{"id":485,"date":"2023-07-29T18:17:31","date_gmt":"2023-07-29T18:17:31","guid":{"rendered":"https:\/\/statorials.org\/tr\/rdeki-ancova\/"},"modified":"2023-07-29T18:17:31","modified_gmt":"2023-07-29T18:17:31","slug":"rdeki-ancova","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/rdeki-ancova\/","title":{"rendered":"R'de ancova nas\u0131l yap\u0131l\u0131r"},"content":{"rendered":"

<\/p>\n

\n

Bu e\u011fitimde R’de ANCOVA’n\u0131n<\/a> nas\u0131l ger\u00e7ekle\u015ftirilece\u011fine ili\u015fkin bir \u00f6rnek sunulmaktad\u0131r.<\/span><\/p>\n

\u00d6rnek: R’de ANCOVA<\/strong><\/span><\/h3>\n

\u00c7al\u0131\u015fma tekni\u011finin s\u0131nav sonu\u00e7lar\u0131 \u00fczerinde etkisi olup olmad\u0131\u011f\u0131n\u0131 test etmek i\u00e7in a\u015fa\u011f\u0131daki de\u011fi\u015fkenleri kullanarak bir ANCOVA ger\u00e7ekle\u015ftirece\u011fiz:<\/span><\/p>\n

    \n
  • Teknik \u00e7al\u0131\u015fma<\/strong> : Analiz etmek istedi\u011fimiz ba\u011f\u0131ms\u0131z de\u011fi\u015fken<\/span><\/li>\n
  • Mevcut \u00f6\u011frenci notu<\/strong> : Dikkate almak istedi\u011fimiz ortak de\u011fi\u015fken<\/span><\/li>\n
  • \u0130nceleme Puan\u0131<\/strong> : Analiz etmek istedi\u011fimiz yan\u0131t de\u011fi\u015fkenleri<\/span><\/li>\n<\/ul>\n

    A\u015fa\u011f\u0131daki veri seti rastgele 30 ki\u015filik \u00fc\u00e7 gruba ayr\u0131lan 90 \u00f6\u011frenciye ili\u015fkin bilgileri i\u00e7ermektedir.<\/span><\/p>\n

    Veri seti, her \u00f6\u011frencinin kulland\u0131\u011f\u0131 \u00e7al\u0131\u015fma tekni\u011fini (A, B<\/em> veya C)<\/em> ,<\/em> \u00e7al\u0131\u015fma tekni\u011fini kullanmaya ba\u015flad\u0131klar\u0131nda s\u0131n\u0131ftaki mevcut notlar\u0131n\u0131 ve haz\u0131rlanmak i\u00e7in bir ay boyunca \u00e7al\u0131\u015fma tekni\u011fini kulland\u0131ktan sonra s\u0131navda ald\u0131klar\u0131 notu g\u00f6sterir. S\u0131nav i\u00e7in. s\u0131nav:<\/span><\/p>\n

