{"id":2547,"date":"2023-07-21T19:20:33","date_gmt":"2023-07-21T19:20:33","guid":{"rendered":"https:\/\/statorials.org\/my\/r-in-three-way-anova\/"},"modified":"2023-07-21T19:20:33","modified_gmt":"2023-07-21T19:20:33","slug":"r-in-three-way-anova","status":"publish","type":"post","link":"https:\/\/statorials.org\/my\/r-in-three-way-anova\/","title":{"rendered":"R \u1016\u103c\u1004\u1037\u103a \u101e\u102f\u1036\u1038\u101c\u1019\u103a\u1038\u101e\u103d\u102c\u1038 anova \u1000\u102d\u102f \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1019\u100a\u103a\u1014\u100a\u103a\u1038\u104b"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><strong>\u101e\u102f\u1036\u1038\u101c\u1019\u103a\u1038\u101e\u103d\u102c\u1038 ANOVA \u1000\u102d\u102f \u1021\u1001\u103b\u1000\u103a\u101e\u102f\u1036\u1038\u1001\u103b\u1000\u103a\u1016\u103c\u1004\u1037\u103a<\/strong> \u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1011\u102c\u1038\u101e\u1031\u102c \u1021\u1019\u103e\u102e\u1021\u1001\u102d\u102f\u1000\u1004\u103a\u1038\u101e\u1031\u102c \u1021\u102f\u1015\u103a\u1005\u102f\u101e\u102f\u1036\u1038\u1005\u102f \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1011\u102d\u102f\u1037\u1011\u1000\u103a\u1019\u1000\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\u1001\u103b\u1000\u103a\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1025\u1015\u1019\u102c\u101e\u100a\u103a R \u1010\u103d\u1004\u103a \u101e\u102f\u1036\u1038\u101c\u1019\u103a\u1038\u101e\u103d\u102c\u1038 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 \u1015\u103c\u101e\u1011\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>\u1025\u1015\u1019\u102c- R in \u101e\u102f\u1036\u1038\u101c\u1019\u103a\u1038 ANOVA<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">\u101c\u1031\u1037\u1000\u103b\u1004\u1037\u103a\u101b\u1031\u1038\u1021\u1005\u102e\u1021\u1005\u1009\u103a\u1014\u103e\u1005\u103a\u1001\u102f\u101e\u100a\u103a \u1000\u1031\u102c\u101c\u102d\u1015\u103a\u1018\u1010\u103a\u1005\u1000\u1000\u103a\u1018\u1031\u102c\u1000\u1005\u102c\u1038\u101e\u1019\u102c\u1038\u1019\u103b\u102c\u1038\u1000\u103c\u102c\u1038 \u1001\u102f\u1014\u103a\u1021\u1019\u103c\u1004\u1037\u103a \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1010\u102d\u102f\u1038\u1010\u1000\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1016\u103c\u1005\u103a\u1015\u1031\u102b\u103a\u1005\u1031\u1001\u103c\u1004\u103a\u1038\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u101e\u102f\u1010\u1031\u101e\u102e\u1010\u1005\u103a\u1026\u1038\u1019\u103e \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101c\u102d\u102f\u101e\u100a\u103a\u1006\u102d\u102f\u1015\u102b\u1005\u102d\u102f\u1037\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1000\u103b\u102c\u1038\/\u1019 \u1000\u103d\u1032\u1015\u103c\u102c\u1038\u1001\u103c\u1004\u103a\u1038 (Division I \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a II) \u101e\u100a\u103a \u1021\u1019\u103c\u1004\u1037\u103a\u1001\u102f\u1014\u103a\u1001\u103c\u1004\u103a\u1038\u1021\u1015\u1031\u102b\u103a \u101e\u1000\u103a\u101b\u1031\u102c\u1000\u103a\u1019\u103e\u102f\u101b\u103e\u102d\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u101f\u102f \u101e\u102f\u1010\u1031\u101e\u102e\u1000 \u101e\u1036\u101e\u101a\u101b\u103e\u102d\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u1024\u1021\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a \u1015\u1010\u103a\u101e\u1000\u103a\u101e\u1031\u102c \u1021\u1001\u103b\u1000\u103a\u1021\u101c\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1005\u102f\u1006\u1031\u102c\u1004\u103a\u1038\u1001\u1032\u1037\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u101e\u1030\u104f \u101b\u100a\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103b\u1000\u103a\u1019\u103e\u102c \u101c\u1031\u1037\u1000\u103b\u1004\u1037\u103a\u101b\u1031\u1038\u1021\u1005\u102e\u1021\u1005\u1009\u103a\u104a \u1000\u103b\u102c\u1038\u104a \u1019 \u1014\u103e\u1004\u1037\u103a \u1000\u103d\u1032\u1015\u103c\u102c\u1038\u1019\u103e\u102f\u1021\u1015\u1031\u102b\u103a \u1019\u100a\u103a\u1000\u1032\u1037\u101e\u102d\u102f\u1037 \u1001\u102f\u1014\u103a\u1021\u1019\u103c\u1004\u1037\u103a\u1000\u102d\u102f \u101e\u1000\u103a\u101b\u1031\u102c\u1000\u103a\u101e\u100a\u103a\u1000\u102d\u102f \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a \u101e\u102f\u1036\u1038\u101c\u1019\u103a\u1038 ANOVA \u1000\u102d\u102f \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1014\u103a\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1024\u101e\u102f\u1036\u1038\u1014\u100a\u103a\u1038 ANOVA \u1000\u102d\u102f R \u1010\u103d\u1004\u103a\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\u1000\u102d\u102f \u101c\u102d\u102f\u1000\u103a\u1014\u102c\u1015\u102b\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 1: \u1012\u1031\u1010\u102c\u1000\u102d\u102f\u1016\u1014\u103a\u1010\u102e\u1038\u1015\u102b\u104b<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1015\u1011\u1019\u1026\u1038\u1005\u103d\u102c\u104a \u1012\u1031\u1010\u102c\u1000\u102d\u102f\u1011\u102d\u1014\u103a\u1038\u1011\u102c\u1038\u101b\u1014\u103a \u1012\u1031\u1010\u102c\u1018\u1031\u102c\u1004\u103a\u1010\u1005\u103a\u1001\u102f \u1016\u1014\u103a\u1010\u102e\u1038\u1000\u103c\u1015\u102b\u1005\u102d\u102f\u1037\u104b<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#create dataset\n<\/span>df &lt;- data. <span style=\"color: #3366ff;\">frame<\/span> (program=rep(c(1, 2), each= <span style=\"color: #008000;\">20<\/span> ),\n                 gender=rep(c(' <span style=\"color: #ff0000;\">M<\/span> ', ' <span style=\"color: #ff0000;\">F<\/span> '), each= <span style=\"color: #008000;\">10<\/span> , times= <span style=\"color: #008000;\">2<\/span> ),\n                 division=rep(c(1, 2), each= <span style=\"color: #008000;\">5<\/span> , times= <span style=\"color: #008000;\">4<\/span> ),\n                 height=c(7, 7, 8, 8, 7, 6, 6, 5, 6, 5,\n                          5, 5, 4, 5, 4, 3, 3, 4, 3, 3,\n                          6, 6, 5, 4, 5, 4, 5, 4, 4, 3,\n                          2, 2, 1, 4, 4, 2, 1, 1, 2, 1)) \n\n<span style=\"color: #008080;\">#view first six rows of dataset\n<\/span>head(df)\n\n  program gender division height\n1 1 M 1 7\n2 1 M 1 7\n3 1 M 1 8\n4 1 M 1 8\n5 1 M 1 7\n6 1 M 2 6<\/strong><\/pre>\n<p> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 