101b\u1031\u1038\u1015\u102b\u1019\u103e\u102f\u1021\u1006\u1004\u1037\u103a\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u1004\u1037\u103a\u101e\u100a\u103a\u101f\u102f \u1006\u102d\u102f\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>3. \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1000\u102d\u102f\u101b\u103e\u102c\u1015\u102b\u104b<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u101e\u100a\u103a U \u1000\u102d\u102f\u101b\u100a\u103a\u100a\u103d\u103e\u1014\u103a\u1038\u1015\u103c\u102e\u1038 \u1021\u1031\u102c\u1000\u103a\u1010\u103d\u1004\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1011\u102c\u1038\u101e\u100a\u1037\u103a\u1021\u1010\u102d\u102f\u1004\u103a\u1038 U <sub>1<\/sub> \u1014\u103e\u1004\u1037\u103a U <sub>2<\/sub> \u104f\u101e\u1031\u1038\u1004\u101a\u103a\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u101e\u1010\u102d\u101b\u1015\u102b\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">U <sub>1<\/sub> = n <sub>1<\/sub> n <sub>2<\/sub> + n <sub>1<\/sub> (n <sub>1<\/sub> +1)\/2 \u2013 R <sub>1<\/sub><\/span><\/p>\n<p> <span style=\"color: #000000;\">U <sub>2<\/sub> = n <sub>1<\/sub> n <sub>2<\/sub> + n <sub>2<\/sub> (n <sub>2<\/sub> +1)\/2 \u2013 R <sub>2<\/sub><\/span><\/p>\n<p> <span style=\"color: #000000;\">n <sub>1<\/sub> \u1014\u103e\u1004\u1037\u103a n <sub>2<\/sub> \u101e\u100a\u103a \u1014\u1019\u1030\u1014\u102c\u1021\u101b\u103d\u101a\u103a\u1021\u1005\u102c\u1038 1 \u1014\u103e\u1004\u1037\u103a 2 \u1021\u101e\u102e\u1038\u101e\u102e\u1038\u1016\u103c\u1005\u103a\u1015\u103c\u102e\u1038 R <sub>1<\/sub> \u1014\u103e\u1004\u1037\u103a R <sub>2<\/sub> \u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1014\u1019\u1030\u1014\u102c 1 \u1014\u103e\u1004\u1037\u103a 2 \u1021\u1010\u103d\u1000\u103a \u1021\u1006\u1004\u1037\u103a\u1019\u103b\u102c\u1038\u104f \u1015\u1031\u102b\u1004\u103a\u1038\u101c\u1012\u103a\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> R 1 \u1014\u103e\u1004\u1037\u103a R 2 <span style=\"color: #000000;\">\u1000\u102d\u102f\u101b\u103e\u102c\u1016\u103d\u1031\u101b\u1014\u103a\u1021\u1010\u103d\u1000\u103a<\/span> <span style=\"color: #000000;\"><sub>\u1021\u102f\u1015\u103a\u1005\u102f<\/sub> <sub>\u1014\u103e\u1005\u103a\u1001\u102f<\/sub> \u101c\u102f\u1036\u1038\u1019\u103e \u1019\u103e\u1010\u103a\u101e\u102c\u1038\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1015\u1031\u102b\u1004\u103a\u1038\u1005\u1015\u103a\u1015\u103c\u102e\u1038 \u104e\u1004\u103a\u1038\u1010\u102d\u102f\u1037\u1000\u102d\u102f \u1021\u101e\u1031\u1038\u1004\u101a\u103a\u1006\u102f\u1036\u1038\u1019\u103e \u1021\u1000\u103c\u102e\u1038\u1006\u102f\u1036\u1038\u101e\u102d\u102f\u1037 \u1005\u102e\u101b\u1014\u103a \u101c\u102d\u102f\u1021\u1015\u103a\u101e\u100a\u103a-<\/span><\/p>\n<div style=\"width: 50%;\">\n<table>\n<thead>\n<tr>\n<th style=\"text-align: center;\"> <span style=\"color: #008080;\">\u1006\u1031\u1038\u1021\u101e\u1005\u103a<\/span><\/th>\n<th style=\"text-align: center;\"> <span style=\"color: #ff0000;\">PLACEBO<\/span><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #008080;\"><strong>\u1043<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #ff0000;\"><strong>\u1044<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #008080;\"><strong>\u1045<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #ff0000;\"><strong>\u1048<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #008080;\"><strong>\u1041<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #ff0000;\"><strong>\u1046<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #008080;\"><strong>\u1044<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #ff0000;\"><strong>\u1042<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #008080;\"><strong>\u1043<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #ff0000;\"><strong>\u1041<\/strong><\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #008080;\"><strong>\u1045<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #ff0000;\"><strong>\u1049<\/strong><\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p> <span style=\"color: #000000;\"><strong>\u1005\u102f\u1005\u102f\u1015\u1031\u102b\u1004\u103a\u1038\u1014\u1019\u1030\u1014\u102c- <span style=\"color: #008080;\">1<\/span> \u104a <span style=\"color: #ff0000;\">1<\/span> \u104a <span style=\"color: #ff0000;\">2<\/span> \u104a <span style=\"color: #008080;\">3<\/span> \u104a <span style=\"color: #008080;\">3<\/span> \u104a <span style=\"color: #ff0000;\">4<\/span> \u104a <span style=\"color: #008080;\">4<\/span> \u104a <span style=\"color: #008080;\">5<\/span> \u104a <span style=\"color: #008080;\">5<\/span> \u104a <span style=\"color: #ff0000;\">6<\/span> \u104a <span style=\"color: #ff0000;\">8<\/span> \u104a <span style=\"color: #ff0000;\">9<\/span><\/strong><\/span><\/p>\n<div>\n<p> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a\u1019\u103b\u102c\u1038- <span style=\"color: #008080;\">1.5<\/span> \u104a <span style=\"color: #ff0000;\">1.5<\/span> \u104a <span style=\"color: #ff0000;\">3<\/span> \u104a <span style=\"color: #008080;\">4.5<\/span> \u104a <span style=\"color: #008080;\">4.5<\/span> \u104a <span style=\"color: #ff0000;\">6.5<\/span> \u104a <span style=\"color: #008080;\">6.5<\/span> \u104a <span style=\"color: #008080;\">8.5<\/span> \u104a <span style=\"color: #008080;\">8.5<\/span> \u104a <span style=\"color: #ff0000;\">10<\/span> \u104a <span style=\"color: #ff0000;\">11<\/span> \u104a <span style=\"color: #ff0000;\">12<\/span><\/strong><\/span><\/p>\n<p> <span style=\"color: #008080;\"><strong>R <sub>1<\/sub><\/strong><\/span> <span style=\"color: #000000;\">= \u1014\u1019\u1030\u1014\u102c 1 \u1021\u1010\u103d\u1000\u103a \u1021\u1006\u1004\u1037\u103a\u1015\u1031\u102b\u1004\u103a\u1038 = 1.5+4.5+4.5+6.5+8.5+8.5 = 34<\/span><\/p>\n<p> <span style=\"color: #ff0000;\"><strong>R <sub>2<\/sub><\/strong><\/span> <span style=\"color: #000000;\">= \u1014\u1019\u1030\u1014\u102c 2 \u1021\u1010\u103d\u1000\u103a \u1021\u1006\u1004\u1037\u103a\u1015\u1031\u102b\u1004\u103a\u1038 = 1.5+3+6.5+10+11+12 = 44<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1011\u102d\u102f\u1037\u1014\u1031\u102c\u1000\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f\u1014\u1019\u1030\u1014\u102c\u1021\u101b\u103d\u101a\u103a\u1021\u1005\u102c\u1038 n <sub>1<\/sub> \u1014\u103e\u1004\u1037\u103a n <sub>2<\/sub> \u1021\u1015\u103c\u1004\u103a U <sub>1<\/sub> \u1014\u103e\u1004\u1037\u103a U <sub>2<\/sub> \u1000\u102d\u102f\u101b\u103e\u102c\u1016\u103d\u1031\u101b\u1014\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f\u1021\u1006\u1004\u1037\u103a\u1015\u1031\u102b\u1004\u103a\u1038 R <sub>1<\/sub> \u1014\u103e\u1004\u1037\u103a R <sub>2<\/sub> \u1000\u102d\u102f\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><sub>U1<\/sub> = 6(6) + 6(6+1)\/2 \u2013 34 = 23<\/span><\/p>\n<p> <span style=\"color: #000000;\"><sub>U2<\/sub> = 6(6) + 6(6+1)\/2 \u2013 44 = 13<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1005\u102c\u101b\u1004\u103a\u1038\u1007\u101a\u102c\u1038\u1019\u103b\u102c\u1038\u101e\u100a\u103a <sub>U1<\/sub> \u1014\u103e\u1004\u1037\u103a <sub>U2<\/sub> \u104f\u101e\u1031\u1038\u1004\u101a\u103a\u101e\u100a\u103a\u104a \u104e\u1004\u103a\u1038\u1019\u103e\u102c U=13 \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <em><span style=\"color: #000000;\">\u1019\u103e\u1010\u103a\u1001\u103b\u1000\u103a- U = 13 \u1000\u102d\u102f \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a <a href=\"https:\/\/statorials.org\/my\/mann-whitney-u-\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1002\u100f\u1014\u103a\u1038\u1015\u1031\u102b\u1004\u103a\u1038\u1005\u1000\u103a\/\" target=\"_blank\" rel=\"noopener\">Mann-Whitney U \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1002\u100f\u1014\u103a\u1038\u1010\u103d\u1000\u103a\u1005\u1000\u103a<\/a> \u1000\u102d\u102f\u101c\u100a\u103a\u1038 \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/em><\/p>\n<\/div>\n<p> <span style=\"color: #000000;\"><strong>4. null hypothesis \u1000\u102d\u102f \u1004\u103c\u1004\u103a\u1038\u1015\u101a\u103a\u1001\u103c\u1004\u103a\u1038 \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1004\u103c\u1004\u103a\u1038\u1015\u101a\u103a\u1001\u103c\u1004\u103a\u1038\u1019\u1015\u103c\u102f\u1015\u102b\u1014\u103e\u1004\u1037\u103a\u104b<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">n <sub>1<\/sub> = 6 \u1014\u103e\u1004\u1037\u103a n <sub>2<\/sub> = 6 \u1000\u102d\u102f \u1021\u101b\u1031\u1038\u1015\u102b\u101e\u100a\u1037\u103a\u1021\u1006\u1004\u1037\u103a 0.05 \u1016\u103c\u1004\u1037\u103a\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d Mann-Whitney U \u1007\u101a\u102c\u1038\u1000 \u1021\u101b\u1031\u1038\u1000\u103c\u102e\u1038\u101e\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103e\u102c 5 \u1016\u103c\u1005\u103a\u101e\u100a\u103a-<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1381 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/mw_ex1.png\" alt=\"Mann Whitney U Test Critical Value Table\" width=\"544\" height=\"401\" srcset=\"\" sizes=\"\"><\/p>\n<p> <span style=\"color: #000000;\">\u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038 (13) \u101e\u100a\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f\u1021\u101b\u1031\u1038\u1000\u103c\u102e\u1038\u101e\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038 (5) \u1011\u1000\u103a\u1000\u103c\u102e\u1038\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a null hypothesis \u1000\u102d\u102f \u1004\u103c\u1004\u103a\u1038\u1015\u101a\u103a\u101b\u1014\u103a\u1015\u103b\u1000\u103a\u1000\u103d\u1000\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>5. \u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1018\u102c\u101e\u102c\u1015\u103c\u1014\u103a\u1015\u102b\u104b<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a null hypothesis \u1000\u102d\u102f \u1004\u103c\u1004\u103a\u1038\u1006\u102d\u102f\u101b\u1014\u103a \u1015\u103b\u1000\u103a\u1000\u103d\u1000\u103a\u1001\u1032\u1037\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a\u104a placebo \u1021\u102f\u1015\u103a\u1005\u102f\u101b\u103e\u102d \u101c\u1030\u1014\u102c\u1019\u103b\u102c\u1038\u1001\u1036\u1005\u102c\u1038\u101b\u101e\u1031\u102c \u1011\u102d\u1010\u103a\u101c\u1014\u1037\u103a\u1010\u102d\u102f\u1000\u103a\u1001\u102d\u102f\u1000\u103a\u1019\u103e\u102f\u1021\u101b\u1031\u1021\u1010\u103d\u1000\u103a\u101e\u100a\u103a \u1006\u1031\u1038\u101d\u102b\u1038\u1021\u102f\u1015\u103a\u1005\u102f\u1021\u101e\u1005\u103a\u1010\u103d\u1004\u103a \u1000\u103d\u1032\u1015\u103c\u102c\u1038\u101e\u100a\u103a\u101f\u102f\u1006\u102d\u102f\u101b\u1014\u103a \u101c\u102f\u1036\u101c\u1031\u102c\u1000\u103a\u101e\u1031\u102c \u1021\u1011\u1031\u102c\u1000\u103a\u1021\u1011\u102c\u1038\u1019\u101b\u103e\u102d\u1015\u102b\u104b<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u1025\u1015\u1019\u102c \u1042<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u1010\u1005\u103a\u1015\u1010\u103a\u101c\u103b\u103e\u1004\u103a \u1019\u102d\u1014\u1005\u103a 30 \u101c\u1031\u1037\u101c\u102c\u1001\u103c\u1004\u103a\u1038\u101e\u100a\u103a \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u1019\u103b\u102c\u1038\u1021\u102c\u1038 \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u1010\u1005\u103a\u1001\u102f\u1010\u103d\u1004\u103a \u1015\u102d\u102f\u1019\u102d\u102f\u1000\u1031\u102c\u1004\u103a\u1038\u1019\u103d\u1014\u103a\u1005\u103d\u102c\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1014\u102d\u102f\u1004\u103a\u1005\u1031\u1019\u100a\u103a\u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u102d\u1001\u103b\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b \u1005\u102f\u1005\u102f\u1015\u1031\u102b\u1004\u103a\u1038\u101c\u1030\u1014\u102c 15 \u1026\u1038\u1000\u102d\u102f \u1000\u103b\u1015\u1014\u103a\u1038\u101c\u1031\u1037\u101c\u102c\u101b\u1014\u103a \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u101c\u1031\u1037\u101c\u102c\u1019\u103e\u102f\u1021\u1016\u103d\u1032\u1037\u1019\u101b\u103e\u102d\u1015\u102b \u104b \u1010\u1005\u103a\u1015\u1010\u103a\u1021\u1000\u103c\u102c\u1010\u103d\u1004\u103a \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u1021\u102c\u1038\u101c\u102f\u1036\u1038 \u1010\u1030\u100a\u102e\u101e\u1031\u102c \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u1000\u102d\u102f \u1016\u103c\u1031\u1000\u103c\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u102f\u1015\u103a\u1005\u102f\u1014\u103e\u1005\u103a\u1001\u102f\u101c\u102f\u1036\u1038\u1021\u1010\u103d\u1000\u103a \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1021\u1031\u102c\u1000\u103a\u1010\u103d\u1004\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1011\u102c\u1038\u101e\u100a\u103a-<\/span><\/p>\n<div style=\"width: 50%;\">\n<table>\n<thead>\n<tr>\n<th style=\"text-align: center;\"> <span style=\"color: #000000;\">\u101c\u1031\u1037\u101c\u102c\u1001\u103b\u1000\u103a<\/span><\/th>\n<th style=\"text-align: center;\"> <span style=\"color: #000000;\">\u101c\u1031\u1037\u101c\u102c\u1019\u103e\u102f\u1019\u101b\u103e\u102d\u1015\u102b\u104b<\/span><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">\u1048\u1049<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">\u1048\u1048<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">\u1049\u1042<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">\u1049\u1043<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">\u1049\u1044<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">\u1049\u1045<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">\u1049\u1046<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">\u1047\u1045<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">\u1049\u1041<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">\u1047\u1042<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">\u1049\u1049<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">\u1048\u1040<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">\u1048\u1044<\/span><\/td>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">\u1048\u1041<\/span><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #000000;\">\u1049\u1040<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p> <span style=\"color: #000000;\"><em><strong>Mann-Whitney U \u1005\u1005\u103a\u1006\u1031\u1038\u1019\u103e\u102f\u1000\u102d\u102f \u101c\u1031\u1037\u101c\u102c\u1019\u103e\u102f\u1021\u102f\u1015\u103a\u1005\u102f\u1021\u1010\u103d\u1000\u103a \u101c\u1031\u1037\u101c\u102c\u1019\u103e\u102f\u1019\u101b\u103e\u102d\u101e\u1031\u102c\u1021\u1016\u103d\u1032\u1037\u1014\u103e\u1004\u1037\u103a \u1014\u103e\u102d\u102f\u1004\u103a\u1038\u101a\u103e\u1009\u103a\u1015\u102b\u1000 \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u101b\u1019\u103e\u1010\u103a\u1019\u103b\u102c\u1038 \u1000\u103d\u102c\u1001\u103c\u102c\u1038\u1019\u103e\u102f\u101b\u103e\u102d\u1019\u101b\u103e\u102d\u1000\u102d\u102f \u1000\u103c\u100a\u1037\u103a\u101b\u103e\u102f\u1015\u102b\u104b \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u1019\u103e\u102f\u1021\u1006\u1004\u1037\u103a 0.01 \u1000\u102d\u102f\u101e\u102f\u1036\u1038\u1015\u102b\u104b<\/strong><\/em><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. \u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b\u104b<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub> :<\/strong> \u101c\u1030\u1026\u1038\u101b\u1031 \u1014\u103e\u1005\u103a\u1001\u102f\u101e\u100a\u103a \u100a\u102e\u1019\u103b\u103e\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>H <sub>a<\/sub> :<\/strong> \u101c\u1030\u1026\u1038\u101b\u1031\u1014\u103e\u1005\u103a\u1001\u102f\u1000 \u1019\u100a\u102e\u1018\u1030\u1038\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. \u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1021\u1010\u103d\u1000\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101b\u1014\u103a \u1021\u101b\u1031\u1038\u1015\u102b\u1019\u103e\u102f\u1021\u1006\u1004\u1037\u103a\u1000\u102d\u102f \u101e\u1010\u103a\u1019\u103e\u1010\u103a\u1015\u102b\u104b<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1015\u103c\u103f\u1014\u102c\u1000 \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a 0.01 \u104f \u1021\u101b\u1031\u1038\u1015\u102b\u1019\u103e\u102f\u1021\u1006\u1004\u1037\u103a\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u1004\u1037\u103a\u101e\u100a\u103a\u101f\u102f \u1006\u102d\u102f\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>3. \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1000\u102d\u102f\u101b\u103e\u102c\u1015\u102b\u104b<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u101e\u100a\u103a