{"id":853,"date":"2023-07-28T13:03:16","date_gmt":"2023-07-28T13:03:16","guid":{"rendered":"https:\/\/statorials.org\/my\/python-anova-bidirectional\/"},"modified":"2023-07-28T13:03:16","modified_gmt":"2023-07-28T13:03:16","slug":"python-anova-bidirectional","status":"publish","type":"post","link":"https:\/\/statorials.org\/my\/python-anova-bidirectional\/","title":{"rendered":"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"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/my\/\u1014\u103e\u1005\u103a\u101c\u1019\u103a\u1038-anova\/\" target=\"_blank\" rel=\"noopener\">\u1014\u103e\u1005\u103a\u101c\u1019\u103a\u1038\u101e\u103d\u102c\u1038 ANOVA \u1000\u102d\u102f \u1021\u1001\u103b\u1000\u103a\u1014\u103e\u1005\u103a\u1001\u103b\u1000\u103a<\/a> \u1001\u103d\u1032\u1015\u103c\u102e\u1038 \u1001\u103d\u1032\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\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1014\u103e\u1005\u103a\u101c\u1019\u103a\u1038\u101e\u103d\u102c\u1038 ANOVA \u104f \u101b\u100a\u103a\u101b\u103d\u101a\u103a\u1001\u103b\u1000\u103a\u1019\u103e\u102c \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1010\u1005\u103a\u1001\u102f\u1021\u1015\u1031\u102b\u103a \u1021\u1001\u103b\u1000\u103a\u1014\u103e\u1005\u103a\u1001\u103b\u1000\u103a\u104f \u1021\u1000\u103b\u102d\u102f\u1038\u101e\u1000\u103a\u101b\u1031\u102c\u1000\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a\u1014\u103e\u1004\u1037\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1015\u1031\u102b\u103a\u101b\u103e\u102d \u1021\u1001\u103b\u1000\u103a\u1014\u103e\u1005\u103a\u1001\u102f\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\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1024\u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u1010\u103d\u1004\u103a Python \u1010\u103d\u1004\u103a \u1014\u103e\u1005\u103a\u101c\u1019\u103a\u1038\u101e\u103d\u102c\u1038 ANOVA \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1014\u100a\u103a\u1038\u1000\u102d\u102f \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1011\u102c\u1038\u101e\u100a\u103a\u104b<\/span><\/p>\n<h2> <span style=\"color: #000000;\"><strong>\u1025\u1015\u1019\u102c- Python \u101b\u103e\u102d \u1014\u103e\u1005\u103a\u101c\u1019\u103a\u1038\u101e\u103d\u102c\u1038 ANOVA<\/strong><\/span><\/h2>\n<p> <span style=\"color: #000000;\">\u101b\u102f\u1000\u1039\u1001\u1017\u1031\u1012\u1015\u100a\u102c\u101b\u103e\u1004\u103a\u1010\u1005\u103a\u1026\u1038\u101e\u100a\u103a \u1014\u1031\u101b\u1031\u102c\u1004\u103a\u1001\u103c\u100a\u103a\u1014\u103e\u1004\u1037\u103a \u1011\u102d\u1010\u103d\u1031\u1037\u1019\u103e\u102f\u1021\u1000\u103c\u102d\u1019\u103a\u101b\u1031\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u1021\u1015\u1004\u103a\u1000\u103c\u102e\u1038\u1011\u103d\u102c\u1038\u1019\u103e\u102f\u1021\u1015\u1031\u102b\u103a \u101c\u103d\u103e\u1019\u103a\u1038\u1019\u102d\u102f\u1038\u1019\u103e\u102f\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u101e\u102d\u101c\u102d\u102f\u101e\u100a\u103a\u104b \u1021\u1005\u1031\u1037 30 \u1000\u102d\u102f \u1005\u102d\u102f\u1000\u103a\u1015\u103b\u102d\u102f\u1038\u1015\u103c\u102e\u1038 \u1014\u1031\u101b\u1031\u102c\u1004\u103a\u1001\u103c\u100a\u103a\u1014\u103e\u1004\u1037\u103a \u101b\u1031\u101c\u1031\u102c\u1004\u103a\u1038\u1000\u103c\u102d\u1019\u103a\u1014\u103e\u102f\u1014\u103a\u1038 \u1019\u1010\u1030\u100a\u102e\u101e\u1031\u102c \u1021\u1001\u103c\u1031\u1021\u1014\u1031\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a \u1014\u103e\u1005\u103a\u101c\u1000\u103c\u102c \u1000\u103c\u102e\u1038\u1011\u103d\u102c\u1038\u1005\u1031\u1015\u102b\u101e\u100a\u103a\u104b \u1014\u103e\u1005\u103a\u101c\u1000\u103c\u102c\u1015\u103c\u102e\u1038\u1014\u1031\u102c\u1000\u103a \u1021\u1015\u1004\u103a\u1010\u1005\u103a\u1015\u1004\u103a\u1001\u103b\u1004\u103a\u1038\u1005\u102e\u104f \u1021\u1019\u103c\u1004\u1037\u103a\u1000\u102d\u102f \u101c\u1000\u103a\u1019\u1016\u103c\u1004\u1037\u103a \u1019\u103e\u1010\u103a\u1010\u1019\u103a\u1038\u1010\u1004\u103a\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u101b\u1031\u101c\u1031\u102c\u1004\u103a\u1038\u101e\u100a\u1037\u103a\u1021\u1000\u103c\u102d\u1019\u103a\u101b\u1031\u1014\u103e\u1004\u1037\u103a \u1014\u1031\u101b\u1031\u102c\u1004\u103a\u1001\u103c\u100a\u103a\u1011\u102d\u1010\u103d\u1031\u1037\u1019\u103e\u102f\u101e\u100a\u103a \u1021\u1015\u1004\u103a\u1000\u103c\u102e\u1038\u1011\u103d\u102c\u1038\u1019\u103e\u102f\u1021\u1015\u1031\u102b\u103a \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\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a\u1014\u103e\u1004\u1037\u103a \u101b\u1031\u1000\u103c\u102d\u1019\u103a\u1014\u103e\u102f\u1014\u103a\u1038\u1014\u103e\u1004\u1037\u103a \u1014\u1031\u101b\u1031\u102c\u1004\u103a\u1001\u103c\u100a\u103a\u1011\u102d\u1010\u103d\u1031\u1037\u1019\u103e\u102f\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\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a \u1021\u1031\u102c\u1000\u103a\u1016\u1031\u102c\u103a\u1015\u103c\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 \u101b\u1031\u101c\u1031\u102c\u1004\u103a\u1038\u1001\u103c\u1004\u103a\u1038\u1014\u103e\u1004\u1037\u103a \u1014\u1031\u101b\u1031\u102c\u1004\u103a\u1001\u103c\u100a\u103a\u1014\u103e\u1004\u1037\u103a\u1011\u102d\u1010\u103d\u1031\u1037\u1001\u103c\u1004\u103a\u1038\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 1: \u1012\u1031\u1010\u102c\u1000\u102d\u102f\u1011\u100a\u1037\u103a\u1015\u102b\u104b<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">\u1015\u1011\u1019\u1026\u1038\u1005\u103d\u102c\u104a \u1021\u1031\u102c\u1000\u103a\u1015\u102b variable \u101e\u102f\u1036\u1038\u1001\u102f\u1015\u102b\u101b\u103e\u102d\u101e\u1031\u102c pandas DataFrame \u1010\u1005\u103a\u1001\u102f\u1000\u102d\u102f \u1016\u1014\u103a\u1010\u102e\u1038\u1015\u102b\u1019\u100a\u103a\u104b<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u101b\u1031-<\/strong> \u1021\u1015\u1004\u103a\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1000\u102d\u102f \u1019\u100a\u103a\u1019\u103b\u103e\u1021\u1000\u103c\u102d\u1019\u103a\u101b\u1031\u101c\u1031\u102c\u1004\u103a\u1038\u101e\u100a\u103a- \u1014\u1031\u1037\u1005\u1009\u103a \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1021\u1015\u1010\u103a\u1005\u1009\u103a<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u1014\u1031-<\/strong> \u1014\u1031\u101b\u1031\u102c\u1004\u103a\u1001\u103c\u100a\u103a \u1011\u102d\u1010\u103d\u1031\u1037\u1019\u103e\u102f \u1015\u1019\u102c\u100f- \u1021\u1014\u102d\u1019\u1037\u103a\u104a \u1021\u101c\u1010\u103a \u101e\u102d\u102f\u1037\u1019\u101f\u102f\u1010\u103a \u1021\u1019\u103c\u1004\u1037\u103a<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u1021\u1019\u103c\u1004\u1037\u103a-<\/strong> \u1014\u103e\u1005\u103a\u101c\u1021\u1000\u103c\u102c\u1010\u103d\u1004\u103a \u1021\u1015\u1004\u103a\u1010\u1005\u103a\u1015\u1004\u103a\u104f\u1021\u1019\u103c\u1004\u1037\u103a (\u101c\u1000\u103a\u1019)<\/span><\/li>\n<\/ul>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #107d3f;\">import<\/span> numpy <span style=\"color: #107d3f;\">as<\/span> np\n<span style=\"color: #107d3f;\">import<\/span> pandas <span style=\"color: #107d3f;\">as<\/span> pd\n\n<span style=\"color: #008080;\">#create data<\/span>\ndf = pd.DataFrame({'water': np.repeat(['daily', 'weekly'], 15),\n                   'sun': np.tile(np.repeat(['low', 'med', 'high'], 5), 2),\n                   'height': [6, 6, 6, 5, 6, 5, 5, 6, 4, 5,\n                              6, 6, 7, 8, 7, 3, 4, 4, 4, 5,\n                              4, 4, 4, 4, 4, 5, 6, 6, 7, 8]})\n\n<span style=\"color: #008080;\">#view first ten rows of data<\/span> \ndf[:10]\n\n\twater sun height\n0 daily low 6\n1 daily low 6\n2 daily low 6\n3 daily low 5\n4 daily low 6\n5 daily med 5\n6 daily med 5\n7 daily med 6\n8 daily med 4\n9 daily med 5\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\"><strong>\u1021\u1006\u1004\u1037\u103a 2- \u1014\u103e\u1005\u103a\u101c\u1019\u103a\u1038\u101e\u103d\u102c\u1038 ANOVA \u1000\u102d\u102f \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1015\u102b\u104b<\/strong><\/span><\/p>\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 statsmodels \u1005\u102c\u1000\u103c\u100a\u1037\u103a\u1010\u102d\u102f\u1000\u103a\u1019\u103e <a href=\"https:\/\/www.statsmodels.org\/dev\/generated\/statsmodels.stats.anova.anova_lm.html\" target=\"_blank\" rel=\"noopener\">anova_lm() \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1001\u103b\u1000\u103a\u1000\u102d\u102f<\/a> \u1021\u101e\u102f\u1036\u1038\u1015\u103c\u102f\u104d \u1014\u103e\u1005\u103a\u101c\u1019\u103a\u1038 ANOVA \u1000\u102d\u102f \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1015\u102b\u1019\u100a\u103a-<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #107d3f;\">import<\/span> statsmodels.api <span style=\"color: #107d3f;\">as<\/span> sm\n<span style=\"color: #107d3f;\">from<\/span> statsmodels.formula.api <span style=\"color: #107d3f;\">import<\/span> ols\n\n<span style=\"color: #008080;\">#perform two-way ANOVA<\/span>\nmodel = ols('height ~ C(water) + C(sun) + C(water):C(sun)', data=df).fit()\nsm.stats.anova_lm(model, typ=2)\n\n\t           sum_sq df F PR(&gt;F)\nC(water) 8.533333 1.0 16.0000 0.000527\nC(sun) 24.866667 2.0 23.3125 0.000002\nC(water):C(sun) 2.466667 2.0 2.3125 0.120667\nResidual 12.800000 24.0 NaN NaN\n<\/strong><\/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;\">\u1007\u101a\u102c\u1038\u101b\u103e\u102d \u1021\u1001\u103b\u1000\u103a\u1010\u1005\u103a\u1001\u102f\u1005\u102e\u1021\u1010\u103d\u1000\u103a \u1021\u1031\u102c\u1000\u103a\u1015\u102b p-\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103b\u102c\u1038\u1000\u102d\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037 \u1019\u103c\u1004\u103a\u1014\u102d\u102f\u1004\u103a\u101e\u100a\u103a-<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>water:<\/strong> p-value = 0.000527<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>sun:<\/strong> p-value = 0.0000002<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u101b\u1031*\u1014\u1031-<\/strong> p-\u1010\u1014\u103a\u1016\u102d\u102f\u1038 = 0.120667<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u101b\u1031\u1014\u103e\u1004\u1037\u103a\u1014\u1031\u104f p-\u1010\u1014\u103a\u1016\u102d\u102f\u1038\u1019\u103b\u102c\u1038\u101e\u100a\u103a 0.05 \u1011\u1000\u103a\u1014\u100a\u103a\u1038\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a\u104a \u1006\u102d\u102f\u101c\u102d\u102f\u101e\u100a\u103a\u1019\u103e\u102c \u1021\u1001\u103b\u1000\u103a\u1014\u103e\u1005\u103a\u1001\u103b\u1000\u103a\u1005\u101c\u102f\u1036\u1038\u101e\u100a\u103a \u1021\u1015\u1004\u103a\u1021\u1019\u103c\u1004\u1037\u103a\u1021\u1015\u1031\u102b\u103a \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1021\u101b \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u101e\u1031\u102c\u1021\u1000\u103b\u102d\u102f\u1038\u101e\u1000\u103a\u101b\u1031\u102c\u1000\u103a\u1019\u103e\u102f\u101b\u103e\u102d\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\">\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\u1021\u1010\u103d\u1000\u103a p-\u1010\u1014\u103a\u1016\u102d\u102f\u1038 (0.120667) \u101e\u100a\u103a 0.05 \u1011\u1000\u103a\u1019\u1014\u100a\u103a\u1038\u101e\u1031\u102c\u1000\u103c\u1031\u102c\u1004\u1037\u103a\u104a \u104e\u1004\u103a\u1038\u101e\u100a\u103a \u1014\u1031\u1014\u103e\u1004\u1037\u103a\u1011\u102d\u1010\u103d\u1031\u1037\u1019\u103e\u102f\u1014\u103e\u1004\u1037\u103a \u101b\u1031\u101c\u1031\u102c\u1004\u103a\u1038\u1000\u103c\u102d\u1019\u103a\u1014\u103e\u102f\u1014\u103a\u1038\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\u1021\u1000\u103b\u102d\u102f\u1038\u101e\u1000\u103a\u101b\u1031\u102c\u1000\u103a\u1019\u103e\u102f\u1019\u101b\u103e\u102d\u101f\u102f \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1000\u102d\u102f\u1015\u103c\u1031\u102c\u1015\u103c\u101e\u100a\u103a\u104b<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u1019\u103e\u1010\u103a\u1001\u103b\u1000\u103a-<\/strong> ANOVA \u101b\u101c\u1012\u103a\u1019\u103b\u102c\u1038\u1000 \u1000\u103b\u103d\u1014\u103a\u102f\u1015\u103a\u1010\u102d\u102f\u1037\u1021\u102c\u1038 \u101b\u1031\u101c\u1031\u102c\u1004\u103a\u1038\u101e\u100a\u1037\u103a\u1021\u1000\u103c\u102d\u1019\u103a\u101b\u1031\u1014\u103e\u1004\u1037\u103a \u1014\u1031\u101b\u1031\u102c\u1004\u103a\u1001\u103c\u100a\u103a\u1011\u102d\u1010\u103d\u1031\u1037\u1019\u103e\u102f\u101e\u100a\u103a \u1021\u1015\u1004\u103a\u1021\u1019\u103c\u1004\u1037\u103a\u1021\u1015\u1031\u102b\u103a \u1000\u102d\u1014\u103a\u1038\u1002\u100f\u1014\u103a\u1038\u1021\u101b \u101e\u102d\u101e\u102c\u1011\u1004\u103a\u101b\u103e\u102c\u1038\u101e\u1031\u102c\u1021\u1000\u103b\u102d\u102f\u1038\u101e\u1000\u103a\u101b\u1031\u102c\u1000\u103a\u1019\u103e\u102f\u101b\u103e\u102d\u101e\u100a\u103a\u1000\u102d\u102f \u1015\u103c\u1031\u102c\u1015\u103c\u101e\u1031\u102c\u103a\u101c\u100a\u103a\u1038\u104a \u101b\u1031\u1014\u103e\u1004\u1037\u103a\u1014\u1031\u101b\u1031\u102c\u1004\u103a\u1001\u103c\u100a\u103a\u101e\u100a\u103a \u1021\u1015\u1004\u103a\u1021\u1019\u103c\u1004\u1037\u103a\u1021\u1015\u1031\u102b\u103a \u1019\u100a\u103a\u1019\u103b\u103e\u1000\u103d\u1032\u1015\u103c\u102c\u1038\u101e\u1031\u102c\u1021\u1006\u1004\u1037\u103a\u1000\u102d\u102f \u1021\u1010\u102d\u1021\u1000\u103b\u101e\u102d\u101b\u103e\u102d\u1014\u102d\u102f\u1004\u103a\u1005\u1031\u101b\u1014\u103a\u1021\u1010\u103d\u1000\u103a <a href=\"https:\/\/statorials.org\/my\/post-hoc-anova-\u1005\u1019\u103a\u1038\u101e\u1015\u103a\u1019\u103e\u102f\u1019\u103b\u102c\u1038\/\" target=\"_blank\" rel=\"noopener\">\u1014\u1031\u102c\u1000\u103a\u1015\u102d\u102f\u1004\u103a\u1038\u1010\u103d\u1004\u103a \u1005\u1019\u103a\u1038\u101e\u1015\u103a\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<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 \u1010\u103d\u1004\u103a \u1021\u1001\u103c\u102c\u1038\u101e\u1031\u102c \u1021\u101e\u102f\u1036\u1038\u1019\u103b\u102c\u1038\u101e\u1031\u102c \u1021\u101c\u102f\u1015\u103a\u1019\u103b\u102c\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\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\/\u101e\u102f\u1036\u1038\u101c\u1019\u103a\u1038-anova-python\/\" target=\"_blank\" rel=\"noopener\">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<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u1014\u103e\u1005\u103a\u101c\u1019\u103a\u1038\u101e\u103d\u102c\u1038 ANOVA \u1000\u102d\u102f \u1021\u1001\u103b\u1000\u103a\u1014\u103e\u1005\u103a\u1001\u103b\u1000\u103a \u1001\u103d\u1032\u1015\u103c\u102e\u1038 \u1001\u103d\u1032\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\u101e\u100a\u103a\u104b \u1014\u103e\u1005\u103a\u101c\u1019\u103a\u1038\u101e\u103d\u102c\u1038 ANOVA \u104f \u101b\u100a\u103a\u101b\u103d\u101a\u103a\u1001\u103b\u1000\u103a\u1019\u103e\u102c \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1010\u1005\u103a\u1001\u102f\u1021\u1015\u1031\u102b\u103a \u1021\u1001\u103b\u1000\u103a\u1014\u103e\u1005\u103a\u1001\u103b\u1000\u103a\u104f \u1021\u1000\u103b\u102d\u102f\u1038\u101e\u1000\u103a\u101b\u1031\u102c\u1000\u103a\u1019\u103e\u102f\u1000\u102d\u102f \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a\u1014\u103e\u1004\u1037\u103a \u1010\u102f\u1036\u1037\u1015\u103c\u1014\u103a\u1019\u103e\u102f\u1000\u102d\u1014\u103a\u1038\u101b\u103e\u1004\u103a\u1015\u1031\u102b\u103a\u101b\u103e\u102d \u1021\u1001\u103b\u1000\u103a\u1014\u103e\u1005\u103a\u1001\u102f\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\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u1006\u102f\u1036\u1038\u1016\u103c\u1010\u103a\u101b\u1014\u103a\u1016\u103c\u1005\u103a\u101e\u100a\u103a\u104b \u1024\u101e\u1004\u103a\u1001\u1014\u103a\u1038\u1005\u102c\u1010\u103d\u1004\u103a Python \u1010\u103d\u1004\u103a \u1014\u103e\u1005\u103a\u101c\u1019\u103a\u1038\u101e\u103d\u102c\u1038 ANOVA \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1014\u100a\u103a\u1038\u1000\u102d\u102f \u101b\u103e\u1004\u103a\u1038\u1015\u103c\u1011\u102c\u1038\u101e\u100a\u103a\u104b \u1025\u1015\u1019\u102c- Python \u101b\u103e\u102d \u1014\u103e\u1005\u103a\u101c\u1019\u103a\u1038\u101e\u103d\u102c\u1038 ANOVA \u101b\u102f\u1000\u1039\u1001\u1017\u1031\u1012\u1015\u100a\u102c\u101b\u103e\u1004\u103a\u1010\u1005\u103a\u1026\u1038\u101e\u100a\u103a \u1014\u1031\u101b\u1031\u102c\u1004\u103a\u1001\u103c\u100a\u103a\u1014\u103e\u1004\u1037\u103a \u1011\u102d\u1010\u103d\u1031\u1037\u1019\u103e\u102f\u1021\u1000\u103c\u102d\u1019\u103a\u101b\u1031\u1000\u103c\u1031\u102c\u1004\u1037\u103a \u1021\u1015\u1004\u103a\u1000\u103c\u102e\u1038\u1011\u103d\u102c\u1038\u1019\u103e\u102f\u1021\u1015\u1031\u102b\u103a \u101c\u103d\u103e\u1019\u103a\u1038\u1019\u102d\u102f\u1038\u1019\u103e\u102f\u101b\u103e\u102d\u1019\u101b\u103e\u102d \u101e\u102d\u101c\u102d\u102f\u101e\u100a\u103a\u104b \u1021\u1005\u1031\u1037 30 \u1000\u102d\u102f \u1005\u102d\u102f\u1000\u103a\u1015\u103b\u102d\u102f\u1038\u1015\u103c\u102e\u1038 \u1014\u1031\u101b\u1031\u102c\u1004\u103a\u1001\u103c\u100a\u103a\u1014\u103e\u1004\u1037\u103a \u101b\u1031\u101c\u1031\u102c\u1004\u103a\u1038\u1000\u103c\u102d\u1019\u103a\u1014\u103e\u102f\u1014\u103a\u1038 \u1019\u1010\u1030\u100a\u102e\u101e\u1031\u102c \u1021\u1001\u103c\u1031\u1021\u1014\u1031\u1019\u103b\u102c\u1038\u1010\u103d\u1004\u103a \u1014\u103e\u1005\u103a\u101c\u1000\u103c\u102c [&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 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<\/title>\n<meta name=\"description\" content=\"Python \u1010\u103d\u1004\u103a two-way ANOVA \u101c\u102f\u1015\u103a\u1006\u1031\u102c\u1004\u103a\u1014\u100a\u103a\u1038\u1021\u1010\u103d\u1000\u103a \u101b\u102d\u102f\u1038\u101b\u103e\u1004\u103a\u1038\u101e\u1031\u102c \u101b\u103e\u1004\u103a\u1038\u101c\u1004\u103a\u1038\u1001\u103b\u1000\u103a\u104b\" \/>\n<meta name=\"robots\" content=\"index, follow, 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