{"id":488,"date":"2023-07-29T18:02:44","date_gmt":"2023-07-29T18:02:44","guid":{"rendered":"https:\/\/statorials.org\/tr\/anova-ra-iki-yonlu\/"},"modified":"2023-07-29T18:02:44","modified_gmt":"2023-07-29T18:02:44","slug":"anova-ra-iki-yonlu","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/anova-ra-iki-yonlu\/","title":{"rendered":"R'de iki y\u00f6nl\u00fc anova nas\u0131l ger\u00e7ekle\u015ftirilir"},"content":{"rendered":"

<\/p>\n

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\u0130ki fakt\u00f6re b\u00f6l\u00fcnm\u00fc\u015f \u00fc\u00e7 veya daha fazla ba\u011f\u0131ms\u0131z grubun ortalamalar\u0131 aras\u0131nda istatistiksel olarak anlaml\u0131 bir fark olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in iki y\u00f6nl\u00fc ANOVA<\/a> (“varyans analizi”) kullan\u0131l\u0131r.<\/span><\/p>\n

Bu e\u011fitimde R’de iki y\u00f6nl\u00fc ANOVA’n\u0131n nas\u0131l ger\u00e7ekle\u015ftirilece\u011fi a\u00e7\u0131klanmaktad\u0131r.<\/span><\/p>\n

\u00d6rnek: R’de iki y\u00f6nl\u00fc ANOVA<\/strong><\/span><\/h3>\n

Diyelim ki egzersiz yo\u011funlu\u011funun ve cinsiyetin kilo kayb\u0131n\u0131 etkileyip etkilemedi\u011fini belirlemek istiyoruz. Bu durumda, bakt\u0131\u011f\u0131m\u0131z iki fakt\u00f6r egzersiz<\/em> ve cinsiyettir<\/em> ve yan\u0131t de\u011fi\u015fkeni ise kilo cinsinden \u00f6l\u00e7\u00fclen kilo kayb\u0131d\u0131r<\/em> .<\/span><\/p>\n

Egzersizin ve cinsiyetin kilo kayb\u0131n\u0131 etkileyip etkilemedi\u011fini belirlemek ve egzersiz ile cinsiyet aras\u0131nda kilo kayb\u0131nda bir etkile\u015fim olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in iki y\u00f6nl\u00fc bir ANOVA ger\u00e7ekle\u015ftirebiliriz.<\/span><\/p>\n

Her birinden 10’unu bir ay boyunca egzersizsiz, hafif egzersiz veya yo\u011fun egzersiz program\u0131n\u0131 takip edecek \u015fekilde rastgele atad\u0131\u011f\u0131m\u0131z bir deneye kat\u0131lmak \u00fczere 30 erkek ve 30 kad\u0131n topluyoruz.<\/span><\/p>\n

