{"id":1284,"date":"2023-07-27T00:38:59","date_gmt":"2023-07-27T00:38:59","guid":{"rendered":"https:\/\/statorials.org\/my\/%e1%80%a1%e1%80%8a%e1%80%ad%e1%80%af%e1%80%9b%e1%80%b1%e1%80%ac%e1%80%84%e1%80%ba-forsythe-test-in-r\/"},"modified":"2023-07-27T00:38:59","modified_gmt":"2023-07-27T00:38:59","slug":"%e1%80%a1%e1%80%8a%e1%80%ad%e1%80%af%e1%80%9b%e1%80%b1%e1%80%ac%e1%80%84%e1%80%ba-forsythe-test-in-r","status":"publish","type":"post","link":"https:\/\/statorials.org\/my\/%e1%80%a1%e1%80%8a%e1%80%ad%e1%80%af%e1%80%9b%e1%80%b1%e1%80%ac%e1%80%84%e1%80%ba-forsythe-test-in-r\/","title":{"rendered":"R \u1010\u103d\u1004\u103a brown\u2013forsythe \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f- \u1021\u1006\u1004\u1037\u103a\u1006\u1004\u1037\u103a \u1025\u1015\u1019\u102c"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/my\/one-way-anova\/\" target=\"_blank\" rel=\"noopener\">\u1010\u1005\u103a\u101c\u1019\u103a\u1038\u101e\u103d\u102c\u1038 ANOVA \u1000\u102d\u102f<\/a> \u101e\u102f\u1036\u1038\u101e\u1031\u102c \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1011\u102d\u102f\u1037\u1011\u1000\u103a\u1019\u1000\u101e\u1031\u102c \u101e\u102e\u1038\u1001\u103c\u102c\u1038\u1021\u102f\u1015\u103a\u1005\u102f\u1019\u103b\u102c\u1038\u104f \u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1019\u103b\u102c\u1038\u1000\u103c\u102c\u1038 \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u101e\u1031\u102c \u1001\u103c\u102c\u1038\u1014\u102c\u1038\u1019\u103e\u102f \u101b\u103e\u102d\u104a \u1019\u101b\u103e\u102d \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1010\u1005\u103a\u101c\u1019\u103a\u1038\u101e\u103d\u102c\u1038 ANOVA \u104f <a href=\"https:\/\/statorials.org\/my\/danova-\u101a\u1030\u1006\u1001\u103b\u1000\u103a\/\" target=\"_blank\" rel=\"noopener\">\u101a\u1030\u1006\u1001\u103b\u1000\u103a<\/a> \u1010\u1005\u103a\u1001\u102f\u101e\u100a\u103a <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\u1019\u103b\u102c\u1038\u1000\u102d\u102f<\/a> \u1011\u102f\u1010\u103a\u101a\u1030\u101e\u100a\u1037\u103a \u101c\u1030\u1026\u1038\u101b\u1031\u104f \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1010\u1030\u100a\u102e\u101e\u100a\u103a\u101f\u102f \u1006\u102d\u102f\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u104e\u1004\u103a\u1038\u1000\u102d\u102f\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u101b\u1014\u103a \u1021\u101e\u102f\u1036\u1038\u1021\u1019\u103b\u102c\u1038\u1006\u102f\u1036\u1038\u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1010\u1005\u103a\u1001\u102f\u1019\u103e\u102c \u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b <a href=\"https:\/\/statorials.org\/my\/\u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1001\u103c\u1004\u103a\u1038-\u1041\/\" target=\"_blank\" rel=\"noopener\">\u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f<\/a> \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u1037\u103a \u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1006\u102d\u102f\u1004\u103a\u101b\u102c\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u1037\u103a <strong>Brown-Forsythe test \u1000\u102d\u102f<\/strong> \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1001\u103c\u1004\u103a\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>H <sub>0<\/sub> :<\/strong> \u101c\u1030\u1026\u1038\u101b\u1031\u1019\u103b\u102c\u1038\u1000\u103c\u102c\u1038 \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1010\u1014\u103a\u1038\u1010\u1030\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>H <sub>A<\/sub><\/strong> : \u101c\u1030\u1026\u1038\u101b\u1031 \u1000\u103d\u102c\u101f\u1001\u103b\u1000\u103a\u1000 \u1019\u100a\u102e\u1019\u103b\u103e\u1015\u102b\u1018\u1030\u1038\u104b<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u104f <a href=\"https:\/\/statorials.org\/my\/p-\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103b\u102c\u1038\u101e\u100a\u103a-\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1006\u102d\u102f\u1004\u103a\u101b\u102c-\u1021\u101b\u1031\u1038\u1015\u102b\u1019\u103e\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b\/\" target=\"_blank\" rel=\"noopener\">p-\u1010\u1014\u103a\u1016\u102d\u102f\u1038<\/a> \u101e\u100a\u103a \u1021\u1001\u103b\u102d\u102f\u1037\u101e\u1031\u102c \u1021\u101b\u1031\u1038\u1015\u102b\u1019\u103e\u102f\u1021\u1006\u1004\u1037\u103a\u1021\u1031\u102c\u1000\u103a\u1010\u103d\u1004\u103a \u101b\u103e\u102d\u1015\u102b\u1000 (\u1025\u1015\u1019\u102c \u03b1 = 0.05)\u104a \u1011\u102d\u102f\u1037\u1014\u1031\u102c\u1000\u103a null hypothesis \u1000\u102d\u102f \u1004\u103c\u1004\u103a\u1038\u1015\u101a\u103a\u1015\u103c\u102e\u1038 \u1019\u1010\u1030\u100a\u102e\u101e\u1031\u102c \u101c\u1030\u1026\u1038\u101b\u1031\u1019\u103b\u102c\u1038\u1000\u103c\u102c\u1038\u1010\u103d\u1004\u103a \u1000\u103d\u1032\u1015\u103c\u102c\u1038\u1019\u103e\u102f\u1019\u103b\u102c\u1038 \u1019\u100a\u102e\u1019\u103b\u103e\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1000\u1031\u102c\u1000\u103a\u1001\u103b\u1000\u103a\u1001\u103b\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1024\u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u101e\u100a\u103a R \u1010\u103d\u1004\u103a Brown-Forsythe \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1015\u103c\u102f\u101c\u102f\u1015\u103a\u1015\u102f\u1036\u1021\u1006\u1004\u1037\u103a\u1006\u1004\u1037\u103a\u1000\u102d\u102f \u1025\u1015\u1019\u102c\u1015\u1031\u1038\u1011\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 1: \u1012\u1031\u1010\u102c\u1000\u102d\u102f\u1011\u100a\u1037\u103a\u1015\u102b\u104b<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u1019\u1010\u1030\u100a\u102e\u1010\u1032\u1037 \u101c\u1031\u1037\u1000\u103b\u1004\u1037\u103a\u1001\u1014\u103a\u1038 \u1021\u1005\u102e\u1021\u1005\u1009\u103a\u101e\u102f\u1036\u1038\u1001\u102f\u1000 \u1019\u1010\u1030\u100a\u102e\u1010\u1032\u1037 \u1000\u102d\u102f\u101a\u103a\u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a\u1000\u102d\u102f \u101c\u103b\u1031\u102c\u1037\u1000\u103b\u1005\u1031\u101e\u101c\u102c\u1038\u1006\u102d\u102f\u1010\u102c\u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u101e\u102d\u101c\u102d\u102f\u101e\u100a\u103a\u1006\u102d\u102f\u1015\u102b\u1005\u102d\u102f\u1037\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u104e\u1004\u103a\u1038\u1000\u102d\u102f\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u101b\u1014\u103a\u1021\u1010\u103d\u1000\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u101c\u1030 90 \u1000\u102d\u102f\u1005\u102f\u1006\u1031\u102c\u1004\u103a\u1038\u1015\u103c\u102e\u1038 \u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1000\u102d\u102f\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101b\u1014\u103a 30 \u1000\u102d\u102f \u1000\u103b\u1015\u1014\u103a\u1038\u101e\u1010\u103a\u1019\u103e\u1010\u103a\u1015\u1031\u1038\u1015\u102b\u101e\u100a\u103a\u104b \u1011\u102d\u102f\u1037\u1014\u1031\u102c\u1000\u103a \u1010\u1005\u103a\u101c\u1021\u1000\u103c\u102c\u1010\u103d\u1004\u103a \u101c\u1030\u1010\u1005\u103a\u1026\u1038\u1005\u102e\u104f \u1000\u102d\u102f\u101a\u103a\u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a\u1000\u102d\u102f \u1010\u102d\u102f\u1004\u103a\u1038\u1010\u102c\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b \u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u1010\u103d\u1004\u103a \u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1010\u103d\u1004\u103a \u1006\u102f\u1036\u1038\u101b\u103e\u102f\u1036\u1038\u101e\u103d\u102c\u1038\u101e\u1031\u102c \u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a\u1015\u1019\u102c\u100f\u1006\u102d\u102f\u1004\u103a\u101b\u102c \u1021\u1001\u103b\u1000\u103a\u1021\u101c\u1000\u103a\u1015\u102b\u101b\u103e\u102d\u101e\u100a\u103a\u104b<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#make this example reproducible\n<\/span>set.seed(0)\n\n<span style=\"color: #008080;\">#create data frame\n<\/span>data &lt;- data.frame(program = <span style=\"color: #3366ff;\">as<\/span> . <span style=\"color: #3366ff;\">factor<\/span> ( <span style=\"color: #3366ff;\">rep<\/span> (c(\" <span style=\"color: #008000;\">A<\/span> \", \" <span style=\"color: #008000;\">B<\/span> \", \" <span style=\"color: #008000;\">C<\/span> \"), <span style=\"color: #3366ff;\">each<\/span> = 30)),\n                   weight_loss = c( <span style=\"color: #3366ff;\">runif<\/span> (30, 0, 3),\n                                   <span style=\"color: #3366ff;\">runif<\/span> (30, 0, 5),\n                                   <span style=\"color: #3366ff;\">runif<\/span> (30, 1, 7)))\n\n<span style=\"color: #008080;\">#view first six rows of data frame\n<\/span>head(data)\n\n# program weight_loss\n#1 A 2.6900916\n#2 A 0.7965260\n#3 A 1.1163717\n#4 A 1.7185601\n#5 A 2.7246234\n#6 A 0.6050458<\/strong><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 2- \u1012\u1031\u1010\u102c\u1000\u102d\u102f \u1021\u1000\u103b\u1009\u103a\u1038\u1001\u103b\u102f\u1015\u103a\u1015\u103c\u102e\u1038 \u1019\u103c\u1004\u103a\u101a\u1031\u102c\u1004\u103a\u1000\u103c\u100a\u1037\u103a\u1015\u102b\u104b<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">Brown-Forsythe \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1019\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1019\u102e\u104a \u1021\u102f\u1015\u103a\u1005\u102f\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1021\u1010\u103d\u1000\u103a \u1000\u102d\u102f\u101a\u103a\u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a\u1000\u103b\u1001\u103c\u1004\u103a\u1038\u104f \u1000\u103d\u1032\u1015\u103c\u102c\u1038\u1019\u103e\u102f\u1000\u102d\u102f \u1019\u103c\u1004\u103a\u101e\u102c\u1005\u1031\u101b\u1014\u103a \u1021\u1000\u103d\u1000\u103a\u1000\u103d\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1016\u1014\u103a\u1010\u102e\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a-<\/span> <\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong>boxplot(weight_loss ~ program, data = data)\n<\/strong><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\"aligncenter wp-image-12614 \" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/test1.png\" alt=\"\" width=\"437\" height=\"395\" srcset=\"\" sizes=\"\"><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u102f\u1015\u103a\u1005\u102f\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u101b\u103e\u102d \u1000\u102d\u102f\u101a\u103a\u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a\u1000\u103b\u1001\u103c\u1004\u103a\u1038\u104f \u1000\u103d\u1032\u1015\u103c\u102c\u1038\u1019\u103e\u102f\u1000\u102d\u102f\u101c\u100a\u103a\u1038 \u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#load dplyr package<\/span>\n<span style=\"color: #993300;\">library<\/span> (dplyr)\n\n<span style=\"color: #008080;\">#calculate variance of weight loss by group\n<\/span>data %&gt;%\n<span style=\"color: #3366ff;\">group_by<\/span> (program) %&gt;%\n  <span style=\"color: #3366ff;\">summarize<\/span> (var=var(weight_loss))\n\n# A tibble: 3 x 2\n  program var\n     \n1 A 0.819\n2 B 1.53 \n3 C 2.46<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u1021\u1016\u103d\u1032\u1037\u1019\u103b\u102c\u1038\u1000\u103c\u102c\u1038 \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1019\u103b\u102c\u1038 \u1000\u103d\u1032\u1015\u103c\u102c\u1038\u101e\u100a\u103a\u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1010\u103d\u1031\u1037\u1019\u103c\u1004\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c\u103a\u101c\u100a\u103a\u1038 \u1024\u1000\u103d\u102c\u1001\u103c\u102c\u1038\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u101e\u100a\u103a <a href=\"https:\/\/statorials.org\/my\/\u101c\u1000\u103a\u1010\u103d\u1031\u1037\u1000\u103b\u101e\u1031\u102c-\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1006\u102d\u102f\u1004\u103a\u101b\u102c-\u1021\u101b\u1031\u1038\u1015\u102b\u1019\u103e\u102f\/\" target=\"_blank\" rel=\"noopener\">\u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1021\u101b \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u1001\u103c\u1004\u103a\u1038<\/a> \u101b\u103e\u102d\u1019\u101b\u103e\u102d \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a Brown-Forsythe \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 3- Brown-Forsythe \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1015\u102b\u104b<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">R \u1010\u103d\u1004\u103a Brown-Forsythe \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1000\u102d\u102f \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 <a href=\"https:\/\/www.rdocumentation.org\/packages\/onewaytests\/versions\/2.4\/topics\/bf.test\" target=\"_blank\" rel=\"noopener\">onewaytests<\/a> \u1015\u1000\u103a\u1000\u1031\u1037\u1001\u103a\u103b\u1019\u103e <strong>bf.test()<\/strong> \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u103b\u1000\u103a\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#load onewaytests package<\/span>\n<span style=\"color: #993300;\">library<\/span> (onewaytests)\n\n<span style=\"color: #008080;\">#perform Brown-Forsythe test<\/span>\nbf.test(weight_loss ~ program, data = data)\n\n  Brown-Forsythe Test (alpha = 0.05) \n-------------------------------------------------- ----------- \n  data: weight_loss and program \n\n  statistic: 30.83304 \n  num df: 2 \n  name df: 74.0272 \n  p.value: 1.816529e-10 \n\n  Result: Difference is statistically significant. \n-------------------------------------------------- -----------<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u1005\u1005\u103a\u1006\u1031\u1038\u1019\u103e\u102f\u104f p-value \u101e\u100a\u103a 0.000 \u1011\u1000\u103a\u1014\u100a\u103a\u1038\u1015\u103c\u102e\u1038 \u101b\u101c\u1012\u103a\u1000\u1016\u1031\u102c\u103a\u1015\u103c\u101e\u100a\u1037\u103a\u1021\u1010\u102d\u102f\u1004\u103a\u1038 \u1021\u102f\u1015\u103a\u1005\u102f\u101e\u102f\u1036\u1038\u1005\u102f\u1000\u103c\u102c\u1038\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1021\u101b \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<h3> <strong>\u1014\u1031\u102c\u1000\u103a\u1010\u1005\u103a\u1006\u1004\u1037\u103a<\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Brown-Forsythe \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u104f null hypothesis \u1000\u102d\u102f \u101e\u1004\u103a \u1019\u1004\u103c\u1004\u103a\u1038\u1015\u101a\u103a\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u1000\u104a \u101e\u1004\u103a\u101e\u100a\u103a data \u1015\u1031\u102b\u103a\u1010\u103d\u1004\u103a one-way ANOVA \u1000\u102d\u102f \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u101e\u102d\u102f\u1037\u101b\u102c\u1010\u103d\u1004\u103a\u104a \u101e\u1004\u103a\u101e\u100a\u103a null hypothesis \u1000\u102d\u102f \u1004\u103c\u1004\u103a\u1038\u1015\u101a\u103a\u1015\u102b\u1000\u104a \u1000\u103d\u1032\u1015\u103c\u102c\u1038\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u104f \u1010\u1014\u103a\u1038\u1010\u1030\u100a\u102e\u1019\u103b\u103e\u1019\u103e\u102f\u104f \u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1000\u102d\u102f \u1001\u103b\u102d\u102f\u1038\u1016\u1031\u102c\u1000\u103a\u101e\u100a\u103a\u101f\u102f \u1006\u102d\u102f\u101c\u102d\u102f\u101e\u100a\u103a\u104b \u1024\u1000\u102d\u1005\u1039\u1005\u1010\u103d\u1004\u103a\u104a \u101e\u1004\u1037\u103a\u1010\u103d\u1004\u103a \u101b\u103d\u1031\u1038\u1001\u103b\u101a\u103a\u1005\u101b\u102c\u1014\u103e\u1005\u103a\u1001\u102f\u101b\u103e\u102d\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. ANOVA \u1010\u1005\u103a\u1000\u103c\u1031\u102c\u1004\u103a\u1038\u1010\u100a\u103a\u1038\u101c\u102f\u1015\u103a\u1015\u102b\u104b<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u1000\u103c\u102e\u1038\u1006\u102f\u1036\u1038\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u101e\u100a\u103a \u1021\u101e\u1031\u1038\u1004\u101a\u103a\u1006\u102f\u1036\u1038\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f 4 \u1006\u1011\u1000\u103a\u1019\u1015\u102d\u102f\u101e\u101b\u103d\u1031\u1037 \u1010\u1005\u103a\u101c\u1019\u103a\u1038\u101e\u103d\u102c\u1038 ANOVA \u101e\u100a\u103a \u1019\u100a\u102e\u1019\u103b\u103e\u101e\u1031\u102c\u1000\u103d\u1032\u101c\u103d\u1032\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a \u1001\u102d\u102f\u1004\u103a\u1001\u1036\u1037\u1019\u103e\u102f\u101b\u103e\u102d\u101e\u100a\u103a \u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u1011\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b \u1025\u1015\u1019\u102c\u104f \u1021\u1006\u1004\u1037\u103a 2 \u1010\u103d\u1004\u103a\u104a \u1021\u101e\u1031\u1038\u1004\u101a\u103a\u1006\u102f\u1036\u1038\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1019\u103e\u102c 0.819 \u1016\u103c\u1005\u103a\u1015\u103c\u102e\u1038 \u1021\u1000\u103c\u102e\u1038\u1006\u102f\u1036\u1038\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1019\u103e\u102c 2.46 \u1016\u103c\u1005\u103a\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1010\u103d\u1031\u1037\u101b\u103e\u102d\u101b\u1015\u102b\u101e\u100a\u103a\u104b \u1011\u102d\u102f\u1037\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u1021\u1000\u103c\u102e\u1038\u1006\u102f\u1036\u1038\u1014\u103e\u1004\u1037\u103a \u1021\u1004\u101a\u103a\u1006\u102f\u1036\u1038\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u104f \u1021\u1001\u103b\u102d\u102f\u1038\u101e\u100a\u103a 2.46 \/ 0.819 = <strong>3.003<\/strong> \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1024\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u101e\u100a\u103a 4 \u1011\u1000\u103a\u1014\u100a\u103a\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 one-way ANOVA \u1000\u102d\u102f \u101b\u102d\u102f\u1038\u101b\u103e\u1004\u103a\u1038\u1005\u103d\u102c\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. Kruskal-Wallis \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1015\u103c\u102f\u101c\u102f\u1015\u103a\u1015\u102b\u104b<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u1004\u101a\u103a\u1006\u102f\u1036\u1038\u1000\u103d\u1032\u101c\u103d\u1032\u1001\u103b\u1000\u103a\u1014\u103e\u1004\u1037\u103a \u1021\u1000\u103c\u102e\u1038\u1006\u102f\u1036\u1038\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u104f\u1021\u1001\u103b\u102d\u102f\u1038\u101e\u100a\u103a 4 \u1011\u1000\u103a\u1000\u103c\u102e\u1038\u1015\u102b\u1000\u104a \u104e\u1004\u103a\u1038\u1021\u1005\u102c\u1038 <a href=\"https:\/\/statorials.org\/my\/kruskal-wallis-\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\/\" target=\"_blank\" rel=\"noopener\">Kruskal-Wallis \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1000\u102d\u102f<\/a> \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1014\u103a \u101b\u103d\u1031\u1038\u1001\u103b\u101a\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b \u104e\u1004\u103a\u1038\u1000\u102d\u102f \u1010\u1005\u103a\u101c\u1019\u103a\u1038\u1019\u1031\u102c\u1004\u103a\u1038 