{"id":483,"date":"2023-07-29T18:17:31","date_gmt":"2023-07-29T18:17:31","guid":{"rendered":"https:\/\/statorials.org\/hi\/%e0%a4%86%e0%a4%b0-%e0%a4%ae%e0%a5%87%e0%a4%82-%e0%a4%8f%e0%a4%82%e0%a4%95%e0%a5%8b%e0%a4%b5%e0%a4%be\/"},"modified":"2023-07-29T18:17:31","modified_gmt":"2023-07-29T18:17:31","slug":"%e0%a4%86%e0%a4%b0-%e0%a4%ae%e0%a5%87%e0%a4%82-%e0%a4%8f%e0%a4%82%e0%a4%95%e0%a5%8b%e0%a4%b5%e0%a4%be","status":"publish","type":"post","link":"https:\/\/statorials.org\/hi\/%e0%a4%86%e0%a4%b0-%e0%a4%ae%e0%a5%87%e0%a4%82-%e0%a4%8f%e0%a4%82%e0%a4%95%e0%a5%8b%e0%a4%b5%e0%a4%be\/","title":{"rendered":"\u0906\u0930 \u092e\u0947\u0902 ancova \u0915\u093e \u0938\u0902\u091a\u093e\u0932\u0928 \u0915\u0948\u0938\u0947 \u0915\u0930\u0947\u0902"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">\u092f\u0939 \u091f\u094d\u092f\u0942\u091f\u094b\u0930\u093f\u092f\u0932 R \u092e\u0947\u0902 <a href=\"https:\/\/statorials.org\/hi\/\u0906\u0930-\u092e\u0947\u0902-\u090f\u0902\u0915\u094b\u0935\u093e\/\" target=\"_blank\" rel=\"noopener noreferrer\">ANCOVA<\/a> \u0928\u093f\u0937\u094d\u092a\u093e\u0926\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u093e \u0909\u0926\u093e\u0939\u0930\u0923 \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u0909\u0926\u093e\u0939\u0930\u0923: \u0906\u0930 \u092e\u0947\u0902 \u090f\u0928\u094d\u0915\u094b\u0935\u093e<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0939\u092e \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u091a\u0930 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u092f\u0939 \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 ANCOVA \u0928\u093f\u0937\u094d\u092a\u093e\u0926\u093f\u0924 \u0915\u0930\u0947\u0902\u0917\u0947 \u0915\u093f \u0905\u0927\u094d\u092f\u092f\u0928 \u0924\u0915\u0928\u0940\u0915 \u0915\u093e \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u092a\u0930\u093f\u0923\u093e\u092e\u094b\u0902 \u092a\u0930 \u092a\u094d\u0930\u092d\u093e\u0935 \u092a\u0921\u093c\u0924\u093e \u0939\u0948 \u092f\u093e \u0928\u0939\u0940\u0902:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u0924\u0915\u0928\u0940\u0915\u0940 \u0905\u0927\u094d\u092f\u092f\u0928<\/strong> : \u0935\u0939 \u0938\u094d\u0935\u0924\u0902\u0924\u094d\u0930 \u091a\u0930 \u091c\u093f\u0938\u0915\u093e \u0939\u092e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0928\u093e \u091a\u093e\u0939\u0924\u0947 \u0939\u0948\u0902<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u0935\u0930\u094d\u0924\u092e\u093e\u0928 \u091b\u093e\u0924\u094d\u0930 \u0917\u094d\u0930\u0947\u0921<\/strong> : \u0935\u0939 \u0938\u0939\u0938\u0902\u092f\u094b\u091c\u0915 \u091c\u093f\u0938\u0947 \u0939\u092e \u0927\u094d\u092f\u093e\u0928 \u092e\u0947\u0902 \u0930\u0916\u0928\u093e \u091a\u093e\u0939\u0924\u0947 \u0939\u0948\u0902<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u0938\u092e\u0940\u0915\u094d\u0937\u093e \u0938\u094d\u0915\u094b\u0930<\/strong> : \u092a\u094d\u0930\u0924\u093f\u0915\u094d\u0930\u093f\u092f\u093e \u091a\u0930 \u091c\u093f\u0938\u0915\u093e \u0939\u092e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0928\u093e \u091a\u093e\u0939\u0924\u0947 \u0939\u0948\u0902<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0921\u0947\u091f\u093e\u0938\u0947\u091f \u092e\u0947\u0902 90 \u091b\u093e\u0924\u094d\u0930\u094b\u0902 \u0915\u0940 \u091c\u093e\u0928\u0915\u093e\u0930\u0940 \u0939\u0948 \u091c\u094b \u092f\u093e\u0926\u0943\u091a\u094d\u091b\u093f\u0915 \u0930\u0942\u092a \u0938\u0947 30 \u0915\u0947 \u0924\u0940\u0928 \u0938\u092e\u0942\u0939\u094b\u0902 \u092e\u0947\u0902 \u0935\u093f\u092d\u093e\u091c\u093f\u0924 \u0939\u0948\u0902\u0964<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0921\u0947\u091f\u093e\u0938\u0947\u091f \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u091b\u093e\u0924\u094d\u0930 \u0926\u094d\u0935\u093e\u0930\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0940 \u091c\u093e\u0928\u0947 \u0935\u093e\u0932\u0940 \u0905\u0927\u094d\u092f\u092f\u0928 \u0924\u0915\u0928\u0940\u0915 <em>(\u090f, \u092c\u0940<\/em> , \u092f\u093e <em>\u0938\u0940)<\/em> <em>,<\/em> \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0909\u0928\u0915\u0947 \u0935\u0930\u094d\u0924\u092e\u093e\u0928 \u0917\u094d\u0930\u0947\u0921 \u0915\u094b \u0926\u0930\u094d\u0936\u093e\u0924\u093e \u0939\u0948 \u091c\u092c \u0909\u0928\u094d\u0939\u094b\u0902\u0928\u0947 \u0905\u0927\u094d\u092f\u092f\u0928 \u0924\u0915\u0928\u0940\u0915 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0928\u093e \u0936\u0941\u0930\u0942 \u0915\u093f\u092f\u093e \u0925\u093e, \u0914\u0930 \u0924\u0948\u092f\u093e\u0930\u0940 \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 \u092e\u0939\u0940\u0928\u0947 \u0924\u0915 \u0905\u0927\u094d\u092f\u092f\u0928 \u0924\u0915\u0928\u0940\u0915 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0928\u0947 \u0915\u0947 \u092c\u093e\u0926 \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0909\u0928\u094d\u0939\u0947\u0902 \u091c\u094b \u0917\u094d\u0930\u0947\u0921 \u092e\u093f\u0932\u093e \u0925\u093e\u0964 \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u0915\u0947 \u0932\u093f\u090f\u0964 \u092a\u0930\u0940\u0915\u094d\u0937\u093e:<\/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>\u091a\u0930\u0923 1: \u0921\u0947\u091f\u093e \u0915\u093e \u0905\u0928\u094d\u0935\u0947\u0937\u0923 \u0915\u0930\u0947\u0902<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">ANCOVA \u092e\u0949\u0921\u0932 \u0915\u094b \u092b\u093f\u091f \u0915\u0930\u0928\u0947 \u0938\u0947 \u092a\u0939\u0932\u0947, \u0939\u092e\u0947\u0902 \u0907\u0938\u0947 \u092c\u0947\u0939\u0924\u0930 \u0922\u0902\u0917 \u0938\u0947 \u0938\u092e\u091d\u0928\u0947 \u0914\u0930 \u092f\u0939 \u0938\u0924\u094d\u092f\u093e\u092a\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0921\u0947\u091f\u093e \u0915\u093e \u092a\u0924\u093e \u0932\u0917\u093e\u0928\u0947 \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0939\u0948 \u0915\u093f \u0915\u094b\u0908 \u091a\u0930\u092e \u0906\u0909\u091f\u0932\u0947\u0930 \u0928\u0939\u0940\u0902 \u0939\u0948\u0902 \u091c\u094b \u092a\u0930\u093f\u0923\u093e\u092e\u094b\u0902 \u0915\u094b \u0935\u093f\u0915\u0943\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902\u0964<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0938\u092c\u0938\u0947 \u092a\u0939\u0932\u0947, \u0939\u092e \u0921\u0947\u091f\u093e\u0938\u0947\u091f \u092e\u0947\u0902 \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u091a\u0930 \u0915\u093e \u0938\u093e\u0930\u093e\u0902\u0936 \u092a\u094d\u0930\u0926\u0930\u094d\u0936\u093f\u0924 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/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;\">\u0939\u092e \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0905\u0927\u094d\u092f\u092f\u0928 \u0924\u0915\u0928\u0940\u0915 \u092e\u093e\u0928 ( <em>\u090f, \u092c\u0940<\/em> \u0914\u0930 <em>\u0938\u0940)<\/em> \u0921\u0947\u091f\u093e \u092e\u0947\u0902 30 \u092c\u093e\u0930 \u0926\u093f\u0916\u093e\u0908 \u0926\u0947\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0939\u092e \u092f\u0939 \u092d\u0940 \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0940 \u0936\u0941\u0930\u0941\u0906\u0924 \u092e\u0947\u0902 \u091b\u093e\u0924\u094d\u0930\u094b\u0902 \u0915\u0947 \u0935\u0930\u094d\u0924\u092e\u093e\u0928 \u0905\u0902\u0915 \u0915\u0948\u0938\u0947 \u0935\u093f\u0924\u0930\u093f\u0924 \u0915\u093f\u090f \u0917\u090f \u0925\u0947\u0964 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u0905\u0902\u0915 65.43, \u0905\u0927\u093f\u0915\u0924\u092e 93.84 \u0914\u0930 \u0914\u0938\u0924 78.15 \u0925\u093e\u0964<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0907\u0938\u0940 \u092a\u094d\u0930\u0915\u093e\u0930, \u0939\u092e \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0928\u094d\u092f\u0942\u0928\u0924\u092e \u0905\u0902\u0915 71.17 \u0925\u093e, \u0905\u0927\u093f\u0915\u0924\u092e \u0905\u0902\u0915 94.76 \u0925\u093e \u0914\u0930 \u0914\u0938\u0924 83.38 \u0925\u093e\u0964<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u092b\u093f\u0930 \u0939\u092e \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0905\u0927\u094d\u092f\u092f\u0928 \u0924\u0915\u0928\u0940\u0915 \u0915\u0947 \u0932\u093f\u090f \u0935\u0930\u094d\u0924\u092e\u093e\u0928 \u0917\u094d\u0930\u0947\u0921 \u0914\u0930 \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u092a\u0930\u093f\u0923\u093e\u092e\u094b\u0902 \u0915\u0947 \u092e\u093e\u0927\u094d\u092f \u0914\u0930 \u092e\u093e\u0928\u0915 \u0935\u093f\u091a\u0932\u0928 \u0915\u094b \u0906\u0938\u093e\u0928\u0940 \u0938\u0947 \u0916\u094b\u091c\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f <strong>dplyr<\/strong> \u092a\u0948\u0915\u0947\u091c \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/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;\">\u0939\u092e \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u092a\u094d\u0930\u0924\u094d\u092f\u0947\u0915 \u0905\u0927\u094d\u092f\u092f\u0928 \u0924\u0915\u0928\u0940\u0915 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0928\u0947 \u0935\u093e\u0932\u0947 \u091b\u093e\u0924\u094d\u0930\u094b\u0902 \u0915\u0947 \u0935\u0930\u094d\u0924\u092e\u093e\u0928 \u0917\u094d\u0930\u0947\u0921 \u0915\u093e \u092e\u093e\u0927\u094d\u092f \u0914\u0930 \u092e\u093e\u0928\u0915 \u0935\u093f\u091a\u0932\u0928 \u0932\u0917\u092d\u0917 \u0938\u092e\u093e\u0928 \u0939\u0948\u0964<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0939\u092e \u092f\u0939 \u092d\u0940 \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0924\u0915\u0928\u0940\u0915 <em>\u092c\u0940<\/em> \u0914\u0930 <em>\u0938\u0940<\/em> \u0915\u0940 \u0924\u0941\u0932\u0928\u093e \u092e\u0947\u0902 \u0905\u0927\u094d\u092f\u092f\u0928 \u0924\u0915\u0928\u0940\u0915 <em>\u090f<\/em> \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0928\u0947 \u0935\u093e\u0932\u0947 \u091b\u093e\u0924\u094d\u0930\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0914\u0938\u0924 \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u0938\u094d\u0915\u094b\u0930 \u0915\u093e\u092b\u0940 \u0905\u0927\u093f\u0915 \u0939\u0948\u0964<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0939\u092e <a href=\"https:\/\/statorials.org\" target=\"_blank\" rel=\"noopener noreferrer\">\u092c\u0949\u0915\u094d\u0938\u092a\u094d\u0932\u0949\u091f \u0915\u093e<\/a> \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u0905\u0927\u094d\u092f\u092f\u0928 \u0924\u0915\u0928\u0940\u0915 \u0915\u0947 \u0906\u0927\u093e\u0930 \u092a\u0930 \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u092a\u0930\u093f\u0923\u093e\u092e\u094b\u0902 \u0915\u0947 \u0935\u093f\u0924\u0930\u0923 \u0915\u0940 \u0915\u0932\u094d\u092a\u0928\u093e \u092d\u0940 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/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;\">\u0907\u0938\u0940 \u0924\u0930\u0939, \u0939\u092e \u0905\u0927\u094d\u092f\u092f\u0928 \u0924\u0915\u0928\u0940\u0915 \u0915\u0947 \u0906\u0927\u093e\u0930 \u092a\u0930 <em>\u0935\u0930\u094d\u0924\u092e\u093e\u0928 \u0917\u094d\u0930\u0947\u0921<\/em> \u0915\u0947 \u0935\u093f\u0924\u0930\u0923 \u0915\u0940 \u0915\u0932\u094d\u092a\u0928\u093e \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u092c\u0949\u0915\u094d\u0938\u092a\u094d\u0932\u0949\u091f \u0915\u093e \u092d\u0940 \u0909\u092a\u092f\u094b\u0917 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/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>\u091a\u0930\u0923 2: \u092e\u0949\u0921\u0932 \u092e\u093e\u0928\u094d\u092f\u0924\u093e\u0913\u0902 \u0915\u0940 \u091c\u093e\u0901\u091a \u0915\u0930\u0947\u0902<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u090f\u0915 \u092c\u093e\u0930 \u091c\u092c \u0939\u092e \u0915\u0941\u091b \u092c\u0941\u0928\u093f\u092f\u093e\u0926\u0940 \u0921\u0947\u091f\u093e \u0905\u0928\u094d\u0935\u0947\u0937\u0923 \u0915\u0930 \u0932\u0947\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u0921\u0947\u091f\u093e \u0938\u0947 \u092a\u0930\u093f\u091a\u093f\u0924 \u0939\u094b \u091c\u093e\u0924\u0947 \u0939\u0948\u0902, \u0924\u094b \u0939\u092e\u0947\u0902 \u092f\u0939 \u0938\u0924\u094d\u092f\u093e\u092a\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0939\u094b\u0924\u0940 \u0939\u0948 \u0915\u093f ANCOVA \u0915\u0947 \u0932\u093f\u090f \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u0927\u093e\u0930\u0923\u093e\u090f\u0901 \u092a\u0942\u0930\u0940 \u0939\u094b\u0924\u0940 \u0939\u0948\u0902:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>\u0938\u0939\u0938\u0902\u092f\u094b\u091c\u0915 \u0914\u0930 \u0909\u092a\u091a\u093e\u0930 \u0938\u094d\u0935\u0924\u0902\u0924\u094d\u0930 \u0939\u0948\u0902<\/strong> &#8211; \u092f\u0939 \u0938\u0924\u094d\u092f\u093e\u092a\u093f\u0924 \u0915\u0930\u0928\u093e \u0906\u0935\u0936\u094d\u092f\u0915 \u0939\u0948 \u0915\u093f \u0938\u0939\u0938\u0902\u092f\u094b\u091c\u0915 ( <em>\u0935\u0930\u094d\u0924\u092e\u093e\u0928 \u0917\u094d\u0930\u0947\u0921)<\/em> \u0914\u0930 \u0909\u092a\u091a\u093e\u0930 <em>(\u0905\u0927\u094d\u092f\u092f\u0928 \u0924\u0915\u0928\u0940\u0915)<\/em> \u090f\u0915 \u0926\u0942\u0938\u0930\u0947 \u0938\u0947 \u0938\u094d\u0935\u0924\u0902\u0924\u094d\u0930 \u0939\u0948\u0902, \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u092e\u0949\u0921\u0932 \u092e\u0947\u0902 \u0938\u0939\u0938\u0902\u092f\u094b\u091c\u0915 \u0936\u092c\u094d\u0926 \u091c\u094b\u0921\u093c\u0928\u093e \u0924\u092d\u0940 \u0938\u093e\u0930\u094d\u0925\u0915 \u0939\u0948 \u091c\u092c \u0938\u0939\u0938\u0902\u092f\u094b\u091c\u0915 \u0914\u0930 \u0909\u092a\u091a\u093e\u0930 \u092a\u094d\u0930\u0924\u093f\u0915\u094d\u0930\u093f\u092f\u093e \u091a\u0930 ( <em>\u092a\u0930\u0940\u0915\u094d\u0937\u093e<\/em> ) \u092a\u0930 \u0938\u094d\u0935\u0924\u0902\u0924\u094d\u0930 \u0930\u0942\u092a \u0938\u0947 \u0915\u093e\u0930\u094d\u092f \u0915\u0930\u0924\u093e \u0939\u0948\u0964<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>\u092a\u094d\u0930\u0938\u0930\u0923 \u0915\u0940 \u0938\u092e\u0930\u0942\u092a\u0924\u093e<\/strong> &#8211; \u0939\u092e\u0947\u0902 \u092f\u0939 \u091c\u093e\u0902\u091a\u0928\u0947 \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0939\u0948 \u0915\u093f \u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u0947 \u092c\u0940\u091a \u092a\u094d\u0930\u0938\u0930\u0923 \u092c\u0930\u093e\u092c\u0930 \u0939\u0948\u0902<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">\u092f\u0939 \u0938\u0924\u094d\u092f\u093e\u092a\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f \u0938\u0939\u0938\u0902\u092f\u094b\u091c\u0915 \u0914\u0930 \u0909\u092a\u091a\u093e\u0930 \u0938\u094d\u0935\u0924\u0902\u0924\u094d\u0930 \u0939\u0948\u0902, \u0939\u092e \u092a\u094d\u0930\u0924\u093f\u0915\u094d\u0930\u093f\u092f\u093e \u091a\u0930 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 <em>\u0935\u0930\u094d\u0924\u092e\u093e\u0928 \u0917\u094d\u0930\u0947\u0921 \u0915\u093e<\/em> \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u090f\u0928\u094b\u0935\u093e \u0915\u093e \u092a\u094d\u0930\u0926\u0930\u094d\u0936\u0928 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0914\u0930 \u092d\u0935\u093f\u0937\u094d\u092f\u0935\u0915\u094d\u0924\u093e \u091a\u0930 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 <em>\u0905\u0927\u094d\u092f\u092f\u0928 \u0924\u0915\u0928\u0940\u0915 \u0915\u093e<\/em> \u0909\u092a\u092f\u094b\u0917 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/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;\">\u092a\u0940-\u092e\u093e\u0928 0.05 \u0938\u0947 \u0905\u0927\u093f\u0915 \u0939\u0948, \u0907\u0938\u0932\u093f\u090f \u0938\u0939\u0938\u0902\u092f\u094b\u091c\u0915 ( <em>\u0935\u0930\u094d\u0924\u092e\u093e\u0928 \u0917\u094d\u0930\u0947\u0921)<\/em> \u0914\u0930 \u0909\u092a\u091a\u093e\u0930 ( <em>\u0905\u0927\u094d\u092f\u092f\u0928 \u0924\u0915\u0928\u0940\u0915<\/em> ) \u0938\u094d\u0935\u0924\u0902\u0924\u094d\u0930 \u0926\u093f\u0916\u093e\u0908 \u0926\u0947\u0924\u0947 \u0939\u0948\u0902\u0964<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u092b\u093f\u0930, \u092f\u0939 \u091c\u093e\u0902\u091a\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f \u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u0947 \u092c\u0940\u091a \u092d\u093f\u0928\u094d\u0928\u0924\u093e \u0915\u0940 \u090f\u0915\u0930\u0942\u092a\u0924\u093e \u0939\u0948, \u0939\u092e \u0932\u0947\u0935\u0947\u0928\u0947 \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/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;\">\u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u093e \u092a\u0940-\u092e\u093e\u0928 0.0001961 \u0915\u0947 \u092c\u0930\u093e\u092c\u0930 \u0939\u0948, \u091c\u094b \u0907\u0902\u0917\u093f\u0924 \u0915\u0930\u0924\u093e \u0939\u0948 \u0915\u093f \u0938\u092e\u0942\u0939\u094b\u0902 \u0915\u0947 \u092c\u0940\u091a \u092d\u093f\u0928\u094d\u0928\u0924\u093e\u090f\u0902 \u0938\u092e\u093e\u0928 \u0928\u0939\u0940\u0902 \u0939\u0948\u0902\u0964 \u0939\u093e\u0932\u093e\u0901\u0915\u093f \u0939\u092e \u0907\u0938 \u0938\u092e\u0938\u094d\u092f\u093e \u0915\u094b \u0920\u0940\u0915 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0921\u0947\u091f\u093e \u092e\u0947\u0902 \u092a\u0930\u093f\u0935\u0930\u094d\u0924\u0928 \u0915\u093e \u092a\u094d\u0930\u092f\u093e\u0938 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902, \u0939\u092e \u0907\u0938 \u0938\u092e\u092f \u092d\u093f\u0928\u094d\u0928\u0924\u093e \u0915\u0947 \u0905\u0902\u0924\u0930 \u0915\u0947 \u092c\u093e\u0930\u0947 \u092e\u0947\u0902 \u092c\u0939\u0941\u0924 \u0905\u0927\u093f\u0915 \u091a\u093f\u0902\u0924\u093e \u0928\u0939\u0940\u0902 \u0915\u0930\u0947\u0902\u0917\u0947\u0964<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u091a\u0930\u0923 3: ANCOVA \u092e\u0949\u0921\u0932 \u0915\u094b \u0938\u092e\u093e\u092f\u094b\u091c\u093f\u0924 \u0915\u0930\u0947\u0902<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0907\u0938\u0915\u0947 \u092c\u093e\u0926, \u0939\u092e \u092a\u094d\u0930\u0924\u093f\u0915\u094d\u0930\u093f\u092f\u093e \u091a\u0930 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 <em>\u092a\u0930\u0940\u0915\u094d\u0937\u093e \u0938\u094d\u0915\u094b\u0930<\/em> , \u092d\u0935\u093f\u0937\u094d\u092f\u0935\u0915\u094d\u0924\u093e (\u092f\u093e &#8220;\u0909\u092a\u091a\u093e\u0930&#8221;) \u091a\u0930 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 <em>\u0905\u0927\u094d\u092f\u092f\u0928 \u0924\u0915\u0928\u0940\u0915<\/em> \u0914\u0930 \u0938\u0939\u0938\u0902\u092f\u094b\u091c\u0915 \u0915\u0947 \u0930\u0942\u092a \u092e\u0947\u0902 <em>\u0935\u0930\u094d\u0924\u092e\u093e\u0928 \u0917\u094d\u0930\u0947\u0921 \u0915\u093e<\/em> \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 ANCOVA \u092e\u0949\u0921\u0932 \u0915\u094b \u092b\u093f\u091f \u0915\u0930\u0947\u0902\u0917\u0947\u0964<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0939\u092e \u092a\u0948\u0915\u0947\u091c \u092e\u0947\u0902 \u090f\u0928\u094b\u0935\u093e() \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0947\u0902\u0917\u0947 \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0910\u0938\u093e \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u0915\u0947\u0935\u0932 \u092f\u0939 \u0928\u093f\u0930\u094d\u0926\u093f\u0937\u094d\u091f \u0915\u0930\u0928\u0947 \u092e\u0947\u0902 \u0938\u0915\u094d\u0937\u092e \u0939\u094b\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0915\u093f \u0939\u092e \u092e\u0949\u0921\u0932 \u0915\u0947 \u0932\u093f\u090f \u092a\u094d\u0930\u0915\u093e\u0930 III \u0935\u0930\u094d\u0917\u094b\u0902 \u0915\u0947 \u092f\u094b\u0917 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0928\u093e \u091a\u093e\u0939\u0924\u0947 \u0939\u0948\u0902, \u0915\u094d\u092f\u094b\u0902\u0915\u093f \u0935\u0930\u094d\u0917\u094b\u0902 \u0915\u093e \u092a\u094d\u0930\u0915\u093e\u0930 I \u092f\u094b\u0917 \u0909\u0938 \u0915\u094d\u0930\u092e \u092a\u0930 \u0928\u093f\u0930\u094d\u092d\u0930 \u0915\u0930\u0924\u093e \u0939\u0948 \u091c\u093f\u0938\u092e\u0947\u0902 \u092d\u0935\u093f\u0937\u094d\u092f\u0935\u0915\u094d\u0924\u093e\u0913\u0902 \u0915\u094b \u092e\u0949\u0921\u0932 \u092e\u0947\u0902 \u0926\u0930\u094d\u091c \u0915\u093f\u092f\u093e \u0917\u092f\u093e \u0939\u0948:<\/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;\">\u0939\u092e \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f <em>\u0924\u0915\u0928\u0940\u0915<\/em> \u0915\u0947 \u0932\u093f\u090f \u092a\u0940-\u0935\u0948\u0932\u094d\u092f\u0942 \u092c\u0947\u0939\u0926 \u0915\u092e \u0939\u0948, \u092f\u0939 \u0926\u0930\u094d\u0936\u093e\u0924\u093e \u0939\u0948 \u0915\u093f \u0935\u0930\u094d\u0924\u092e\u093e\u0928 \u0917\u094d\u0930\u0947\u0921 \u0915\u0947 \u0932\u093f\u090f \u0928\u093f\u092f\u0902\u0924\u094d\u0930\u0923 \u0915\u0947 \u092c\u093e\u0926 \u092d\u0940 \u0905\u0927\u094d\u092f\u092f\u0928 \u0924\u0915\u0928\u0940\u0915 \u0915\u093e \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u0938\u094d\u0915\u094b\u0930 \u092a\u0930 \u0938\u093e\u0902\u0916\u094d\u092f\u093f\u0915\u0940\u092f \u0930\u0942\u092a \u0938\u0947 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u092a\u094d\u0930\u092d\u093e\u0935 \u092a\u0921\u093c\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u091a\u0930\u0923 4: \u092a\u094b\u0938\u094d\u091f-\u0939\u0949\u0915 \u092a\u0930\u0940\u0915\u094d\u0937\u0923<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\">\u0939\u093e\u0932\u093e\u0901\u0915\u093f ANCOVA \u092a\u0930\u093f\u0923\u093e\u092e\u094b\u0902 \u0928\u0947 \u0939\u092e\u0947\u0902 \u092c\u0924\u093e\u092f\u093e \u0915\u093f <em>\u0905\u0927\u094d\u092f\u092f\u0928 \u0924\u0915\u0928\u0940\u0915 \u0915\u093e<\/em> \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u0905\u0902\u0915\u094b\u0902 \u092a\u0930 \u0938\u093e\u0902\u0916\u094d\u092f\u093f\u0915\u0940\u092f \u0930\u0942\u092a \u0938\u0947 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u092a\u094d\u0930\u092d\u093e\u0935 \u092a\u0921\u093c\u093e \u0939\u0948, \u0939\u092e\u0947\u0902 \u092f\u0939 \u0928\u093f\u0930\u094d\u0927\u093e\u0930\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f <a href=\"https:\/\/statorials.org\" target=\"_blank\" rel=\"noopener noreferrer\">\u092a\u094b\u0938\u094d\u091f \u0939\u0949\u0915 \u092a\u0930\u0940\u0915\u094d\u0937\u0923<\/a> \u0915\u0930\u0928\u0947 \u0915\u0940 \u0906\u0935\u0936\u094d\u092f\u0915\u0924\u093e \u0939\u0948 \u0915\u093f \u0915\u094c\u0928 \u0938\u0940 \u0905\u0927\u094d\u092f\u092f\u0928 \u0924\u0915\u0928\u0940\u0915 \u090f\u0915 \u0926\u0942\u0938\u0930\u0947 \u0938\u0947 \u092d\u093f\u0928\u094d\u0928 \u0939\u0948\u0902\u0964<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0910\u0938\u093e \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f, \u0939\u092e \u090f\u0915\u093e\u0927\u093f\u0915 \u0924\u0941\u0932\u0928\u093e\u0913\u0902 \u0915\u0947 \u0932\u093f\u090f \u0924\u0941\u0915\u0940 \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u0906\u0930 \u092e\u0947\u0902 <strong>\u092e\u0932\u094d\u091f\u0940\u0915\u0949\u092e\u094d\u092a<\/strong> \u092a\u0948\u0915\u0947\u091c \u092e\u0947\u0902 glht() \u092b\u093c\u0902\u0915\u094d\u0936\u0928 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902:<\/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;\">\u092a\u0930\u093f\u0923\u093e\u092e \u0938\u0947, \u0939\u092e \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0924\u0915\u0928\u0940\u0915 <em>\u090f \u0915\u093e<\/em> \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0930\u0928\u0947 \u0914\u0930 \u0924\u0915\u0928\u0940\u0915 <em>\u092c\u0940<\/em> \u0915\u093e \u0905\u0927\u094d\u092f\u092f\u0928 \u0915\u0930\u0928\u0947 (\u092a\u0940-\u092e\u0942\u0932\u094d\u092f: 0,000109) \u0915\u0947 \u0938\u093e\u0925-\u0938\u093e\u0925 \u0924\u0915\u0928\u0940\u0915 <em>\u090f<\/em> \u0914\u0930 \u0924\u0915\u0928\u0940\u0915 <em>\u0938\u0940<\/em> \u0915\u0947 \u092c\u0940\u091a \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u092a\u0930\u093f\u0923\u093e\u092e\u094b\u0902 \u092e\u0947\u0902 \u0938\u093e\u0902\u0916\u094d\u092f\u093f\u0915\u0940\u092f \u0930\u0942\u092a \u0938\u0947 \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0905\u0902\u0924\u0930 (\u03b1 = 0.05 \u092a\u0930) \u0939\u0948\u0964 (\u092a\u0940-\u092e\u093e\u0928: &lt;1e-04)\u0964<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0939\u092e \u092f\u0939 \u092d\u0940 \u0926\u0947\u0916 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0924\u0915\u0928\u0940\u0915 <em>\u092c\u0940<\/em> \u0914\u0930 <em>\u0938\u0940<\/em> \u0915\u0947 \u092c\u0940\u091a \u0915\u094b\u0908 \u0938\u093e\u0902\u0916\u094d\u092f\u093f\u0915\u0940\u092f \u092e\u0939\u0924\u094d\u0935\u092a\u0942\u0930\u094d\u0923 \u0905\u0902\u0924\u0930 (\u03b1 = 0.05 \u092a\u0930) <em>\u0928\u0939\u0940\u0902<\/em> \u0939\u0948\u0964<\/span> <span style=\"color: #000000;\">\u0924\u0915\u0928\u0940\u0915\u094b\u0902 \u0915\u0947 \u092c\u0940\u091a \u0906\u0924\u094d\u092e\u0935\u093f\u0936\u094d\u0935\u093e\u0938 \u0905\u0902\u0924\u0930\u093e\u0932 \u092d\u0940 \u0907\u0928 \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937\u094b\u0902 \u0915\u093e \u0938\u092e\u0930\u094d\u0925\u0928 \u0915\u0930\u0924\u0947 \u0939\u0948\u0902\u0964<\/span><\/p>\n<p> <span style=\"color: #000000;\">\u0907\u0938 \u092a\u094d\u0930\u0915\u093e\u0930, \u0939\u092e \u092f\u0939 \u0928\u093f\u0937\u094d\u0915\u0930\u094d\u0937 \u0928\u093f\u0915\u093e\u0932 \u0938\u0915\u0924\u0947 \u0939\u0948\u0902 \u0915\u093f \u0905\u0927\u094d\u092f\u092f\u0928 \u0924\u0915\u0928\u0940\u0915 <em>\u090f<\/em> \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0928\u0947 \u0938\u0947 \u0915\u0915\u094d\u0937\u093e \u092e\u0947\u0902 \u091b\u093e\u0924\u094d\u0930 \u0915\u0947 \u0935\u0930\u094d\u0924\u092e\u093e\u0928 \u0917\u094d\u0930\u0947\u0921 \u0915\u094b \u0928\u093f\u092f\u0902\u0924\u094d\u0930\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u0947 \u092c\u093e\u0926 \u092d\u0940 \u0924\u0915\u0928\u0940\u0915 <em>\u092c\u0940<\/em> \u0914\u0930 <em>\u0938\u0940<\/em> \u0915\u0940 \u0924\u0941\u0932\u0928\u093e \u092e\u0947\u0902 \u091b\u093e\u0924\u094d\u0930\u094b\u0902 \u0915\u0947 \u0932\u093f\u090f \u0938\u093e\u0902\u0916\u094d\u092f\u093f\u0915\u0940\u092f \u0930\u0942\u092a \u0938\u0947 \u0915\u093e\u092b\u0940 \u0909\u091a\u094d\u091a \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u0917\u094d\u0930\u0947\u0921 \u092a\u094d\u0930\u093e\u092a\u094d\u0924 \u0939\u094b\u0924\u093e \u0939\u0948\u0964<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u092f\u0939 \u091f\u094d\u092f\u0942\u091f\u094b\u0930\u093f\u092f\u0932 R \u092e\u0947\u0902 ANCOVA \u0928\u093f\u0937\u094d\u092a\u093e\u0926\u093f\u0924 \u0915\u0930\u0928\u0947 \u0915\u093e \u0909\u0926\u093e\u0939\u0930\u0923 \u092a\u094d\u0930\u0926\u093e\u0928 \u0915\u0930\u0924\u093e \u0939\u0948\u0964 \u0909\u0926\u093e\u0939\u0930\u0923: \u0906\u0930 \u092e\u0947\u0902 \u090f\u0928\u094d\u0915\u094b\u0935\u093e \u0939\u092e \u0928\u093f\u092e\u094d\u0928\u0932\u093f\u0916\u093f\u0924 \u091a\u0930 \u0915\u093e \u0909\u092a\u092f\u094b\u0917 \u0915\u0930\u0915\u0947 \u092f\u0939 \u092a\u0930\u0940\u0915\u094d\u0937\u0923 \u0915\u0930\u0928\u0947 \u0915\u0947 \u0932\u093f\u090f \u090f\u0915 ANCOVA \u0928\u093f\u0937\u094d\u092a\u093e\u0926\u093f\u0924 \u0915\u0930\u0947\u0902\u0917\u0947 \u0915\u093f \u0905\u0927\u094d\u092f\u092f\u0928 \u0924\u0915\u0928\u0940\u0915 \u0915\u093e \u092a\u0930\u0940\u0915\u094d\u0937\u093e \u092a\u0930\u093f\u0923\u093e\u092e\u094b\u0902 \u092a\u0930 \u092a\u094d\u0930\u092d\u093e\u0935 \u092a\u0921\u093c\u0924\u093e \u0939\u0948 \u092f\u093e \u0928\u0939\u0940\u0902: \u0924\u0915\u0928\u0940\u0915\u0940 \u0905\u0927\u094d\u092f\u092f\u0928 : \u0935\u0939 \u0938\u094d\u0935\u0924\u0902\u0924\u094d\u0930 \u091a\u0930 \u091c\u093f\u0938\u0915\u093e \u0939\u092e \u0935\u093f\u0936\u094d\u0932\u0947\u0937\u0923 \u0915\u0930\u0928\u093e \u091a\u093e\u0939\u0924\u0947 \u0939\u0948\u0902 [&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":[],"class_list":["post-483","post","type-post","status-publish","format-standard","hentry","category-3"],"yoast_head":"<!-- This site is optimized with the Yoast SEO 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