A\u015fa\u011f\u0131daki kod \u00e7al\u0131\u015faca\u011f\u0131m\u0131z veri \u00e7er\u00e7evesini olu\u015fturur:<\/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
 Verileri ke\u015ffedin<\/strong><\/span><\/h3>\n
 \u0130ki y\u00f6nl\u00fc ANOVA modelini bile yerle\u015ftirmeden \u00f6nce, dplyr<\/strong> paketini kullanarak alt\u0131 tedavi grubunun her biri i\u00e7in kilo kayb\u0131n\u0131n ortalamas\u0131n\u0131 ve standart sapmas\u0131n\u0131 bularak verileri daha iyi anlayabiliriz:<\/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
 Ayr\u0131ca her grup i\u00e7in kilo kayb\u0131 da\u011f\u0131l\u0131m\u0131n\u0131 g\u00f6rselle\u015ftirmek amac\u0131yla alt\u0131 tedavi grubunun her biri i\u00e7in bir kutu grafi\u011fi olu\u015fturabiliriz:<\/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
 Yo\u011fun<\/em> egzersiz yapan iki grubun kilo verme de\u011ferlerinin daha y\u00fcksek oldu\u011funu hemen g\u00f6rebiliyoruz. Ayr\u0131ca hem yo\u011fun<\/em> hem de hafif<\/em> egzersiz gruplar\u0131nda erkeklerin kad\u0131nlara g\u00f6re kilo verme de\u011ferlerinin daha y\u00fcksek oldu\u011funu g\u00f6rebiliyoruz.<\/span><\/p>\n
 Daha sonra, bu g\u00f6rsel farkl\u0131l\u0131klar\u0131n ger\u00e7ekten istatistiksel olarak anlaml\u0131 olup olmad\u0131\u011f\u0131n\u0131 g\u00f6rmek i\u00e7in iki y\u00f6nl\u00fc ANOVA modelini verilerimize uyarlayaca\u011f\u0131z.<\/span><\/p>\n
 \u0130ki y\u00f6nl\u00fc ANOVA modelinin tak\u0131lmas\u0131<\/strong><\/span><\/h3>\n
 R’ye iki y\u00f6nl\u00fc bir ANOVA modeli yerle\u015ftirmek i\u00e7in genel s\u00f6zdizimi \u015f\u00f6yledir:<\/span><\/p>\n
 aov(yan\u0131t de\u011fi\u015fkeni ~predictor_variable1 *predictor_variable2, veri = veri k\u00fcmesi)<\/span><\/strong><\/p>\n
 \u0130ki yorday\u0131c\u0131 de\u011fi\u015fken aras\u0131ndaki *<\/strong> i\u015faretinin, iki yorday\u0131c\u0131 de\u011fi\u015fken aras\u0131ndaki etkile\u015fim etkisini de test etmek istedi\u011fimizi g\u00f6sterdi\u011fini unutmay\u0131n.<\/span><\/p>\n
 \u00d6rne\u011fimizde, yan\u0131t de\u011fi\u015fkeni olarak kilo_kayb\u0131n\u0131<\/em> ve iki yorday\u0131c\u0131 de\u011fi\u015fken olarak cinsiyet<\/em> ve egzersizi<\/em> kullanarak iki y\u00f6nl\u00fc ANOVA modeline uymak i\u00e7in a\u015fa\u011f\u0131daki kodu kullanabiliriz.<\/span><\/p>\n
 Daha sonra modelimizin sonucunu g\u00f6r\u00fcnt\u00fclemek i\u00e7in Summary()<\/strong> fonksiyonunu kullanabiliriz:<\/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
 Model sonu\u00e7lar\u0131ndan cinsiyet<\/em> , egzersiz<\/em> ve iki de\u011fi\u015fken aras\u0131ndaki etkile\u015fimin istatistiksel olarak 0,05 anlaml\u0131l\u0131k d\u00fczeyinde anlaml\u0131 oldu\u011funu g\u00f6rebiliriz.<\/span><\/p>\n
 Model varsay\u0131mlar\u0131n\u0131n kontrol edilmesi<\/strong><\/span><\/h3>\n
 Daha ileri gitmeden \u00f6nce, model sonu\u00e7lar\u0131m\u0131z\u0131n g\u00fcvenilir olmas\u0131 i\u00e7in modelimizin varsay\u0131mlar\u0131n\u0131n kar\u015f\u0131land\u0131\u011f\u0131n\u0131 do\u011frulamam\u0131z gerekir. \u00d6zellikle iki y\u00f6nl\u00fc bir ANOVA \u015funu varsayar:<\/span><\/p>\n
 1. Ba\u011f\u0131ms\u0131zl\u0131k<\/strong> \u2013 her grubun g\u00f6zlemleri birbirinden ba\u011f\u0131ms\u0131z olmal\u0131d\u0131r.<\/span> Rastgelele\u015ftirilmi\u015f bir tasar\u0131m kulland\u0131\u011f\u0131m\u0131z i\u00e7in<\/span> bu varsay\u0131m\u0131n kar\u015f\u0131lanmas\u0131 gerekir, b\u00f6ylece bu konuda \u00e7ok fazla endi\u015felenmemize gerek kalmaz.<\/span><\/p>\n
 2. Normallik<\/strong> \u2013 ba\u011f\u0131ml\u0131 de\u011fi\u015fken, iki fakt\u00f6rden olu\u015fan gruplar\u0131n her bir kombinasyonu i\u00e7in yakla\u015f\u0131k olarak normal bir da\u011f\u0131l\u0131ma sahip olmal\u0131d\u0131r.<\/span><\/p>\n
 Bu varsay\u0131m\u0131 test etmenin bir yolu model art\u0131klar\u0131n\u0131n histogram\u0131n\u0131 olu\u015fturmakt\u0131r. Art\u0131klar yakla\u015f\u0131k olarak normal da\u011f\u0131l\u0131yorsa, bu varsay\u0131m kar\u015f\u0131lanmal\u0131d\u0131r.<\/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