     #make this example reproducible<\/span>\nset.seed(10)\n\n#create dataset<\/span>\ndata <- 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#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
     1. Ad\u0131m: Verileri ke\u015ffedin<\/strong><\/span><\/h3>\n
     ANCOVA modelini yerle\u015ftirmeden \u00f6nce, verileri daha iyi anlamak i\u00e7in ara\u015ft\u0131rmam\u0131z ve sonu\u00e7lar\u0131 \u00e7arp\u0131tabilecek a\u015f\u0131r\u0131 u\u00e7 de\u011ferlerin olmad\u0131\u011f\u0131n\u0131 do\u011frulamam\u0131z gerekiyor.<\/span><\/p>\n
     \u0130lk olarak veri k\u00fcmesindeki her de\u011fi\u015fkenin \u00f6zetini g\u00f6r\u00fcnt\u00fcleyebiliriz:<\/span><\/p>\n
     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
     Her bir \u00e7al\u0131\u015fma tekni\u011fi de\u011ferinin ( A, B<\/em> ve C)<\/em> verilerde 30 kez g\u00f6r\u00fcnd\u00fc\u011f\u00fcn\u00fc g\u00f6rebiliriz.<\/span><\/p>\n
     Ayr\u0131ca \u00e7al\u0131\u015fman\u0131n ba\u015f\u0131nda \u00f6\u011frencilerin mevcut puanlar\u0131n\u0131n nas\u0131l da\u011f\u0131ld\u0131\u011f\u0131n\u0131 da g\u00f6rebiliyoruz. S\u0131n\u0131f\u0131n en d\u00fc\u015f\u00fck puan\u0131 65,43, en y\u00fcksek puan\u0131 93,84, ortalamas\u0131 ise 78,15 oldu.<\/span><\/p>\n
     Benzer \u015fekilde s\u0131navda al\u0131nan minimum puan\u0131n 71,17, maksimum puan\u0131n 94,76, ortalaman\u0131n ise 83,38 oldu\u011funu g\u00f6r\u00fcyoruz.<\/span><\/p>\n
     Daha sonra her \u00e7al\u0131\u015fma tekni\u011fi i\u00e7in ge\u00e7erli notlar\u0131n ve s\u0131nav sonu\u00e7lar\u0131n\u0131n ortalamas\u0131n\u0131 ve standart sapmas\u0131n\u0131 kolayca bulmak i\u00e7in dplyr<\/strong> paketini kullanabiliriz:<\/span><\/p>\n
     #load dplyr<\/em><\/span>\nlibrary(dplyr)\n\ndata %>%\n  group_by<\/span> (technical) %>%\n  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
     Her \u00e7al\u0131\u015fma tekni\u011fini kullanan \u00f6\u011frencilerin mevcut notlar\u0131n\u0131n ortalama ve standart sapmalar\u0131n\u0131n yakla\u015f\u0131k olarak benzer oldu\u011funu g\u00f6rebiliriz.<\/span><\/p>\n
     Ayr\u0131ca A<\/em> \u00e7al\u0131\u015fma tekni\u011fini kullanan \u00f6\u011frencilerin ortalama s\u0131nav puan\u0131n\u0131n, B<\/em> ve C<\/em> tekniklerine k\u0131yasla \u00f6nemli \u00f6l\u00e7\u00fcde daha y\u00fcksek oldu\u011funu da g\u00f6rebiliriz.<\/span><\/p>\n
     Ayr\u0131ca kutu grafiklerini kullanarak \u00e7al\u0131\u015fma tekni\u011fine dayal\u0131 s\u0131nav sonu\u00e7lar\u0131n\u0131n da\u011f\u0131l\u0131m\u0131n\u0131 da g\u00f6rselle\u015ftirebiliriz:<\/span><\/p>\n
     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>\n
     Benzer \u015fekilde, \u00e7al\u0131\u015fma tekni\u011fine dayal\u0131 olarak mevcut notlar\u0131n<\/em> da\u011f\u0131l\u0131m\u0131n\u0131 g\u00f6rselle\u015ftirmek i\u00e7in kutu grafiklerini de kullanabiliriz:<\/span><\/p>\n
     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
     2. Ad\u0131m: Model varsay\u0131mlar\u0131n\u0131 kontrol edin<\/strong><\/span><\/h3>\n
     Baz\u0131 temel veri ara\u015ft\u0131rmalar\u0131n\u0131 ger\u00e7ekle\u015ftirdikten ve verilere a\u015fina olduktan sonra, ANCOVA i\u00e7in a\u015fa\u011f\u0131daki varsay\u0131mlar\u0131n kar\u015f\u0131land\u0131\u011f\u0131n\u0131 do\u011frulamam\u0131z gerekir:<\/span><\/p>\n
      \n
