{"id":485,"date":"2023-07-29T18:02:44","date_gmt":"2023-07-29T18:02:44","guid":{"rendered":"https:\/\/statorials.org\/ar\/%d8%a7%d9%94%d9%86%d9%88%d9%81%d8%a7-%d8%b1%d8%a7-%d8%a7%d8%aa%d8%ac%d8%a7%d9%87%d9%8a%d9%86\/"},"modified":"2023-07-29T18:02:44","modified_gmt":"2023-07-29T18:02:44","slug":"%d8%a7%d9%94%d9%86%d9%88%d9%81%d8%a7-%d8%b1%d8%a7-%d8%a7%d8%aa%d8%ac%d8%a7%d9%87%d9%8a%d9%86","status":"publish","type":"post","link":"https:\/\/statorials.org\/ar\/%d8%a7%d9%94%d9%86%d9%88%d9%81%d8%a7-%d8%b1%d8%a7-%d8%a7%d8%aa%d8%ac%d8%a7%d9%87%d9%8a%d9%86\/","title":{"rendered":"\u0643\u064a\u0641\u064a\u0629 \u0625\u062c\u0631\u0627\u0621 anova \u062b\u0646\u0627\u0626\u064a \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0641\u064a r"},"content":{"rendered":"

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\u0645\u062b\u0627\u0644: \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u062a\u0628\u0627\u064a\u0646 \u062b\u0646\u0627\u0626\u064a \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0641\u064a R<\/strong><\/span><\/h3>\n

\u0644\u0646\u0641\u062a\u0631\u0636 \u0623\u0646\u0646\u0627 \u0646\u0631\u064a\u062f \u062a\u062d\u062f\u064a\u062f \u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0634\u062f\u0629 \u0627\u0644\u062a\u0645\u0631\u064a\u0646 \u0648\u0627\u0644\u062c\u0646\u0633 \u064a\u0624\u062b\u0631\u0627\u0646 \u0639\u0644\u0649 \u0641\u0642\u062f\u0627\u0646 \u0627\u0644\u0648\u0632\u0646. \u0641\u064a \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0629\u060c \u0627\u0644\u0639\u0627\u0645\u0644\u0627\u0646 \u0627\u0644\u0644\u0630\u0627\u0646 \u0646\u0646\u0638\u0631 \u0625\u0644\u064a\u0647\u0645\u0627 \u0647\u0645\u0627 \u0627\u0644\u062a\u0645\u0631\u064a\u0646<\/em> \u0648\u0627\u0644\u062c\u0646\u0633<\/em> \u060c \u0648\u0645\u062a\u063a\u064a\u0631 \u0627\u0644\u0627\u0633\u062a\u062c\u0627\u0628\u0629 \u0647\u0648 \u0641\u0642\u062f\u0627\u0646 \u0627\u0644\u0648\u0632\u0646\u060c<\/em> \u0645\u0642\u0627\u0633\u064b\u0627 \u0628\u0627\u0644\u062c\u0646\u064a\u0647.<\/span><\/p>\n

\u064a\u0645\u0643\u0646\u0646\u0627 \u0625\u062c\u0631\u0627\u0621 \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u062a\u0628\u0627\u064a\u0646 (ANOVA) \u062b\u0646\u0627\u0626\u064a \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0644\u062a\u062d\u062f\u064a\u062f \u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646 \u0627\u0644\u062a\u0645\u0631\u064a\u0646 \u0648\u0627\u0644\u062c\u0646\u0633 \u064a\u0624\u062b\u0631\u0627\u0646 \u0639\u0644\u0649 \u0641\u0642\u062f\u0627\u0646 \u0627\u0644\u0648\u0632\u0646 \u0648\u0644\u062a\u062d\u062f\u064a\u062f \u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646 \u0647\u0646\u0627\u0643 \u062a\u0641\u0627\u0639\u0644 \u0628\u064a\u0646 \u0627\u0644\u062a\u0645\u0631\u064a\u0646 \u0648\u0627\u0644\u062c\u0646\u0633 \u0639\u0644\u0649 \u0641\u0642\u062f\u0627\u0646 \u0627\u0644\u0648\u0632\u0646.<\/span><\/p>\n

\u0646\u0642\u0648\u0645 \u0628\u062a\u062c\u0646\u064a\u062f 30 \u0631\u062c\u0644\u0627\u064b \u064830 \u0627\u0645\u0631\u0623\u0629 \u0644\u0644\u0645\u0634\u0627\u0631\u0643\u0629 \u0641\u064a \u062a\u062c\u0631\u0628\u0629 \u0646\u062e\u0635\u0635 \u0641\u064a\u0647\u0627 10 \u0645\u0646 \u0643\u0644 \u0645\u0646\u0647\u0645 \u0628\u0634\u0643\u0644 \u0639\u0634\u0648\u0627\u0626\u064a \u0644\u0645\u062a\u0627\u0628\u0639\u0629 \u0628\u0631\u0646\u0627\u0645\u062c \u0639\u062f\u0645 \u0645\u0645\u0627\u0631\u0633\u0629 \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u0631\u064a\u0627\u0636\u064a\u0629 \u0623\u0648 \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u062e\u0641\u064a\u0641\u0629 \u0623\u0648 \u0628\u0631\u0646\u0627\u0645\u062c \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u0645\u0643\u062b\u0641\u0629 \u0644\u0645\u062f\u0629 \u0634\u0647\u0631.<\/span><\/p>\n