 Art\u0131klar yakla\u015f\u0131k olarak normal da\u011f\u0131l\u0131ma sahip oldu\u011fundan normallik varsay\u0131m\u0131n\u0131n kar\u015f\u0131land\u0131\u011f\u0131n\u0131 varsayabiliriz.<\/span><\/p>\n
 3. E\u015fit varyans<\/strong> \u2013 her grubun varyanslar\u0131 e\u015fit veya yakla\u015f\u0131k olarak e\u015fittir.<\/span><\/p>\n
 Bu varsay\u0131m\u0131 kontrol etmenin bir yolu, araba<\/strong> paketini kullanarak varyanslar\u0131n e\u015fitli\u011fi i\u00e7in Levene testi yapmakt\u0131r:<\/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
 Testin p de\u011feri bizim anlaml\u0131l\u0131k d\u00fczeyimiz olan 0,05’ten b\u00fcy\u00fck oldu\u011fundan gruplar aras\u0131 varyanslar\u0131n e\u015fitli\u011fi varsay\u0131m\u0131m\u0131z\u0131n kar\u015f\u0131land\u0131\u011f\u0131n\u0131 varsayabiliriz.<\/span><\/p>\n
 Tedavi farkl\u0131l\u0131klar\u0131n\u0131 analiz edin<\/strong><\/span><\/h3>\n
 Model varsay\u0131mlar\u0131n\u0131n kar\u015f\u0131land\u0131\u011f\u0131n\u0131 do\u011frulad\u0131ktan sonra, hangi tedavi gruplar\u0131n\u0131n birbirinden farkl\u0131 oldu\u011funu tam olarak belirlemek i\u00e7in bir post hoc testi ger\u00e7ekle\u015ftirebiliriz.<\/span><\/p>\n
 Post hoc testimizde, \u00e7oklu kar\u015f\u0131la\u015ft\u0131rmalar i\u00e7in Tukey testini ger\u00e7ekle\u015ftirmek \u00fczere TukeyHSD()<\/strong> i\u015flevini kullanaca\u011f\u0131z:<\/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
 P de\u011feri, her grup aras\u0131nda istatistiksel olarak anlaml\u0131 bir fark olup olmad\u0131\u011f\u0131n\u0131 g\u00f6sterir.<\/span><\/p>\n
 \u00d6rne\u011fin, yukar\u0131daki son sat\u0131rda, egzersiz yapmayan erkek grubunun, egzersiz yapmayan kad\u0131n grubuna k\u0131yasla kilo kayb\u0131nda istatistiksel olarak anlaml\u0131 bir fark ya\u015famad\u0131\u011f\u0131n\u0131 g\u00f6r\u00fcyoruz (p de\u011feri: 0,990364).<\/span><\/p>\n
 Ayr\u0131ca Tukey testinden elde edilen %95 g\u00fcven aral\u0131klar\u0131n\u0131 R’dekiplot ()<\/strong> fonksiyonunu kullanarak g\u00f6rselle\u015ftirebiliriz:<\/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
 \u0130ki Y\u00f6nl\u00fc ANOVA Sonu\u00e7lar\u0131n\u0131n Raporlanmas\u0131<\/span><\/strong><\/h3>\n
 Son olarak iki y\u00f6nl\u00fc ANOVA sonu\u00e7lar\u0131n\u0131 \u00f6zetleyecek \u015fekilde raporlayabiliriz:<\/span><\/p>\n
 Cinsiyetin ( erkek, kad\u0131n)<\/em> ve egzersiz program\u0131n\u0131n (yok, hafif, yo\u011fun)<\/em> kilo kayb\u0131 (kilo cinsinden \u00f6l\u00e7\u00fcl\u00fcr) \u00fczerindeki etkilerini incelemek i\u00e7in iki y\u00f6nl\u00fc bir ANOVA yap\u0131ld\u0131.<\/em> Cinsiyet ve egzersizin kilo kayb\u0131na etkisi aras\u0131nda istatistiksel olarak anlaml\u0131 bir etkile\u015fim vard\u0131 (F(2, 54) = 4,615, p = 0,0141).<\/span> Post-hoc Tukey’in HSD testleri yap\u0131ld\u0131.<\/span><\/p>\n
 Erkekler i\u00e7in yo\u011fun<\/em> bir egzersiz program\u0131, hafif bir<\/em> programa (p < 0,0001) veya egzersiz yap\u0131lmayan programa<\/em> (p < 0,0001) g\u00f6re \u00f6nemli \u00f6l\u00e7\u00fcde daha fazla kilo kayb\u0131yla sonu\u00e7land\u0131. Ek olarak erkeklerde hafif<\/em> bir diyet, egzersiz yapmamaya<\/em> k\u0131yasla \u00f6nemli \u00f6l\u00e7\u00fcde daha fazla kilo kayb\u0131yla sonu\u00e7land\u0131 (p < 0,0001).<\/span><\/p>\n
 Kad\u0131nlar i\u00e7in yo\u011fun<\/em> bir egzersiz program\u0131, hafif bir<\/em> programa (p < 0,0001) veya egzersiz yap\u0131lmayan programa<\/em> (p < 0,0001) g\u00f6re \u00f6nemli \u00f6l\u00e7\u00fcde daha fazla kilo kayb\u0131yla sonu\u00e7land\u0131.<\/span><\/p>\n
 ANOVA’n\u0131n varsay\u0131mlar\u0131n\u0131n kar\u015f\u0131land\u0131\u011f\u0131n\u0131 do\u011frulamak i\u00e7in normallik kontrolleri ve Levene testi yap\u0131ld\u0131.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"