    •  Ortak de\u011fi\u015fken ve tedavi ba\u011f\u0131ms\u0131zd\u0131r<\/strong> – ortak de\u011fi\u015fkenin ( mevcut derece)<\/em> ve tedavinin (\u00e7al\u0131\u015fma tekni\u011fi)<\/em> birbirinden ba\u011f\u0131ms\u0131z oldu\u011funu do\u011frulamak gerekir, \u00e7\u00fcnk\u00fc modele bir ortak de\u011fi\u015fken terimi eklemek yaln\u0131zca ortak de\u011fi\u015fken ve Tedavi yan\u0131t de\u011fi\u015fkenine ( s\u0131nav<\/em> ) g\u00f6re ba\u011f\u0131ms\u0131z olarak hareket eder.<\/span><\/li>\n
    •  Varyans\u0131n homojenli\u011fi<\/strong> \u2013 gruplar aras\u0131ndaki varyanslar\u0131n e\u015fit olup olmad\u0131\u011f\u0131n\u0131 kontrol etmemiz gerekir<\/span><\/li>\n<\/ul>\n
       Ortak de\u011fi\u015fkenin ve tedavinin ba\u011f\u0131ms\u0131z oldu\u011funu do\u011frulamak i\u00e7in, yan\u0131t de\u011fi\u015fkeni olarak mevcut notu<\/em> ve yorday\u0131c\u0131 de\u011fi\u015fken olarak \u00e7al\u0131\u015fma tekni\u011fini<\/em> kullanarak bir ANOVA ger\u00e7ekle\u015ftirebiliriz:<\/span><\/p>\n
       #fit anova model\n<\/span>anova_model <- aov(current_grade ~ technique, data = data)\n#view summary of anova model\n<\/span>summary(anova_model)\n\n# Df Sum Sq Mean Sq F value Pr(>F)\n#technical 2 74 37.21 0.599 0.552\n#Residuals 87 5406 62.14    \n<\/strong><\/pre>\n
       P de\u011feri 0,05’ten b\u00fcy\u00fckt\u00fcr, dolay\u0131s\u0131yla ortak de\u011fi\u015fken ( mevcut derece)<\/em> ve tedavi ( \u00e7al\u0131\u015fma tekni\u011fi<\/em> ) ba\u011f\u0131ms\u0131z g\u00f6r\u00fcnmektedir.<\/span><\/p>\n
       Daha sonra gruplar aras\u0131nda varyans\u0131n homojenli\u011fini kontrol etmek i\u00e7in Levene testini yapabiliriz:<\/span><\/p>\n
       #load car<\/em> library to conduct Levene's Test<\/span>\nlibary(car)\n\n#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(>F)    \n#group 2 9.4324 0.0001961 ***\n#87   \n<\/strong><\/pre>\n
       Testin p de\u011ferinin 0,0001961’e e\u015fit olmas\u0131 gruplar aras\u0131ndaki varyanslar\u0131n e\u015fit olmad\u0131\u011f\u0131n\u0131 g\u00f6stermektedir. Bu sorunu d\u00fczeltmek i\u00e7in veriler \u00fczerinde bir d\u00f6n\u00fc\u015ft\u00fcrme giri\u015fiminde bulunabilsek de, \u015fu anda varyans farkl\u0131l\u0131klar\u0131 konusunda \u00e7ok fazla endi\u015felenmeyece\u011fiz.<\/span><\/p>\n
       3. Ad\u0131m: ANCOVA modelini ayarlay\u0131n<\/strong><\/span><\/h3>\n
       Daha sonra, yan\u0131t de\u011fi\u015fkeni olarak s\u0131nav puan\u0131n\u0131<\/em> , yorday\u0131c\u0131 (veya “tedavi”) de\u011fi\u015fkeni olarak \u00e7al\u0131\u015fma tekni\u011fini<\/em> ve ortak de\u011fi\u015fken olarak mevcut notu<\/em> kullanarak ANCOVA modelini uygulayaca\u011f\u0131z.<\/span><\/p>\n
       Pakette Anova() fonksiyonunu kullanaca\u011f\u0131z \u00e7\u00fcnk\u00fc bunu yapmak i\u00e7in, sadece model i\u00e7in tip III kareler toplam\u0131n\u0131 kullanmak istedi\u011fimizi belirtebilmek i\u00e7in, \u00e7\u00fcnk\u00fc tip I kareler toplam\u0131 hangi s\u0131raya g\u00f6re de\u011fi\u015fir? Tahminciler modele girilir:<\/span><\/p>\n
       #load car<\/em> library<\/span>\nlibrary(car)\n\n#fit ANCOVA model\n<\/span>ancova_model <- aov(exam ~ technique + current_grade, data = data)\n\n#view summary of model\n<\/span>Anova(ancova_model, type=\"III\") \n\n#Answer: exam\n# Sum Sq Df F value Pr(>F)    \n#(Intercept) 7161.2 1 201.4621 < 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