\u0627\u0644\u0643\u0648\u062f \u0627\u0644\u062a\u0627\u0644\u064a \u064a\u0646\u0634\u0626 \u0625\u0637\u0627\u0631 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0630\u064a \u0633\u0646\u0639\u0645\u0644 \u0645\u0639\u0647:<\/span><\/p>\n

 #make this example reproducible\n<\/span>set.seed(10)\n\n#create data frame\n<\/span>data <- data.frame(gender = rep(c(\"Male\", \"Female\"), each = 30),\n                   exercise = rep(c(\"None\", \"Light\", \"Intense\"), each = 10, times = 2),\n                   weight_loss = c(runif(10, -3, 3), runif(10, 0, 5), runif(10, 5, 9),\n                                   runif(10, -4, 2), runif(10, 0, 3), runif(10, 3, 8)))\n\n#view first six rows of data frame\n<\/span>head(data)\n\n# gender exercise weight_loss\n#1 Male None 0.04486922\n#2 Male None -1.15938896\n#3 Male None -0.43855400\n#4 Male None 1.15861249\n#5 Male None -2.48918419\n#6 Male None -1.64738030\n\n#see how many participants are in each group<\/span>\ntable(data$gender, data$exercise)\n\n# Intense Light None\n# Female 10 10 10\n# Male 10 10 10\n<\/strong><\/pre>\n
 \u0627\u0633\u062a\u0643\u0634\u0641 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a<\/strong><\/span><\/h3>\n
 \u0642\u0628\u0644 \u062d\u062a\u0649 \u062a\u0631\u0643\u064a\u0628 \u0646\u0645\u0648\u0630\u062c ANOVA \u062b\u0646\u0627\u0626\u064a \u0627\u0644\u0627\u062a\u062c\u0627\u0647\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0641\u0647\u0645 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0628\u0634\u0643\u0644 \u0623\u0641\u0636\u0644 \u0645\u0646 \u062e\u0644\u0627\u0644 \u0625\u064a\u062c\u0627\u062f \u0627\u0644\u0645\u062a\u0648\u0633\u0637 \u0648\u0627\u0644\u0627\u0646\u062d\u0631\u0627\u0641 \u0627\u0644\u0645\u0639\u064a\u0627\u0631\u064a \u0644\u0641\u0642\u062f\u0627\u0646 \u0627\u0644\u0648\u0632\u0646 \u0644\u0643\u0644 \u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u0646 \u0645\u062c\u0645\u0648\u0639\u0627\u062a \u0627\u0644\u0639\u0644\u0627\u062c \u0627\u0644\u0633\u062a \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062d\u0632\u0645\u0629 dplyr<\/strong> :<\/span><\/p>\n
 #load dplyr<\/em> package<\/span>\nlibrary(dplyr)\n\n#find mean and standard deviation of weight loss for each treatment group<\/span>\ndata %>%\n  group_by<\/span> (gender, exercise) %>%\n  summarize<\/span> (mean = mean(weight_loss),\n            sd = sd(weight_loss))\n\n# A tibble: 6 x 4\n# Groups: gender [2]\n# gender exercise means sd\n#          \n#1 Female Intense 5.31 1.02 \n#2 Female Light 0.920 0.835\n#3 Female None -0.501 1.77 \n#4 Male Intense 7.37 0.928\n#5 Male Light 2.13 1.22 \n#6 Male None -0.698 1.12 \n<\/strong><\/pre>\n
 \u064a\u0645\u0643\u0646\u0646\u0627 \u0623\u064a\u0636\u064b\u0627 \u0625\u0646\u0634\u0627\u0621 \u0645\u062e\u0637\u0637 \u0645\u0631\u0628\u0639 \u0644\u0643\u0644 \u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u0646 \u0645\u062c\u0645\u0648\u0639\u0627\u062a \u0627\u0644\u0639\u0644\u0627\u062c \u0627\u0644\u0633\u062a \u0644\u062a\u0635\u0648\u0631 \u062a\u0648\u0632\u064a\u0639 \u0641\u0642\u062f\u0627\u0646 \u0627\u0644\u0648\u0632\u0646 \u0644\u0643\u0644 \u0645\u062c\u0645\u0648\u0639\u0629:<\/span><\/p>\n
 #set margins so that axis labels on boxplot don't get cut off<\/span>\nby(mar=c(8, 4.1, 4.1, 2.1))\n\n#create boxplots\n<\/span>boxplot(weight_loss ~ gender:exercise,\ndata = data,\nmain = \"Weight Loss Distribution by Group\",\nxlab = \"Group\",\nylab = \"Weight Loss\",\ncol = \"steelblue\",\nborder = \"black\", \nlas = 2 #make x-axis labels perpendicular<\/span>\n)<\/strong><\/pre>\n
