{"id":483,"date":"2023-07-29T18:17:31","date_gmt":"2023-07-29T18:17:31","guid":{"rendered":"https:\/\/statorials.org\/my\/ancova-in-r\/"},"modified":"2023-07-29T18:17:31","modified_gmt":"2023-07-29T18:17:31","slug":"ancova-in-r","status":"publish","type":"post","link":"https:\/\/statorials.org\/my\/ancova-in-r\/","title":{"rendered":"R \u1016\u103c\u1004\u1037\u103a ancova \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;\">\u1024\u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u101e\u100a\u103a R \u1016\u103c\u1004\u1037\u103a <a href=\"https:\/\/statorials.org\/my\/ancova-in-r\/\" target=\"_blank\" rel=\"noopener noreferrer\">ANCOVA \u1000\u102d\u102f<\/a> \u1019\u100a\u103a\u101e\u102d\u102f\u1037\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1019\u100a\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>\u1025\u1015\u1019\u102c- R in ANCOVA<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u101c\u1031\u1037\u101c\u102c\u1019\u103e\u102f\u1014\u100a\u103a\u1038\u1015\u100a\u102c\u101e\u100a\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u1021\u1015\u1031\u102b\u103a \u101e\u1000\u103a\u101b\u1031\u102c\u1000\u103a\u1019\u103e\u102f\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u101b\u1014\u103a ANCOVA \u1000\u102d\u102f \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1015\u102b\u1019\u100a\u103a\u104b<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u1014\u100a\u103a\u1038\u1015\u100a\u102c\u101c\u1031\u1037\u101c\u102c\u1019\u103e\u102f<\/strong> &#8211; \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u101c\u102d\u102f\u101e\u1031\u102c \u101e\u102e\u1038\u1001\u103c\u102c\u1038\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u101c\u1000\u103a\u101b\u103e\u102d \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u1021\u1006\u1004\u1037\u103a<\/strong> &#8211; \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u1011\u100a\u1037\u103a\u101e\u103d\u1004\u103a\u1038\u1005\u1009\u103a\u1038\u1005\u102c\u1038\u101c\u102d\u102f\u101e\u1031\u102c \u1021\u1005\u102f\u1021\u101d\u1031\u1038<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u101e\u102f\u1036\u1038\u101e\u1015\u103a\u1001\u103b\u1000\u103a\u101b\u1019\u103e\u1010\u103a<\/strong> &#8211; \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u101c\u102d\u102f\u101e\u1031\u102c \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038<\/span><\/li>\n<\/ul>\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 \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038 90 \u1026\u1038\u1021\u102c\u1038 \u1000\u103b\u1015\u1014\u103a\u1038\u1021\u102f\u1015\u103a\u1005\u102f 30 \u1019\u103e \u1021\u102f\u1015\u103a\u1005\u102f\u101e\u102f\u1036\u1038\u1005\u102f\u1001\u103d\u1032\u1011\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u1010\u103d\u1004\u103a \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u1010\u1005\u103a\u1026\u1038\u1005\u102e\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u1031\u102c \u101c\u1031\u1037\u101c\u102c\u1019\u103e\u102f\u1014\u100a\u103a\u1038\u1005\u1014\u1005\u103a <em>(A\u104a B<\/em> \u104a \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a <em>C)<\/em> <em>\u104a<\/em> \u101c\u1031\u1037\u101c\u102c\u1019\u103e\u102f\u1014\u100a\u103a\u1038\u1015\u100a\u102c\u1000\u102d\u102f \u1005\u1010\u1004\u103a\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1001\u103b\u102d\u1014\u103a\u1010\u103d\u1004\u103a \u1021\u1010\u1014\u103a\u1038\u1010\u103d\u1004\u103a\u1038\u101b\u103e\u102d \u104e\u1004\u103a\u1038\u1010\u102d\u102f\u1037\u104f \u101c\u1000\u103a\u101b\u103e\u102d\u1021\u1010\u1014\u103a\u1038\u1014\u103e\u1004\u1037\u103a \u101c\u1031\u1037\u101c\u102c\u1019\u103e\u102f\u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1000\u102d\u102f \u1010\u1005\u103a\u101c\u1000\u103c\u102c\u1015\u103c\u1004\u103a\u1006\u1004\u103a\u1015\u103c\u102e\u1038\u1014\u1031\u102c\u1000\u103a \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u1010\u103d\u1004\u103a \u101b\u101b\u103e\u102d\u101e\u100a\u1037\u103a\u1021\u1006\u1004\u1037\u103a\u1000\u102d\u102f \u1015\u103c\u101e\u101e\u100a\u103a \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u1021\u1010\u103d\u1000\u103a\u104b \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032:<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#make this example reproducible<\/span>\nset.seed(10)\n\n<span style=\"color: #008080;\">#create dataset<\/span>\ndata &lt;- data.frame(technique = rep(c(\"A\", \"B\", \"C\"), each = 30),\n                   current_grade = runif(90, 65, 95),\n                   exam = c(runif(30, 80, 95), runif(30, 70, 95), runif(30, 70, 90)))\n\n<span style=\"color: #008080;\">#view first six lines of dataset<\/span>\nhead(data)\n\n# technical current_grade exam\n#1 A 80.22435 87.32759\n#2 A 74.20306 90.67114\n#3 A 77.80723 88.87902\n#4 A 85.79306 87.75735\n#5 A 67.55408 85.72442\n#6 A 71.76310 92.52167\n<\/strong><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 1: \u1012\u1031\u1010\u102c\u1000\u102d\u102f\u1005\u1030\u1038\u1005\u1019\u103a\u1038\u1015\u102b\u104b<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">ANCOVA \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1000\u102d\u102f \u1021\u1036\u1019\u101d\u1004\u103a\u1019\u102e\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u104e\u1004\u103a\u1038\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\u101b\u1014\u103a \u1012\u1031\u1010\u102c\u1000\u102d\u102f \u1005\u1030\u1038\u1005\u1019\u103a\u1038\u101c\u1031\u1037\u101c\u102c\u1015\u103c\u102e\u1038 \u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u101c\u103e\u100a\u1037\u103a\u1005\u102c\u1038\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u1037\u103a \u101c\u103d\u1014\u103a\u1000\u1032\u101e\u1031\u102c \u1021\u1005\u103d\u1014\u103a\u1038\u1021\u1011\u1004\u103a\u1038\u1019\u103b\u102c\u1038 \u1019\u101b\u103e\u102d\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1005\u1005\u103a\u1006\u1031\u1038\u101b\u1014\u103a \u101c\u102d\u102f\u1021\u1015\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1026\u1038\u1005\u103d\u102c\u104a dataset \u1021\u1010\u103d\u1004\u103a\u1038\u101b\u103e\u102d variable \u1010\u1005\u103a\u1001\u102f\u1005\u102e\u104f \u1021\u1000\u103b\u1009\u103a\u1038\u1001\u103b\u102f\u1015\u103a\u1000\u102d\u102f \u1015\u103c\u101e\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a-<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong>summary(data)\n\n# technical current_grade exam      \n#A:30 Min. :65.43 Min. :71.17  \n# B:30 1st Qu.:71.79 1st Qu.:77.27  \n# C:30 Median:77.84 Median:84.69  \n# Mean:78.15 Mean:83.38  \n# 3rd Qu.:83.65 3rd Qu.:89.22  \n# Max. :93.84 Max. :94.76  \n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u101c\u1031\u1037\u101c\u102c\u1019\u103e\u102f\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u104f\u1014\u100a\u103a\u1038\u1015\u100a\u102c\u1010\u1014\u103a\u1016\u102d\u102f\u1038 ( <em>A\u104a B<\/em> \u1014\u103e\u1004\u1037\u103a <em>C)<\/em> \u101e\u100a\u103a \u1021\u1001\u103b\u1000\u103a\u1021\u101c\u1000\u103a\u1010\u103d\u1004\u103a \u1021\u1006 30 \u1015\u1031\u102b\u103a\u101c\u102c\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;\">\u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u1019\u103b\u102c\u1038\u104f \u101c\u1000\u103a\u101b\u103e\u102d\u101b\u1019\u103e\u1010\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u101c\u1031\u1037\u101c\u102c\u1019\u103e\u102f\u1005\u1010\u1004\u103a\u1001\u103b\u102d\u1014\u103a\u1010\u103d\u1004\u103a \u1019\u100a\u103a\u1000\u1032\u1037\u101e\u102d\u102f\u1037 \u1016\u103c\u1014\u1037\u103a\u101d\u1031\u101e\u100a\u103a\u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101c\u100a\u103a\u1038 \u1000\u103c\u100a\u1037\u103a\u101b\u103e\u102f\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b \u1021\u1010\u1014\u103a\u1038\u1010\u103d\u1004\u103a \u1021\u1014\u102d\u1019\u1037\u103a\u1006\u102f\u1036\u1038\u101b\u1019\u103e\u1010\u103a\u1019\u103e\u102c \u1046\u1045.\u1044\u1043\u104a \u1021\u1019\u103c\u1004\u1037\u103a\u1006\u102f\u1036\u1038\u1019\u103e\u102c \u1049\u1043.\u1048\u1044 \u1016\u103c\u1005\u103a\u1015\u103c\u102e\u1038 \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e\u1019\u103e\u102c \u1047\u1048.\u1041\u1045 \u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1021\u101c\u102c\u1038\u1010\u1030\u104a \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u1010\u103d\u1004\u103a\u101b\u101b\u103e\u102d\u101e\u1031\u102c \u1021\u1014\u102d\u1019\u1037\u103a\u1006\u102f\u1036\u1038\u101b\u1019\u103e\u1010\u103a\u1019\u103e\u102c \u1047\u1041.\u1041\u1047\u104a \u1021\u1019\u103c\u1004\u1037\u103a\u1006\u102f\u1036\u1038\u101b\u1019\u103e\u1010\u103a\u1019\u103e\u102c \u1049\u1044.\u1047\u1046 \u1016\u103c\u1005\u103a\u1015\u103c\u102e\u1038 \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e \u1048\u1043.\u1043\u1048 \u1016\u103c\u1005\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 \u101c\u1031\u1037\u101c\u102c\u1019\u103e\u102f\u1014\u100a\u103a\u1038\u1015\u100a\u102c\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1021\u1010\u103d\u1000\u103a \u101c\u1000\u103a\u101b\u103e\u102d\u1021\u1006\u1004\u1037\u103a\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u101b\u101c\u1012\u103a\u1019\u103b\u102c\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 \u1021\u101c\u103d\u101a\u103a\u1010\u1000\u1030\u101b\u103e\u102c\u1016\u103d\u1031\u101b\u1014\u103a <strong>dplyr<\/strong> package \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 <em>dplyr<\/em><\/span>\nlibrary(dplyr)\n\ndata %&gt;%\n  <span style=\"color: #800080;\">group_by<\/span> (technical) %&gt;%\n  <span style=\"color: #800080;\">summarize<\/span> (mean_grade = mean(current_grade),\n            sd_grade = sd(current_grade),\n            mean_exam = mean(exam),\n            sd_exam = sd(exam))\n\n# A tibble: 3 x 5\n# technique mean_grade sd_grade mean_exam sd_exam                      \n#1 A 79.0 7.00 88.5 3.88\n#2 B 78.5 8.33 81.8 7.62\n#3 C 76.9 8.24 79.9 5.71<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u101c\u1031\u1037\u101c\u102c\u1019\u103e\u102f\u1014\u100a\u103a\u1038\u101c\u1019\u103a\u1038\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1000\u102d\u102f\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u100a\u1037\u103a \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u1019\u103b\u102c\u1038\u104f \u101c\u1000\u103a\u101b\u103e\u102d\u1021\u1010\u1014\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\u1019\u103b\u102c\u1038\u101e\u100a\u103a \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u1001\u103c\u1031\u1021\u102c\u1038\u1016\u103c\u1004\u1037\u103a \u1006\u1004\u103a\u1010\u1030\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \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;\">\u1014\u100a\u103a\u1038\u1005\u1014\u1005\u103a <em>B<\/em> \u1014\u103e\u1004\u1037\u103a <em>C<\/em> \u1014\u103e\u1004\u1037\u103a \u1014\u103e\u102d\u102f\u1004\u103a\u1038\u101a\u103e\u1009\u103a\u1015\u102b\u1000 \u101c\u1031\u1037\u101c\u102c\u1019\u103e\u102f\u1014\u100a\u103a\u1038\u1015\u100a\u102c <em>A<\/em> \u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u1031\u102c \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u1019\u103b\u102c\u1038\u1021\u1010\u103d\u1000\u103a \u1015\u103b\u1019\u103a\u1038\u1019\u103b\u103e \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u101b\u1019\u103e\u1010\u103a\u101e\u100a\u103a \u101e\u102d\u101e\u102d\u101e\u102c\u101e\u102c \u1019\u103c\u1004\u1037\u103a\u1019\u102c\u1038\u101e\u100a\u103a\u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u1010\u103d\u1031\u1037\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\" target=\"_blank\" rel=\"noopener noreferrer\">boxplots \u1000\u102d\u102f<\/a> \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d \u101c\u1031\u1037\u101c\u102c\u1019\u103e\u102f\u1014\u100a\u103a\u1038\u1015\u100a\u102c\u1021\u1015\u1031\u102b\u103a \u1021\u1001\u103c\u1031\u1001\u1036\u104d \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038 \u1016\u103c\u1014\u1037\u103a\u101d\u1031\u1019\u103e\u102f\u1000\u102d\u102f\u101c\u100a\u103a\u1038 \u1019\u103c\u1004\u103a\u101a\u1031\u102c\u1004\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a-<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong>boxplot(exam ~ technique,\ndata = data,\nmain = \"Exam Score by Studying Technique\",\nxlab = \"Studying Technique\",\nylab = \"Exam Score\",\ncol = \"steelblue\",\nborder = \"black\"\n)<\/strong><\/pre>\n<h3><\/h3>\n<p> <span style=\"color: #000000;\">\u1021\u101c\u102c\u1038\u1010\u1030\u104a \u101c\u1031\u1037\u101c\u102c\u1019\u103e\u102f\u1014\u100a\u103a\u1038\u1015\u100a\u102c\u1021\u1015\u1031\u102b\u103a\u1021\u1001\u103c\u1031\u1001\u1036\u104d <em>\u101c\u1000\u103a\u101b\u103e\u102d\u1021\u1006\u1004\u1037\u103a\u1019\u103b\u102c\u1038<\/em> \u1001\u103d\u1032\u101d\u1031\u1019\u103e\u102f\u1000\u102d\u102f \u1019\u103c\u1004\u103a\u101e\u102c\u1005\u1031\u101b\u1014\u103a boxplots \u1019\u103b\u102c\u1038\u1000\u102d\u102f\u101c\u100a\u103a\u1038 \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>boxplot(current_grade ~ technical,\ndata = data,\nmain = \"Current Grade by Studying Technique\",\nxlab = \"Studying Technique\",\nylab = \"Current Grade\",\ncol = \"steelblue\",\nborder = \"black\"\n)<\/strong><\/pre>\n<h3> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 2- \u1019\u1031\u102c\u103a\u1012\u101a\u103a \u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1000\u102d\u102f \u1005\u1005\u103a\u1006\u1031\u1038\u1015\u102b\u104b<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1021\u1001\u103c\u1031\u1001\u1036\u1012\u1031\u1010\u102c\u101b\u103e\u102c\u1016\u103d\u1031\u101b\u1031\u1038\u1021\u1001\u103b\u102d\u102f\u1037\u1000\u102d\u102f \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1015\u103c\u102e\u1038 \u1012\u1031\u1010\u102c\u1014\u103e\u1004\u1037\u103a\u101b\u1004\u103a\u1038\u1014\u103e\u102e\u1038\u1015\u103c\u102e\u1038\u101e\u100a\u103a\u1014\u103e\u1004\u1037\u103a\u104a ANCOVA \u1021\u1010\u103d\u1000\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u101a\u1030\u1006\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1014\u103e\u1004\u1037\u103a \u1000\u102d\u102f\u1000\u103a\u100a\u102e\u1019\u103e\u102f\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u1005\u1005\u103a\u1006\u1031\u1038\u101b\u1014\u103a \u101c\u102d\u102f\u1021\u1015\u103a\u101e\u100a\u103a-<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>covariate \u1014\u103e\u1004\u1037\u103a \u1000\u102f\u101e\u1019\u103e\u102f\u101e\u100a\u103a \u101e\u102e\u1038\u1001\u103c\u102c\u1038\u1016\u103c\u1005\u103a\u101e\u100a\u103a<\/strong> &#8211; covariate ( <em>\u101c\u1000\u103a\u101b\u103e\u102d\u1021\u1006\u1004\u1037\u103a)<\/em> \u1014\u103e\u1004\u1037\u103a \u1000\u102f\u101e\u1019\u103e\u102f <em>(\u101c\u1031\u1037\u101c\u102c\u101b\u1031\u1038\u1014\u100a\u103a\u1038\u1015\u100a\u102c)<\/em> \u101e\u100a\u103a \u1010\u1005\u103a\u1001\u102f\u1014\u103e\u1004\u1037\u103a\u1010\u1005\u103a\u1001\u102f \u101e\u102e\u1038\u1001\u103c\u102c\u1038\u1019\u1000\u1004\u103a\u1038\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1005\u1005\u103a\u1006\u1031\u1038\u101b\u1014\u103a \u101c\u102d\u102f\u1021\u1015\u103a\u101e\u100a\u103a\u104a \u1021\u1018\u101a\u103a\u1000\u103c\u1031\u102c\u1004\u1037\u103a\u1006\u102d\u102f\u101e\u1031\u102c\u103a \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1010\u103d\u1004\u103a covariate \u101f\u1030\u101e\u1031\u102c\u1021\u101e\u102f\u1036\u1038\u1021\u1014\u103e\u102f\u1014\u103a\u1038\u1000\u102d\u102f \u1011\u100a\u1037\u103a\u101e\u103d\u1004\u103a\u1038\u1001\u103c\u1004\u103a\u1038\u101e\u100a\u103a covariate \u1019\u103e\u101e\u102c\u101c\u103b\u103e\u1004\u103a \u1021\u1013\u102d\u1015\u1039\u1015\u102c\u101a\u103a\u101b\u103e\u102d\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a\u104a \u1000\u102f\u101e\u1019\u103e\u102f\u101e\u100a\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1015\u103c\u1031\u102c\u1004\u103a\u1038\u101c\u1032\u1019\u103e\u102f ( <em>\u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032<\/em> ) \u1010\u103d\u1004\u103a \u101e\u102e\u1038\u1001\u103c\u102c\u1038\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u104f \u1010\u1030\u100a\u102e\u1001\u103c\u1004\u103a\u1038<\/strong> &#8211; \u1021\u102f\u1015\u103a\u1005\u102f\u1019\u103b\u102c\u1038\u1000\u103c\u102c\u1038 \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1019\u103b\u102c\u1038 \u1010\u1030\u100a\u102e\u1019\u103e\u102f\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u1005\u1005\u103a\u1006\u1031\u1038\u101b\u1014\u103a \u101c\u102d\u102f\u1021\u1015\u103a\u101e\u100a\u103a\u104b<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">covariate \u1014\u103e\u1004\u1037\u103a \u1000\u102f\u101e\u1019\u103e\u102f\u101e\u100a\u103a \u101e\u102e\u1038\u1001\u103c\u102c\u1038\u1016\u103c\u1005\u103a\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1021\u1010\u100a\u103a\u1015\u103c\u102f\u101b\u1014\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\u1014\u103e\u1004\u1037\u103a <em>\u101c\u1031\u1037\u101c\u102c\u1019\u103e\u102f\u1014\u100a\u103a\u1038\u1005\u1014\u1005\u103a<\/em> \u1021\u1016\u103c\u1005\u103a <em>\u101c\u1000\u103a\u101b\u103e\u102d\u1021\u1006\u1004\u1037\u103a\u1000\u102d\u102f<\/em> \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d