{"id":526,"date":"2023-07-29T14:56:51","date_gmt":"2023-07-29T14:56:51","guid":{"rendered":"https:\/\/statorials.org\/my\/welchs-t-%e1%80%85%e1%80%99%e1%80%ba%e1%80%b8%e1%80%9e%e1%80%95%e1%80%ba%e1%80%99%e1%80%be%e1%80%af\/"},"modified":"2023-07-29T14:56:51","modified_gmt":"2023-07-29T14:56:51","slug":"welchs-t-%e1%80%85%e1%80%99%e1%80%ba%e1%80%b8%e1%80%9e%e1%80%95%e1%80%ba%e1%80%99%e1%80%be%e1%80%af","status":"publish","type":"post","link":"https:\/\/statorials.org\/my\/welchs-t-%e1%80%85%e1%80%99%e1%80%ba%e1%80%b8%e1%80%9e%e1%80%95%e1%80%ba%e1%80%99%e1%80%be%e1%80%af\/","title":{"rendered":"Welch \u104f t \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f- \u1019\u100a\u103a\u101e\u100a\u1037\u103a\u1021\u1001\u103b\u102d\u1014\u103a\u1010\u103d\u1004\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101b\u1019\u100a\u103a + \u1025\u1015\u1019\u102c\u1019\u103b\u102c\u1038"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u1021\u1019\u103e\u102e\u1021\u1001\u102d\u102f\u1000\u1004\u103a\u1038\u101e\u1031\u102c\u1021\u102f\u1015\u103a\u1005\u102f\u1014\u103e\u1005\u103a\u1001\u102f\u104f\u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1014\u103e\u102d\u102f\u1004\u103a\u1038\u101a\u103e\u1009\u103a\u101c\u102d\u102f\u101e\u1031\u102c\u1021\u1001\u102b\u104a \u1019\u1010\u1030\u100a\u102e\u101e\u1031\u102c\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1014\u103e\u1005\u103a\u1001\u102f\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d \u101b\u103d\u1031\u1038\u1001\u103b\u101a\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a-<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u104f t-test-<\/strong> \u1024\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1010\u103d\u1004\u103a \u1012\u1031\u1010\u102c\u1021\u102f\u1015\u103a\u1005\u102f\u1014\u103e\u1005\u103a\u1005\u102f\u1000\u102d\u102f <a href=\"https:\/\/statorials.org\/my\/\u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u1019\u103e\u102f\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1019\u103e\u102f<\/a> \u1014\u1031\u102c\u1000\u103a\u101e\u102d\u102f\u1037\u101c\u102d\u102f\u1000\u103a\u101e\u1031\u102c \u101c\u1030\u1026\u1038\u101b\u1031\u1019\u103b\u102c\u1038\u1019\u103e\u1014\u1019\u1030\u1014\u102c\u101a\u1030\u1011\u102c\u1038\u1015\u103c\u102e\u1038 \u101c\u1030\u1026\u1038\u101b\u1031\u1014\u103e\u1005\u103a\u1001\u102f\u101e\u100a\u103a \u1010\u1030\u100a\u102e\u101e\u1031\u102c\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u101b\u103e\u102d\u101e\u100a\u103a\u101f\u102f \u101a\u1030\u1006\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>Welch \u104f t-test-<\/strong> \u1024\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1010\u103d\u1004\u103a \u1012\u1031\u1010\u102c\u1021\u102f\u1015\u103a\u1005\u102f\u1014\u103e\u1005\u103a\u1001\u102f\u1005\u101c\u102f\u1036\u1038\u101e\u100a\u103a \u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1019\u103e\u102f\u1014\u1031\u102c\u1000\u103a\u101e\u102d\u102f\u1037\u101c\u102d\u102f\u1000\u103a\u101e\u1031\u102c \u101c\u1030\u1026\u1038\u101b\u1031\u1019\u103b\u102c\u1038\u1019\u103e\u1014\u1019\u1030\u1014\u102c\u101a\u1030\u1011\u102c\u1038\u101e\u100a\u103a\u101f\u102f \u101a\u1030\u1006\u101e\u1031\u102c\u103a\u101c\u100a\u103a\u1038 <em>\u1024\u101c\u1030\u1026\u1038\u101b\u1031\u1014\u103e\u1005\u103a\u1001\u102f\u101e\u100a\u103a \u1010\u1030\u100a\u102e\u101e\u1031\u102c\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u101b\u103e\u102d\u101e\u100a\u103a\u101f\u102f \u1019\u101a\u1030\u1006\u1015\u102b<\/em> \u104b<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Student&#8217;s t-test \u1014\u103e\u1004\u1037\u103a Welch&#8217;s t-test \u1000\u103d\u102c\u1001\u103c\u102c\u1038\u1001\u103b\u1000\u103a<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\"><span style=\"color: #000000;\">Student&#8217;s t-test \u1014\u103e\u1004\u1037\u103a Welch&#8217;s t-test \u101c\u102f\u1015\u103a\u1015\u102f\u1036 \u1000\u103d\u102c\u1001\u103c\u102c\u1038\u1001\u103b\u1000\u103a \u1014\u103e\u1005\u103a\u1001\u102f\u101b\u103e\u102d\u101e\u100a\u103a\u104b<\/span><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><span style=\"color: #000000;\"><strong>\u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038<\/strong><\/span><\/span><\/li>\n<li> <span style=\"color: #000000;\"><span style=\"color: #000000;\"><strong>\u101c\u103d\u1010\u103a\u101c\u1015\u103a\u1019\u103e\u102f\u1012\u102e\u1002\u101b\u102e<\/strong><\/span><\/span><\/li>\n<\/ul>\n<h3> <span style=\"color: #000000;\"><strong>\u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u104f t-test-<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><strong>\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038-<\/strong> ( <span style=\"border-top: 1px solid black;\">x<\/span> <sub>1<\/sub> \u2013 <span style=\"border-top: 1px solid black;\">x<\/span> <sub>2<\/sub> ) \/ s <sub>p<\/sub> (\u221a <span style=\"border-top: 1px solid black;\">1\/n <sub>1<\/sub> + 1\/n <sub>2<\/sub><\/span> )<\/span><\/p>\n<p> <span style=\"color: #000000;\"><span style=\"border-top: 1px solid black;\">x<\/span> <sub>1<\/sub> \u1014\u103e\u1004\u1037\u103a <span style=\"border-top: 1px solid black;\">x<\/span> <sub>2<\/sub> \u101e\u100a\u103a \u1014\u1019\u1030\u1014\u102c\u1006\u102d\u102f\u101c\u102d\u102f\u101e\u100a\u103a\u1019\u103e\u102c \u1021\u1018\u101a\u103a\u1019\u103e\u102c\u1014\u100a\u103a\u1038\u104a n <sub>1<\/sub> \u1014\u103e\u1004\u1037\u103a n <sub>2<\/sub> \u101e\u100a\u103a \u1014\u1019\u1030\u1014\u102c 1 \u1014\u103e\u1004\u1037\u103a \u1014\u1019\u1030\u1014\u102c 2 \u1021\u1010\u103d\u1000\u103a \u1014\u1019\u1030\u1014\u102c\u1021\u101b\u103d\u101a\u103a\u1021\u1005\u102c\u1038\u1019\u103b\u102c\u1038\u1016\u103c\u1005\u103a\u1015\u103c\u102e\u1038 s <sub>p<\/sub> \u1000\u102d\u102f \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1021\u1010\u102d\u102f\u1004\u103a\u1038 \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101e\u100a\u103a-<\/span><\/p>\n<p> <span style=\"color: #000000;\">s <sub>p<\/sub><\/span> = <span style=\"color: #000000;\">\u221a <span style=\"border-top: 1px solid black;\">(n <sub>1<\/sub> -1)s <sub>1<\/sub> <sup>2<\/sup> + (n <sub>2<\/sub> -1)s <sub>2<\/sub> <sup>2<\/sup> \/ (n <sub>1<\/sub> +n <sub>2<\/sub> -2)\u104a<\/span><\/span><\/p>\n<p> <span style=\"color: #000000;\">s <sub>1<\/sub> <sup>2<\/sup> \u1014\u103e\u1004\u1037\u103a s <sub>2<\/sub> <sup>2<\/sup> \u101e\u100a\u103a \u1014\u1019\u1030\u1014\u102c\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u101c\u103d\u1010\u103a\u101c\u1015\u103a\u1019\u103e\u102f\u1012\u102e\u1002\u101b\u102e-<\/strong> n <sub>1<\/sub> + n <sub>2<\/sub> \u2013 2<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>Welch \u104f T-test<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><strong>\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038-<\/strong> ( <span style=\"border-top: 1px solid black;\">x<\/span> <sub>1<\/sub> \u2013 <span style=\"border-top: 1px solid black;\">x<\/span> <sub>2<\/sub> ) \/ (\u221a <span style=\"border-top: 1px solid black;\">s <sub>1<\/sub> <sup>2<\/sup> \/n <sub>1<\/sub> + s <sub>2<\/sub> <sup>2<\/sup> \/n <sub>2<\/sub><\/span> )<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u101c\u103d\u1010\u103a\u101c\u1015\u103a\u1019\u103e\u102f\u1012\u102e\u1002\u101b\u102e-<\/strong><\/span> <span style=\"color: #000000;\">(s <sub>1<\/sub> <sup>2<\/sup> \/n <sub>1<\/sub> + s <sub>2<\/sub> <sup>2<\/sup> \/n <sub>2<\/sub> ) <sup>2<\/sup> \/ { [ (s <sub>1<\/sub> <sup>2<\/sup> \/ n <sub>1<\/sub> ) <sup>2<\/sup> \/ (n <sub>1<\/sub> \u2013 1) ] + [ (s <sub>2<\/sub> <sup>2<\/sup> \/ n <sub>2<\/sub> ) <sup>\u1042<\/sup> \/ (\u100e <sub>\u1042<\/sub> \u2013 \u1041) ] }<\/span><\/p>\n<p> <span style=\"color: #000000;\">Welch \u104f t-test \u1021\u1010\u103d\u1000\u103a \u101c\u103d\u1010\u103a\u101c\u1015\u103a\u1019\u103e\u102f\u1012\u102e\u1002\u101b\u102e\u1000\u102d\u102f \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u101b\u1014\u103a \u1016\u1031\u102c\u103a\u1019\u103c\u1030\u101c\u102c\u101e\u100a\u103a \u1005\u1036\u101e\u103d\u1031\u1016\u100a\u103a\u1019\u103e\u102f\u1014\u103e\u1005\u103a\u1001\u102f\u1000\u103c\u102c\u1038 \u1000\u103d\u102c\u1001\u103c\u102c\u1038\u1001\u103b\u1000\u103a\u1000\u102d\u102f \u1011\u100a\u1037\u103a\u101e\u103d\u1004\u103a\u1038\u1005\u1009\u103a\u1038\u1005\u102c\u1038\u101e\u100a\u103a\u104b <a href=\"https:\/\/statorials.org\/my\/\u101c\u1030\u1025\u102e\u1038\u101b\u1031\u1014\u103e\u1004\u1037\u103a-\u1014\u1019\u1030\u1014\u102c-1\/\" target=\"_blank\" rel=\"noopener\">\u1014\u1019\u1030\u1014\u102c<\/a> \u1014\u103e\u1005\u103a\u1001\u102f\u1010\u103d\u1004\u103a \u1005\u1036\u101e\u103d\u1031\u1016\u100a\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038 \u1010\u1030\u100a\u102e\u1015\u102b\u1000 Welch&#8217;s t-test \u104f \u101c\u103d\u1010\u103a\u101c\u1015\u103a\u1019\u103e\u102f\u1012\u102e\u1002\u101b\u102e\u101e\u100a\u103a \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u104f t-test \u104f \u101c\u103d\u1010\u103a\u101c\u1015\u103a\u1019\u103e\u102f\u1012\u102e\u1002\u101b\u102e\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a \u1021\u1010\u102d\u1021\u1000\u103b\u1010\u1030\u100a\u102e\u1019\u100a\u103a\u1016\u103c\u1005\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a\u104a \u1014\u1019\u1030\u1014\u102c\u1014\u103e\u1005\u103a\u1001\u102f\u1021\u1010\u103d\u1000\u103a \u1005\u1036\u101e\u103d\u1031\u1016\u100a\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u1019\u103e\u102c \u1019\u1010\u1030\u100a\u102e\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a Welch&#8217;s t-test \u104f \u101c\u103d\u1010\u103a\u101c\u1015\u103a\u1019\u103e\u102f\u1012\u102e\u1002\u101b\u102e\u101e\u100a\u103a \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u104f t-test \u104f \u101c\u103d\u1010\u103a\u101c\u1015\u103a\u1019\u103e\u102f\u1012\u102e\u1002\u101b\u102e\u1011\u1000\u103a \u101e\u1031\u1038\u1004\u101a\u103a\u1014\u1031\u1010\u1010\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">Welch \u104f t-test \u1010\u103d\u1004\u103a \u101c\u103d\u1010\u103a\u101c\u1015\u103a\u1019\u103e\u102f\u1012\u102e\u1002\u101b\u102e\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u101a\u1031\u1018\u102f\u101a\u103b\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a \u1000\u102d\u1014\u103a\u1038\u1015\u103c\u100a\u1037\u103a\u1019\u101f\u102f\u1010\u103a\u1000\u103c\u1031\u102c\u1004\u103a\u1038\u1000\u102d\u102f\u101c\u100a\u103a\u1038 \u101e\u1010\u102d\u1015\u103c\u102f\u101b\u1014\u103a \u1021\u101b\u1031\u1038\u1000\u103c\u102e\u1038\u1015\u102b\u101e\u100a\u103a\u104b \u101e\u1004\u103a\u1000\u102d\u102f\u101a\u103a\u1010\u102d\u102f\u1004\u103a \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1014\u1031\u1015\u102b\u1000\u104a \u1021\u1014\u102d\u1019\u1037\u103a\u1006\u102f\u1036\u1038\u1014\u1036\u1015\u102b\u1010\u103a\u1010\u1005\u103a\u1001\u102f\u101c\u102f\u1036\u1038\u101e\u102d\u102f\u1037 \u101c\u103e\u100a\u1037\u103a\u1001\u103c\u1004\u103a\u1038\u101e\u100a\u103a \u1021\u1000\u1031\u102c\u1004\u103a\u1038\u1006\u102f\u1036\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b <em>R<\/em> \u1000\u1032\u1037\u101e\u102d\u102f\u1037\u101e\u1031\u102c \u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1006\u1031\u102c\u1037\u1016\u103a\u101d\u1032\u1000\u102d\u102f \u101e\u1004\u103a\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1015\u102b\u1000\u104a \u1006\u1031\u102c\u1037\u1016\u103a\u101d\u1032\u101e\u100a\u103a \u101c\u103d\u1010\u103a\u101c\u1015\u103a\u1019\u103e\u102f\u1012\u102e\u1002\u101b\u102e\u1019\u103b\u102c\u1038\u104f \u1012\u103f\u1019\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1000\u102d\u102f \u1015\u1031\u1038\u1006\u1031\u102c\u1004\u103a\u1014\u102d\u102f\u1004\u103a\u1019\u100a\u103a\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<h2> <strong><span style=\"color: #000000;\">Welch t-test \u1000\u102d\u102f \u1018\u101a\u103a\u1021\u1001\u103b\u102d\u1014\u103a\u1019\u103e\u102c \u101e\u102f\u1036\u1038\u101e\u1004\u1037\u103a\u101c\u1032\u104b<\/span><\/strong><\/h2>\n<p> <span style=\"color: #000000;\"><a href=\"https:\/\/daniellakens.blogspot.com\/2015\/01\/always-use-welchs-t-test-instead-of.html\" target=\"_blank\" rel=\"noopener noreferrer\">Welch \u104f t-test \u101e\u100a\u103a \u1021\u1019\u103e\u102e\u1021\u1001\u102d\u102f\u1000\u1004\u103a\u1038\u101e\u1031\u102c\u1021\u102f\u1015\u103a\u1005\u102f\u1014\u103e\u1005\u103a\u1001\u102f\u104f\u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1014\u103e\u102d\u102f\u1004\u103a\u1038\u101a\u103e\u1009\u103a\u1001\u103c\u1004\u103a\u1038\u1021\u1010\u103d\u1000\u103a \u1015\u102f\u1036\u101e\u1031\u101b\u103d\u1031\u1038\u1001\u103b\u101a\u103a\u1019\u103e\u102f\u1016\u103c\u1005\u103a\u101e\u1004\u1037\u103a\u101e\u100a\u103a\u101f\u102f<\/a> \u1005\u1031\u102c\u1012\u1000\u1010\u1000\u103a\u1000\u103c\u1015\u103c\u102e\u1038 \u1014\u1019\u1030\u1014\u102c\u1021\u101b\u103d\u101a\u103a\u1021\u1005\u102c\u1038\u1014\u103e\u1004\u1037\u103a \u1000\u103d\u1032\u1015\u103c\u102c\u1038\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1021\u102f\u1015\u103a\u1005\u102f\u1019\u103b\u102c\u1038\u1000\u103c\u102c\u1038\u1010\u103d\u1004\u103a \u1014\u1019\u1030\u1014\u102c\u1021\u101b\u103d\u101a\u103a\u1021\u1005\u102c\u1038\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a \u1019\u1010\u1030\u100a\u102e\u101e\u100a\u1037\u103a\u1021\u1001\u102b\u1010\u103d\u1004\u103a \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u104f t-test \u1011\u1000\u103a \u1015\u102d\u102f\u1019\u102d\u102f\u1000\u1031\u102c\u1004\u103a\u1038\u1019\u103d\u1014\u103a\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u104e\u1004\u103a\u1038\u101e\u100a\u103a \u1014\u1019\u1030\u1014\u102c\u1021\u101b\u103d\u101a\u103a\u1021\u1005\u102c\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1010\u1030\u100a\u102e\u101e\u100a\u1037\u103a\u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u1015\u1031\u1038\u1006\u1031\u102c\u1004\u103a\u101e\u100a\u103a \u1019\u1010\u1030\u1000\u103c\u1015\u102b\u104b \u1000\u103d\u102c\u1001\u103c\u102c\u1038\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1010\u1014\u103a\u1038\u1010\u1030\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u101c\u1000\u103a\u1010\u103d\u1031\u1037\u1010\u103d\u1004\u103a\u104a \u1021\u102f\u1015\u103a\u1005\u102f\u1014\u103e\u1005\u103a\u1001\u102f\u104f\u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1014\u103e\u102d\u102f\u1004\u103a\u1038\u101a\u103e\u1009\u103a\u1000\u103c\u100a\u1037\u103a\u101e\u1031\u102c\u1021\u1001\u102b\u104a \u1021\u102f\u1015\u103a\u1005\u102f\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u104f \u1005\u1036\u101e\u103d\u1031\u1016\u100a\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u1019\u103e\u102c \u1010\u1030\u100a\u102e\u101c\u102d\u1019\u1037\u103a\u1019\u100a\u103a\u1019\u1011\u1004\u103a\u1015\u102b\u104b \u1011\u102d\u102f\u1037\u1000\u103c\u1031\u102c\u1004\u1037\u103a Welch&#8217;s t-test \u1000\u102d\u102f \u1021\u1019\u103c\u1032\u101e\u102f\u1036\u1038\u101b\u1014\u103a \u1005\u102d\u1010\u103a\u1000\u1030\u1038\u1000\u1031\u102c\u1004\u103a\u1038\u1015\u102b\u101e\u100a\u103a\u104a \u1011\u102d\u102f\u1037\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u1019\u1010\u1030\u100a\u102e\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u104f \u101e\u102c\u1010\u1030\u100a\u102e\u1019\u103b\u103e\u1019\u103e\u102f\u1014\u103e\u1004\u1037\u103a\u1015\u1010\u103a\u101e\u1000\u103a\u104d \u101a\u1030\u1006\u101b\u1014\u103a \u1019\u101c\u102d\u102f\u1021\u1015\u103a\u1015\u102b\u104b<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>Welch&#8217;s t-test \u1000\u102d\u102f\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1015\u102f\u1036 \u1014\u1019\u1030\u1014\u102c\u1019\u103b\u102c\u1038<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">\u1011\u102d\u102f\u1037\u1014\u1031\u102c\u1000\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1014\u1019\u1030\u1014\u102c\u1014\u103e\u1005\u103a\u1001\u102f\u1010\u103d\u1004\u103a Welch \u104f t-test \u1000\u102d\u102f\u1015\u103c\u102f\u101c\u102f\u1015\u103a\u1015\u103c\u102e\u1038 \u104e\u1004\u103a\u1038\u1010\u102d\u102f\u1037\u104f\u101c\u1030\u1026\u1038\u101b\u1031\u104f\u1021\u1013\u102d\u1015\u1039\u1015\u102b\u101a\u103a\u1019\u103e\u102c 0.05 \u1021\u101b\u1031\u1038\u1015\u102b\u1019\u103e\u102f\u1021\u1006\u1004\u1037\u103a\u1010\u103d\u1004\u103a \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u1005\u103d\u102c\u1000\u103d\u102c\u1001\u103c\u102c\u1038\u1019\u103e\u102f\u101b\u103e\u102d\u1019\u101b\u103e\u102d\u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1015\u102b\u1019\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u1014\u1019\u1030\u1014\u102c 1:<\/strong> 14\u104a 15\u104a 15\u104a 15\u104a 16\u104a 18\u104a 22\u104a 23\u104a 24\u104a 25\u104a 25<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u1014\u1019\u1030\u1014\u102c \u1042-<\/strong> \u1041\u1040\u104a \u1041\u1042\u104a \u1041\u1044\u104a \u1041\u1045\u104a \u1041\u1048\u104a \u1042\u1042\u104a \u1042\u1044\u104a \u1042\u1047\u104a \u1043\u1041\u104a \u1043\u1043\u104a \u1043\u1044\u104a \u1043\u1044\u104a \u1043\u1044<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u1000\u102d\u102f \u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u101e\u102f\u1036\u1038\u1019\u103b\u102d\u102f\u1038\u1016\u103c\u1004\u1037\u103a \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1019\u100a\u103a\u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u101e\u101b\u102f\u1015\u103a\u1016\u1031\u102c\u103a\u1015\u102b\u1019\u100a\u103a\u104b<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u101c\u1000\u103a\u1016\u103c\u1004\u1037\u103a<\/span><\/li>\n<li> <span style=\"color: #000000;\">Microsoft Excel \u1000\u102d\u102f\u101e\u102f\u1036\u1038\u1015\u102b\u104b<\/span><\/li>\n<li> <span style=\"color: #000000;\"><em>R<\/em> \u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a\u1038\u1019\u1004\u103a\u1038\u1018\u102c\u101e\u102c\u1005\u1000\u102c\u1038\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1015\u102b\u104b<\/span><\/li>\n<\/ul>\n<h3> <span style=\"color: #000000;\"><strong>Welch&#8217;s T \u1000\u102d\u102f \u101c\u1000\u103a\u1016\u103c\u1004\u1037\u103a \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u101e\u100a\u103a\u104b<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Welch t-test \u1000\u102d\u102f \u101c\u1000\u103a\u1016\u103c\u1004\u1037\u103a\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1014\u103a\u104a \u1014\u1019\u1030\u1014\u102c\u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1019\u103b\u102c\u1038\u104a \u1014\u1019\u1030\u1014\u102c\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a \u1014\u1019\u1030\u1014\u102c\u1021\u101b\u103d\u101a\u103a\u1021\u1005\u102c\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1026\u1038\u1005\u103d\u102c\u101b\u103e\u102c\u1016\u103d\u1031\u101b\u1014\u103a \u101c\u102d\u102f\u1021\u1015\u103a\u101e\u100a\u103a-<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong><span style=\"border-top: 1px solid black;\">x1<\/span> <sub>\u2013<\/sub><\/strong> 19.27<br \/><\/span> <span style=\"color: #000000;\"><strong><span style=\"border-top: 1px solid black;\">x2<\/span> <sub>\u2013<\/sub><\/strong> 23.69<br \/> <strong>s <sub>1<\/sub> <sup>2<\/sup><\/strong> \u2013 8:42 pm<br \/><\/span> <span style=\"color: #000000;\"><strong>\u1021\u1014\u102f\u1015\u100a\u102c <sub>2<\/sub> <sup>2<\/sup><\/strong> \u2013 83.23<br \/> <strong>#<\/strong> <sub><strong>\u1041\u2013\u1041\u1041<\/strong><\/sub> <strong><br \/>#<\/strong> <sub><strong>\u1042<\/strong><\/sub> \u2013 \u1041\u1043<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1011\u102d\u102f\u1037\u1014\u1031\u102c\u1000\u103a \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u101b\u103e\u102c\u1016\u103d\u1031\u101b\u1014\u103a \u1024\u1014\u1036\u1015\u102b\u1010\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u101b\u102d\u102f\u1000\u103a\u1011\u100a\u1037\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a-<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038-<\/strong> ( <span style=\"border-top: 1px solid black;\">x <sub>1<\/sub><\/span> \u2013 <span style=\"border-top: 1px solid black;\">x <sub>2<\/sub><\/span> ) \/ (\u221a <span style=\"border-top: 1px solid black;\">s <sub>1<\/sub> <sup>2<\/sup> \/n <sub>1<\/sub> + s <sub>2<\/sub> <sup>2<\/sup> \/n <sub>2<\/sub><\/span> )<\/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- (19.27 \u2013 23.69) \/ (\u221a <span style=\"border-top: 1px solid black;\">20.42\/11 + 83.23\/13<\/span> ) = -4.42 \/ 2.873 = <strong>-1.538<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u101c\u103d\u1010\u103a\u101c\u1015\u103a\u1019\u103e\u102f\u1012\u102e\u1002\u101b\u102e-<\/strong> (s <sub>1<\/sub> <sup>2<\/sup> \/n <sub>1<\/sub> + s <sub>2<\/sub> <sup>2<\/sup> \/n <sub>2<\/sub> ) <sup>2<\/sup> \/ { [ (s <sub>1<\/sub> <sup>2<\/sup> \/ n <sub>1<\/sub> ) <sup>2<\/sup> \/ (n <sub>1<\/sub> \u2013 1) ] + [ (s <sub>2<\/sub> <sup>2<\/sup> \/ n <sub>2<\/sub> ) <sup>\u1042<\/sup> \/ (\u100e <sub>\u1042<\/sub> \u2013 \u1041) ] }<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u101c\u103d\u1010\u103a\u101c\u1015\u103a\u1019\u103e\u102f\u1012\u102e\u1002\u101b\u102e- (20.42\/11 + 83.23\/13) <sup>2<\/sup> \/ { [ (20.42\/11) <sup>2<\/sup> \/ (11 \u2013 1) ] + [ (83.23\/13) <sup>2<\/sup> \/ (13 \u2013 1) ] } = 18.137 \u104b \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1024\u101b\u101c\u1012\u103a\u1000\u102d\u102f \u1021\u1014\u102e\u1038\u1006\u102f\u1036\u1038\u1000\u102d\u1014\u103a\u1038\u1015\u103c\u100a\u1037\u103a\u104a <strong>18<\/strong> \u101e\u102d\u102f\u1037 \u101d\u102d\u102f\u1004\u103a\u1038\u1011\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1014\u1031\u102c\u1000\u103a\u1006\u102f\u1036\u1038\u1010\u103d\u1004\u103a\u104a \u101c\u103d\u1010\u103a\u101c\u1015\u103a\u1019\u103e\u102f 18 \u1012\u102e\u1002\u101b\u102e\u1021\u1010\u103d\u1000\u103a alpha = 0.05 \u1016\u103c\u1004\u1037\u103a \u1014\u103e\u1005\u103a\u1018\u1000\u103a\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1001\u103b\u1000\u103a\u1014\u103e\u1004\u1037\u103a \u101e\u1000\u103a\u1006\u102d\u102f\u1004\u103a\u101e\u100a\u1037\u103a t \u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u101b\u1031\u1038\u1007\u101a\u102c\u1038\u1010\u103d\u1004\u103a \u1021\u101b\u1031\u1038\u1000\u103c\u102e\u1038\u101e\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038 <em>t<\/em> \u1000\u102d\u102f \u1010\u103d\u1031\u1037\u101b\u103e\u102d\u1015\u102b\u1019\u100a\u103a\u104b<\/span> <\/p>\n<p><img decoding=\"async\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/t_dist.png\" alt=\"\u1016\u103c\u1014\u1037\u103a\u1016\u103c\u1030\u1038\u101b\u1031\u1038\u1007\u101a\u102c\u1038 T\" srcset=\"\" sizes=\"\"><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u101b\u1031\u1038\u1000\u103c\u102e\u1038\u101e\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038 t \u101e\u100a\u103a <strong>2.101<\/strong> \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b \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 (1.538) \u104f \u1015\u1000\u1010\u102d\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u101e\u100a\u103a \u1021\u101b\u1031\u1038\u1000\u103c\u102e\u1038\u101e\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038 t \u1011\u1000\u103a\u1019\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 \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u104f 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 \u101c\u1030\u1026\u1038\u101b\u1031\u1014\u103e\u1005\u103a\u1001\u102f\u104f \u1021\u1013\u102d\u1015\u1039\u1015\u102b\u101a\u103a\u1019\u103e\u102c \u101e\u102d\u101e\u102d\u101e\u102c\u101e\u102c\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>Excel \u1016\u103c\u1004\u1037\u103a Welch \u104f T-test<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Welch \u104f t-test \u1000\u102d\u102f Excel \u1010\u103d\u1004\u103a\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1014\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1021\u1001\u1019\u1032\u1037 Analysis ToolPak \u1006\u1031\u102c\u1037\u1016\u103a\u101d\u1032\u101c\u103a\u1000\u102d\u102f \u1026\u1038\u1005\u103d\u102c\u1012\u1031\u102b\u1004\u103a\u1038\u101c\u102f\u1012\u103a\u101c\u102f\u1015\u103a\u101b\u1014\u103a \u101c\u102d\u102f\u1021\u1015\u103a\u1015\u102b\u101e\u100a\u103a\u104b Excel \u1019\u103e\u102c \u1012\u1031\u102b\u1004\u103a\u1038\u101c\u102f\u1012\u103a\u1019\u101c\u102f\u1015\u103a\u101b\u101e\u1031\u1038\u101b\u1004\u103a <a href=\"https:\/\/statorials.org\/my\/\u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c-toolpak-\u1000\u102d\u102f-excel-\u1010\u103d\u1004\u103a\u1019\u100a\u103a\u101e\u102d\u102f\u1037\u1010\u1004\u103a\u101b\u1019\u100a\u103a\u1014\u100a\u103a\u1038\u104b\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u1012\u1031\u102b\u1004\u103a\u1038\u101c\u102f\u1012\u103a\u101c\u102f\u1015\u103a\u1014\u100a\u103a\u1038\u1000\u102d\u102f \u1021\u1019\u103c\u1014\u103a<\/a> \u101b\u1031\u1038\u1011\u102c\u1038\u1015\u102b\u1010\u101a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">Analysis ToolPak \u1000\u102d\u102f \u101e\u1004\u103a\u1012\u1031\u102b\u1004\u103a\u1038\u101c\u102f\u1012\u103a\u101c\u102f\u1015\u103a\u1015\u103c\u102e\u1038\u101e\u100a\u103a\u1014\u103e\u1004\u1037\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f\u1014\u1019\u1030\u1014\u102c\u1014\u103e\u1005\u103a\u1001\u102f\u1010\u103d\u1004\u103a