U \u1000\u102d\u102f\u101b\u100a\u103a\u100a\u103d\u103e\u1014\u103a\u1038\u1015\u103c\u102e\u1038 \u1021\u1031\u102c\u1000\u103a\u1010\u103d\u1004\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1011\u102c\u1038\u101e\u100a\u1037\u103a\u1021\u1010\u102d\u102f\u1004\u103a\u1038 U <sub>1<\/sub> \u1014\u103e\u1004\u1037\u103a U <sub>2<\/sub> \u104f\u101e\u1031\u1038\u1004\u101a\u103a\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u101e\u1010\u102d\u101b\u1015\u102b\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">U <sub>1<\/sub> = n <sub>1<\/sub> n <sub>2<\/sub> + n <sub>1<\/sub> (n <sub>1<\/sub> +1)\/2 \u2013 R <sub>1<\/sub><\/span><\/p>\n<p> <span style=\"color: #000000;\">U <sub>2<\/sub> = n <sub>1<\/sub> n <sub>2<\/sub> + n <sub>2<\/sub> (n <sub>2<\/sub> +1)\/2 \u2013 R <sub>2<\/sub><\/span><\/p>\n<p> <span style=\"color: #000000;\">n <sub>1<\/sub> \u1014\u103e\u1004\u1037\u103a n <sub>2<\/sub> \u101e\u100a\u103a \u1014\u1019\u1030\u1014\u102c\u1021\u101b\u103d\u101a\u103a\u1021\u1005\u102c\u1038 1 \u1014\u103e\u1004\u1037\u103a 2 \u1021\u101e\u102e\u1038\u101e\u102e\u1038\u1016\u103c\u1005\u103a\u1015\u103c\u102e\u1038 R <sub>1<\/sub> \u1014\u103e\u1004\u1037\u103a R <sub>2<\/sub> \u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1014\u1019\u1030\u1014\u102c 1 \u1014\u103e\u1004\u1037\u103a 2 \u1021\u1010\u103d\u1000\u103a \u1021\u1006\u1004\u1037\u103a\u1019\u103b\u102c\u1038\u104f \u1015\u1031\u102b\u1004\u103a\u1038\u101c\u1012\u103a\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> R 1 \u1014\u103e\u1004\u1037\u103a R 2 <span style=\"color: #000000;\">\u1000\u102d\u102f\u101b\u103e\u102c\u1016\u103d\u1031\u101b\u1014\u103a\u1021\u1010\u103d\u1000\u103a<\/span> <span style=\"color: #000000;\"><sub>\u1021\u102f\u1015\u103a\u1005\u102f<\/sub> <sub>\u1014\u103e\u1005\u103a\u1001\u102f<\/sub> \u101c\u102f\u1036\u1038\u1019\u103e \u1019\u103e\u1010\u103a\u101e\u102c\u1038\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1015\u1031\u102b\u1004\u103a\u1038\u1005\u1015\u103a\u1015\u103c\u102e\u1038 \u104e\u1004\u103a\u1038\u1010\u102d\u102f\u1037\u1000\u102d\u102f \u1021\u101e\u1031\u1038\u1004\u101a\u103a\u1006\u102f\u1036\u1038\u1019\u103e \u1021\u1000\u103c\u102e\u1038\u1006\u102f\u1036\u1038\u101e\u102d\u102f\u1037 \u1005\u102e\u101b\u1014\u103a \u101c\u102d\u102f\u1021\u1015\u103a\u101e\u100a\u103a-<\/span><\/p>\n<div style=\"width: 50%;\">\n<table>\n<thead>\n<tr>\n<th style=\"text-align: center;\"> <strong><span style=\"color: #008080;\">\u101c\u1031\u1037\u101c\u102c\u1001\u103b\u1000\u103a<\/span><\/strong><\/th>\n<th style=\"text-align: center;\"> <span style=\"color: #ff0000;\">\u101c\u1031\u1037\u101c\u102c\u1019\u103e\u102f\u1019\u101b\u103e\u102d\u1015\u102b\u104b<\/span><\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td style=\"text-align: center;\"> <span style=\"color: #008080;\"><strong>\u1048\u1049<\/strong><\/span><\/td>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #ff0000;\">\u1048\u1048<\/span><\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #008080;\">\u1049\u1042<\/span><\/strong><\/td>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #ff0000;\">\u1049\u1043<\/span><\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #008080;\">\u1049\u1044<\/span><\/strong><\/td>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #ff0000;\">\u1049\u1045<\/span><\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #008080;\">\u1049\u1046<\/span><\/strong><\/td>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #ff0000;\">\u1047\u1045<\/span><\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #008080;\">\u1049\u1041<\/span><\/strong><\/td>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #ff0000;\">\u1047\u1042<\/span><\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #008080;\">\u1049\u1049<\/span><\/strong><\/td>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #ff0000;\">\u1048\u1040<\/span><\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #008080;\">\u1048\u1044<\/span><\/strong><\/td>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #ff0000;\">\u1048\u1041<\/span><\/strong><\/td>\n<\/tr>\n<tr>\n<td