2- \u1016\u1031\u102c\u103a\u1015\u103c\u1001\u103b\u1000\u103a\u1005\u102c\u101b\u1004\u103a\u1038\u1007\u101a\u102c\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1000\u103c\u100a\u1037\u103a\u1015\u102b\u104b<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u101e\u102f\u1036\u1038\u101c\u1019\u103a\u1038\u101e\u103d\u102c\u1038 ANOVA \u1000\u102d\u102f \u1019\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1019\u102e\u104a \u101c\u1031\u1037\u1000\u103b\u1004\u1037\u103a\u101b\u1031\u1038\u1021\u1005\u102e\u1021\u1005\u1009\u103a\u104a \u1000\u103b\u102c\u1038\u104a \u1019 \u1014\u103e\u1004\u1037\u103a \u1021\u1015\u102d\u102f\u1004\u103a\u1038\u1021\u101c\u102d\u102f\u1000\u103a \u1021\u102f\u1015\u103a\u1005\u102f\u1016\u103d\u1032\u1037\u1011\u102c\u1038\u101e\u1031\u102c \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1001\u102f\u1014\u103a\u1014\u103e\u102f\u1014\u103a\u1038\u1010\u102d\u102f\u1038\u1014\u103e\u102f\u1014\u103a\u1038\u1000\u102d\u102f \u101c\u103b\u1004\u103a\u1019\u103c\u1014\u103a\u1005\u103d\u102c \u1021\u1000\u103b\u1009\u103a\u1038\u1001\u103b\u102f\u1015\u103a\u1016\u1031\u102c\u103a\u1015\u103c\u101b\u1014\u103a <a href=\"https:\/\/dplyr.tidyverse.org\/\" target=\"_blank\" rel=\"noopener\">dplyr<\/a> \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: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008000;\">library<\/span> (dplyr)\n\n<span style=\"color: #008080;\">#calculate mean jumping height increase grouped by program, gender, and division\n<\/span>df %&gt;%\n  group_by(program, gender, division) %&gt;%\n  summarize(mean_height = mean(height))\n\n# A tibble: 8 x 4\n# Groups: program, gender [4]\n  program gender division mean_height\n                 \n1 1 F 1 4.6\n2 1 F 2 3.2\n3 1 M 1 7.4\n4 1 M 2 5.6\n5 2 F 1 2.6\n6 2 F 2 1.4\n7 2 M 1 5.2\n8 2 M 2 4  \n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u1024\u101e\u100a\u103a\u1019\u103e\u102c \u101b\u101c\u1012\u103a\u1000\u102d\u102f \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u1021\u1013\u102d\u1015\u1039\u1015\u102c\u101a\u103a\u1016\u103d\u1004\u1037\u103a\u1006\u102d\u102f\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a-<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Training Program 1 \u1000\u102d\u102f\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u1031\u102c Division I \u1021\u1019\u103b\u102d\u102f\u1038\u101e\u1019\u102e\u1038\u1019\u103b\u102c\u1038\u1021\u1010\u103d\u1000\u103a \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1001\u102f\u1014\u103a\u1014\u103e\u102f\u1014\u103a\u1038\u101e\u100a\u103a <strong>4.6 \u101c\u1000\u103a\u1019<\/strong> \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/li>\n<li> <span style=\"color: #000000;\">Training Program 1 \u1000\u102d\u102f\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u1031\u102c Division II \u1021\u1019\u103b\u102d\u102f\u1038\u101e\u1019\u102e\u1038\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1001\u102f\u1014\u103a\u1014\u103e\u102f\u1014\u103a\u1038\u101e\u100a\u103a <strong>3.2 \u101c\u1000\u103a\u1019<\/strong> \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/li>\n<li> <span style=\"color: #000000;\">Training Program 1 \u1000\u102d\u102f\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u1031\u102c Division I \u1021\u1019\u103b\u102d\u102f\u1038\u101e\u102c\u1038\u1019\u103b\u102c\u1038\u1021\u1000\u103c\u102c\u1038 \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1001\u102f\u1014\u103a\u1014\u103e\u102f\u1014\u103a\u1038\u101e\u100a\u103a <strong>7.4 \u101c\u1000\u103a\u1019<\/strong> \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u1014\u1031\u102c\u1000\u103a &#8230; \u1015\u103c\u102e\u1038\u1010\u1031\u102c\u1037\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 3- ANOVA \u101e\u102f\u1036\u1038\u101b\u1015\u103a\u1000\u102d\u102f \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1015\u102b\u104b<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1014\u1031\u102c\u1000\u103a\u1010\u1005\u103a\u1001\u102f\u104a \u101e\u102f\u1036\u1038\u101c\u1019\u103a\u1038 ANOVA \u1000\u102d\u102f\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1014\u103a <strong>aov()<\/strong> \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u103b\u1000\u103a\u1000\u102d\u102f\u101e\u102f\u1036\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#perform three-way ANOVA<\/span>\nmodel &lt;- aov(height ~ program * gender * division, data=df)\n\n<span style=\"color: #008080;\">#view summary of three-way ANOVA\n<\/span>summary(model)\n\n                        Df Sum Sq Mean Sq F value Pr(&gt;F)    \nprogram 1 36.1 36.10 65.636 2.98e-09 ***\ngender 1 67.6 67.60 122.909 1.71e-12 ***\ndivision 1 19.6 19.60 35.636 1.19e-06 ***\nprogram:gender 1 0.0 0.00 0.000 1.000    \nprogram:division 1 0.4 0.40 0.727 0.400    \ngender:division 1 0.1 0.10 0.182 0.673    \nprogram:gender:division 1 0.1 0.10 0.182 0.673    \nResiduals 32 17.6 0.55                     \n---\nSignificant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\"><strong>Pr(&gt;F)<\/strong> \u1000\u1031\u102c\u103a\u101c\u1036\u101e\u100a\u103a \u1021\u1001\u103b\u1000\u103a\u1010\u1005\u103a\u1001\u102f\u1001\u103b\u1004\u103a\u1038\u1005\u102e\u1021\u1010\u103d\u1000\u103a p-value \u1014\u103e\u1004\u1037\u103a \u1021\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u103c\u102c\u1038 \u1021\u1015\u103c\u1014\u103a\u1021\u101c\u103e\u1014\u103a\u1021\u1000\u103b\u102d\u102f\u1038\u101e\u1000\u103a\u101b\u1031\u102c\u1000\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1015\u103c\u101e\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u1019\u103e\u104a \u1021\u1001\u103b\u1000\u103a\u101e\u102f\u1036\u1038\u1001\u103b\u1000\u103a\u1021\u1000\u103c\u102c\u1038 \u1021\u1015\u103c\u1014\u103a\u1021\u101c\u103e\u1014\u103a\u1021\u1000\u103b\u102d\u102f\u1038\u101e\u1000\u103a\u101b\u1031\u102c\u1000\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1021\u101b \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u1019\u103e\u102f\u1019\u101b\u103e\u102d\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;\">\u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a\u104a \u1000\u103b\u102c\u1038\u104a \u1019 \u1014\u103e\u1004\u1037\u103a \u1000\u103d\u1032\u1015\u103c\u102c\u1038\u1001\u103c\u1004\u103a\u1038 \u1005\u101e\u100a\u1037\u103a \u1021\u1001\u103b\u1000\u103a\u101e\u102f\u1036\u1038\u1001\u103b\u1000\u103a\u1005\u102e\u101e\u100a\u103a \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1021\u101b \u1021\u101b\u1031\u1038\u1015\u102b\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\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a\u104a \u1000\u103b\u102c\u1038\u104a \u1019 \u1014\u103e\u1004\u1037\u103a \u1015\u102d\u102f\u1004\u103a\u1038\u1001\u103c\u102c\u1038\u1019\u103e\u102f\u1021\u1010\u103d\u1000\u103a \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1001\u102f\u1014\u103a\u1014\u103e\u102f\u1014\u103a\u1038\u1010\u102d\u102f\u1038\u1019\u103e\u102f\u1000\u102d\u102f \u101b\u103e\u102c\u1016\u103d\u1031\u101b\u1014\u103a \u101a\u1001\u102f dplyr \u1000\u102d\u102f \u1011\u1015\u103a\u1019\u1036\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a-<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\"><span style=\"color: #000000;\"><span style=\"color: #008000;\">library<\/span> (dplyr)\n<\/span>\n#find mean jumping increase by program<\/span>\ndf %&gt;%\n  group_by(program) %&gt;%\n  summarize(mean_height = mean(height))\n\n# A tibble: 2 x 2\n  program mean_height\n           \n1 1 5.2\n2 2 3.3\n\n<span style=\"color: #008080;\">#find mean jumping increase by gender\n<\/span>df %&gt;%\n  group_by(gender) %&gt;%\n  summarize(mean_height = mean(height))\n\n# A tibble: 2 x 2\n  gender mean_height\n          \n1 F 2.95\n2M 5.55\n\n<span style=\"color: #008080;\">#find mean jumping increase by division\n<\/span>df %&gt;%\ngroup_by(division) %&gt;%\nsummarize(mean_height = mean(height))\n\n# A tibble: 2 x 2\n  division mean_height\n            \n1 1 4.95\n2 2 3.55<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u101b\u101c\u1012\u103a\u1021\u1014\u1031\u1016\u103c\u1004\u1037\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1010\u102d\u102f\u1037\u1000\u102d\u102f \u101c\u1031\u1037\u101c\u102c\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u101c\u1031\u1037\u1000\u103b\u1004\u1037\u103a\u101b\u1031\u1038\u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a 1 ( <strong>5.2 \u101c\u1000\u103a\u1019<\/strong> ) \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u1031\u102c \u1010\u1005\u103a\u1026\u1038\u1001\u103b\u1004\u103a\u1038\u1005\u102e\u1021\u1010\u103d\u1000\u103a \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e \u1001\u102f\u1014\u103a\u1014\u103e\u102f\u1014\u103a\u1038 \u1019\u103c\u1004\u1037\u103a\u1010\u1000\u103a\u101c\u102c\u1019\u103e\u102f\u101e\u100a\u103a \u101c\u1031\u1037\u1000\u103b\u1004\u1037\u103a\u101b\u1031\u1038 \u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a 2 <strong>(3.3 \u101c\u1000\u103a\u1019<\/strong> ) \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u1030\u1019\u103b\u102c\u1038\u1021\u1010\u103d\u1000\u103a \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e \u1010\u102d\u102f\u1038\u1014\u103e\u102f\u1014\u103a\u1038\u1011\u1000\u103a \u1015\u102d\u102f\u1019\u103b\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/li>\n<li> <span style=\"color: #000000;\">\u1021\u1019\u103b\u102d\u102f\u1038\u101e\u102c\u1038\u1019\u103b\u102c\u1038\u1021\u1010\u103d\u1000\u103a \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e \u1001\u102f\u1014\u103a\u1021\u1019\u103c\u1004\u1037\u103a ( <strong>5.55\u101c\u1000\u103a\u1019<\/strong> ) \u101e\u100a\u103a \u1021\u1019\u103b\u102d\u102f\u1038\u101e\u1019\u102e\u1038\u1019\u103b\u102c\u1038\u1021\u1010\u103d\u1000\u103a \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1010\u102d\u102f\u1038\u1014\u103e\u102f\u1014\u103a\u1038 <strong>(2.95\u101c\u1000\u103a\u1019<\/strong> )\u1011\u1000\u103a \u1015\u102d\u102f\u1019\u103b\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/li>\n<li> <span style=\"color: #000000;\">Division 1 \u1000\u1005\u102c\u1038\u101e\u1019\u102c\u1038\u1019\u103b\u102c\u1038\u1021\u1000\u103c\u102c\u1038 \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e \u1001\u102f\u1014\u103a\u1014\u103e\u102f\u1014\u103a\u1038 \u1019\u103c\u1004\u1037\u103a\u1010\u1000\u103a\u101c\u102c\u1019\u103e\u102f ( <strong>\u1044.\u1049\u1045 \u101c\u1000\u103a\u1019<\/strong> ) \u101e\u100a\u103a Division 2 \u1000\u1005\u102c\u1038\u101e\u1019\u102c\u1038\u1019\u103b\u102c\u1038\u1021\u1000\u103c\u102c\u1038 \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e \u1010\u102d\u102f\u1038\u1019\u103c\u1004\u1037\u103a\u1019\u103e\u102f <strong>(\u1043.\u1045\u1045 \u101c\u1000\u103a\u1019<\/strong> ) \u1011\u1000\u103a \u1015\u102d\u102f\u1019\u103b\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u1014\u102d\u1002\u102f\u1036\u1038\u1001\u103b\u102f\u1015\u103a\u1021\u1014\u1031\u1014\u1032\u1037\u1015\u103c\u1031\u102c\u101b\u1019\u101a\u103a\u1006\u102d\u102f\u101b\u1004\u103a \u101c\u1031\u1037\u1000\u103b\u1004\u1037\u103a\u101b\u1031\u1038\u1021\u1005\u102e\u1021\u1005\u1009\u103a\u104a \u1000\u103b\u102c\u1038\u104a\u1019 \u1000\u103d\u1032\u1015\u103c\u102c\u1038\u1019\u103e\u102f\u1010\u103d\u1031\u101f\u102c \u1000\u1005\u102c\u1038\u101e\u1019\u102c\u1038\u1010\u103d\u1031\u101b\u1032\u1037 \u1001\u102f\u1014\u103a\u1014\u103e\u102f\u1014\u103a\u1038\u1019\u103c\u1004\u1037\u103a\u101c\u102c\u1019\u103e\u102f\u101b\u1032\u1037 \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u1010\u1032\u1037 \u1021\u100a\u103d\u103e\u1014\u103a\u1038\u1000\u102d\u1014\u103a\u1038\u1010\u103d\u1031\u1015\u102b\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1024\u1021\u1001\u103b\u1000\u103a\u101e\u102f\u1036\u1038\u1001\u103b\u1000\u103a\u1000\u103c\u102c\u1038\u1010\u103d\u1004\u103a \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u101e\u1031\u102c \u1021\u1015\u103c\u1014\u103a\u1021\u101c\u103e\u1014\u103a\u101e\u1000\u103a\u101b\u1031\u102c\u1000\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038 \u1019\u101b\u103e\u102d\u101f\u102f\u101c\u100a\u103a\u1038 \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1015\u103c\u1031\u102c\u1015\u102b\u1019\u100a\u103a\u104b<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>\u1011\u1015\u103a\u101c\u1031\u102c\u1004\u103a\u1038\u1021\u101b\u1004\u103a\u1038\u1021\u1019\u103c\u1005\u103a\u1019\u103b\u102c\u1038<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">\u1021\u1031\u102c\u1000\u103a\u1015\u102b\u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u1019\u103b\u102c\u1038\u101e\u100a\u103a R \u1010\u103d\u1004\u103a\u1021\u1001\u103c\u102c\u1038 ANOVA \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a\u1021\u1036\u101d\u1004\u103a\u1001\u103d\u1004\u103a\u1000\u103b\u1016\u103c\u1005\u103a\u1015\u102f\u1036\u1000\u102d\u102f\u101b\u103e\u1004\u103a\u1038\u1015\u103c\u101e\u100a\u103a<\/span><\/p>\n<p> <a