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 \u0628\u0639\u062f \u0630\u0644\u0643\u060c \u0633\u0648\u0641 \u0646\u0644\u0627\u0626\u0645 \u0646\u0645\u0648\u0630\u062c ANOVA \u062b\u0646\u0627\u0626\u064a \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0645\u0639 \u0628\u064a\u0627\u0646\u0627\u062a\u0646\u0627 \u0644\u0645\u0639\u0631\u0641\u0629 \u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0647\u0630\u0647 \u0627\u0644\u0627\u062e\u062a\u0644\u0627\u0641\u0627\u062a \u0627\u0644\u0645\u0631\u0626\u064a\u0629 \u0630\u0627\u062a \u062f\u0644\u0627\u0644\u0629 \u0625\u062d\u0635\u0627\u0626\u064a\u0629 \u0628\u0627\u0644\u0641\u0639\u0644.<\/span><\/p>\n
 \u062a\u0631\u0643\u064a\u0628 \u0646\u0645\u0648\u0630\u062c ANOVA \u062b\u0646\u0627\u0626\u064a \u0627\u0644\u0627\u062a\u062c\u0627\u0647<\/strong><\/span><\/h3>\n
 \u0628\u0646\u0627\u0621 \u0627\u0644\u062c\u0645\u0644\u0629 \u0627\u0644\u0639\u0627\u0645 \u0644\u062a\u0631\u0643\u064a\u0628 \u0646\u0645\u0648\u0630\u062c ANOVA \u062b\u0646\u0627\u0626\u064a \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0641\u064a R \u0647\u0648:<\/span><\/p>\n
 aov (\u0645\u062a\u063a\u064a\u0631 \u0627\u0644\u0627\u0633\u062a\u062c\u0627\u0628\u0629 ~predictor_variable1 *predictor_variable2\u060c \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a = \u0645\u062c\u0645\u0648\u0639\u0629 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a)<\/span><\/strong><\/p>\n
 \u0644\u0627\u062d\u0638 \u0623\u0646 *<\/strong> \u0628\u064a\u0646 \u0645\u062a\u063a\u064a\u0631\u064a \u0627\u0644\u062a\u0648\u0642\u0639 \u064a\u0634\u064a\u0631 \u0625\u0644\u0649 \u0623\u0646\u0646\u0627 \u0646\u0631\u064a\u062f \u0623\u064a\u0636\u064b\u0627 \u0627\u062e\u062a\u0628\u0627\u0631 \u062a\u0623\u062b\u064a\u0631 \u0627\u0644\u062a\u0641\u0627\u0639\u0644 \u0628\u064a\u0646 \u0645\u062a\u063a\u064a\u0631\u064a \u0627\u0644\u062a\u0648\u0642\u0639.<\/span><\/p>\n
 \u0641\u064a \u0645\u062b\u0627\u0644\u0646\u0627\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u0643\u0648\u062f \u0627\u0644\u062a\u0627\u0644\u064a \u0644\u0645\u0644\u0627\u0621\u0645\u0629 \u0646\u0645\u0648\u0630\u062c ANOVA \u062b\u0646\u0627\u0626\u064a \u0627\u0644\u0627\u062a\u062c\u0627\u0647\u060c \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 Weight_loss<\/em> \u0643\u0645\u062a\u063a\u064a\u0631 \u0627\u0644\u0627\u0633\u062a\u062c\u0627\u0628\u0629 \u0648\u0627\u0644\u062c\u0646\u0633<\/em> \u0648\u0627\u0644\u062a\u0645\u0631\u064a\u0646<\/em> \u0643\u0645\u062a\u063a\u064a\u0631\u064a\u0646 \u0645\u062a\u0648\u0642\u0639\u064a\u0646.<\/span><\/p>\n
 \u064a\u0645\u0643\u0646\u0646\u0627 \u0628\u0639\u062f \u0630\u0644\u0643 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062f\u0627\u0644\u0629 Summary()<\/strong> \u0644\u0639\u0631\u0636 \u0646\u062a\u064a\u062c\u0629 \u0646\u0645\u0648\u0630\u062c\u0646\u0627:<\/span><\/p>\n
 #fit the two-way ANOVA model<\/span>\nmodel <- aov(weight_loss ~ gender * exercise, data = data)\n\n#view the model output<\/span>\nsummary(model)\n\n# Df Sum Sq Mean Sq F value Pr(>F)    \n#gender 1 15.8 15.80 11.197 0.0015 ** \n#exercise 2 505.6 252.78 179.087 <2e-16 ***\n#gender:exercise 2 13.0 6.51 4.615 0.0141 *  \n#Residuals 54 76.2 1.41                   \n#---\n#Significant. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n<\/strong><\/pre>\n
 \u0648\u0645\u0646 \u0646\u062a\u0627\u0626\u062c \u0627\u0644\u0646\u0645\u0648\u0630\u062c \u064a\u0645\u0643\u0646\u0646\u0627 \u0623\u0646 \u0646\u0631\u0649 \u0623\u0646 \u0627\u0644\u062c\u0646\u0633<\/em> \u0648\u0627\u0644\u062a\u0645\u0631\u064a\u0646<\/em> \u0648\u0627\u0644\u062a\u0641\u0627\u0639\u0644 \u0628\u064a\u0646 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u064a\u0646 \u0643\u0644\u0647\u0627 \u0630\u0627\u062a \u062f\u0644\u0627\u0644\u0629 \u0625\u062d\u0635\u0627\u0626\u064a\u0629 \u0639\u0646\u062f \u0645\u0633\u062a\u0648\u0649 \u062f\u0644\u0627\u0644\u0629 0.05.<\/span><\/p>\n