ANOVA \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;\">#fit anova model\n<\/span>anova_model &lt;- aov(current_grade ~ technique, data = data)\n<span style=\"color: #008080;\">#view summary of anova model\n<\/span>summary(anova_model)\n\n# Df Sum Sq Mean Sq F value Pr(&gt;F)\n#technical 2 74 37.21 0.599 0.552\n#Residuals 87 5406 62.14    \n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">p-value \u101e\u100a\u103a 0.05 \u1011\u1000\u103a \u1000\u103c\u102e\u1038\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a covariate ( <em>\u101c\u1000\u103a\u101b\u103e\u102d\u1021\u1006\u1004\u1037\u103a)<\/em> \u1014\u103e\u1004\u1037\u103a \u1000\u102f\u101e\u1019\u103e\u102f ( <em>\u101c\u1031\u1037\u101c\u102c\u1019\u103e\u102f\u1014\u100a\u103a\u1038\u1015\u100a\u102c<\/em> ) \u101e\u100a\u103a \u101e\u102e\u1038\u1001\u103c\u102c\u1038\u1016\u103c\u1005\u103a\u1014\u1031\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1011\u102d\u102f\u1037\u1014\u1031\u102c\u1000\u103a\u104a \u1021\u102f\u1015\u103a\u1005\u102f\u1019\u103b\u102c\u1038\u1000\u103c\u102c\u1038 \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f \u1010\u1030\u100a\u102e\u1019\u103e\u102f\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u1005\u1005\u103a\u1006\u1031\u1038\u101b\u1014\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a 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 <em>car<\/em> library to conduct Levene's Test<\/span>\nlibary(car)\n\n<span style=\"color: #008080;\">#conduct Levene's Test<\/span>\nleveneTest(technical exam, data = data)\n\n#Levene's Test for Homogeneity of Variance (center = median)\n# Df F value Pr(&gt;F)    \n#group 2 9.4324 0.0001961 ***\n#87   \n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u1005\u1005\u103a\u1006\u1031\u1038\u1019\u103e\u102f\u104f p-value \u101e\u100a\u103a 0.0001961 \u1014\u103e\u1004\u1037\u103a \u100a\u102e\u1019\u103b\u103e\u101e\u100a\u103a\u104a \u104e\u1004\u103a\u1038\u101e\u100a\u103a \u1021\u102f\u1015\u103a\u1005\u102f\u1019\u103b\u102c\u1038\u1000\u103c\u102c\u1038\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1019\u103b\u102c\u1038 \u1019\u100a\u102e\u1019\u103b\u103e\u1000\u103c\u1031\u102c\u1004\u103a\u1038\u1016\u1031\u102c\u103a\u1015\u103c\u101e\u100a\u103a\u104b \u1024\u1015\u103c\u103f\u1014\u102c\u1000\u102d\u102f \u1015\u103c\u102f\u1015\u103c\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 \u101a\u1001\u102f\u1021\u1001\u103b\u102d\u1014\u103a\u1010\u103d\u1004\u103a \u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f \u1000\u103d\u1032\u1015\u103c\u102c\u1038\u1019\u103e\u102f\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1021\u101c\u103d\u1014\u103a\u1005\u102d\u102f\u1038\u101b\u102d\u1019\u103a\u1019\u100a\u103a\u1019\u101f\u102f\u1010\u103a\u1015\u102b\u104b<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 3- ANCOVA \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1000\u102d\u102f \u1001\u103b\u102d\u1014\u103a\u100a\u103e\u102d\u1015\u102b\u104b<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u1011\u102d\u102f\u1037\u1014\u1031\u102c\u1000\u103a\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1019\u1015\u103c\u1031\u102c\u1004\u103a\u1038\u101c\u1032\u1014\u102d\u102f\u1004\u103a\u101e\u1031\u102c\u104a \u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u101e\u1030 (\u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a &#8220; \u1000\u102f\u101e\u1019\u103e\u102f&#8221; ) \u1000\u102d\u1014\u103a\u1038 <em>\u101b\u103e\u1004\u103a<\/em> \u1021\u1016\u103c\u1005\u103a <em>\u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u101b\u1019\u103e\u1010\u103a\u1000\u102d\u102f<\/em> \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d ANCOVA \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1014\u103e\u1004\u1037\u103a <em>\u1021\u1036\u101d\u1004\u103a\u1001\u103d\u1004\u103a\u1000\u103b<\/em> \u1016\u103c\u1005\u103a\u1015\u102b\u1019\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u104e\u1004\u103a\u1038\u1000\u102d\u102f\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1014\u103a\u1021\u1010\u103d\u1000\u103a \u1015\u1000\u103a\u1000\u1031\u1037\u1002\u103b\u103a\u101b\u103e\u102d Anova() \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u103b\u1000\u103a\u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1021\u1010\u103d\u1000\u103a \u1021\u1019\u103b\u102d\u102f\u1038\u1021\u1005\u102c\u1038 III \u1015\u1031\u102b\u1004\u103a\u1038\u101c\u1012\u103a\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101c\u102d\u102f\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u101e\u1010\u103a\u1019\u103e\u1010\u103a\u1014\u102d\u102f\u1004\u103a\u1005\u1031\u101b\u1014\u103a\u1021\u1010\u103d\u1000\u103a \u1021\u1019\u103b\u102d\u102f\u1038\u1021\u1005\u102c\u1038 I sum \u104f \u1005\u1010\u102f\u101b\u1014\u103a\u1038\u1021\u1019\u103b\u102d\u102f\u1038\u1021\u1005\u102c\u1038\u101e\u100a\u103a \u1019\u100a\u103a\u101e\u100a\u1037\u103a\u1021\u1005\u102e\u1021\u1005\u1025\u103a\u1015\u1031\u102b\u103a\u1010\u103d\u1004\u103a\u1019\u1030\u1010\u100a\u103a\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a\u104a \u1000\u103c\u102d\u102f\u1010\u1004\u103a\u1001\u1014\u1037\u103a\u1019\u103e\u1014\u103a\u1038\u101e\u1030\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1019\u1031\u102c\u103a\u1012\u101a\u103a\u1011\u1032\u101e\u102d\u102f\u1037 \u1011\u100a\u1037\u103a\u101e\u103d\u1004\u103a\u1038\u1011\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#load <em>car<\/em> library<\/span>\nlibrary(car)\n\n<span style=\"color: #008080;\">#fit ANCOVA model\n<\/span>ancova_model &lt;- aov(exam ~ technique + current_grade, data = data)\n\n<span style=\"color: #008080;\">#view summary of model\n<\/span>Anova(ancova_model, type=\"III\") \n\n#Answer: exam\n# Sum Sq Df F value Pr(&gt;F)    \n#(Intercept) 7161.2 1 201.4621 &lt; 2.2e-16 ***\n#technical 1242.9 2 17.4830 4.255e-07 ***\n#current_grade 12.3 1 0.3467 0.5576    \n#Residuals 3057.0 86         \n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\"><em>\u1014\u100a\u103a\u1038\u1015\u100a\u102c<\/em> \u1021\u1010\u103d\u1000\u103a p-\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u101e\u100a\u103a \u1021\u101c\u103d\u1014\u103a\u1014\u102d\u1019\u1037\u103a\u1000\u103b\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\u104a \u101c\u1031\u1037\u101c\u102c\u1019\u103e\u102f\u1014\u100a\u103a\u1038\u1015\u100a\u102c\u101e\u100a\u103a \u101c\u1000\u103a\u101b\u103e\u102d\u1021\u1010\u1014\u103a\u1038\u1000\u102d\u102f \u1011\u102d\u1014\u103a\u1038\u1001\u103b\u102f\u1015\u103a\u1015\u103c\u102e\u1038\u1014\u1031\u102c\u1000\u103a\u1010\u103d\u1004\u103a\u1015\u1004\u103a \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u101b\u1019\u103e\u1010\u103a\u1019\u103b\u102c\u1038\u1021\u1015\u1031\u102b\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 \u1021\u1000\u103b\u102d\u102f\u1038\u101e\u1000\u103a\u101b\u1031\u102c\u1000\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u100a\u103d\u103e\u1014\u103a\u1015\u103c\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 4- Post-hoc \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1001\u103c\u1004\u103a\u1038\u104b<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">ANCOVA \u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u1000 <em>\u101c\u1031\u1037\u101c\u102c\u1019\u103e\u102f\u1014\u100a\u103a\u1038\u1015\u100a\u102c\u101e\u100a\u103a<\/em> \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u101b\u1019\u103e\u1010\u103a\u1019\u103b\u102c\u1038\u1021\u1015\u1031\u102b\u103a \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1021\u1001\u103b\u1000\u103a\u1021\u101c\u1010\u103a\u1019\u103b\u102c\u1038 \u101e\u102d\u101e\u102d\u101e\u102c\u101e\u102c\u101e\u1000\u103a\u101b\u1031\u102c\u1000\u103a\u1019\u103e\u102f\u101b\u103e\u102d\u1000\u103c\u1031\u102c\u1004\u103a\u1038 \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1021\u102c\u1038\u1015\u103c\u1031\u102c\u1015\u103c\u101e\u1031\u102c\u103a\u101c\u100a\u103a\u1038 \u1019\u100a\u103a\u101e\u100a\u1037\u103a\u101c\u1031\u1037\u101c\u102c\u1019\u103e\u102f\u1014\u100a\u103a\u1038\u1015\u100a\u102c\u1019\u103b\u102c\u1038 \u1000\u103d\u102c\u1001\u103c\u102c\u1038\u101e\u100a\u103a\u1000\u102d\u102f \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u101e\u100a\u103a <a href=\"https:\/\/statorials.org\" target=\"_blank\" rel=\"noopener noreferrer\">post hoc \u1005\u1005\u103a\u1006\u1031\u1038\u1019\u103e\u102f<\/a> \u1015\u103c\u102f\u101c\u102f\u1015\u103a\u101b\u1014\u103a \u101c\u102d\u102f\u1021\u1015\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u104e\u1004\u103a\u1038\u1000\u102d\u102f\u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u101b\u1014\u103a\u104a \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 R \u101b\u103e\u102d <strong>multcomp<\/strong> \u1015\u1000\u103a\u1000\u1031\u1037\u1002\u103a\u101b\u103e\u102d glht() \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u103b\u1000\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\u101e\u100a\u103a-<\/span><\/p>\n<pre style=\"background-color: #e5e5e5; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#load the <em>multcomp<\/em> library<\/span>\nlibrary(multicomp)\n\n<span style=\"color: #008080;\">#fit the ANCOVA model\n<\/span>ancova_model &lt;- aov(exam ~ technique + current_grade, data = data)\n\n<span style=\"color: #008080;\">#define the post hoc comparisons to make\n<\/span>postHocs &lt;- glht(ancova_model, linfct = mcp(technique = \"Tukey\"))\n\n<span style=\"color: #008080;\">#view a summary of the post hoc comparisons\n<\/span>summary(postHocs)\n\n#Multiple Comparisons of Means: Tukey Contrasts\n#\n#Fit: aov(formula = exam ~ technique + current_grade, data = data)\n#\n#Linear Assumptions:\n#Estimate Std. Error t value Pr(&gt;|t|)    \n#B - A == 0 -6.711 1.540 -4.358 0.000109 ***\n#C - A == 0 -8.736 1.549 -5.640 &lt; 1e-04 ***\n#C - B == 0 -2.025 1.545 -1.311 0.393089    \n\n<span style=\"color: #008080;\">#view the confidence intervals associated with the multiple comparisons\n<\/span>confint(postHocs)\n\n# Simultaneous Confidence Intervals\n#\n#Multiple Comparisons of Means: Tukey Contrasts\n#\n#Fit: aov(formula = exam ~ technique + current_grade, data = data)\n#\n#Quantile = 2.3845\n#95% family-wise confidence level\n#\n#Linear Assumptions:\n# Estimate lwr upr     \n#B - A == 0 -6.7112 -10.3832 -3.0392\n#C - A == 0 -8.7364 -12.4302 -5.0426\n#C - B == 0 -2.0252 -5.7091 1.6588\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u101b\u101c\u1012\u103a\u1019\u103e\u104a \u101c\u1031\u1037\u101c\u102c\u1001\u103c\u1004\u103a\u1038\u1014\u100a\u103a\u1038\u1015\u100a\u102c <em>A<\/em> \u1014\u103e\u1004\u1037\u103a \u101c\u1031\u1037\u101c\u102c\u1001\u103c\u1004\u103a\u1038\u1014\u100a\u103a\u1038\u1015\u100a\u102c <em>B<\/em> (p-value: 0,000109) \u1021\u1000\u103c\u102c\u1038 \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u101b\u101c\u1012\u103a\u1019\u103b\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\u1001\u103b\u1000\u103a ( <em>\u03b1<\/em> = 0.05) \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\u101e\u100a\u103a <em>\u104b<\/em> (p-value: &lt;1e-04)\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1014\u100a\u103a\u1038\u1015\u100a\u102c\u1019\u103b\u102c\u1038 <em>B<\/em> \u1014\u103e\u1004\u1037\u103a <em>C<\/em> \u1021\u1000\u103c\u102c\u1038\u1010\u103d\u1004\u103a \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\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 (\u03b1 = 