{"id":3348,"date":"2023-07-17T23:22:52","date_gmt":"2023-07-17T23:22:52","guid":{"rendered":"https:\/\/statorials.org\/my\/%e1%80%9e%e1%80%af%e1%80%b6%e1%80%b8%e1%80%9c%e1%80%99%e1%80%ba%e1%80%b8-anova-python\/"},"modified":"2023-07-17T23:22:52","modified_gmt":"2023-07-17T23:22:52","slug":"%e1%80%9e%e1%80%af%e1%80%b6%e1%80%b8%e1%80%9c%e1%80%99%e1%80%ba%e1%80%b8-anova-python","status":"publish","type":"post","link":"https:\/\/statorials.org\/my\/%e1%80%9e%e1%80%af%e1%80%b6%e1%80%b8%e1%80%9c%e1%80%99%e1%80%ba%e1%80%b8-anova-python\/","title":{"rendered":"Python \u1010\u103d\u1004\u103a three-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\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 Python \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- Python \u101b\u103e\u102d \u101e\u102f\u1036\u1038\u101c\u1019\u103a\u1038\u101e\u103d\u102c\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;\">Python \u1010\u103d\u1004\u103a \u1024\u101e\u102f\u1036\u1038\u1014\u100a\u103a\u1038 ANOVA \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 \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\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 pandas DataFrame \u1000\u102d\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;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008000;\">import<\/span> numpy <span style=\"color: #008000;\">as<\/span> np\n<span style=\"color: #008000;\">import<\/span> pandas <span style=\"color: #008000;\">as<\/span> pd\n\n<span style=\"color: #008080;\">#createDataFrame\n<\/span>df = pd. <span style=\"color: #3366ff;\">DataFrame<\/span> ({' <span style=\"color: #ff0000;\">program<\/span> ': <span style=\"color: #3366ff;\">np.repeat<\/span> ([1,2],20),\n                   ' <span style=\"color: #ff0000;\">gender<\/span> ': np. <span style=\"color: #3366ff;\">tile<\/span> (np. <span style=\"color: #3366ff;\">repeat<\/span> (['M', 'F'], 10), 2),\n                   ' <span style=\"color: #ff0000;\">division<\/span> ': np. <span style=\"color: #3366ff;\">tile<\/span> (np. <span style=\"color: #3366ff;\">repeat<\/span> ([1, 2], 5), 4),\n                   ' <span style=\"color: #ff0000;\">height<\/span> ': [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 ten rows of DataFrame \n<\/span>df[:10]\n\n\tprogram gender division height\n0 1 M 1 7\n1 1 M 1 7\n2 1 M 1 8\n3 1 M 1 8\n4 1 M 1 7\n5 1 M 2 6\n6 1 M 2 6\n7 1 M 2 5\n8 1 M 2 6\n9 1 M 2 5\n<\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 2- 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>statsmodels<\/strong> \u1005\u102c\u1000\u103c\u100a\u1037\u103a\u1010\u102d\u102f\u1000\u103a\u1019\u103e <strong>anova_lm()<\/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\u101e\u100a\u103a\u104b<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <span style=\"color: #000000;\"><strong><span style=\"color: #008000;\">import<\/span> statsmodels. <span style=\"color: #3366ff;\">api<\/span> <span style=\"color: #008000;\">as<\/span> sm\n<span style=\"color: #008000;\">from<\/span> statsmodels. <span style=\"color: #3366ff;\">formula<\/span> . <span style=\"color: #3366ff;\">api<\/span> <span style=\"color: #008000;\">import<\/span> ols\n\n<span style=\"color: #008080;\">#perform three-way ANOVA\n<\/span>model = ols(\"\"\"height ~ C(program) + C(gender) + C(division) +\n               C(program):C(gender) + C(program):C(division) + C(gender):C(division) +\n               C(program):C(gender):C(division)\"\"\", data=df) <span style=\"color: #3366ff;\">.fit<\/span> ()\n\nsm. <span style=\"color: #3366ff;\">stats<\/span> . <span style=\"color: #3366ff;\">anova_lm<\/span> (model, typ= <span style=\"color: #008000;\">2<\/span> )\n\n\t                          sum_sq df F