 \u0627\u0644\u062a\u062d\u0642\u0642 \u0645\u0646 \u0627\u0641\u062a\u0631\u0627\u0636\u0627\u062a \u0627\u0644\u0646\u0645\u0648\u0630\u062c<\/strong><\/span><\/h3>\n
 \u0642\u0628\u0644 \u0623\u0646 \u0646\u0630\u0647\u0628 \u0625\u0644\u0649 \u0623\u0628\u0639\u062f \u0645\u0646 \u0630\u0644\u0643\u060c \u0646\u062d\u062a\u0627\u062c \u0625\u0644\u0649 \u0627\u0644\u062a\u062d\u0642\u0642 \u0645\u0646 \u0627\u0633\u062a\u064a\u0641\u0627\u0621 \u0627\u0641\u062a\u0631\u0627\u0636\u0627\u062a \u0646\u0645\u0648\u0630\u062c\u0646\u0627 \u0628\u062d\u064a\u062b \u062a\u0643\u0648\u0646 \u0646\u062a\u0627\u0626\u062c \u0646\u0645\u0648\u0630\u062c\u0646\u0627 \u0645\u0648\u062b\u0648\u0642\u0629. \u0639\u0644\u0649 \u0648\u062c\u0647 \u0627\u0644\u062e\u0635\u0648\u0635\u060c \u064a\u0641\u062a\u0631\u0636 ANOVA \u062b\u0646\u0627\u0626\u064a \u0627\u0644\u0627\u062a\u062c\u0627\u0647:<\/span><\/p>\n
 1. \u0627\u0644\u0627\u0633\u062a\u0642\u0644\u0627\u0644<\/strong> \u2013 \u064a\u062c\u0628 \u0623\u0646 \u062a\u0643\u0648\u0646 \u0645\u0644\u0627\u062d\u0638\u0627\u062a \u0643\u0644 \u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u0633\u062a\u0642\u0644\u0629 \u0639\u0646 \u0628\u0639\u0636\u0647\u0627 \u0627\u0644\u0628\u0639\u0636. \u0646\u0638\u0631\u064b\u0627 \u0644\u0623\u0646\u0646\u0627 \u0627\u0633\u062a\u062e\u062f\u0645\u0646\u0627<\/span> \u062a\u0635\u0645\u064a\u0645\u064b\u0627 \u0639\u0634\u0648\u0627\u0626\u064a\u064b\u0627 \u060c \u0641\u064a\u062c\u0628 \u062a\u0644\u0628\u064a\u0629 \u0647\u0630\u0627 \u0627\u0644\u0627\u0641\u062a\u0631\u0627\u0636\u060c \u0644\u0630\u0644\u0643 \u0644\u0627 \u062f\u0627\u0639\u064a \u0644\u0644\u0642\u0644\u0642 \u0643\u062b\u064a\u0631\u064b\u0627 \u0628\u0634\u0623\u0646\u0647.<\/span><\/p>\n
 2. \u0627\u0644\u062d\u0627\u0644\u0629 \u0627\u0644\u0637\u0628\u064a\u0639\u064a\u0629<\/strong> \u2013 \u064a\u062c\u0628 \u0623\u0646 \u064a\u0643\u0648\u0646 \u0644\u0644\u0645\u062a\u063a\u064a\u0631 \u0627\u0644\u062a\u0627\u0628\u0639 \u062a\u0648\u0632\u064a\u0639 \u0637\u0628\u064a\u0639\u064a \u062a\u0642\u0631\u064a\u0628\u064b\u0627 \u0644\u0643\u0644 \u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u0646 \u0645\u062c\u0645\u0648\u0639\u0627\u062a \u0627\u0644\u0639\u0627\u0645\u0644\u064a\u0646.<\/span><\/p>\n
 \u0625\u062d\u062f\u0649 \u0627\u0644\u0637\u0631\u0642 \u0644\u0627\u062e\u062a\u0628\u0627\u0631 \u0647\u0630\u0627 \u0627\u0644\u0627\u0641\u062a\u0631\u0627\u0636 \u0647\u064a \u0625\u0646\u0634\u0627\u0621 \u0631\u0633\u0645 \u0628\u064a\u0627\u0646\u064a \u0644\u0628\u0642\u0627\u064a\u0627 \u0627\u0644\u0646\u0645\u0648\u0630\u062c. \u0648\u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0627\u0644\u0628\u0642\u0627\u064a\u0627 \u0645\u0648\u0632\u0639\u0629 \u0628\u0634\u0643\u0644 \u0637\u0628\u064a\u0639\u064a \u062a\u0642\u0631\u064a\u0628\u064b\u0627\u060c \u0641\u064a\u062c\u0628 \u0627\u0633\u062a\u064a\u0641\u0627\u0621 \u0647\u0630\u0627 \u0627\u0644\u0627\u0641\u062a\u0631\u0627\u0636.<\/span><\/p>\n
 #define model residuals\n<\/b><\/span>reside <- model$residuals<\/strong>\n\n#create histogram of residuals<\/strong><\/span>\nhist(resid, main = \"Histogram of Residuals\", xlab = \"Residuals\", col = \"steelblue\")<\/strong><\/pre>\n
 \u064a\u062a\u0645 \u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0628\u0642\u0627\u064a\u0627 \u0628\u0634\u0643\u0644 \u0637\u0628\u064a\u0639\u064a \u062a\u0642\u0631\u064a\u0628\u064b\u0627\u060c \u0644\u0630\u0644\u0643 \u064a\u0645\u0643\u0646\u0646\u0627 \u0623\u0646 \u0646\u0641\u062a\u0631\u0636 \u0623\u0646 \u0627\u0641\u062a\u0631\u0627\u0636 \u0627\u0644\u062d\u0627\u0644\u0629 \u0627\u0644\u0637\u0628\u064a\u0639\u064a\u0629 \u0642\u062f \u062a\u0645 \u0627\u0633\u062a\u064a\u0641\u0627\u0621\u0647.<\/span><\/p>\n
 3. \u0627\u0644\u062a\u0628\u0627\u064a\u0646 \u0627\u0644\u0645\u062a\u0633\u0627\u0648\u064a<\/strong> \u2013 \u0627\u0644\u062a\u0628\u0627\u064a\u0646\u0627\u062a \u0644\u0643\u0644 \u0645\u062c\u0645\u0648\u0639\u0629 \u0645\u062a\u0633\u0627\u0648\u064a\u0629 \u0623\u0648 \u0645\u062a\u0633\u0627\u0648\u064a\u0629 \u062a\u0642\u0631\u064a\u0628\u064b\u0627.<\/span><\/p>\n
 \u0625\u062d\u062f\u0649 \u0627\u0644\u0637\u0631\u0642 \u0644\u0644\u062a\u062d\u0642\u0642 \u0645\u0646 \u0647\u0630\u0627 \u0627\u0644\u0627\u0641\u062a\u0631\u0627\u0636 \u0647\u064a \u0625\u062c\u0631\u0627\u0621 \u0627\u062e\u062a\u0628\u0627\u0631 \u0644\u064a\u0641\u064a\u0646 \u0644\u0645\u0633\u0627\u0648\u0627\u0629 \u0627\u0644\u062a\u0628\u0627\u064a\u0646\u0627\u062a \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u062d\u0632\u0645\u0629 \u0627\u0644\u0633\u064a\u0627\u0631\u0629<\/strong> :<\/span><\/p>\n
 #load car<\/em> package<\/span>\nlibrary(car)\n\n#conduct Levene's Test for equality of variances<\/span>\nleveneTest(weight_loss ~ gender * exercise, data = data)\n\n#Levene's Test for Homogeneity of Variance (center = median)\n# Df F value Pr(>F)\n#group 5 1.8547 0.1177\n#54  \n<\/strong><\/pre>\n
 \u0646\u0638\u0631\u064b\u0627 \u0644\u0623\u0646 \u0627\u0644\u0642\u064a\u0645\u0629 p \u0644\u0644\u0627\u062e\u062a\u0628\u0627\u0631 \u0623\u0643\u0628\u0631 \u0645\u0646 \u0645\u0633\u062a\u0648\u0649 \u0627\u0644\u0623\u0647\u0645\u064a\u0629 \u0644\u062f\u064a\u0646\u0627 \u0648\u0647\u0648 0.05\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0623\u0646 \u0646\u0641\u062a\u0631\u0636 \u0623\u0646 \u0627\u0641\u062a\u0631\u0627\u0636\u0646\u0627 \u0644\u0644\u0645\u0633\u0627\u0648\u0627\u0629 \u0641\u064a \u0627\u0644\u062a\u0628\u0627\u064a\u0646 \u0628\u064a\u0646 \u0627\u0644\u0645\u062c\u0645\u0648\u0639\u0627\u062a \u0642\u062f \u062a\u0645 \u0627\u0633\u062a\u064a\u0641\u0627\u0621\u0647.<\/span><\/p>\n
 \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0627\u062e\u062a\u0644\u0627\u0641\u0627\u062a \u0627\u0644\u0639\u0644\u0627\u062c\u064a\u0629<\/strong><\/span><\/h3>\n
 \u0628\u0645\u062c\u0631\u062f \u0627\u0644\u062a\u062d\u0642\u0642 \u0645\u0646 \u0627\u0633\u062a\u064a\u0641\u0627\u0621 \u0627\u0641\u062a\u0631\u0627\u0636\u0627\u062a \u0627\u0644\u0646\u0645\u0648\u0630\u062c\u060c \u064a\u0645\u0643\u0646\u0646\u0627 \u0628\u0639\u062f \u0630\u0644\u0643 \u0625\u062c\u0631\u0627\u0621 \u0627\u062e\u062a\u0628\u0627\u0631 \u0644\u0627\u062d\u0642 \u0644\u062a\u062d\u062f\u064a\u062f \u0645\u062c\u0645\u0648\u0639\u0627\u062a \u0627\u0644\u0639\u0644\u0627\u062c \u0627\u0644\u062a\u064a \u062a\u062e\u062a\u0644\u0641 \u0639\u0646 \u0628\u0639\u0636\u0647\u0627 \u0627\u0644\u0628\u0639\u0636 \u0628\u0627\u0644\u0636\u0628\u0637.<\/span><\/p>\n
 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0627\u062e\u062a\u0628\u0627\u0631 \u0627\u0644\u0644\u0627\u062d\u0642 \u0627\u0644\u062e\u0627\u0635 \u0628\u0646\u0627\u060c \u0633\u0646\u0633\u062a\u062e\u062f\u0645 \u0627\u0644\u062f\u0627\u0644\u0629 TukeyHSD()<\/strong> \u0644\u0625\u062c\u0631\u0627\u0621 \u0627\u062e\u062a\u0628\u0627\u0631 Tukey \u0644\u0625\u062c\u0631\u0627\u0621 \u0645\u0642\u0627\u0631\u0646\u0627\u062a \u0645\u062a\u0639\u062f\u062f\u0629:<\/span><\/p>\n