Welch&#8217;s t-test \u1000\u102d\u102f\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1014\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1021\u1006\u1004\u1037\u103a\u1019\u103b\u102c\u1038\u1021\u1010\u102d\u102f\u1004\u103a\u1038 \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a-<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. \u1021\u1001\u103b\u1000\u103a\u1021\u101c\u1000\u103a\u1011\u100a\u1037\u103a\u1015\u102b\u104b<\/strong> \u1000\u1031\u102c\u103a\u101c\u1036 A \u1014\u103e\u1004\u1037\u103a B \u1010\u103d\u1004\u103a \u1014\u1019\u1030\u1014\u102c\u1014\u103e\u1005\u103a\u1001\u102f\u1021\u1010\u103d\u1000\u103a \u1012\u1031\u1010\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1000\u1031\u102c\u103a\u101c\u1036\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u104f \u1015\u1011\u1019\u1006\u1032\u101c\u103a\u1010\u103d\u1004\u103a <em>\u1014\u1019\u1030\u1014\u102c 1<\/em> \u1014\u103e\u1004\u1037\u103a <em>\u1014\u1019\u1030\u1014\u102c 2<\/em> \u1001\u1031\u102b\u1004\u103a\u1038\u1005\u1009\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1011\u100a\u1037\u103a\u1015\u102b\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. Analysis ToolPak \u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d Welch \u104f t-test \u1000\u102d\u102f \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1015\u102b\u104b<\/strong> \u1011\u102d\u1015\u103a\u1016\u1032\u1000\u103c\u102d\u102f\u1038\u1010\u1005\u103a\u101c\u103b\u103e\u1031\u102c\u1000\u103a <strong>\u1012\u1031\u1010\u102c<\/strong> \u1010\u1000\u103a\u1018\u103a\u101e\u102d\u102f\u1037 \u101e\u103d\u102c\u1038\u1015\u102b\u104b \u1011\u102d\u102f\u1037\u1014\u1031\u102c\u1000\u103a\u104a <strong>\u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u1019\u103e\u102f<\/strong> \u1021\u102f\u1015\u103a\u1005\u102f\u1021\u1031\u102c\u1000\u103a\u101b\u103e\u102d \u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u1001\u103c\u1004\u103a\u1038\u1000\u102d\u101b\u102d\u101a\u102c\u1010\u1014\u103a\u1006\u102c\u1015\u101c\u102c\u1021\u102d\u102f\u1004\u103a\u1000\u103d\u1014\u103a\u1000\u102d\u102f \u1014\u103e\u102d\u1015\u103a\u1015\u102b\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1015\u1031\u102b\u103a\u101c\u102c\u101e\u100a\u1037\u103a \u1012\u102d\u102f\u1004\u103a\u101a\u102c\u101c\u1031\u102c\u1037\u1002\u103a\u1018\u1031\u102c\u1000\u103a\u1005\u103a\u1010\u103d\u1004\u103a\u104a <strong>t-test \u1000\u102d\u102f \u1014\u103e\u102d\u1015\u103a\u1015\u102b- \u1019\u100a\u102e\u1019\u103b\u103e\u101e\u1031\u102c\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u101f\u102f \u101a\u1030\u1006\u101e\u100a\u1037\u103a \u1014\u1019\u1030\u1014\u102c\u1014\u103e\u1005\u103a\u1001\u102f\u1000\u102d\u102f<\/strong> \u1014\u103e\u102d\u1015\u103a\u1015\u102b\u104a \u1011\u102d\u102f\u1037\u1014\u1031\u102c\u1000\u103a OK \u1000\u102d\u102f\u1014\u103e\u102d\u1015\u103a\u1015\u102b\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1014\u1031\u102c\u1000\u103a\u1006\u102f\u1036\u1038\u1010\u103d\u1004\u103a\u104a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f\u1016\u103c\u100a\u1037\u103a\u1015\u103c\u102e\u1038 OK \u1000\u102d\u102f\u1014\u103e\u102d\u1015\u103a\u1015\u102b\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u1031\u102c\u1000\u103a\u1015\u102b\u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038 \u1015\u1031\u102b\u103a\u101c\u102c\u101e\u1004\u1037\u103a\u101e\u100a\u103a-<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1024\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u104f\u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1000\u102d\u102f\u101a\u103a\u1010\u102d\u102f\u1004\u103a\u101b\u101b\u103e\u102d\u101e\u1031\u102c\u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a \u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u101e\u1010\u102d\u1015\u103c\u102f\u1015\u102b\u104b<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u101e\u100a\u103a <strong>-1.5379<\/strong> \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u1014\u103e\u1005\u103a\u1018\u1000\u103a\u1021\u101b\u1031\u1038\u1021\u101e\u102c\u1038\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u101e\u100a\u103a <strong>2.1009<\/strong> \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u1005\u1005\u103a\u1006\u1031\u1038\u1019\u103e\u102f\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u104f \u1015\u1000\u1010\u102d\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u101e\u100a\u103a \u1021\u1019\u103c\u102e\u1038\u1014\u103e\u1005\u103a\u1015\u102d\u102f\u1004\u103a\u1038\u1021\u101b\u1031\u1038\u1015\u102b\u101e\u1031\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1011\u1000\u103a \u1019\u1015\u102d\u102f\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a\u104a \u101c\u1030\u1026\u1038\u101b\u1031\u1014\u103e\u1005\u103a\u1001\u102f\u104f \u1021\u1013\u102d\u1015\u1039\u1015\u102b\u101a\u103a\u1019\u103e\u102c \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1021\u101b \u1019\u1010\u1030\u100a\u102e\u1015\u102b\u104b<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u1011\u102d\u102f\u1037\u1021\u1015\u103c\u1004\u103a\u104a \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u104f \u1021\u1019\u103c\u102e\u1038\u1014\u103e\u1005\u103a\u1015\u102d\u102f\u1004\u103a\u1038 p-\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u101e\u100a\u103a 0.14 \u1016\u103c\u1005\u103a\u1015\u103c\u102e\u1038 0.05 \u1011\u1000\u103a \u1015\u102d\u102f\u1019\u103b\u102c\u1038\u1015\u103c\u102e\u1038 \u101c\u1030\u1026\u1038\u101b\u1031\u1014\u103e\u1005\u103a\u1001\u102f\u104f \u1021\u1013\u102d\u1015\u1039\u1015\u102b\u101a\u103a\u1019\u103e\u102c \u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1021\u101b \u1000\u103d\u1032\u1015\u103c\u102c\u1038\u1001\u103c\u1004\u103a\u1038\u1019\u101b\u103e\u102d\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1021\u1010\u100a\u103a\u1015\u103c\u102f\u101e\u100a\u103a\u104b<\/span><\/li>\n<\/ul>\n<h3> <span style=\"color: #000000;\"><strong>R \u1000\u102d\u102f\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d Welch \u104f t-test<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1000\u102f\u1012\u103a\u101e\u100a\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f\u1014\u1019\u1030\u1014\u102c\u1014\u103e\u1005\u103a\u1001\u102f\u1021\u1010\u103d\u1000\u103a Welch \u104f t-test \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 <em>R<\/em> statistical programming language \u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d \u1016\u1031\u102c\u103a\u1015\u103c\u101e\u100a\u103a<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create two vectors to hold sample data values\n<\/span>sample1 &lt;- c(14, 15, 15, 15, 16, 18, 22, 23, 24, 25, 25)\nsample2 &lt;- c(10, 12, 14, 15, 18, 22, 24, 27, 31, 33, 34, 34, 34)\n\n<span style=\"color: #008080;\">#conduct Welch's test\n<\/span><span style=\"color: #800080;\">t.test(<\/span> sample1, sample2)\n\n# Welch Two Sample t-test\n#\n#data: sample1 and sample2\n#t = -1.5379, df = 18.137, p-value = 0.1413\n#alternative hypothesis: true difference in means is not equal to 0\n#95 percent confidence interval:\n#-10.453875 1.614714\n#sample estimates:\n#mean of x mean of y \n#19.27273 23.69231 \n#<\/strong><\/pre>\n<p> <span style=\"color: #000000;\"><strong>t.test()<\/strong> \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u103b\u1000\u103a\u101e\u100a\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b \u101e\u1000\u103a\u1006\u102d\u102f\u1004\u103a\u101b\u102c \u101b\u101c\u1012\u103a\u1000\u102d\u102f \u1015\u103c\u101e\u101e\u100a\u103a-<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>t:<\/strong> \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038 = <strong>-1.5379<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>df<\/strong> : \u101c\u103d\u1010\u103a\u101c\u1015\u103a\u1019\u103e\u102f\u1012\u102e\u1002\u101b\u102e = <strong>18.137<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>p-value-<\/strong> \u1021\u1019\u103c\u102e\u1038\u1014\u103e\u1005\u103a\u1001\u102f\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u104f p-\u1010\u1014\u103a\u1016\u102d\u102f\u1038 = <strong>0.1413<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>95% \u101a\u102f\u1036\u1000\u103c\u100a\u103a\u1019\u103e\u102f\u1000\u103c\u102c\u1038\u1000\u102c\u101c<\/strong> : \u101c\u1030\u1026\u1038\u101b\u1031\u1021\u1010\u103d\u1000\u103a \u1005\u1005\u103a\u1019\u103e\u1014\u103a\u101e\u1031\u102c\u1001\u103c\u102c\u1038\u1014\u102c\u1038\u1001\u103b\u1000\u103a\u1021\u1010\u103d\u1000\u103a 95% <a href=\"https:\/\/statorials.org\/my\/\u101a\u102f\u1036\u1000\u103c\u100a\u103a\u1019\u103e\u102f\u1000\u103c\u102c\u1038\u1000\u102c\u101c\u1019\u103b\u102c\u1038\/\" target=\"_blank\" rel=\"noopener noreferrer\">\u101a\u102f\u1036\u1000\u103c\u100a\u103a\u1019\u103e\u102f\u1000\u103c\u102c\u1038\u1000\u102c\u101c<\/a> \u1006\u102d\u102f\u101e\u100a\u103a\u1019\u103e\u102c = <strong>(-10.45\u104a 1.61)<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u1024\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u104f\u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1000\u102d\u102f\u101a\u103a\u1010\u102d\u102f\u1004\u103a\u1014\u103e\u1004\u1037\u103a Excel \u1000\u102d\u102f\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d \u101b\u101b\u103e\u102d\u101e\u1031\u102c\u101e\u1030\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a \u101e\u1000\u103a\u1006\u102d\u102f\u1004\u103a\u101e\u100a\u103a- \u1024\u101c\u1030\u1026\u1038\u101b\u1031\u1014\u103e\u1005\u103a\u1001\u102f\u1021\u1010\u103d\u1000\u103a \u1021\u1013\u102d\u1015\u1039\u1015\u102b\u101a\u103a\u1019\u103e\u102c alpha = 0.05 \u1021\u1006\u1004\u1037\u103a\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\u1001\u103c\u1004\u103a\u1038\u1019\u101b\u103e\u102d\u1015\u102b\u104b<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u1021\u1019\u103e\u102e\u1021\u1001\u102d\u102f\u1000\u1004\u103a\u1038\u101e\u1031\u102c\u1021\u102f\u1015\u103a\u1005\u102f\u1014\u103e\u1005\u103a\u1001\u102f\u104f\u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1014\u103e\u102d\u102f\u1004\u103a\u1038\u101a\u103e\u1009\u103a\u101c\u102d\u102f\u101e\u1031\u102c\u1021\u1001\u102b\u104a \u1019\u1010\u1030\u100a\u102e\u101e\u1031\u102c\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1014\u103e\u1005\u103a\u1001\u102f\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d \u101b\u103d\u1031\u1038\u1001\u103b\u101a\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a- \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u104f t-test- \u1024\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1010\u103d\u1004\u103a \u1012\u1031\u1010\u102c\u1021\u102f\u1015\u103a\u1005\u102f\u1014\u103e\u1005\u103a\u1005\u102f\u1000\u102d\u102f \u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1019\u103e\u102f \u1014\u1031\u102c\u1000\u103a\u101e\u102d\u102f\u1037\u101c\u102d\u102f\u1000\u103a\u101e\u1031\u102c \u101c\u1030\u1026\u1038\u101b\u1031\u1019\u103b\u102c\u1038\u1019\u103e\u1014\u1019\u1030\u1014\u102c\u101a\u1030\u1011\u102c\u1038\u1015\u103c\u102e\u1038 \u101c\u1030\u1026\u1038\u101b\u1031\u1014\u103e\u1005\u103a\u1001\u102f\u101e\u100a\u103a \u1010\u1030\u100a\u102e\u101e\u1031\u102c\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u101b\u103e\u102d\u101e\u100a\u103a\u101f\u102f \u101a\u1030\u1006\u101e\u100a\u103a\u104b Welch \u104f t-test- \u1024\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1010\u103d\u1004\u103a \u1012\u1031\u1010\u102c\u1021\u102f\u1015\u103a\u1005\u102f\u1014\u103e\u1005\u103a\u1001\u102f\u1005\u101c\u102f\u1036\u1038\u101e\u100a\u103a \u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1019\u103e\u102f\u1014\u1031\u102c\u1000\u103a\u101e\u102d\u102f\u1037\u101c\u102d\u102f\u1000\u103a\u101e\u1031\u102c \u101c\u1030\u1026\u1038\u101b\u1031\u1019\u103b\u102c\u1038\u1019\u103e\u1014\u1019\u1030\u1014\u102c\u101a\u1030\u1011\u102c\u1038\u101e\u100a\u103a\u101f\u102f \u101a\u1030\u1006\u101e\u1031\u102c\u103a\u101c\u100a\u103a\u1038 \u1024\u101c\u1030\u1026\u1038\u101b\u1031\u1014\u103e\u1005\u103a\u1001\u102f\u101e\u100a\u103a \u1010\u1030\u100a\u102e\u101e\u1031\u102c\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u101b\u103e\u102d\u101e\u100a\u103a\u101f\u102f \u1019\u101a\u1030\u1006\u1015\u102b \u104b Student&#8217;s t-test \u1014\u103e\u1004\u1037\u103a Welch&#8217;s t-test \u1000\u103d\u102c\u1001\u103c\u102c\u1038\u1001\u103b\u1000\u103a Student&#8217;s t-test \u1014\u103e\u1004\u1037\u103a Welch&#8217;s t-test \u101c\u102f\u1015\u103a\u1015\u102f\u1036 \u1000\u103d\u102c\u1001\u103c\u102c\u1038\u1001\u103b\u1000\u103a \u1014\u103e\u1005\u103a\u1001\u102f\u101b\u103e\u102d\u101e\u100a\u103a\u104b \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038 \u101c\u103d\u1010\u103a\u101c\u1015\u103a\u1019\u103e\u102f\u1012\u102e\u1002\u101b\u102e \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u104f t-test- \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038- ( x 1 \u2013 x 2 ) \/ s [&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>Welch \u104f t-test- \u1019\u100a\u103a\u101e\u100a\u1037\u103a\u1021\u1001\u103b\u102d\u1014\u103a\u1010\u103d\u1004\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101b\u1019\u100a\u103a + \u1025\u1015\u1019\u102c\u1019\u103b\u102c\u1038 - Statorials<\/title>\n<meta name=\"description\" content=\"Welch&#039;s t-test \u1000\u102d\u102f\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1015\u102f\u1036\u1014\u103e\u1004\u1037\u103a \u1019\u100a\u103a\u101e\u100a\u1037\u103a\u1021\u1001\u103b\u102d\u1014\u103a\u1010\u103d\u1004\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101b\u1019\u100a\u103a\u1000\u102d\u102f \u1025\u1015\u1019\u102c\u1019\u103b\u102c\u1038\u1005\u103d\u102c\u1016\u103c\u1004\u1037\u103a \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1011\u102c\u1038\u101e\u100a\u1037\u103a \u101b\u102d\u102f\u1038\u101b\u103e\u1004\u103a\u1038\u101e\u1031\u102c\u101c\u1019\u103a\u1038\u100a\u103d\u103e\u1014\u103a\u1001\u103b\u1000\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\/welchs-t-\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\/\" \/>\n<meta property=\"og:locale\" content=\"my_MM\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Welch \u104f t-test- \u1019\u100a\u103a\u101e\u100a\u1037\u103a\u1021\u1001\u103b\u102d\u1014\u103a\u1010\u103d\u1004\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101b\u1019\u100a\u103a + \u1025\u1015\u1019\u102c\u1019\u103b\u102c\u1038 - Statorials\" \/>\n<meta property=\"og:description\" content=\"Welch&#039;s t-test \u1000\u102d\u102f\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1015\u102f\u1036\u1014\u103e\u1004\u1037\u103a \u1019\u100a\u103a\u101e\u100a\u1037\u103a\u1021\u1001\u103b\u102d\u1014\u103a\u1010\u103d\u1004\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101b\u1019\u100a\u103a\u1000\u102d\u102f \u1025\u1015\u1019\u102c\u1019\u103b\u102c\u1038\u1005\u103d\u102c\u1016\u103c\u1004\u1037\u103a \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1011\u102c\u1038\u101e\u100a\u1037\u103a \u101b\u102d\u102f\u1038\u101b\u103e\u1004\u103a\u1038\u101e\u1031\u102c\u101c\u1019\u103a\u1038\u100a\u103d\u103e\u1014\u103a\u1001\u103b\u1000\u103a\u104b\" \/>\n<meta property=\"og:url\" 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