href=\"https:\/\/statorials.org\/my\/one-way-anova-r\/\" target=\"_blank\" rel=\"noopener\">\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<\/a><br \/> <a href=\"https:\/\/statorials.org\/my\/anova-ra-\u1014\u103e\u1005\u103a\u101c\u1019\u103a\u1038\/\" target=\"_blank\" rel=\"noopener\">R \u1016\u103c\u1004\u1037\u103a \u1014\u103e\u1005\u103a\u101c\u1019\u103a\u1038\u101e\u103d\u102c\u1038 ANOVA \u1000\u102d\u102f \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1019\u100a\u103a\u1014\u100a\u103a\u1038\u104b<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u101e\u102f\u1036\u1038\u101c\u1019\u103a\u1038\u101e\u103d\u102c\u1038 ANOVA \u1000\u102d\u102f \u1021\u1001\u103b\u1000\u103a\u101e\u102f\u1036\u1038\u1001\u103b\u1000\u103a\u1016\u103c\u1004\u1037\u103a \u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1011\u102c\u1038\u101e\u1031\u102c \u1021\u1019\u103e\u102e\u1021\u1001\u102d\u102f\u1000\u1004\u103a\u1038\u101e\u1031\u102c \u1021\u102f\u1015\u103a\u1005\u102f\u101e\u102f\u1036\u1038\u1005\u102f \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1011\u102d\u102f\u1037\u1011\u1000\u103a\u1019\u1000\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\u1001\u103b\u1000\u103a\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1015\u102b\u101e\u100a\u103a\u104b \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1025\u1015\u1019\u102c\u101e\u100a\u103a R \u1010\u103d\u1004\u103a \u101e\u102f\u1036\u1038\u101c\u1019\u103a\u1038\u101e\u103d\u102c\u1038 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 \u1015\u103c\u101e\u1011\u102c\u1038\u101e\u100a\u103a\u104b \u1025\u1015\u1019\u102c- R in \u101e\u102f\u1036\u1038\u101c\u1019\u103a\u1038 ANOVA \u101c\u1031\u1037\u1000\u103b\u1004\u1037\u103a\u101b\u1031\u1038\u1021\u1005\u102e\u1021\u1005\u1009\u103a\u1014\u103e\u1005\u103a\u1001\u102f\u101e\u100a\u103a \u1000\u1031\u102c\u101c\u102d\u1015\u103a\u1018\u1010\u103a\u1005\u1000\u1000\u103a\u1018\u1031\u102c\u1000\u1005\u102c\u1038\u101e\u1019\u102c\u1038\u1019\u103b\u102c\u1038\u1000\u103c\u102c\u1038 \u1001\u102f\u1014\u103a\u1021\u1019\u103c\u1004\u1037\u103a \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1010\u102d\u102f\u1038\u1010\u1000\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1016\u103c\u1005\u103a\u1015\u1031\u102b\u103a\u1005\u1031\u1001\u103c\u1004\u103a\u1038\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u101e\u102f\u1010\u1031\u101e\u102e\u1010\u1005\u103a\u1026\u1038\u1019\u103e \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101c\u102d\u102f\u101e\u100a\u103a\u1006\u102d\u102f\u1015\u102b\u1005\u102d\u102f\u1037\u104b \u1000\u103b\u102c\u1038\/\u1019 \u1000\u103d\u1032\u1015\u103c\u102c\u1038\u1001\u103c\u1004\u103a\u1038 (Division I \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a II) \u101e\u100a\u103a \u1021\u1019\u103c\u1004\u1037\u103a\u1001\u102f\u1014\u103a\u1001\u103c\u1004\u103a\u1038\u1021\u1015\u1031\u102b\u103a \u101e\u1000\u103a\u101b\u1031\u102c\u1000\u103a\u1019\u103e\u102f\u101b\u103e\u102d\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u101f\u102f \u101e\u102f\u1010\u1031\u101e\u102e\u1000 \u101e\u1036\u101e\u101a\u101b\u103e\u102d\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a 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