 #perform Tukey's Test for multiple comparisons\n<\/span>TukeyHSD(model, conf.level=.95) \n\n#Tukey multiple comparisons of means\n# 95% family-wise confidence level\n#\n#Fit: aov(formula = weight_loss ~ gender * exercise, data = data)\n#\n#$gender\n# diff lwr upr p adj\n#Male-Female 1.026456 0.4114451 1.641467 0.0014967\n#\n#$exercise\n# diff lwr upr p adj\n#Light-Intense -4.813064 -5.718493 -3.907635 0.0e+00\n#None-Intense -6.938966 -7.844395 -6.033537 0.0e+00\n#None-Light -2.125902 -3.031331 -1.220473 1.8e-06\n#\n#$`gender:exercise`\n# diff lwr upr p adj\n#Male:Intense-Female:Intense 2.0628297 0.4930588 3.63260067 0.0036746\n#Female:Light-Female:Intense -4.3883563 -5.9581272 -2.81858535 0.0000000\n#Male:Light-Female:Intense -3.1749419 -4.7447128 -1.60517092 0.0000027\n#Female:None-Female:Intense -5.8091131 -7.3788841 -4.23934219 0.0000000\n#Male:None-Female:Intense -6.0059891 -7.5757600 -4.43621813 0.0000000\n#Female:Light-Male:Intense -6.4511860 -8.0209570 -4.88141508 0.0000000\n#Male:Light-Male:Intense -5.2377716 -6.8075425 -3.66800066 0.0000000\n#Female:None-Male:Intense -7.8719429 -9.4417138 -6.30217192 0.0000000\n#Male:None-Male:Intense -8.0688188 -9.6385897 -6.49904786 0.0000000\n#Male:Light-Female:Light 1.2134144 -0.3563565 2.78318536 0.2185439\n#Female:None-Female:Light -1.4207568 -2.9905278 0.14901410 0.0974193\n#Male:None-Female:Light -1.6176328 -3.1874037 -0.04786184 0.0398106\n#Female:None-Male:Light -2.6341713 -4.2039422 -1.06440032 0.0001050\n#Male:None-Male:Light -2.8310472 -4.4008181 -1.26127627 0.0000284\n#Male:None-Female:None -0.1968759 -1.7666469 1.37289500 0.9990364<\/strong><\/pre>\n
 \u062a\u0634\u064a\u0631 \u0627\u0644\u0642\u064a\u0645\u0629 p \u0625\u0644\u0649 \u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646 \u0647\u0646\u0627\u0643 \u0641\u0631\u0642 \u0630\u0648 \u062f\u0644\u0627\u0644\u0629 \u0625\u062d\u0635\u0627\u0626\u064a\u0629 \u0628\u064a\u0646 \u0643\u0644 \u0645\u062c\u0645\u0648\u0639\u0629 \u0623\u0645 \u0644\u0627.<\/span><\/p>\n
 \u0639\u0644\u0649 \u0633\u0628\u064a\u0644 \u0627\u0644\u0645\u062b\u0627\u0644\u060c \u0641\u064a \u0627\u0644\u0635\u0641 \u0627\u0644\u0623\u062e\u064a\u0631 \u0623\u0639\u0644\u0627\u0647\u060c \u0646\u0631\u0649 \u0623\u0646 \u0645\u062c\u0645\u0648\u0639\u0629 \u0627\u0644\u0631\u062c\u0627\u0644 \u0627\u0644\u0630\u064a\u0646 \u0644\u0645 \u064a\u0645\u0627\u0631\u0633\u0648\u0627 \u0627\u0644\u0631\u064a\u0627\u0636\u0629 \u0644\u0645 \u062a\u0634\u0647\u062f \u0641\u0631\u0642\u064b\u0627 \u0630\u0648 \u062f\u0644\u0627\u0644\u0629 \u0625\u062d\u0635\u0627\u0626\u064a\u0629 \u0641\u064a \u0641\u0642\u062f\u0627\u0646 \u0627\u0644\u0648\u0632\u0646 \u0645\u0642\u0627\u0631\u0646\u0629 \u0628\u0645\u062c\u0645\u0648\u0639\u0629 \u0627\u0644\u0646\u0633\u0627\u0621 \u0627\u0644\u062a\u064a \u0644\u0645 \u062a\u0645\u0627\u0631\u0633 \u0627\u0644\u0631\u064a\u0627\u0636\u0629 (\u0642\u064a\u0645\u0629 p: 0.990364).<\/span><\/p>\n
 \u064a\u0645\u0643\u0646\u0646\u0627 \u0623\u064a\u0636\u064b\u0627 \u062a\u0635\u0648\u0631 \u0641\u0648\u0627\u0635\u0644 \u0627\u0644\u062b\u0642\u0629 95% \u0627\u0644\u0646\u0627\u062a\u062c\u0629 \u0639\u0646 \u0627\u062e\u062a\u0628\u0627\u0631 Tukey \u0628\u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062f\u0627\u0644\u0629 plot()<\/strong> \u0641\u064a R:<\/span><\/p>\n
 #set axis margins so labels don't get cut off\n<\/span>by(mar=c(4.1, 13, 4.1, 2.1))\n\n#create confidence interval for each comparison\n<\/span>plot(TukeyHSD(model, conf.level=.95), las = 2)\n<\/strong><\/pre>\n
 \u0627\u0644\u0625\u0628\u0644\u0627\u063a \u0639\u0646 \u0646\u062a\u0627\u0626\u062c ANOVA \u062b\u0646\u0627\u0626\u064a\u0629 \u0627\u0644\u0627\u062a\u062c\u0627\u0647<\/span><\/strong><\/h3>\n
 \u0648\u0623\u062e\u064a\u0631\u0627\u064b \u064a\u0645\u0643\u0646\u0646\u0627 \u062a\u0642\u0631\u064a\u0631 \u0646\u062a\u0627\u0626\u062c \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u062a\u0628\u0627\u064a\u0646 \u0627\u0644\u062b\u0646\u0627\u0626\u064a \u0628\u0637\u0631\u064a\u0642\u0629 \u062a\u0644\u062e\u0635 \u0627\u0644\u0646\u062a\u0627\u0626\u062c:<\/span><\/p>\n