PR(&gt;F)\nC(program) 3.610000e+01 1.0 6.563636e+01 2.983934e-09\nC(gender) 6.760000e+01 1.0 1.229091e+02 1.714432e-12\nC(division) 1.960000e+01 1.0 3.563636e+01 1.185218e-06\nC(program):C(gender) 2.621672e-30 1.0 4.766677e-30 1.000000e+00\nC(program):C(division) 4.000000e-01 1.0 7.272727e-01 4.001069e-01\nC(gender):C(division) 1.000000e-01 1.0 1.818182e-01 6.726702e-01\nC(program):C(gender):C(division) 1.000000e-01 1.0 1.818182e-01 6.726702e-01\nResidual 1.760000e+01 32.0 NaN NaN<\/strong><\/span><\/pre>\n<p> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 3- \u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1018\u102c\u101e\u102c\u1015\u103c\u1014\u103a\u1015\u102b\u104b<\/strong><\/span><\/p>\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;\">\u1021\u1001\u103b\u1000\u103a\u101e\u102f\u1036\u1038\u1001\u103b\u1000\u103a\u1005\u102e (\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\u1019\u103e\u102f) \u101e\u100a\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b p-\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103b\u102c\u1038\u1016\u103c\u1004\u1037\u103a \u1005\u102c\u101b\u1004\u103a\u1038\u1021\u1004\u103a\u1038\u1021\u101b \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u1000\u103c\u1031\u102c\u1004\u103a\u1038\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><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u1015\u101b\u102d\u102f\u1002\u101b\u1019\u103a<\/strong> P-\u1010\u1014\u103a\u1016\u102d\u102f\u1038- 0.00000000298<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>Gender<\/strong> P-value: 0.00000000000171<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u100c\u102c\u1014\u1001\u103d\u1032<\/strong> P-\u1010\u1014\u103a\u1016\u102d\u102f\u1038: 0.00000185<\/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 Python \u101b\u103e\u102d \u1021\u1001\u103c\u102c\u1038\u101e\u1031\u102c 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-python\/\" target=\"_blank\" rel=\"noopener\">Python \u1010\u103d\u1004\u103a One-Way ANOVA \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1014\u100a\u103a\u1038<\/a><br \/> <a href=\"https:\/\/statorials.org\/my\/python-anova-bidirectional\/\" target=\"_blank\" rel=\"noopener\">Python \u1010\u103d\u1004\u103a Two-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\u1014\u100a\u103a\u1038\u104b<\/a><br \/> <a href=\"https:\/\/statorials.org\/my\/\u1011\u1015\u103a\u1001\u102b\u1010\u101c\u1032\u101c\u1032-\u1010\u102d\u102f\u1004\u103a\u1038\u1010\u102c\u1019\u103e\u102f-anova-python\/\" target=\"_blank\" rel=\"noopener\">Python \u1010\u103d\u1004\u103a \u1011\u1015\u103a\u1001\u102b\u1010\u101c\u1032\u101c\u1032 \u1010\u102d\u102f\u1004\u103a\u1038\u1010\u102c\u1014\u100a\u103a\u1038 ANOVA \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1014\u100a\u103a\u1038<\/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 Python \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- Python \u101b\u103e\u102d \u101e\u102f\u1036\u1038\u101c\u1019\u103a\u1038\u101e\u103d\u102c\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 \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 \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 [&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>Python - Statorials \u1010\u103d\u1004\u103a Three-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\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 Python \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 \u1025\u1015\u1019\u102c\u1010\u1005\u103a\u1001\u102f\u1016\u103c\u1004\u1037\u103a \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\/\u101e\u102f\u1036\u1038\u101c\u1019\u103a\u1038-anova-python\/\" 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