style=\"text-align: center;\"> <strong><span style=\"color: #008080;\">\u1049\u1040<\/span><\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p> <span style=\"color: #000000;\"><strong><span style=\"color: #000000;\">\u1005\u102f\u1005\u102f\u1015\u1031\u102b\u1004\u103a\u1038\u1014\u1019\u1030\u1014\u102c- <span style=\"color: #ff0000;\">72<\/span> , <span style=\"color: #ff0000;\">75<\/span> <span style=\"color: #008080;\">,<\/span> <span style=\"color: #ff0000;\">80<\/span> , 81 , 84 , <span style=\"color: #ff0000;\">88<\/span> , <span style=\"color: #008080;\">89<\/span> , <span style=\"color: #ff0000;\">90<\/span> , <span style=\"color: #008080;\">91<\/span> , <span style=\"color: #008080;\">92<\/span> , <span style=\"color: #008080;\">93<\/span> , <span style=\"color: #008080;\">94<\/span> , <span style=\"color: #ff0000;\">95<\/span> , <span style=\"color: #008080;\">96<\/span> <span style=\"color: #008080;\">,<\/span> <span style=\"color: #ff0000;\">99<\/span><\/span><\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong><span style=\"color: #000000;\">\u1021\u1010\u1014\u103a\u1038\u1019\u103b\u102c\u1038- <span style=\"color: #ff0000;\">1<\/span> \u104a <span style=\"color: #ff0000;\">2<\/span> \u104a <span style=\"color: #ff0000;\">3<\/span> \u104a <span style=\"color: #ff0000;\">4<\/span> \u104a <span style=\"color: #008080;\">5<\/span> \u104a <span style=\"color: #ff0000;\">6<\/span> \u104a <span style=\"color: #008080;\">7<\/span> \u104a <span style=\"color: #008080;\">8<\/span> \u104a <span style=\"color: #008080;\">9<\/span> \u104a <span style=\"color: #008080;\">10<\/span> \u104a <span style=\"color: #ff0000;\">11<\/span> \u104a <span style=\"color: #008080;\">12<\/span> \u104a <span style=\"color: #ff0000;\">13<\/span> \u104a <span style=\"color: #008080;\">14<\/span> \u104a <span style=\"color: #008080;\">15<\/span><\/span><\/strong><\/span><\/p>\n<p> <span style=\"color: #008080;\"><strong>R <sub>1<\/sub><\/strong><\/span> <span style=\"color: #000000;\">= \u1014\u1019\u1030\u1014\u102c 1 \u1021\u1010\u103d\u1000\u103a \u1021\u1006\u1004\u1037\u103a\u1015\u1031\u102b\u1004\u103a\u1038 = 5+7+8+9+10+12+14+15 = 80<\/span><\/p>\n<p> <span style=\"color: #ff0000;\"><strong>R <sub>2<\/sub><\/strong><\/span> <span style=\"color: #000000;\">= \u1014\u1019\u1030\u1014\u102c 2 \u1021\u1010\u103d\u1000\u103a \u1021\u1006\u1004\u1037\u103a\u1015\u1031\u102b\u1004\u103a\u1038 = 1+2+3+4+6+11+13 = 40<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1011\u102d\u102f\u1037\u1014\u1031\u102c\u1000\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f\u1014\u1019\u1030\u1014\u102c\u1021\u101b\u103d\u101a\u103a\u1021\u1005\u102c\u1038 n <sub>1<\/sub> \u1014\u103e\u1004\u1037\u103a n <sub>2<\/sub> \u1021\u1015\u103c\u1004\u103a U <sub>1<\/sub> \u1014\u103e\u1004\u1037\u103a U <sub>2<\/sub> \u1000\u102d\u102f\u101b\u103e\u102c\u1016\u103d\u1031\u101b\u1014\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f\u1021\u1006\u1004\u1037\u103a\u1015\u1031\u102b\u1004\u103a\u1038 R <sub>1<\/sub> \u1014\u103e\u1004\u1037\u103a R <sub>2<\/sub> \u1000\u102d\u102f\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><sub>U1<\/sub> = 8(7) + 8(8+1)\/2 \u2013 80 = 12<\/span><\/p>\n<p> <span style=\"color: #000000;\"><sub>U2<\/sub> = 8(7) + 7(7+1)\/2 \u2013 40 = 44<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1005\u102c\u101b\u1004\u103a\u1038\u1007\u101a\u102c\u1038\u1019\u103b\u102c\u1038\u101e\u100a\u103a <sub>U1<\/sub> \u1014\u103e\u1004\u1037\u103a <sub>U2<\/sub> \u104f\u101e\u1031\u1038\u1004\u101a\u103a\u101e\u100a\u103a\u104a \u104e\u1004\u103a\u1038\u1019\u103e\u102c U=12 \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <em><span style=\"color: #000000;\">\u1019\u103e\u1010\u103a\u1001\u103b\u1000\u103a- U = 12 \u1000\u102d\u102f \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a <a href=\"https:\/\/statorials.org\/my\/mann-whitney-u-\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1002\u100f\u1014\u103a\u1038\u1015\u1031\u102b\u1004\u103a\u1038\u1005\u1000\u103a\/\" target=\"_blank\" rel=\"noopener\">Mann-Whitney U \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1002\u100f\u1014\u103a\u1038\u1010\u103d\u1000\u103a\u1005\u1000\u103a<\/a> \u1000\u102d\u102f\u101c\u100a\u103a\u1038 \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/em><\/p>\n<p> <span style=\"color: #000000;\"><strong>4. null hypothesis \u1000\u102d\u102f \u1004\u103c\u1004\u103a\u1038\u1015\u101a\u103a\u1001\u103c\u1004\u103a\u1038 \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1004\u103c\u1004\u103a\u1038\u1015\u101a\u103a\u1001\u103c\u1004\u103a\u1038\u1019\u1015\u103c\u102f\u1015\u102b\u1014\u103e\u1004\u1037\u103a\u104b<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">n <sub>1<\/sub> = 8 \u1014\u103e\u1004\u1037\u103a n <sub>2<\/sub> = 7 \u1000\u102d\u102f 0.01 \u104f \u1021\u101b\u1031\u1038\u1015\u102b\u101e\u1031\u102c\u1021\u1006\u1004\u1037\u103a\u1016\u103c\u1004\u1037\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d Mann-Whitney U \u1007\u101a\u102c\u1038\u1000 \u1021\u101b\u1031\u1038\u1000\u103c\u102e\u1038\u101e\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103e\u102c 6 \u1016\u103c\u1005\u103a\u101e\u100a\u103a-<\/span> <\/p>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-1383 size-full\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/mw_ex2.png\" alt=\"Mann Whitney U Test Critical Value Table\" width=\"544\" height=\"401\" srcset=\"\" sizes=\"\"><\/p>\n<p> <span style=\"color: #000000;\">\u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038 (12) \u101e\u100a\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f\u1021\u101b\u1031\u1038\u1000\u103c\u102e\u1038\u101e\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038 (6) \u1011\u1000\u103a\u1000\u103c\u102e\u1038\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a null hypothesis \u1000\u102d\u102f \u1004\u103c\u1004\u103a\u1038\u1015\u101a\u103a\u101b\u1014\u103a\u1015\u103b\u1000\u103a\u1000\u103d\u1000\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>5. \u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1018\u102c\u101e\u102c\u1015\u103c\u1014\u103a\u1015\u102b\u104b<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">null hypothesis \u1000\u102d\u102f \u1004\u103c\u1004\u103a\u1038\u1006\u102d\u102f\u101b\u1014\u103a \u1015\u103b\u1000\u103a\u1000\u103d\u1000\u103a\u1001\u1032\u1037\u101e\u1016\u103c\u1004\u1037\u103a \u101c\u1031\u1037\u101c\u102c\u1001\u1032\u1037\u101e\u1031\u102c \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u1019\u103b\u102c\u1038\u104f \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u101b\u1019\u103e\u1010\u103a\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1005\u102c\u1019\u1000\u103b\u1000\u103a\u101e\u1031\u102c \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a \u1000\u103d\u1032\u1015\u103c\u102c\u1038\u101e\u100a\u103a\u101f\u102f \u1006\u102d\u102f\u101b\u1014\u103a \u101c\u102f\u1036\u101c\u1031\u102c\u1000\u103a\u101e\u1031\u102c \u1021\u1011\u1031\u102c\u1000\u103a\u1021\u1011\u102c\u1038 \u1019\u101b\u103e\u102d\u1015\u102b\u104b<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>\u1011\u1015\u103a\u101c\u1031\u102c\u1004\u103a\u1038\u1021\u101b\u1004\u103a\u1038\u1021\u1019\u103c\u1005\u103a\u1019\u103b\u102c\u1038<\/strong><\/span><\/h2>\n<p> <a href=\"https:\/\/statorials.org\/my\/mann-whitney-u-\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1002\u100f\u1014\u103a\u1038\u1015\u1031\u102b\u1004\u103a\u1038\u1005\u1000\u103a\/\" target=\"_blank\" rel=\"noopener\">Mann-Whitney U \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1002\u100f\u1014\u103a\u1038\u1015\u1031\u102b\u1004\u103a\u1038\u1005\u1000\u103a<\/a><br \/> Mann-Whitney U Table<br \/> <a href=\"https:\/\/statorials.org\/my\/mann-whitney-u-test-\u1000\u102d\u102f-excel-\u1019\u103e\u102c-\u1018\u101a\u103a\u101c\u102d\u102f\u1016\u103c\u1031\u101b\u1019\u101c\u1032\/\" target=\"_blank\" rel=\"noopener\">Excel \u1010\u103d\u1004\u103a Mann-Whitney U Test \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<\/a><br \/> <a href=\"https:\/\/statorials.org\/my\/mann-whitney-u-test-r\/\" target=\"_blank\" rel=\"noopener\">R \u1010\u103d\u1004\u103a Mann-Whitney U \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1015\u103c\u102f\u101c\u102f\u1015\u103a\u1014\u100a\u103a\u1038<\/a><br \/> <a href=\"https:\/\/statorials.org\/my\/mann-whitney-u-\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1005\u1015\u102b\u1038\u1021\u102f\u1036\u1038\/\">Python \u1010\u103d\u1004\u103a Mann-Whitney U Test \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<\/a><br \/> <a href=\"https:\/\/statorials.org\/my\/mann-whitney-u-test-spss\/\" target=\"_blank\" rel=\"noopener\">SPSS \u1010\u103d\u1004\u103a Mann-Whitney U Test \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<\/a><br \/> <a href=\"https:\/\/statorials.org\/my\/mann-whitney-u-\u1005\u1019\u103a\u1038\u1000\u103c\u100a\u1037\u103a\u1010\u101a\u103a\u104b\/\" target=\"_blank\" rel=\"noopener\">Stata \u101b\u103e\u102d Mann-Whitney U \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1015\u103c\u102f\u101c\u102f\u1015\u103a\u1014\u100a\u103a\u1038<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Mann-Whitney U \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f (\u1010\u1005\u103a\u1001\u102b\u1010\u1005\u103a\u101b\u1036 Wilcoxon rank sum test \u101f\u102f\u1001\u1031\u102b\u103a\u101e\u100a\u103a) \u1000\u102d\u102f\u1014\u1019\u1030\u1014\u102c\u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1019\u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1018\u1032\u1014\u103e\u1004\u1037\u103a \u1014\u1019\u1030\u1014\u102c\u1021\u101b\u103d\u101a\u103a\u1021\u1005\u102c\u1038\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u101e\u1031\u1038\u1004\u101a\u103a\u101e\u100a\u103a (n &lt;30) \u1010\u103d\u1004\u103a \u101e\u102e\u1038\u1001\u103c\u102c\u1038\u1014\u1019\u1030\u1014\u102c\u1014\u103e\u1005\u103a\u1001\u102f\u1000\u103c\u102c\u1038 \u1000\u103d\u102c\u1001\u103c\u102c\u1038\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1014\u103e\u102d\u102f\u1004\u103a\u1038\u101a\u103e\u1009\u103a\u101b\u1014\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a\u104b \u101c\u103d\u1010\u103a\u101c\u1015\u103a\u101e\u1031\u102c\u1014\u1019\u1030\u1014\u102c\u1014\u103e\u1005\u103a\u1001\u102f t \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f \u104f parametric \u100a\u102e\u1019\u103b\u103e\u1001\u103c\u1004\u103a\u1038\u101f\u102f \u101a\u1030\u1006\u101e\u100a\u103a\u104b \u1024\u101e\u100a\u103a\u1019\u103e\u102c Mann-Whitney U \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u101e\u1004\u103a\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u1037\u103a\u1021\u1001\u102b \u1025\u1015\u1019\u102c\u1021\u1001\u103b\u102d\u102f\u1037\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b \u1010\u1000\u1039\u1000\u101e\u102d\u102f\u101c\u103a A \u1019\u103e \u1018\u103d\u1032\u1037\u101b\u1004\u102b\u1038\u1026\u1038\u104f \u101c\u1005\u102c\u1014\u103e\u1004\u1037\u103a \u1010\u1000\u1039\u1000\u101e\u102d\u102f\u101c\u103a B \u1018\u103d\u1032\u1037\u101b\u1004\u102b\u1038\u1026\u1038\u104f \u101c\u1005\u102c\u1010\u102d\u102f\u1037\u1000\u102d\u102f \u1014\u103e\u102d\u102f\u1004\u103a\u1038\u101a\u103e\u1009\u103a\u101c\u102d\u102f\u101e\u100a\u103a\u104b \u101c\u1005\u102c\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1001\u103d\u1032\u101d\u1031\u1015\u1031\u1038\u1019\u100a\u103a\u1019\u101f\u102f\u1010\u103a\u1015\u102b\u104b \u1000\u102d\u102f\u101a\u103a\u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a\u1000\u103b\u1001\u103c\u1004\u103a\u1038\u1021\u1010\u103d\u1000\u103a \u1021\u102f\u1015\u103a\u1005\u102f\u1014\u103e\u1005\u103a\u1005\u102f\u1000\u103d\u1032\u1015\u103c\u102c\u1038\u1019\u103e\u102f\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u101e\u102d\u101c\u102d\u102f\u1015\u102b\u101e\u100a\u103a- \u1021\u1005\u102c\u1038\u1021\u101e\u1031\u102c\u1000\u103a A \u1000\u102d\u102f\u101e\u102f\u1036\u1038\u101e\u1031\u102c \u101c\u1030 \u1041\u1042 \u1026\u1038\u1014\u103e\u1004\u1037\u103a \u1021\u1005\u102c\u1038\u1021\u101e\u1031\u102c\u1000\u103a [&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>Mann-Whitney U \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f - Statorials<\/title>\n<meta name=\"description\" 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