 \u062a\u0645 \u0625\u062c\u0631\u0627\u0621 ANOVA \u062b\u0646\u0627\u0626\u064a \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0644\u0641\u062d\u0635 \u0622\u062b\u0627\u0631 \u0627\u0644\u062c\u0646\u0633 ( \u0630\u0643\u0631\u060c \u0623\u0646\u062b\u0649)<\/em> \u0648\u0628\u0631\u0646\u0627\u0645\u062c \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 (\u0644\u0627 \u0634\u064a\u0621\u060c \u062e\u0641\u064a\u0641\u060c \u0645\u0643\u062b\u0641)<\/em> \u0639\u0644\u0649 \u0641\u0642\u062f\u0627\u0646 \u0627\u0644\u0648\u0632\u0646 (\u064a\u0642\u0627\u0633 \u0628\u0627\u0644\u062c\u0646\u064a\u0647).<\/em> \u0643\u0627\u0646 \u0647\u0646\u0627\u0643 \u062a\u0641\u0627\u0639\u0644 \u0630\u0648 \u062f\u0644\u0627\u0644\u0629 \u0625\u062d\u0635\u0627\u0626\u064a\u0629 \u0628\u064a\u0646 \u0622\u062b\u0627\u0631 \u0627\u0644\u062c\u0646\u0633 \u0648\u0645\u0645\u0627\u0631\u0633\u0629 \u0627\u0644\u0631\u064a\u0627\u0636\u0629 \u0639\u0644\u0649 \u0641\u0642\u062f\u0627\u0646 \u0627\u0644\u0648\u0632\u0646 (F(2\u060c 54) = 4.615\u060c \u0639 = 0.0141).<\/span> \u062a\u0645 \u0625\u062c\u0631\u0627\u0621 \u0627\u062e\u062a\u0628\u0627\u0631\u0627\u062a HSD \u0627\u0644\u062e\u0627\u0635\u0629 \u0628\u0640 Tukey.<\/span><\/p>\n
 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0631\u062c\u0627\u0644\u060c \u0623\u062f\u0649 \u0628\u0631\u0646\u0627\u0645\u062c \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u0645\u0643\u062b\u0641\u0629<\/em> \u0625\u0644\u0649 \u0641\u0642\u062f\u0627\u0646 \u0627\u0644\u0648\u0632\u0646 \u0628\u0634\u0643\u0644 \u0623\u0643\u0628\u0631 \u0628\u0643\u062b\u064a\u0631 \u0645\u0646 \u0627\u0644\u0628\u0631\u0646\u0627\u0645\u062c \u0627\u0644\u062e\u0641\u064a\u0641<\/em> (P <0.0001) \u0623\u0648 \u0639\u062f\u0645 \u0648\u062c\u0648\u062f \u0628\u0631\u0646\u0627\u0645\u062c \u062a\u0645\u0631\u064a\u0646<\/em> (P <0.0001). \u0628\u0627\u0644\u0625\u0636\u0627\u0641\u0629 \u0625\u0644\u0649 \u0630\u0644\u0643\u060c \u0623\u062f\u0649 \u0627\u062a\u0628\u0627\u0639 \u0646\u0638\u0627\u0645 \u063a\u0630\u0627\u0626\u064a \u062e\u0641\u064a\u0641<\/em> \u0644\u062f\u0649 \u0627\u0644\u0631\u062c\u0627\u0644 \u0625\u0644\u0649 \u0641\u0642\u062f\u0627\u0646 \u0627\u0644\u0648\u0632\u0646 \u0628\u0634\u0643\u0644 \u0623\u0643\u0628\u0631 \u0628\u0643\u062b\u064a\u0631 \u0645\u0646 \u0639\u062f\u0645 \u0645\u0645\u0627\u0631\u0633\u0629 \u0623\u064a \u0646\u0638\u0627\u0645 \u0631\u064a\u0627\u0636\u064a<\/em> (P <0.0001).<\/span><\/p>\n
 \u0628\u0627\u0644\u0646\u0633\u0628\u0629 \u0644\u0644\u0646\u0633\u0627\u0621\u060c \u0623\u062f\u0649 \u0628\u0631\u0646\u0627\u0645\u062c \u0627\u0644\u062a\u0645\u0627\u0631\u064a\u0646 \u0627\u0644\u0645\u0643\u062b\u0641\u0629<\/em> \u0625\u0644\u0649 \u0641\u0642\u062f\u0627\u0646 \u0627\u0644\u0648\u0632\u0646 \u0628\u0634\u0643\u0644 \u0623\u0643\u0628\u0631 \u0628\u0643\u062b\u064a\u0631 \u0645\u0646 \u0627\u0644\u0628\u0631\u0646\u0627\u0645\u062c \u0627\u0644\u062e\u0641\u064a\u0641<\/em> (P <0.0001) \u0623\u0648 \u0639\u062f\u0645 \u0648\u062c\u0648\u062f \u0628\u0631\u0646\u0627\u0645\u062c \u062a\u0645\u0631\u064a\u0646<\/em> (P <0.0001).<\/span><\/p>\n
 \u062a\u0645 \u0625\u062c\u0631\u0627\u0621 \u0641\u062d\u0648\u0635\u0627\u062a \u0627\u0644\u062d\u0627\u0644\u0629 \u0627\u0644\u0637\u0628\u064a\u0639\u064a\u0629 \u0648\u0627\u062e\u062a\u0628\u0627\u0631 \u0644\u064a\u0641\u064a\u0646 \u0644\u0644\u062a\u062d\u0642\u0642 \u0645\u0646 \u0627\u0633\u062a\u064a\u0641\u0627\u0621 \u0627\u0641\u062a\u0631\u0627\u0636\u0627\u062a ANOVA.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"