\u0130ki fakt\u00f6re b\u00f6l\u00fcnm\u00fc\u015f \u00fc\u00e7 veya daha fazla ba\u011f\u0131ms\u0131z grubun ortalamalar\u0131 aras\u0131nda istatistiksel olarak anlaml\u0131 bir fark olup olmad\u0131\u011f\u0131n\u0131 belirlemek i\u00e7in iki y\u00f6nl\u00fc ANOVA (“varyans analizi”) kullan\u0131l\u0131r. Bu e\u011fitimde R’de iki y\u00f6nl\u00fc ANOVA’n\u0131n nas\u0131l ger\u00e7ekle\u015ftirilece\u011fi a\u00e7\u0131klanmaktad\u0131r. \u00d6rnek: R’de iki y\u00f6nl\u00fc ANOVA Diyelim ki egzersiz yo\u011funlu\u011funun ve cinsiyetin kilo kayb\u0131n\u0131 etkileyip etkilemedi\u011fini belirlemek istiyoruz. Bu durumda, bakt\u0131\u011f\u0131m\u0131z […]<\/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":[],"class_list":["post-488","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"\nR - Statorials'da iki y\u00f6nl\u00fc ANOVA nas\u0131l ger\u00e7ekle\u015ftirilir?<\/title>\n<meta name=\"description\" content=\"Bu e\u011fitimde, R'de iki y\u00f6nl\u00fc ANOVA'n\u0131n kolayca nas\u0131l ger\u00e7ekle\u015ftirilece\u011fi a\u00e7\u0131klanmaktad\u0131r.\" \/>\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\/tr\/anova-ra-iki-yonlu\/\" \/>\n<meta property=\"og:locale\" content=\"tr_TR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"R - Statorials'da iki y\u00f6nl\u00fc ANOVA nas\u0131l ger\u00e7ekle\u015ftirilir?\" \/>\n<meta property=\"og:description\" content=\"Bu e\u011fitimde, R'de iki y\u00f6nl\u00fc ANOVA'n\u0131n kolayca nas\u0131l ger\u00e7ekle\u015ftirilece\u011fi a\u00e7\u0131klanmaktad\u0131r.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/tr\/anova-ra-iki-yonlu\/\" \/>\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=\"Dr.benjamin anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Yazan:\" \/>\n\t<meta name=\"twitter:data1\" content=\"Dr.benjamin anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Tahmini okuma s\u00fcresi\" \/>\n\t<meta name=\"twitter:data2\" content=\"7 dakika\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/tr\/anova-ra-iki-yonlu\/\",\"url\":\"https:\/\/statorials.org\/tr\/anova-ra-iki-yonlu\/\",\"name\":\"R - Statorials'da iki y\u00f6nl\u00fc ANOVA nas\u0131l ger\u00e7ekle\u015ftirilir?\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/tr\/#website\"},\"datePublished\":\"2023-07-29T18:02:44+00:00\",\"dateModified\":\"2023-07-29T18:02:44+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\"},\"description\":\"Bu e\u011fitimde, R'de iki y\u00f6nl\u00fc ANOVA'n\u0131n kolayca nas\u0131l ger\u00e7ekle\u015ftirilece\u011fi a\u00e7\u0131klanmaktad\u0131r.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/tr\/anova-ra-iki-yonlu\/#breadcrumb\"},\"inLanguage\":\"tr\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/tr\/anova-ra-iki-yonlu\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/tr\/anova-ra-iki-yonlu\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Ev\",\"item\":\"https:\/\/statorials.org\/tr\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"R'de iki y\u00f6nl\u00fc anova nas\u0131l ger\u00e7ekle\u015ftirilir\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/tr\/#website\",\"url\":\"https:\/\/statorials.org\/tr\/\",\"name\":\"Statorials\",\"description\":\"\u0130statistik okuryazarl\u0131\u011f\u0131 rehberiniz!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/tr\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"tr\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/365dc158a39a7c8ae256355451e3de48\",\"name\":\"Dr.benjamin anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"tr\",\"@id\":\"https:\/\/statorials.org\/tr\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/tr\/wp-content\/uploads\/2023\/10\/Dr.-Benjamin-Anderson-96x96.jpg\",\"caption\":\"Dr.benjamin anderson\"},\"description\":\"Merhaba, ben Benjamin, emekli bir istatistik profes\u00f6r\u00fc ve Statorials \u00f6\u011fretmenine d\u00f6n\u00fc\u015ft\u00fcm. \u0130statistik alan\u0131ndaki kapsaml\u0131 deneyimim ve uzmanl\u0131\u011f\u0131mla, \u00f6\u011frencilerimi Statorials arac\u0131l\u0131\u011f\u0131yla g\u00fc\u00e7lendirmek i\u00e7in bilgilerimi payla\u015fmaya can at\u0131yorum. 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