{"id":491,"date":"2023-07-29T17:42:56","date_gmt":"2023-07-29T17:42:56","guid":{"rendered":"https:\/\/statorials.org\/my\/one-way-anova-r\/"},"modified":"2023-07-29T17:42:56","modified_gmt":"2023-07-29T17:42:56","slug":"one-way-anova-r","status":"publish","type":"post","link":"https:\/\/statorials.org\/my\/one-way-anova-r\/","title":{"rendered":"R \u1010\u103d\u1004\u103a\u1010\u1005\u103a\u101c\u1019\u103a\u1038\u1019\u1031\u102c\u1004\u103a\u1038 anova \u1000\u102d\u102f\u1019\u100a\u103a\u1000\u1032\u1037\u101e\u102d\u102f\u1037\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1019\u100a\u103a\u1014\u100a\u103a\u1038\u104b"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><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\u1015\u102d\u102f\u101e\u1031\u102c \u101c\u103d\u1010\u103a\u101c\u1015\u103a\u101e\u1031\u102c \u1021\u102f\u1015\u103a\u1005\u102f\u1019\u103b\u102c\u1038\u1021\u1000\u103c\u102c\u1038 \u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1006\u102d\u102f\u1004\u103a\u101b\u102c \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u101e\u1031\u102c \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;\">\u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1010\u1005\u103a\u1001\u102f\u1015\u1031\u102b\u103a\u101b\u103e\u102d \u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a <em>\u1010\u1005\u103a\u1001\u102f\u104f<\/em> \u1021\u1000\u103b\u102d\u102f\u1038\u101e\u1000\u103a\u101b\u1031\u102c\u1000\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1015\u102d\u102f\u1004\u103a\u1038\u1001\u103c\u102c\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u1024\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1021\u1019\u103b\u102d\u102f\u1038\u1021\u1005\u102c\u1038\u1000\u102d\u102f <em>\u1010\u1005\u103a\u101c\u1019\u103a\u1038\u101e\u103d\u102c\u1038<\/em> ANOVA \u101f\u102f\u1001\u1031\u102b\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u1019\u103e\u1010\u103a\u1001\u103b\u1000\u103a<\/strong> &#8211; \u1021\u1000\u101a\u103a\u104d \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1010\u1005\u103a\u1001\u102f\u1015\u1031\u102b\u103a\u101b\u103e\u102d \u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1014\u103e\u1005\u103a\u1001\u102f\u104f \u1021\u1000\u103b\u102d\u102f\u1038\u101e\u1000\u103a\u101b\u1031\u102c\u1000\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1005\u102d\u1010\u103a\u101d\u1004\u103a\u1005\u102c\u1038\u1015\u102b\u1000\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a <a href=\"https:\/\/statorials.org\/my\/anova-ra-\u1014\u103e\u1005\u103a\u101c\u1019\u103a\u1038\/\" target=\"_blank\" rel=\"noopener\">\u1014\u103e\u1005\u103a\u101c\u1019\u103a\u1038\u101e\u103d\u102c\u1038 ANOVA \u1000\u102d\u102f<\/a> \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>\u1010\u1005\u103a\u101c\u1019\u103a\u1038\u1019\u1031\u102c\u1004\u103a\u1038 ANOVA \u1000\u102d\u102f R \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\u1014\u100a\u103a\u1038\u104b<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">\u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b \u1025\u1015\u1019\u102c\u101e\u100a\u103a R in one-way ANOVA \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 \u1016\u1031\u102c\u103a\u1015\u103c\u101e\u100a\u103a\u104b<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u1014\u1031\u102c\u1000\u103a\u1001\u1036<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u1019\u1010\u1030\u100a\u102e\u101e\u1031\u102c \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\u101e\u100a\u103a \u1000\u102d\u102f\u101a\u103a\u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a\u1000\u103b\u1001\u103c\u1004\u103a\u1038\u1021\u1015\u1031\u102b\u103a \u1019\u1010\u1030\u100a\u102e\u101e\u1031\u102c\u1021\u1000\u103b\u102d\u102f\u1038\u101e\u1000\u103a\u101b\u1031\u102c\u1000\u103a\u1019\u103e\u102f\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a\u101c\u102d\u102f\u101e\u100a\u103a\u1006\u102d\u102f\u1015\u102b\u1005\u102d\u102f\u1037\u104b \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101c\u1031\u1037\u101c\u102c\u1001\u1032\u1037\u101e\u1031\u102c \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103b\u1000\u103a\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u101e\u100a\u103a <em>\u101c\u1031\u1037\u1000\u103b\u1004\u1037\u103a\u1001\u1014\u103a\u1038\u1021\u1005\u102e\u1021\u1005\u1009\u103a<\/em> \u1016\u103c\u1005\u103a\u1015\u103c\u102e\u1038 <a href=\"https:\/\/statorials.org\/my\/\u1015\u103c\u1031\u102c\u1004\u103a\u1038\u101c\u1032\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c-\u101b\u103e\u1004\u103a\u1038\u101c\u1004\u103a\u1038\u1001\u103b\u1000\u103a-\u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038\/\" target=\"_blank\" rel=\"noopener\">\u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1015\u103c\u1031\u102c\u1004\u103a\u1038\u101c\u1032\u1019\u103e\u102f<\/a> \u1019\u103e\u102c <em>\u1000\u102d\u102f\u101a\u103a\u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a<\/em> \u1015\u1031\u102b\u1004\u103a\u1016\u103c\u1004\u1037\u103a \u1010\u102d\u102f\u1004\u103a\u1038\u1010\u102c\u1001\u103c\u1004\u103a\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a\u101e\u102f\u1036\u1038\u1001\u102f\u1019\u103e \u1011\u103d\u1000\u103a\u1015\u1031\u102b\u103a\u101c\u102c\u101e\u1031\u102c \u1000\u102d\u102f\u101a\u103a\u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a\u1000\u103b\u1001\u103c\u1004\u103a\u1038\u1000\u103c\u102c\u1038\u1010\u103d\u1004\u103a \u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1021\u101b \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u101e\u1031\u102c \u1001\u103c\u102c\u1038\u1014\u102c\u1038\u1001\u103b\u1000\u103a\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a \u1010\u1005\u103a\u101c\u1019\u103a\u1038\u101e\u103d\u102c\u1038 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;\">\u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a A\u104a \u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a B \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a C \u1000\u102d\u102f \u1010\u1005\u103a\u101c\u1000\u103c\u102c \u101c\u102d\u102f\u1000\u103a\u1014\u102c\u101b\u1014\u103a \u101c\u1030 30 \u1000\u102d\u102f \u1000\u103b\u1015\u1014\u103a\u1038\u101e\u1010\u103a\u1019\u103e\u1010\u103a\u1011\u102c\u1038\u101e\u1031\u102c \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1010\u1005\u103a\u1001\u102f\u1010\u103d\u1004\u103a \u1015\u102b\u101d\u1004\u103a\u101b\u1014\u103a \u101c\u1030 90 \u1000\u102d\u102f \u1005\u102f\u1006\u1031\u102c\u1004\u103a\u1038\u1011\u102c\u1038\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\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\u1014\u103e\u1004\u1037\u103a\u1021\u1010\u1030 \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1019\u100a\u1037\u103a \u1012\u1031\u1010\u102c\u1018\u1031\u102c\u1004\u103a\u1000\u102d\u102f \u1016\u1014\u103a\u1010\u102e\u1038\u101e\u100a\u103a-<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#make this example reproducible\n<span style=\"color: #000000;\">set.seed(0)\n<\/span>\n#create data frame\n<span style=\"color: #000000;\">data &lt;- data.frame(program = rep(c(\"A\", \"B\", \"C\"), each = 30),\n                   weight_loss = c(runif(30, 0, 3),\n                                   runif(30, 0, 5),\n                                   runif(30, 1, 7)))<\/span>\n\n#view first six rows of data frame\n<span style=\"color: #000000;\">head(data)\n<\/span>\n<span style=\"color: #000000;\"># 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<\/span>\n<\/span><\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u1012\u1031\u1010\u102c\u1018\u1031\u102c\u1004\u103a\u104f \u1015\u1011\u1019\u1000\u1031\u102c\u103a\u101c\u1036\u1010\u103d\u1004\u103a \u1010\u1005\u103a\u101c\u1000\u103c\u102c\u1015\u102b\u101d\u1004\u103a\u1001\u1032\u1037\u101e\u100a\u1037\u103a \u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a\u1000\u102d\u102f \u1015\u103c\u101e\u1015\u103c\u102e\u1038 \u1012\u102f\u1010\u102d\u101a\u1000\u1031\u102c\u103a\u101c\u1036\u1010\u103d\u1004\u103a \u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a\u104f\u1021\u1006\u102f\u1036\u1038\u1010\u103d\u1004\u103a \u1000\u103c\u102f\u1036\u1010\u103d\u1031\u1037\u1001\u1032\u1037\u101b\u101e\u1030\u104f \u1005\u102f\u1005\u102f\u1015\u1031\u102b\u1004\u103a\u1038\u1000\u102d\u102f\u101a\u103a\u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a\u1000\u102d\u102f \u1015\u1031\u102b\u1004\u103a\u1016\u103c\u1004\u1037\u103a\u1010\u102d\u102f\u1004\u103a\u1038\u1010\u102c\u1000\u102c \u1015\u103c\u101e\u101e\u100a\u103a\u104b<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u1021\u1001\u103b\u1000\u103a\u1021\u101c\u1000\u103a\u1000\u102d\u102f \u1005\u1030\u1038\u1005\u1019\u103a\u1038\u1015\u102b\u104b<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u1010\u1005\u103a\u101c\u1019\u103a\u1038\u101e\u103d\u102c\u1038 ANOVA \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1000\u102d\u102f\u1015\u1004\u103a \u1021\u1036\u1000\u102d\u102f\u1000\u103a\u1019\u1016\u103c\u1005\u103a\u1019\u102e\u104a <strong>dplyr<\/strong> \u1015\u1000\u103a\u1000\u1031\u1037\u1002\u103b\u103a\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d \u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a\u101e\u102f\u1036\u1038\u1001\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 \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1014\u103e\u1004\u1037\u103a \u1005\u1036\u101e\u103d\u1031\u1016\u100a\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u101b\u103e\u102c\u1016\u103d\u1031\u1001\u103c\u1004\u103a\u1038\u1016\u103c\u1004\u1037\u103a \u1012\u1031\u1010\u102c\u1000\u102d\u102f \u1015\u102d\u102f\u1019\u102d\u102f\u1000\u1031\u102c\u1004\u103a\u1038\u1019\u103d\u1014\u103a\u1005\u103d\u102c \u1014\u102c\u1038\u101c\u100a\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a-<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#load <em>dplyr<\/em> package<\/span>\n<span style=\"color: #008000;\">library<\/span> (dplyr)\n\n<span style=\"color: #008080;\">#find mean and standard deviation of weight loss for each treatment group<\/span>\ndata %&gt;%\n  <span style=\"color: #800080;\">group_by<\/span> (program) %&gt;%\n  <span style=\"color: #800080;\">summarize<\/span> (mean = mean(weight_loss),\n            sd = sd(weight_loss))\n\n# A tibble: 3 x 3\n# program mean sd\n#      \n#1 A 1.58 0.905\n#2 B 2.56 1.24 \n#3 C 4.13 1.57  \n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a\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\u101c\u103b\u103e\u1031\u102c\u1037\u1001\u103b\u1001\u103c\u1004\u103a\u1038\u1000\u102d\u102f \u1019\u103c\u1004\u103a\u101e\u102c\u1005\u1031\u101b\u1014\u103a \u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a\u101e\u102f\u1036\u1038\u1001\u102f\u1005\u102e\u1021\u1010\u103d\u1000\u103a <a href=\"https:\/\/statorials.org\" target=\"_blank\" rel=\"noopener\">boxplot<\/a> \u1010\u1005\u103a\u1001\u102f\u1000\u102d\u102f\u101c\u100a\u103a\u1038 \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><span style=\"color: #008080;\">#create boxplots\n<\/span>boxplot(weight_loss ~ program,\ndata = data,\nmain = \"Weight Loss Distribution by Program\",\nxlab = \"Program\",\nylab = \"Weight Loss\",\ncol = \"steelblue\",\nborder = \"black\")<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u1024\u1015\u102f\u1036\u1038\u1000\u103d\u1000\u103a\u1019\u103b\u102c\u1038\u1019\u103e\u104a Program C \u1010\u103d\u1004\u103a\u1015\u102b\u101d\u1004\u103a\u101e\u1030\u1019\u103b\u102c\u1038\u1021\u1010\u103d\u1000\u103a \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1000\u102d\u102f\u101a\u103a\u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a\u101e\u100a\u103a \u1021\u1019\u103c\u1004\u1037\u103a\u1006\u102f\u1036\u1038\u1016\u103c\u1005\u103a\u1015\u103c\u102e\u1038 Program A \u1010\u103d\u1004\u103a\u1015\u102b\u101d\u1004\u103a\u101e\u1030\u1019\u103b\u102c\u1038\u1021\u1010\u103d\u1000\u103a \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1000\u102d\u102f\u101a\u103a\u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a\u101e\u100a\u103a \u1021\u1014\u102d\u1019\u1037\u103a\u1006\u102f\u1036\u1038\u1016\u103c\u1005\u103a\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1010\u103d\u1031\u1037\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <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 \u1005\u1036\u101e\u103d\u1031\u1016\u100a\u103a\u1019\u103e\u102f (&#8220; \u1021\u101b\u103e\u100a\u103a&#8221; ) \u101e\u100a\u103a \u1021\u1001\u103c\u102c\u1038\u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a\u1014\u103e\u1005\u103a\u1001\u102f\u1014\u103e\u1004\u1037\u103a \u1014\u103e\u102d\u102f\u1004\u103a\u1038\u101a\u103e\u1009\u103a\u1015\u102b\u1000 \u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a C \u1010\u103d\u1004\u103a \u1021\u1014\u100a\u103a\u1038\u1004\u101a\u103a\u1015\u102d\u102f\u1019\u103c\u1004\u1037\u103a\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\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1011\u102d\u102f\u1037\u1014\u1031\u102c\u1000\u103a\u104a \u1024\u101b\u102f\u1015\u103a\u1015\u102f\u1036\u1006\u102d\u102f\u1004\u103a\u101b\u102c \u1000\u103d\u102c\u1001\u103c\u102c\u1038\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1021\u1019\u103e\u1014\u103a\u1010\u1000\u101a\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\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u1000\u103c\u100a\u1037\u103a\u101b\u103e\u102f\u101b\u1014\u103a \u1010\u1005\u103a\u101c\u1019\u103a\u1038\u101e\u103d\u102c\u1038 ANOVA \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f\u1012\u1031\u1010\u102c\u1014\u103e\u1004\u1037\u103a \u1021\u1036\u101d\u1004\u103a\u1001\u103d\u1004\u103a\u1000\u103b\u1016\u103c\u1005\u103a\u1005\u1031\u1015\u102b\u1019\u100a\u103a\u104b<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u1010\u1005\u103a\u101c\u1019\u103a\u1038\u1019\u1031\u102c\u1004\u103a\u1038 ANOVA \u1019\u1031\u102c\u103a\u1012\u101a\u103a \u101c\u103b\u1031\u102c\u1000\u103a\u1015\u1010\u103a\u101e\u100a\u103a\u104b<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">R \u1010\u103d\u1004\u103a \u1010\u1005\u103a\u101c\u1019\u103a\u1038\u101e\u103d\u102c\u1038 ANOVA \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1014\u103e\u1004\u1037\u103a \u1021\u1036\u101d\u1004\u103a\u1001\u103d\u1004\u103a\u1000\u103b\u1021\u1010\u103d\u1000\u103a \u101a\u1031\u1018\u1030\u101a\u103b syntax \u101e\u100a\u103a-<\/span><\/p>\n<p style=\"text-align: left;\"> <strong><span style=\"color: #000000;\">aov(\u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a ~ \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u101e\u1030_\u1015\u103c\u1031\u102c\u1004\u103a\u1038\u101c\u1032\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c\u104a \u1012\u1031\u1010\u102c = \u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032)<\/span><\/strong><\/p>\n<p> <span style=\"color: #000000;\">\u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f\u1025\u1015\u1019\u102c\u1010\u103d\u1004\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1021\u1016\u103c\u1005\u103a <em>weight_loss<\/em> \u1014\u103e\u1004\u1037\u103a \u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1021\u1016\u103c\u1005\u103a <em>\u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a\u1000\u102d\u102f<\/em> \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d \u1010\u1005\u103a\u101c\u1019\u103a\u1038\u101e\u103d\u102c\u1038 ANOVA \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1014\u103e\u1004\u1037\u103a\u1000\u102d\u102f\u1000\u103a\u100a\u102e\u101b\u1014\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1000\u102f\u1012\u103a\u1000\u102d\u102f\u101e\u102f\u1036\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b \u1011\u102d\u102f\u1037\u1014\u1031\u102c\u1000\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f\u1019\u1031\u102c\u103a\u1012\u101a\u103a\u101b\u101c\u1012\u103a\u1000\u102d\u102f\u1015\u103c\u101e\u101b\u1014\u103a <strong>summary()<\/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;\">#fit the one-way ANOVA model<\/span>\nmodel &lt;- aov(weight_loss ~ program, data = data)\n\n<span style=\"color: #008080;\">#view the model output<\/span>\nsummary(model)\n\n# Df Sum Sq Mean Sq F value Pr(&gt;F)    \n#program 2 98.93 49.46 30.83 7.55e-11 ***\n#Residuals 87 139.57 1.60                     \n#---\n#Significant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u1019\u1031\u102c\u103a\u1012\u101a\u103a\u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u1019\u103e\u104a \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u101e\u1030\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\u104f <em>\u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a<\/em> \u101e\u100a\u103a 0.05 \u1021\u101b\u1031\u1038\u1015\u102b\u1019\u103e\u102f\u1021\u1006\u1004\u1037\u103a\u1010\u103d\u1004\u103a \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1021\u101b \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1010\u103d\u1031\u1037\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1010\u1005\u103a\u1014\u100a\u103a\u1038\u1006\u102d\u102f\u101b\u101e\u1031\u102c\u103a\u104a \u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a\u101e\u102f\u1036\u1038\u1001\u102f\u1019\u103e \u1011\u103d\u1000\u103a\u1015\u1031\u102b\u103a\u101c\u102c\u101e\u1031\u102c \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1000\u102d\u102f\u101a\u103a\u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a \u101c\u103b\u1031\u102c\u1037\u1000\u103b\u1019\u103e\u102f\u1000\u103c\u102c\u1038\u1010\u103d\u1004\u103a \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1021\u101b \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u101e\u1031\u102c \u1000\u103d\u102c\u1001\u103c\u102c\u1038\u1001\u103b\u1000\u103a \u101b\u103e\u102d\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u1019\u1031\u102c\u103a\u1012\u101a\u103a\u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1005\u1005\u103a\u1006\u1031\u1038\u1001\u103c\u1004\u103a\u1038\u104b<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u101b\u103e\u1031\u1037\u1006\u1000\u103a\u1019\u101e\u103d\u102c\u1038\u1019\u102e\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u101a\u102f\u1036\u1000\u103c\u100a\u103a\u1005\u102d\u1010\u103a\u1001\u103b\u1014\u102d\u102f\u1004\u103a\u1005\u1031\u101b\u1014\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f \u1019\u1031\u102c\u103a\u1012\u101a\u103a\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\u1019\u103b\u102c\u1038<\/a> \u1014\u103e\u1004\u1037\u103a \u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1021\u1010\u100a\u103a\u1015\u103c\u102f\u101b\u1014\u103a \u101c\u102d\u102f\u1021\u1015\u103a\u1015\u102b\u101e\u100a\u103a\u104b \u1021\u1011\u1030\u1038\u101e\u1016\u103c\u1004\u1037\u103a\u104a \u1010\u1005\u103a\u101c\u1019\u103a\u1038\u101e\u103d\u102c\u1038 ANOVA \u1000 \u101a\u1030\u1006\u101e\u100a\u103a-<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. \u101c\u103d\u1010\u103a\u101c\u1015\u103a\u101b\u1031\u1038<\/strong> \u2013 \u1021\u1016\u103d\u1032\u1037\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u104f \u101b\u103e\u102f\u1019\u103c\u1004\u103a\u101e\u102f\u1036\u1038\u101e\u1015\u103a\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1010\u1005\u103a\u1001\u102f\u1014\u103e\u1004\u1037\u103a\u1010\u1005\u103a\u1001\u102f \u1021\u1019\u103e\u102e\u1021\u1001\u102d\u102f\u1000\u1004\u103a\u1038\u101b\u1019\u100a\u103a\u104b \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a<\/span> <span style=\"color: #000000;\">\u1000\u103b\u1015\u1014\u103a\u1038\u1015\u102f\u1036\u1005\u1036\u1012\u102e\u1007\u102d\u102f\u1004\u103a\u1038\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1001\u1032\u1037\u101e\u100a\u103a (\u1006\u102d\u102f\u101c\u102d\u102f\u101e\u100a\u103a\u1019\u103e\u102c\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u101c\u1031\u1037\u1000\u103b\u1004\u1037\u103a\u1001\u1014\u103a\u1038\u1021\u1005\u102e\u1021\u1005\u1009\u103a\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a \u1015\u102b\u101d\u1004\u103a\u101e\u1030\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1000\u103b\u1015\u1014\u103a\u1038\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1015\u1031\u1038\u101e\u100a\u103a) \u1016\u103c\u1005\u103a\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u1024\u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u1021\u101c\u103d\u1014\u103a\u1021\u1000\u103b\u103d\u1036\u1005\u102d\u102f\u1038\u101b\u102d\u1019\u103a\u1005\u101b\u102c\u1019\u101c\u102d\u102f\u1005\u1031\u101b\u1014\u103a\u1021\u1010\u103d\u1000\u103a \u1024\u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1000\u102d\u102f \u1016\u103c\u100a\u1037\u103a\u1006\u100a\u103a\u1038\u1015\u1031\u1038\u101e\u1004\u1037\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. Normality<\/strong> \u2013 \u1019\u103e\u102e\u1001\u102d\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u101e\u100a\u103a \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1010\u103d\u1000\u103a\u1001\u103b\u1000\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1021\u1006\u1004\u1037\u103a\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1021\u1010\u103d\u1000\u103a \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103c\u1031\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a \u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1019\u103e\u102f \u101b\u103e\u102d\u101e\u1004\u1037\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>3. \u1010\u1030\u100a\u102e\u101e\u1031\u102c\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f<\/strong> \u2013 \u1021\u102f\u1015\u103a\u1005\u102f\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1021\u1010\u103d\u1000\u103a \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1010\u1030\u100a\u102e\u101e\u100a\u103a \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\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><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1021\u1001\u103c\u1031\u1021\u1014\u1031<\/strong> \u1014\u103e\u1004\u1037\u103a <strong>\u1010\u1030\u100a\u102e\u101e\u1031\u102c\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f<\/strong> \u104f \u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1005\u1005\u103a\u1006\u1031\u1038\u101b\u1014\u103a \u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1010\u1005\u103a\u1001\u102f\u1019\u103e\u102c \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1005\u1005\u103a\u1006\u1031\u1038\u1001\u103c\u1004\u103a\u1038\u1000\u103d\u1000\u103a \u101c\u1031\u1038\u1001\u102f\u1000\u102d\u102f \u1011\u102f\u1010\u103a\u101c\u102f\u1015\u103a\u1015\u1031\u1038\u101e\u100a\u1037\u103a <strong>plot()<\/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\u1001\u103c\u1004\u103a\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b \u1021\u1011\u1030\u1038\u101e\u1016\u103c\u1004\u1037\u103a\u104a \u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b \u1019\u103c\u1031\u1000\u103d\u1000\u103a\u1014\u103e\u1005\u103a\u1001\u102f\u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u1021\u1011\u1030\u1038\u1005\u102d\u1010\u103a\u101d\u1004\u103a\u1005\u102c\u1038\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a \u1010\u1015\u103a\u1006\u1004\u103a\u1011\u102c\u1038\u101e\u100a\u103a<\/strong> &#8211; \u1024\u1002\u101b\u1015\u103a\u101e\u100a\u103a \u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a \u1010\u1015\u103a\u1006\u1004\u103a\u1011\u102c\u1038\u101e\u1031\u102c \u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103b\u102c\u1038\u1000\u103c\u102c\u1038 \u1006\u1000\u103a\u1014\u103d\u101a\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1015\u103c\u101e\u101e\u100a\u103a\u104b \u1021\u1016\u103d\u1032\u1037\u1019\u103b\u102c\u1038\u1000\u103c\u102c\u1038 \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1019\u103e\u102c \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103c\u1031\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a \u100a\u102e\u1019\u103b\u103e\u1001\u103c\u1004\u103a\u1038 \u101b\u103e\u102d\u104a \u1019\u101b\u103e\u102d \u1021\u1000\u103c\u1019\u103a\u1038\u1016\u103b\u1004\u103a\u1038 \u1021\u1000\u1032\u1016\u103c\u1010\u103a\u101b\u1014\u103a \u1024\u1002\u101b\u1015\u103a\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>QQ \u1000\u103c\u1036\u1005\u100a\u103a\u1019\u103e\u102f<\/strong> &#8211; \u1024\u1000\u103d\u1000\u103a\u1000\u103d\u1000\u103a\u101e\u100a\u103a \u101e\u102e\u1021\u102d\u102f\u101b\u102e\u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a \u1006\u1014\u1037\u103a\u1000\u103b\u1004\u103a\u1018\u1000\u103a\u1005\u1036\u1015\u103c\u102f\u1000\u103b\u1014\u103a\u1014\u1031\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1015\u103c\u101e\u101e\u100a\u103a\u104b \u101e\u102c\u1019\u102c\u1014\u103a\u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1014\u103e\u1004\u1037\u103a\u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1019\u103e\u102f\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u1021\u1000\u103c\u1019\u103a\u1038\u1016\u103b\u1004\u103a\u1038\u1021\u1000\u1032\u1016\u103c\u1010\u103a\u101b\u1014\u103a \u1024\u1002\u101b\u1015\u103a\u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u1024\u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1005\u1005\u103a\u1006\u1031\u1038\u1001\u103c\u1004\u103a\u1038\u1000\u103d\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1011\u102f\u1010\u103a\u101c\u102f\u1015\u103a\u101b\u1014\u103a\u1021\u1010\u103d\u1000\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1000\u102f\u1012\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;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #000000;\">plot(model)<\/span><\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\">\u1021\u1011\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b <em>QQ \u1002\u101b\u1015\u103a\u101e\u100a\u103a<\/em> \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1021\u102c\u1038 \u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1021\u1016\u103c\u1005\u103a\u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1000\u102d\u102f \u1021\u1010\u100a\u103a\u1015\u103c\u102f\u1014\u102d\u102f\u1004\u103a\u1005\u1031\u1015\u102b\u101e\u100a\u103a\u104b \u1021\u1000\u1031\u102c\u1004\u103a\u1038\u1006\u102f\u1036\u1038\u1019\u103e\u102c\u104a \u1005\u1036\u101e\u1010\u103a\u1019\u103e\u1010\u103a\u1011\u102c\u1038\u101e\u1031\u102c \u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1000\u103d\u1000\u103a\u101c\u1015\u103a\u104f \u1016\u103c\u1031\u102c\u1004\u1037\u103a\u1011\u1031\u102c\u1004\u1037\u103a\u1016\u103c\u1010\u103a\u1019\u103b\u1009\u103a\u1038\u1010\u1005\u103a\u101c\u103b\u103e\u1031\u102c\u1000\u103a\u1010\u103d\u1004\u103a \u101b\u103e\u102d\u1014\u1031\u1019\u100a\u103a\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b \u101e\u102d\u102f\u1037\u101b\u102c\u1010\u103d\u1004\u103a\u104a \u1021\u1011\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b\u1002\u101b\u1015\u103a\u1010\u103d\u1004\u103a \u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1019\u103b\u1009\u103a\u1038\u1019\u103e\u1021\u1005\u1014\u103e\u1004\u1037\u103a\u1021\u1006\u102f\u1036\u1038\u101e\u102d\u102f\u1037 \u1021\u1014\u100a\u103a\u1038\u1004\u101a\u103a\u101c\u103d\u1032\u101e\u103d\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\u1015\u102b\u101e\u100a\u103a\u104b \u101a\u1004\u103a\u1038\u1000 \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f \u1015\u102f\u1036\u1019\u103e\u1014\u103a\u1016\u103c\u1005\u103a\u1010\u100a\u103a\u1019\u103e\u102f \u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1000\u102d\u102f \u1001\u103b\u102d\u102f\u1038\u1016\u1031\u102c\u1000\u103a\u1014\u102d\u102f\u1004\u103a\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u100a\u103d\u103e\u1014\u103a\u1015\u103c\u1014\u1031\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><em>\u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a<\/em> \u1021\u1011\u1000\u103a\u1010\u103d\u1004\u103a <em>\u1001\u103b\u102d\u1014\u103a\u100a\u103e\u102d\u1011\u102c\u1038\u101e\u1031\u102c \u1002\u101b\u1015\u103a\u101e\u100a\u103a<\/em> \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f \u1010\u1030\u100a\u102e\u101e\u1031\u102c\u1000\u103d\u1032\u1015\u103c\u102c\u1038\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u104f \u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1000\u102d\u102f \u1021\u1010\u100a\u103a\u1015\u103c\u102f\u1014\u102d\u102f\u1004\u103a\u1005\u1031\u1015\u102b\u101e\u100a\u103a\u104b \u1021\u1000\u1031\u102c\u1004\u103a\u1038\u1006\u102f\u1036\u1038\u1000\u1010\u1031\u102c\u1037\u104a \u1010\u1015\u103a\u1006\u1004\u103a\u1011\u102c\u1038\u101e\u1031\u102c \u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1021\u1006\u1004\u1037\u103a\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1021\u1010\u103d\u1000\u103a \u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1021\u100a\u102e\u1021\u1019\u103b\u103e \u1001\u103d\u1032\u101d\u1031\u1015\u1031\u1038\u1005\u1031\u101c\u102d\u102f\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u1000\u103c\u103d\u1004\u103a\u1038\u1021\u1000\u103b\u1014\u103a\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1015\u102d\u102f\u1019\u102d\u102f\u1019\u103c\u1004\u1037\u103a\u1019\u102c\u1038\u101e\u1031\u102c \u1010\u1015\u103a\u1006\u1004\u103a\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103b\u102c\u1038\u1021\u1010\u103d\u1000\u103a \u1015\u102d\u102f\u1019\u102d\u102f\u1015\u103c\u1014\u1037\u103a\u1014\u103e\u1036\u1037\u101e\u103d\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\u1015\u103c\u102e\u1038\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f <a href=\"https:\/\/statorials.org\/my\/\u1010\u1030\u100a\u102e\u101e\u1031\u102c\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u101a\u1030\u1006\u1001\u103b\u1000\u103a\/\" target=\"_blank\" rel=\"noopener\">\u1010\u1014\u103a\u1038\u1010\u1030\u100a\u102e\u1019\u103b\u103e\u1019\u103e\u102f \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u104f \u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1000\u102d\u102f<\/a> \u1001\u103b\u102d\u102f\u1038\u1016\u1031\u102c\u1000\u103a\u1001\u1036\u101b\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u1000\u102d\u102f \u100a\u103d\u103e\u1014\u103a\u1015\u103c\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1010\u1030\u100a\u102e\u101e\u1031\u102c\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1010\u101b\u102c\u1038\u101d\u1004\u103a\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u101b\u1014\u103a\u104a <strong>\u1000\u102c\u1038<\/strong> \u1015\u1000\u103a\u1000\u1031\u1037\u1001\u103a\u103b\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d Levene \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\u101e\u100a\u103a-<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#load car package\n<\/span><span style=\"color: #008000;\">library<\/span> (car)\n\n<span style=\"color: #008080;\">#conduct Levene's Test for equality of variances\n<\/span>leveneTest(weight_loss ~ program, data = data)\n\n#Levene's Test for Homogeneity of Variance (center = median)\n# Df F value Pr(&gt;F)  \n#group 2 4.1716 0.01862 *\n#87                  \n#---\n#Significant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u104f p-\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u101e\u100a\u103a <strong>0.01862<\/strong> \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b \u1021\u1000\u101a\u103a\u104d \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\u1015\u102b\u1000\u104a \u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a\u101e\u102f\u1036\u1038\u1001\u102f\u1010\u103d\u1004\u103a \u1019\u1010\u1030\u100a\u102e\u101e\u1031\u102c\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\u101f\u1030\u101e\u1031\u102c null hypothesis \u1000\u102d\u102f \u1004\u103c\u1004\u103a\u1038\u1015\u101a\u103a\u1015\u102b\u1019\u100a\u103a\u104b \u101e\u102d\u102f\u1037\u101e\u1031\u102c\u103a\u104a \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\u1015\u102b\u1000\u104a null hypothesis \u1000\u102d\u102f \u1004\u103c\u1004\u103a\u1038\u1015\u101a\u103a\u1019\u100a\u103a\u1019\u101f\u102f\u1010\u103a\u1015\u102b\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f \u101e\u102c\u1010\u1030\u100a\u102e\u1019\u103b\u103e\u1019\u103e\u102f\u1014\u103e\u1004\u1037\u103a \u1000\u103d\u1032\u1015\u103c\u102c\u1038\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u104f \u101e\u102c\u1010\u1030\u100a\u102e\u1019\u103b\u103e\u1019\u103e\u102f\u1006\u102d\u102f\u1004\u103a\u101b\u102c \u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1016\u103c\u100a\u1037\u103a\u1006\u100a\u103a\u1038\u1015\u1031\u1038\u1014\u102d\u102f\u1004\u103a\u101b\u1014\u103a \u1012\u1031\u1010\u102c\u1000\u102d\u102f \u1021\u101e\u103d\u1004\u103a\u1015\u103c\u1031\u102c\u1004\u103a\u1038\u101b\u1014\u103a \u1000\u103c\u102d\u102f\u1038\u1015\u1019\u103a\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c\u103a\u101c\u100a\u103a\u1038\u104a \u101a\u1001\u102f\u1021\u1001\u103b\u102d\u1014\u103a\u1010\u103d\u1004\u103a \u104e\u1004\u103a\u1038\u1014\u103e\u1004\u1037\u103a\u1015\u1010\u103a\u101e\u1000\u103a\u104d \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u1021\u101c\u103d\u1014\u103a\u1005\u102d\u102f\u1038\u101b\u102d\u1019\u103a\u1014\u1031\u1019\u100a\u103a\u1019\u101f\u102f\u1010\u103a\u1015\u102b\u104b<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u1000\u102f\u101e\u1019\u103e\u102f\u1000\u103d\u102c\u1001\u103c\u102c\u1038\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u1015\u102b\u104b<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u1005\u1036\u1015\u103c\u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a \u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1005\u1005\u103a\u1006\u1031\u1038\u1021\u1010\u100a\u103a\u1015\u103c\u102f\u1015\u103c\u102e\u1038\u101e\u100a\u103a\u1014\u103e\u1004\u1037\u103a (\u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1000\u103b\u102d\u102f\u1038\u1000\u103c\u1031\u102c\u1004\u103a\u1038\u1006\u102e\u101c\u103b\u1031\u102c\u103a\u1005\u103d\u102c \u1000\u102d\u102f\u1000\u103a\u100a\u102e\u101e\u100a\u103a)\u104a \u1011\u102d\u102f\u1037\u1014\u1031\u102c\u1000\u103a \u1019\u100a\u103a\u101e\u100a\u1037\u103a\u1000\u102f\u101e\u1019\u103e\u102f\u1021\u102f\u1015\u103a\u1005\u102f\u1019\u103b\u102c\u1038 \u1010\u1005\u103a\u1001\u102f\u1014\u103e\u1004\u1037\u103a\u1010\u1005\u103a\u1001\u102f \u1000\u103d\u1032\u1015\u103c\u102c\u1038\u101e\u100a\u103a\u1000\u102d\u102f \u1010\u102d\u1010\u102d\u1000\u103b\u1000\u103b \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a <a href=\"https:\/\/statorials.org\" target=\"_blank\" rel=\"noopener\">post hoc test<\/a> \u1015\u103c\u102f\u101c\u102f\u1015\u103a\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f post hoc \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u1021\u1010\u103d\u1000\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1014\u103e\u102d\u102f\u1004\u103a\u1038\u101a\u103e\u1009\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u1005\u103d\u102c\u1021\u1010\u103d\u1000\u103a Tukey \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 <strong>TukeyHSD()<\/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\u1015\u102b\u1019\u100a\u103a\u104b<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#perform Tukey's Test for multiple comparisons\n<\/span>TukeyHSD(model, conf.level=.95) \n\n#Tukey multiple comparisons of means\n# 95% family-wise confidence level\n#\n#Fit: aov(formula = weight_loss ~ program, data = data)\n#\n#$program\n# diff lwr upr p adj\n#BA 0.9777414 0.1979466 1.757536 0.0100545\n#CA 2.5454024 1.7656076 3.325197 0.0000000\n#CB 1.5676610 0.7878662 2.347456 0.0000199\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">p-value \u101e\u100a\u103a \u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1000\u103c\u102c\u1038\u1010\u103d\u1004\u103a \u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1006\u102d\u102f\u1004\u103a\u101b\u102c \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u101e\u1031\u102c \u1001\u103c\u102c\u1038\u1014\u102c\u1038\u1001\u103b\u1000\u103a\u101b\u103e\u102d\u1019\u101b\u103e\u102d\u1000\u102d\u102f \u1016\u1031\u102c\u103a\u1015\u103c\u101e\u100a\u103a\u104b \u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u1000 0.05 \u1021\u101b\u1031\u1038\u1015\u102b\u1019\u103e\u102f\u1021\u1006\u1004\u1037\u103a\u1010\u103d\u1004\u103a \u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u104f \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1000\u102d\u102f\u101a\u103a\u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a \u101c\u103b\u1031\u102c\u1037\u1000\u103b\u1019\u103e\u102f\u1000\u103c\u102c\u1038\u1010\u103d\u1004\u103a \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u101e\u102d\u101e\u102d\u101e\u102c\u101e\u102c \u1000\u103d\u102c\u1001\u103c\u102c\u1038\u1019\u103e\u102f\u101b\u103e\u102d\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1015\u103c\u101e\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">R \u1010\u103d\u1004\u103a <strong>plot(TukeyHSD())<\/strong> \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u103b\u1000\u103a\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d Tukey \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1019\u103e \u1011\u103d\u1000\u103a\u1015\u1031\u102b\u103a\u101c\u102c\u101e\u1031\u102c \u101a\u102f\u1036\u1000\u103c\u100a\u103a\u1019\u103e\u102f 95% \u1000\u103c\u102c\u1038\u1000\u102c\u101c\u1000\u102d\u102f\u101c\u100a\u103a\u1038 \u1019\u103c\u1004\u103a\u101a\u1031\u102c\u1004\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a \u104b<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create confidence interval for each comparison\n<\/span>plot(TukeyHSD(model, conf.level=.95), las = 2)\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u101a\u102f\u1036\u1000\u103c\u100a\u103a\u1019\u103e\u102f\u1000\u103c\u102c\u1038\u1000\u102c\u101c\u104f\u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u101e\u102e\u1021\u102d\u102f\u101b\u102e\u1005\u1005\u103a\u1006\u1031\u1038\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u104f\u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a \u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u1011\u1030\u1038\u101e\u1016\u103c\u1004\u1037\u103a\u104a \u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a\u101e\u102f\u1036\u1038\u1001\u102f\u1000\u103c\u102c\u1038\u101b\u103e\u102d \u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a\u1019\u103b\u102c\u1038\u1000\u103c\u102c\u1038\u101b\u103e\u102d \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1000\u102d\u102f\u101a\u103a\u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a\u1021\u1010\u103d\u1000\u103a \u101a\u102f\u1036\u1000\u103c\u100a\u103a\u1019\u103e\u102f\u1000\u103c\u102c\u1038\u1000\u102c\u101c\u1010\u1005\u103a\u1001\u102f\u1019\u103e <em>\u101e\u102f\u100a<\/em> \u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u1015\u102b\u101d\u1004\u103a\u1000\u103c\u1031\u102c\u1004\u103a\u1038\u104a \u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a\u101e\u102f\u1036\u1038\u1001\u102f\u1000\u103c\u102c\u1038 \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1006\u102f\u1036\u1038\u101b\u103e\u102f\u1036\u1038\u1019\u103e\u102f\u1010\u103d\u1004\u103a \u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1021\u101b \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u101e\u1031\u102c \u1000\u103d\u102c\u1001\u103c\u102c\u1038\u1001\u103b\u1000\u103a\u101b\u103e\u102d\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1010\u103d\u1031\u1037\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u104e\u1004\u103a\u1038\u101e\u100a\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u104f <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\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f<\/a> \u1019\u103b\u102c\u1038\u1021\u1010\u103d\u1000\u103a 0.05 \u1011\u1000\u103a\u1014\u100a\u103a\u1038\u101e\u1031\u102c <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\u1019\u103b\u102c\u1038<\/a> \u1021\u102c\u1038\u101c\u102f\u1036\u1038\u1014\u103e\u1004\u1037\u103a \u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<h3> <strong><span style=\"color: #000000;\">\u1010\u1005\u103a\u101c\u1019\u103a\u1038\u1019\u1031\u102c\u1004\u103a\u1038 ANOVA \u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1021\u1005\u102e\u101b\u1004\u103a\u1001\u1036\u1001\u103c\u1004\u103a\u1038\u104b<\/span><\/strong><\/h3>\n<p> <span style=\"color: #000000;\">\u1014\u1031\u102c\u1000\u103a\u1006\u102f\u1036\u1038\u1021\u1014\u1031\u1014\u1032\u1037\u104a \u1010\u1005\u103a\u101c\u1019\u103a\u1038\u101e\u103d\u102c\u1038 ANOVA \u101b\u1032\u1037 \u101b\u101c\u1012\u103a\u1010\u103d\u1031\u1000\u102d\u102f \u101b\u101c\u1012\u103a\u1010\u103d\u1031\u1000\u102d\u102f \u1021\u1000\u103b\u1009\u103a\u1038\u1001\u103b\u102f\u1036\u1037\u1010\u1032\u1037\u1014\u100a\u103a\u1038\u1014\u1032\u1037 \u1021\u1005\u102e\u101b\u1004\u103a\u1001\u1036\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u1010\u101a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u101c\u1031\u1037\u1000\u103b\u1004\u1037\u103a\u1001\u1014\u103a\u1038\u1021\u1005\u102e\u1021\u1005\u1009\u103a\u104f\u1021\u1000\u103b\u102d\u102f\u1038\u101e\u1000\u103a\u101b\u1031\u102c\u1000\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u1000\u102d\u102f\u1005\u1005\u103a\u1006\u1031\u1038\u101b\u1014\u103a\u1010\u1005\u103a\u101c\u1019\u103a\u1038\u101e\u103d\u102c\u1038 ANOVA \u1000\u102d\u102f\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u1032\u1037\u101e\u100a\u103a\u104b <em>&nbsp;<\/em> \u1000\u102d\u102f\u101a\u103a\u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a <em>(\u1015\u1031\u102b\u1004\u103a\u1016\u103c\u1004\u1037\u103a\u1010\u102d\u102f\u1004\u103a\u1038\u1010\u102c\u101e\u100a\u103a)\u104b<\/em> \u1000\u102d\u102f\u101a\u103a\u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a\u1000\u103b\u1001\u103c\u1004\u103a\u1038\u1006\u102d\u102f\u1004\u103a\u101b\u102c \u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a\u101e\u102f\u1036\u1038\u1001\u102f\u104f \u1021\u1000\u103b\u102d\u102f\u1038\u101e\u1000\u103a\u101b\u1031\u102c\u1000\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038 (F(2, 87) = 30.83\u104a p = 7.55e-11) \u1021\u1000\u103c\u102c\u1038 \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1021\u101b \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u101e\u1031\u102c \u1000\u103d\u102c\u1001\u103c\u102c\u1038\u1001\u103b\u1000\u103a\u1010\u1005\u103a\u1001\u102f\u101b\u103e\u102d\u101e\u100a\u103a\u104b<\/span> <span style=\"color: #000000;\">Post-hoc Tukey \u104f HSD \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1015\u103c\u102f\u101c\u102f\u1015\u103a\u1001\u1032\u1037\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a C \u1010\u103d\u1004\u103a\u1015\u102b\u101d\u1004\u103a\u101e\u1030\u1019\u103b\u102c\u1038\u104f\u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1000\u102d\u102f\u101a\u103a\u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a\u101e\u100a\u103a \u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a B (p &lt; 0.0001) \u1010\u103d\u1004\u103a\u1015\u102b\u101d\u1004\u103a\u101e\u1030\u1019\u103b\u102c\u1038\u104f\u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1000\u102d\u102f\u101a\u103a\u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a\u1011\u1000\u103a\u101e\u102d\u101e\u102d\u101e\u102c\u101e\u102c\u1000\u103c\u102e\u1038\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a C \u1010\u103d\u1004\u103a \u1015\u102b\u101d\u1004\u103a\u101e\u1030\u1019\u103b\u102c\u1038\u104f \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1000\u102d\u102f\u101a\u103a\u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a \u101c\u103b\u1031\u102c\u1037\u1000\u103b\u1019\u103e\u102f\u101e\u100a\u103a \u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a A (p &lt; 0.0001) \u1010\u103d\u1004\u103a \u1015\u102b\u101d\u1004\u103a\u101e\u1030\u1019\u103b\u102c\u1038\u104f \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1000\u102d\u102f\u101a\u103a\u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a\u1011\u1000\u103a \u101e\u102d\u101e\u102d\u101e\u102c\u101e\u102c \u1015\u102d\u102f\u1019\u103b\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1011\u102d\u102f\u1037\u1021\u1015\u103c\u1004\u103a\u104a \u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a B \u1010\u103d\u1004\u103a\u1015\u102b\u101d\u1004\u103a\u101e\u1030\u1019\u103b\u102c\u1038\u104f\u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1000\u102d\u102f\u101a\u103a\u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a\u101e\u100a\u103a \u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a A (p = 0.01) \u1010\u103d\u1004\u103a\u1015\u102b\u101d\u1004\u103a\u101e\u1030\u1019\u103b\u102c\u1038\u104f\u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1000\u102d\u102f\u101a\u103a\u1021\u101c\u1031\u1038\u1001\u103b\u102d\u1014\u103a\u1011\u1000\u103a \u101e\u102d\u101e\u102d\u101e\u102c\u101e\u102c\u1000\u103c\u102e\u1038\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<h3> <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><\/h3>\n<p> <span style=\"color: #000000;\">\u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u1015\u102b \u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1010\u1005\u103a\u101c\u1019\u103a\u1038\u101e\u103d\u102c\u1038 ANOVA \u1019\u103b\u102c\u1038\u1021\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1014\u1031\u102c\u1000\u103a\u1011\u1015\u103a\u1021\u1001\u103b\u1000\u103a\u1021\u101c\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1015\u1031\u1038\u1006\u1031\u102c\u1004\u103a\u101e\u100a\u103a-<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/my\/one-way-anova\/\" target=\"_blank\" rel=\"noopener\">One-Way ANOVA \u1019\u102d\u1010\u103a\u1006\u1000\u103a<\/a><br \/> <a href=\"https:\/\/statorials.org\/my\/post-hoc-anova-\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038\/\" target=\"_blank\" rel=\"noopener\">ANOVA \u1016\u103c\u1004\u1037\u103a Post-Hoc Testing \u1000\u102d\u102f\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1001\u103c\u1004\u103a\u1038\u101c\u1019\u103a\u1038\u100a\u103d\u103e\u1014\u103a<\/a><br \/> <a href=\"https:\/\/statorials.org\/my\/anova-\u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f-\u1019\u100a\u103a\u101e\u102d\u102f\u1037\u1021\u1005\u102e\u101b\u1004\u103a\u1001\u1036\u1019\u100a\u103a\u1014\u100a\u103a\u1038\u104b\/\" target=\"_blank\" rel=\"noopener\">\u101c\u1019\u103a\u1038\u100a\u103d\u103e\u1014\u103a\u1001\u103b\u1000\u103a\u1021\u1015\u103c\u100a\u1037\u103a\u1021\u1005\u102f\u1036- ANOVA \u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u1021\u1005\u102e\u101b\u1004\u103a\u1001\u1036\u1019\u100a\u103a\u1014\u100a\u103a\u1038\u104b<\/a><\/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\u1015\u102d\u102f\u101e\u1031\u102c \u101c\u103d\u1010\u103a\u101c\u1015\u103a\u101e\u1031\u102c \u1021\u102f\u1015\u103a\u1005\u102f\u1019\u103b\u102c\u1038\u1021\u1000\u103c\u102c\u1038 \u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1006\u102d\u102f\u1004\u103a\u101b\u102c \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u101e\u1031\u102c \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 \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1010\u1005\u103a\u1001\u102f\u1015\u1031\u102b\u103a\u101b\u103e\u102d \u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a \u1010\u1005\u103a\u1001\u102f\u104f \u1021\u1000\u103b\u102d\u102f\u1038\u101e\u1000\u103a\u101b\u1031\u102c\u1000\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1015\u102d\u102f\u1004\u103a\u1038\u1001\u103c\u102c\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u1024\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1021\u1019\u103b\u102d\u102f\u1038\u1021\u1005\u102c\u1038\u1000\u102d\u102f \u1010\u1005\u103a\u101c\u1019\u103a\u1038\u101e\u103d\u102c\u1038 ANOVA \u101f\u102f\u1001\u1031\u102b\u103a\u101e\u100a\u103a\u104b \u1019\u103e\u1010\u103a\u1001\u103b\u1000\u103a &#8211; \u1021\u1000\u101a\u103a\u104d \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1010\u1005\u103a\u1001\u102f\u1015\u1031\u102b\u103a\u101b\u103e\u102d \u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1014\u103e\u1005\u103a\u1001\u102f\u104f \u1021\u1000\u103b\u102d\u102f\u1038\u101e\u1000\u103a\u101b\u1031\u102c\u1000\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1005\u102d\u1010\u103a\u101d\u1004\u103a\u1005\u102c\u1038\u1015\u102b\u1000\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1014\u103e\u1005\u103a\u101c\u1019\u103a\u1038\u101e\u103d\u102c\u1038 ANOVA \u1000\u102d\u102f 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