\u064a\u062a\u0645 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 ANOVA \u062b\u0646\u0627\u0626\u064a \u0627\u0644\u0627\u062a\u062c\u0627\u0647 (“\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u062a\u0628\u0627\u064a\u0646”) \u0644\u062a\u062d\u062f\u064a\u062f \u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646 \u0647\u0646\u0627\u0643 \u0641\u0631\u0642 \u0630\u0648 \u062f\u0644\u0627\u0644\u0629 \u0625\u062d\u0635\u0627\u0626\u064a\u0629 \u0628\u064a\u0646 \u0645\u062a\u0648\u0633\u0637\u0627\u062a \u062b\u0644\u0627\u062b \u0645\u062c\u0645\u0648\u0639\u0627\u062a \u0645\u0633\u062a\u0642\u0644\u0629 \u0623\u0648 \u0623\u0643\u062b\u0631 \u062a\u0645 \u062a\u0642\u0633\u064a\u0645\u0647\u0627 \u0639\u0628\u0631 \u0639\u0627\u0645\u0644\u064a\u0646 \u0623\u0645 \u0644\u0627. \u064a\u0634\u0631\u062d \u0647\u0630\u0627 \u0627\u0644\u0628\u0631\u0646\u0627\u0645\u062c \u0627\u0644\u062a\u0639\u0644\u064a\u0645\u064a \u0643\u064a\u0641\u064a\u0629 \u0625\u062c\u0631\u0627\u0621 ANOVA \u062b\u0646\u0627\u0626\u064a \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0641\u064a R. \u0645\u062b\u0627\u0644: \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u062a\u0628\u0627\u064a\u0646 \u062b\u0646\u0627\u0626\u064a \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0641\u064a R \u0644\u0646\u0641\u062a\u0631\u0636 \u0623\u0646\u0646\u0627 \u0646\u0631\u064a\u062f \u062a\u062d\u062f\u064a\u062f \u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0634\u062f\u0629 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[11],"tags":[],"yoast_head":"\n\u0643\u064a\u0641\u064a\u0629 \u0625\u062c\u0631\u0627\u0621 ANOVA \u062b\u0646\u0627\u0626\u064a \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0641\u064a R - Statorials<\/title>\n<meta name=\"description\" content=\"\u064a\u0634\u0631\u062d \u0647\u0630\u0627 \u0627\u0644\u0628\u0631\u0646\u0627\u0645\u062c \u0627\u0644\u062a\u0639\u0644\u064a\u0645\u064a \u0643\u064a\u0641\u064a\u0629 \u0625\u062c\u0631\u0627\u0621 ANOVA \u062b\u0646\u0627\u0626\u064a \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0628\u0633\u0647\u0648\u0644\u0629 \u0641\u064a R.\" \/>\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\/ar\/\u0627\u0654\u0646\u0648\u0641\u0627-\u0631\u0627-\u0627\u062a\u062c\u0627\u0647\u064a\u0646\/\" \/>\n<meta property=\"og:locale\" content=\"az_AZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u0643\u064a\u0641\u064a\u0629 \u0625\u062c\u0631\u0627\u0621 ANOVA \u062b\u0646\u0627\u0626\u064a \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0641\u064a R - Statorials\" \/>\n<meta property=\"og:description\" content=\"\u064a\u0634\u0631\u062d \u0647\u0630\u0627 \u0627\u0644\u0628\u0631\u0646\u0627\u0645\u062c \u0627\u0644\u062a\u0639\u0644\u064a\u0645\u064a \u0643\u064a\u0641\u064a\u0629 \u0625\u062c\u0631\u0627\u0621 ANOVA \u062b\u0646\u0627\u0626\u064a \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0628\u0633\u0647\u0648\u0644\u0629 \u0641\u064a R.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/ar\/\u0627\u0654\u0646\u0648\u0641\u0627-\u0631\u0627-\u0627\u062a\u062c\u0627\u0647\u064a\u0646\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-29T18:02:44+00:00\" \/>\n<meta name=\"author\" content=\"\u062f\u0643\u062a\u0648\u0631 \u0628\u0646\u064a\u0627\u0645\u064a\u0646 \u0623\u0646\u062f\u0631\u0633\u0648\u0646\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"\u062f\u0643\u062a\u0648\u0631 \u0628\u0646\u064a\u0627\u0645\u064a\u0646 \u0623\u0646\u062f\u0631\u0633\u0648\u0646\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/ar\/%d8%a7%d9%94%d9%86%d9%88%d9%81%d8%a7-%d8%b1%d8%a7-%d8%a7%d8%aa%d8%ac%d8%a7%d9%87%d9%8a%d9%86\/\",\"url\":\"https:\/\/statorials.org\/ar\/%d8%a7%d9%94%d9%86%d9%88%d9%81%d8%a7-%d8%b1%d8%a7-%d8%a7%d8%aa%d8%ac%d8%a7%d9%87%d9%8a%d9%86\/\",\"name\":\"\u0643\u064a\u0641\u064a\u0629 \u0625\u062c\u0631\u0627\u0621 ANOVA \u062b\u0646\u0627\u0626\u064a \u0627\u0644\u0627\u062a\u062c\u0627\u0647 \u0641\u064a R - 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