0.05) <em>\u1019\u101b\u103e\u102d\u1000\u103c\u1031\u102c\u1004\u103a\u1038<\/em> \u1000\u102d\u102f\u101c\u100a\u103a\u1038 \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> <span style=\"color: #000000;\">\u1014\u100a\u103a\u1038\u1005\u1014\u1005\u103a\u1019\u103b\u102c\u1038\u1000\u103c\u102c\u1038\u1000\u102c\u101c\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a \u101a\u102f\u1036\u1000\u103c\u100a\u103a\u1019\u103e\u102f\u101e\u100a\u103a \u1024\u1010\u103d\u1031\u1037\u101b\u103e\u102d\u1001\u103b\u1000\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1015\u1036\u1037\u1015\u102d\u102f\u1038\u1015\u1031\u1038\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1011\u102d\u102f\u1037\u1000\u103c\u1031\u102c\u1004\u1037\u103a\u104a \u1021\u1010\u1014\u103a\u1038\u1011\u1032\u1010\u103d\u1004\u103a \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u104f \u101c\u1000\u103a\u101b\u103e\u102d\u1021\u1010\u1014\u103a\u1038\u1000\u102d\u102f \u1011\u102d\u1014\u103a\u1038\u1001\u103b\u102f\u1015\u103a\u1015\u103c\u102e\u1038\u1014\u1031\u102c\u1000\u103a\u1010\u103d\u1004\u103a\u1015\u1004\u103a \u1014\u100a\u103a\u1038\u1015\u100a\u102c <em>B<\/em> \u1014\u103e\u1004\u1037\u103a <em>C<\/em> \u1014\u103e\u1004\u1037\u103a \u1014\u103e\u102d\u102f\u1004\u103a\u1038\u101a\u103e\u1009\u103a\u1015\u102b\u1000 \u101c\u1031\u1037\u101c\u102c\u1019\u103e\u102f\u1014\u100a\u103a\u1038\u1005\u1014\u1005\u103a <em>A<\/em> \u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1001\u103c\u1004\u103a\u1038\u1016\u103c\u1004\u1037\u103a \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u1019\u103b\u102c\u1038\u1021\u1010\u103d\u1000\u103a \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u101e\u102d\u101e\u102d\u101e\u102c\u101e\u102c \u1019\u103c\u1004\u1037\u103a\u1019\u102c\u1038\u101e\u1031\u102c \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u1021\u1006\u1004\u1037\u103a\u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u1000\u1031\u102c\u1000\u103a\u1001\u103b\u1000\u103a\u1001\u103b\u1014\u102d\u102f\u1004\u103a\u1015\u102b\u101e\u100a\u103a\u104b<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u1024\u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u101e\u100a\u103a R \u1016\u103c\u1004\u1037\u103a ANCOVA \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 \u1025\u1015\u1019\u102c\u1015\u1031\u1038\u1011\u102c\u1038\u101e\u100a\u103a\u104b \u1025\u1015\u1019\u102c- R in ANCOVA \u101c\u1031\u1037\u101c\u102c\u1019\u103e\u102f\u1014\u100a\u103a\u1038\u1015\u100a\u102c\u101e\u100a\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d \u1005\u102c\u1019\u1031\u1038\u1015\u103d\u1032\u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u1021\u1015\u1031\u102b\u103a \u101e\u1000\u103a\u101b\u1031\u102c\u1000\u103a\u1019\u103e\u102f\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u1005\u1019\u103a\u1038\u101e\u1015\u103a\u101b\u1014\u103a ANCOVA \u1000\u102d\u102f \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1015\u102b\u1019\u100a\u103a\u104b \u1014\u100a\u103a\u1038\u1015\u100a\u102c\u101c\u1031\u1037\u101c\u102c\u1019\u103e\u102f &#8211; \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u101c\u102d\u102f\u101e\u1031\u102c \u101e\u102e\u1038\u1001\u103c\u102c\u1038\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a \u101c\u1000\u103a\u101b\u103e\u102d \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u1021\u1006\u1004\u1037\u103a &#8211; \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u1011\u100a\u1037\u103a\u101e\u103d\u1004\u103a\u1038\u1005\u1009\u103a\u1038\u1005\u102c\u1038\u101c\u102d\u102f\u101e\u1031\u102c \u1021\u1005\u102f\u1021\u101d\u1031\u1038 \u101e\u102f\u1036\u1038\u101e\u1015\u103a\u1001\u103b\u1000\u103a\u101b\u1019\u103e\u1010\u103a &#8211; \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u101c\u102d\u102f\u101e\u1031\u102c \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1019\u103b\u102c\u1038 \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 \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038 90 \u1026\u1038\u1021\u102c\u1038 \u1000\u103b\u1015\u1014\u103a\u1038\u1021\u102f\u1015\u103a\u1005\u102f 30 \u1019\u103e \u1021\u102f\u1015\u103a\u1005\u102f\u101e\u102f\u1036\u1038\u1005\u102f\u1001\u103d\u1032\u1011\u102c\u1038\u101e\u100a\u103a\u104b \u1012\u1031\u1010\u102c\u1021\u1010\u103d\u1032\u1010\u103d\u1004\u103a \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u1010\u1005\u103a\u1026\u1038\u1005\u102e\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u101e\u1031\u102c \u101c\u1031\u1037\u101c\u102c\u1019\u103e\u102f\u1014\u100a\u103a\u1038\u1005\u1014\u1005\u103a (A\u104a B \u104a \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a C) \u104a \u101c\u1031\u1037\u101c\u102c\u1019\u103e\u102f\u1014\u100a\u103a\u1038\u1015\u100a\u102c\u1000\u102d\u102f \u1005\u1010\u1004\u103a\u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u1001\u103b\u102d\u1014\u103a\u1010\u103d\u1004\u103a \u1021\u1010\u1014\u103a\u1038\u1010\u103d\u1004\u103a\u1038\u101b\u103e\u102d \u104e\u1004\u103a\u1038\u1010\u102d\u102f\u1037\u104f [&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 - Statology \u1010\u103d\u1004\u103a ANCOVA \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<\/title>\n<meta name=\"description\" content=\"\u1024\u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u1010\u103d\u1004\u103a R \u1016\u103c\u1004\u1037\u103a ANCOVA (\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1000\u102d\u102f \u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u1001\u103c\u1004\u103a\u1038) \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 \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1011\u102c\u1038\u101e\u100a\u103a\u104b\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/statorials.org\/my\/ancova-in-r\/\" \/>\n<meta