       Tekni\u011fe<\/em> ili\u015fkin p de\u011ferinin son derece d\u00fc\u015f\u00fck oldu\u011funu g\u00f6rebiliyoruz; bu, mevcut not kontrol edildikten sonra bile \u00e7al\u0131\u015fma tekni\u011finin s\u0131nav puanlar\u0131 \u00fczerinde istatistiksel olarak anlaml\u0131 bir etkiye sahip oldu\u011funu g\u00f6steriyor.<\/span><\/p>\n
       Ad\u0131m 4: Post-hoc testi<\/strong><\/span><\/h3>\n
       ANCOVA sonu\u00e7lar\u0131 bize \u00e7al\u0131\u015fma tekni\u011finin<\/em> s\u0131nav puanlar\u0131 \u00fczerinde istatistiksel olarak anlaml\u0131 bir etkiye sahip oldu\u011funu s\u00f6ylese de, hangi \u00e7al\u0131\u015fma tekniklerinin birbirinden farkl\u0131 oldu\u011funu belirlemek i\u00e7in post hoc testler yapmam\u0131z gerekiyor.<\/span><\/p>\n
       Bunu yapmak i\u00e7in \u00e7oklu kar\u015f\u0131la\u015ft\u0131rmalar i\u00e7in Tukey testini ger\u00e7ekle\u015ftirmek amac\u0131yla R’deki multicomp<\/strong> paketindeki glht() fonksiyonunu kullanabiliriz:<\/span><\/p>\n
       #load the multcomp<\/em> library<\/span>\nlibrary(multicomp)\n\n#fit the ANCOVA model\n<\/span>ancova_model <- aov(exam ~ technique + current_grade, data = data)\n\n#define the post hoc comparisons to make\n<\/span>postHocs <- glht(ancova_model, linfct = mcp(technique = \"Tukey\"))\n\n#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(>|t|)    \n#B - A == 0 -6.711 1.540 -4.358 0.000109 ***\n#C - A == 0 -8.736 1.549 -5.640 < 1e-04 ***\n#C - B == 0 -2.025 1.545 -1.311 0.393089    \n\n#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
       Sonu\u00e7tan, A<\/em> tekni\u011fi ile B<\/em> tekni\u011fi \u00fczerinde \u00e7al\u0131\u015fma (p-de\u011feri: 0,000109) ve A<\/em> tekni\u011fi ile C<\/em> tekni\u011fi aras\u0131nda s\u0131nav sonu\u00e7lar\u0131nda istatistiksel olarak anlaml\u0131 bir fark (\u03b1 = 0,05) oldu\u011funu g\u00f6rebiliriz. (p-de\u011feri: <1e-04).<\/span><\/p>\n
       B<\/em> ve C<\/em> teknikleri aras\u0131nda istatistiksel olarak anlaml\u0131 bir fark olmad\u0131\u011f\u0131n\u0131<\/em> da g\u00f6r\u00fcyoruz (\u03b1 = 0,05).<\/span> Teknikler aras\u0131ndaki g\u00fcven aral\u0131klar\u0131 da bu bulgular\u0131 desteklemektedir.<\/span><\/p>\n
       Dolay\u0131s\u0131yla, A<\/em> \u00e7al\u0131\u015fma tekni\u011fini kullanman\u0131n, \u00f6\u011frencinin s\u0131n\u0131ftaki mevcut notu kontrol edildikten sonra bile, B<\/em> ve C<\/em> teknikleriyle kar\u015f\u0131la\u015ft\u0131r\u0131ld\u0131\u011f\u0131nda \u00f6\u011frenciler i\u00e7in istatistiksel olarak anlaml\u0131 derecede daha y\u00fcksek bir s\u0131nav notuna yol a\u00e7t\u0131\u011f\u0131 sonucuna varabiliriz.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"
      Bu e\u011fitimde R’de ANCOVA’n\u0131n nas\u0131l ger\u00e7ekle\u015ftirilece\u011fine ili\u015fkin bir \u00f6rnek sunulmaktad\u0131r. \u00d6rnek: R’de ANCOVA \u00c7al\u0131\u015fma tekni\u011finin s\u0131nav sonu\u00e7lar\u0131 \u00fczerinde etkisi olup olmad\u0131\u011f\u0131n\u0131 test etmek i\u00e7in a\u015fa\u011f\u0131daki de\u011fi\u015fkenleri kullanarak bir ANCOVA ger\u00e7ekle\u015ftirece\u011fiz: Teknik \u00e7al\u0131\u015fma : Analiz etmek istedi\u011fimiz ba\u011f\u0131ms\u0131z de\u011fi\u015fken Mevcut \u00f6\u011frenci notu : Dikkate almak istedi\u011fimiz ortak de\u011fi\u015fken \u0130nceleme Puan\u0131 : Analiz etmek istedi\u011fimiz yan\u0131t de\u011fi\u015fkenleri […]<\/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-485","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"\nR - 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