ANOVA \u104f \u1005\u1036\u1019\u100a\u102e\u101e\u1031\u102c \u1010\u102d\u102f\u1004\u103a\u1038\u1010\u102c\u1019\u103e\u102f \u100a\u102e\u1019\u103b\u103e\u101e\u100a\u103a\u101f\u102f \u101a\u1030\u1006\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">R \u1010\u103d\u1004\u103a Kruskal-Wallis \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u104f \u1021\u1006\u1004\u1037\u103a\u1006\u1004\u1037\u103a \u1025\u1015\u1019\u102c\u1000\u102d\u102f <a href=\"https:\/\/statorials.org\" target=\"_blank\" rel=\"noopener\">\u1024\u1014\u1031\u101b\u102c\u1010\u103d\u1004\u103a<\/a> \u101b\u103e\u102c\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u1010\u1005\u103a\u101c\u1019\u103a\u1038\u101e\u103d\u102c\u1038 ANOVA \u1000\u102d\u102f \u101e\u102f\u1036\u1038\u101e\u1031\u102c \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1011\u102d\u102f\u1037\u1011\u1000\u103a\u1019\u1000\u101e\u1031\u102c \u101e\u102e\u1038\u1001\u103c\u102c\u1038\u1021\u102f\u1015\u103a\u1005\u102f\u1019\u103b\u102c\u1038\u104f \u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1019\u103b\u102c\u1038\u1000\u103c\u102c\u1038 \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u101e\u1031\u102c \u1001\u103c\u102c\u1038\u1014\u102c\u1038\u1019\u103e\u102f \u101b\u103e\u102d\u104a \u1019\u101b\u103e\u102d \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u103a\u104b \u1010\u1005\u103a\u101c\u1019\u103a\u1038\u101e\u103d\u102c\u1038 ANOVA \u104f \u101a\u1030\u1006\u1001\u103b\u1000\u103a \u1010\u1005\u103a\u1001\u102f\u101e\u100a\u103a \u1014\u1019\u1030\u1014\u102c\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1011\u102f\u1010\u103a\u101a\u1030\u101e\u100a\u1037\u103a \u101c\u1030\u1026\u1038\u101b\u1031\u104f \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1010\u1030\u100a\u102e\u101e\u100a\u103a\u101f\u102f \u1006\u102d\u102f\u101e\u100a\u103a\u104b \u104e\u1004\u103a\u1038\u1000\u102d\u102f\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u101b\u1014\u103a \u1021\u101e\u102f\u1036\u1038\u1021\u1019\u103b\u102c\u1038\u1006\u102f\u1036\u1038\u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1010\u1005\u103a\u1001\u102f\u1019\u103e\u102c \u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b \u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u1037\u103a \u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1006\u102d\u102f\u1004\u103a\u101b\u102c\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1016\u103c\u1005\u103a\u101e\u100a\u1037\u103a Brown-Forsythe test \u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1001\u103c\u1004\u103a\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b H 0 : \u101c\u1030\u1026\u1038\u101b\u1031\u1019\u103b\u102c\u1038\u1000\u103c\u102c\u1038 \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1010\u1014\u103a\u1038\u1010\u1030\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b H A : \u101c\u1030\u1026\u1038\u101b\u1031 \u1000\u103d\u102c\u101f\u1001\u103b\u1000\u103a\u1000 \u1019\u100a\u102e\u1019\u103b\u103e\u1015\u102b\u1018\u1030\u1038\u104b \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u104f p-\u1010\u1014\u103a\u1016\u102d\u102f\u1038 \u101e\u100a\u103a \u1021\u1001\u103b\u102d\u102f\u1037\u101e\u1031\u102c \u1021\u101b\u1031\u1038\u1015\u102b\u1019\u103e\u102f\u1021\u1006\u1004\u1037\u103a\u1021\u1031\u102c\u1000\u103a\u1010\u103d\u1004\u103a \u101b\u103e\u102d\u1015\u102b\u1000 (\u1025\u1015\u1019\u102c \u03b1 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>R \u101b\u103e\u102d Brown\u2013Forsythe \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f- \u1021\u1006\u1004\u1037\u103a\u1006\u1004\u1037\u103a \u1025\u1015\u1019\u102c- Statorials<\/title>\n<meta name=\"description\" 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