property=\"og:locale\" content=\"my_MM\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"R - Statology \u1010\u103d\u1004\u103a ANCOVA \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\" \/>\n<meta property=\"og:description\" content=\"\u1024\u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u1010\u103d\u1004\u103a R \u1016\u103c\u1004\u1037\u103a ANCOVA (\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1000\u102d\u102f \u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u1001\u103c\u1004\u103a\u1038) \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 \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1011\u102c\u1038\u101e\u100a\u103a\u104b\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/my\/ancova-in-r\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-29T18:17:31+00:00\" \/>\n<meta name=\"author\" content=\"Benjamin Anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"Benjamin Anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/my\/ancova-in-r\/\",\"url\":\"https:\/\/statorials.org\/my\/ancova-in-r\/\",\"name\":\"R - Statology \u1010\u103d\u1004\u103a ANCOVA \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\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/my\/#website\"},\"datePublished\":\"2023-07-29T18:17:31+00:00\",\"dateModified\":\"2023-07-29T18:17:31+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/my\/#\/schema\/person\/e47470981684a202f7ed4c0cb1e10097\"},\"description\":\"\u1024\u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u1010\u103d\u1004\u103a R \u1016\u103c\u1004\u1037\u103a ANCOVA (\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1000\u102d\u102f \u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u1001\u103c\u1004\u103a\u1038) \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 \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1011\u102c\u1038\u101e\u100a\u103a\u104b\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/my\/ancova-in-r\/#breadcrumb\"},\"inLanguage\":\"my-MM\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/my\/ancova-in-r\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/my\/ancova-in-r\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"\u1021\u102d\u1019\u103a\",\"item\":\"https:\/\/statorials.org\/my\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"R \u1016\u103c\u1004\u1037\u103a ancova \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\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/my\/#website\",\"url\":\"https:\/\/statorials.org\/my\/\",\"name\":\"Statorials\",\"description\":\"\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1006\u102d\u102f\u1004\u103a\u101b\u102c \u1021\u101b\u100a\u103a\u1021\u1001\u103b\u1004\u103a\u1038\u1021\u1010\u103d\u1000\u103a \u101e\u1004\u1037\u103a\u101c\u1019\u103a\u1038\u100a\u103d\u103e\u1014\u103a\u1001\u103b\u1000\u103a\u104b\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/my\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"my-MM\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/my\/#\/schema\/person\/e47470981684a202f7ed4c0cb1e10097\",\"name\":\"Benjamin Anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"my-MM\",\"@id\":\"https:\/\/statorials.org\/my\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/my\/wp-content\/uploads\/2023\/11\/Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/my\/wp-content\/uploads\/2023\/11\/Benjamin-Anderson-96x96.jpg\",\"caption\":\"Benjamin Anderson\"},\"description\":\"\u1019\u1004\u103a\u1039\u1002\u101c\u102c\u1015\u102b\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u101e\u100a\u103a \u1021\u1004\u103c\u102d\u1019\u103a\u1038\u1005\u102c\u1038 \u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038 \u1015\u102b\u1019\u1031\u102c\u1000\u1039\u1001 \u1018\u1004\u103a\u1002\u103b\u1019\u1004\u103a\u1016\u103c\u1005\u103a\u1015\u103c\u102e\u1038 \u101e\u102e\u1038\u101e\u1014\u1037\u103a Statorials \u1006\u101b\u102c\u1021\u1016\u103c\u1005\u103a \u101c\u103e\u100a\u1037\u103a\u1015\u1010\u103a\u1015\u102b\u101e\u100a\u103a\u104b \u1005\u102c\u101b\u1004\u103a\u1038\u1007\u101a\u102c\u1038\u1014\u101a\u103a\u1015\u101a\u103a\u1010\u103d\u1004\u103a \u1000\u103b\u101a\u103a\u1015\u103c\u1014\u1037\u103a\u101e\u1031\u102c\u1021\u1010\u103d\u1031\u1037\u1021\u1000\u103c\u102f\u1036\u1014\u103e\u1004\u1037\u103a \u1000\u103b\u103d\u1019\u103a\u1038\u1000\u103b\u1004\u103a\u1019\u103e\u102f\u1014\u103e\u1004\u1037\u103a\u1021\u1010\u1030\u104a Statorials \u1019\u103e\u1010\u1005\u103a\u1006\u1004\u1037\u103a \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1001\u103d\u1014\u103a\u1021\u102c\u1038\u1016\u103c\u1005\u103a\u1005\u1031\u101b\u1014\u103a\u1021\u1010\u103d\u1000\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u104f\u1021\u101e\u102d\u1015\u100a\u102c\u1000\u102d\u102f \u1019\u103b\u103e\u101d\u1031\u101c\u102d\u102f\u1015\u102b\u101e\u100a\u103a\u104b \u1015\u102d\u102f\u101e\u102d\u1010\u101a\u103a\u104b\",\"sameAs\":[\"https:\/\/statorials.org\/my\"]}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"R - Statology \u1010\u103d\u1004\u103a ANCOVA \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","description":"\u1024\u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u1010\u103d\u1004\u103a R \u1016\u103c\u1004\u1037\u103a ANCOVA (\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1000\u102d\u102f \u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u1001\u103c\u1004\u103a\u1038) \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 \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1011\u102c\u1038\u101e\u100a\u103a\u104b","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/statorials.org\/my\/ancova-in-r\/","og_locale":"my_MM","og_type":"article","og_title":"R - Statology \u1010\u103d\u1004\u103a ANCOVA \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","og_description":"\u1024\u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u1010\u103d\u1004\u103a R \u1016\u103c\u1004\u1037\u103a ANCOVA (\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1000\u102d\u102f \u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u1001\u103c\u1004\u103a\u1038) \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 \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1011\u102c\u1038\u101e\u100a\u103a\u104b","og_url":"https:\/\/statorials.org\/my\/ancova-in-r\/","og_site_name":"Statorials","article_published_time":"2023-07-29T18:17:31+00:00","author":"Benjamin Anderson","twitter_card":"summary_large_image","twitter_misc":{"Written by":"Benjamin Anderson","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/statorials.org\/my\/ancova-in-r\/","url":"https:\/\/statorials.org\/my\/ancova-in-r\/","name":"R - Statology \u1010\u103d\u1004\u103a ANCOVA \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","isPartOf":{"@id":"https:\/\/statorials.org\/my\/#website"},"datePublished":"2023-07-29T18:17:31+00:00","dateModified":"2023-07-29T18:17:31+00:00","author":{"@id":"https:\/\/statorials.org\/my\/#\/schema\/person\/e47470981684a202f7ed4c0cb1e10097"},"description":"\u1024\u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u1010\u103d\u1004\u103a R \u1016\u103c\u1004\u1037\u103a ANCOVA (\u1000\u103d\u1032\u101c\u103d\u1032\u1019\u103e\u102f\u1000\u102d\u102f \u1001\u103d\u1032\u1001\u103c\u1019\u103a\u1038\u1005\u102d\u1010\u103a\u1016\u103c\u102c\u1001\u103c\u1004\u103a\u1038) \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 \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1011\u102c\u1038\u101e\u100a\u103a\u104b","breadcrumb":{"@id":"https:\/\/statorials.org\/my\/ancova-in-r\/#breadcrumb"},"inLanguage":"my-MM","potentialAction":[{"@type":"ReadAction","target":["https:\/\/statorials.org\/my\/ancova-in-r\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/statorials.org\/my\/ancova-in-r\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"\u1021\u102d\u1019\u103a","item":"https:\/\/statorials.org\/my\/"},{"@type":"ListItem","position":2,"name":"R \u1016\u103c\u1004\u1037\u103a ancova \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"}]},{"@type":"WebSite","@id":"https:\/\/statorials.org\/my\/#website","url":"https:\/\/statorials.org\/my\/","name":"Statorials","description":"\u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1006\u102d\u102f\u1004\u103a\u101b\u102c \u1021\u101b\u100a\u103a\u1021\u1001\u103b\u1004\u103a\u1038\u1021\u1010\u103d\u1000\u103a \u101e\u1004\u1037\u103a\u101c\u1019\u103a\u1038\u100a\u103d\u103e\u1014\u103a\u1001\u103b\u1000\u103a\u104b","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/statorials.org\/my\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"my-MM"},{"@type":"Person","@id":"https:\/\/statorials.org\/my\/#\/schema\/person\/e47470981684a202f7ed4c0cb1e10097","name":"Benjamin Anderson","image":{"@type":"ImageObject","inLanguage":"my-MM","@id":"https:\/\/statorials.org\/my\/#\/schema\/person\/image\/","url":"https:\/\/statorials.org\/my\/wp-content\/uploads\/2023\/11\/Benjamin-Anderson-96x96.jpg","contentUrl":"https:\/\/statorials.org\/my\/wp-content\/uploads\/2023\/11\/Benjamin-Anderson-96x96.jpg","caption":"Benjamin Anderson"},"description":"\u1019\u1004\u103a\u1039\u1002\u101c\u102c\u1015\u102b\u104a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u101e\u100a\u103a \u1021\u1004\u103c\u102d\u1019\u103a\u1038\u1005\u102c\u1038 \u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038 \u1015\u102b\u1019\u1031\u102c\u1000\u1039\u1001 \u1018\u1004\u103a\u1002\u103b\u1019\u1004\u103a\u1016\u103c\u1005\u103a\u1015\u103c\u102e\u1038 \u101e\u102e\u1038\u101e\u1014\u1037\u103a Statorials \u1006\u101b\u102c\u1021\u1016\u103c\u1005\u103a \u101c\u103e\u100a\u1037\u103a\u1015\u1010\u103a\u1015\u102b\u101e\u100a\u103a\u104b \u1005\u102c\u101b\u1004\u103a\u1038\u1007\u101a\u102c\u1038\u1014\u101a\u103a\u1015\u101a\u103a\u1010\u103d\u1004\u103a \u1000\u103b\u101a\u103a\u1015\u103c\u1014\u1037\u103a\u101e\u1031\u102c\u1021\u1010\u103d\u1031\u1037\u1021\u1000\u103c\u102f\u1036\u1014\u103e\u1004\u1037\u103a \u1000\u103b\u103d\u1019\u103a\u1038\u1000\u103b\u1004\u103a\u1019\u103e\u102f\u1014\u103e\u1004\u1037\u103a\u1021\u1010\u1030\u104a Statorials \u1019\u103e\u1010\u1005\u103a\u1006\u1004\u1037\u103a \u1000\u103b\u1031\u102c\u1004\u103a\u1038\u101e\u102c\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1001\u103d\u1014\u103a\u1021\u102c\u1038\u1016\u103c\u1005\u103a\u1005\u1031\u101b\u1014\u103a\u1021\u1010\u103d\u1000\u103a \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u104f\u1021\u101e\u102d\u1015\u100a\u102c\u1000\u102d\u102f \u1019\u103b\u103e\u101d\u1031\u101c\u102d\u102f\u1015\u102b\u101e\u100a\u103a\u104b \u1015\u102d\u102f\u101e\u102d\u1010\u101a\u103a\u104b","sameAs":["https:\/\/statorials.org\/my"]}]}},"yoast_meta":{"yoast_wpseo_title":"","yoast_wpseo_metadesc":"","yoast_wpseo_canonical":""},"_links":{"self":[{"href":"https:\/\/statorials.org\/my\/wp-json\/wp\/v2\/posts\/483"}],"collection":[{"href":"https:\/\/statorials.org\/my\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/statorials.org\/my\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/statorials.org\/my\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/statorials.org\/my\/wp-json\/wp\/v2\/comments?post=483"}],"version-history":[{"count":0,"href":"https:\/\/statorials.org\/my\/wp-json\/wp\/v2\/posts\/483\/revisions"}],"wp:attachment":[{"href":"https:\/\/statorials.org\/my\/wp-json\/wp\/v2\/media?parent=483"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/statorials.org\/my\/wp-json\/wp\/v2\/categories?post=483"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/statorials.org\/my\/wp-json\/wp\/v2\/tags?post=483"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}