{"id":1229,"date":"2023-07-27T05:20:12","date_gmt":"2023-07-27T05:20:12","guid":{"rendered":"https:\/\/statorials.org\/tr\/r-cinsinden-guven-araligi\/"},"modified":"2023-07-27T05:20:12","modified_gmt":"2023-07-27T05:20:12","slug":"r-cinsinden-guven-araligi","status":"publish","type":"post","link":"https:\/\/statorials.org\/tr\/r-cinsinden-guven-araligi\/","title":{"rendered":"R&#39;de g\u00fcven aral\u0131klar\u0131 nas\u0131l bulunur (\u00f6rneklerle)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/guvenilirlik-araligi\/\" target=\"_blank\" rel=\"noopener noreferrer\">G\u00fcven aral\u0131\u011f\u0131,<\/a> belirli bir g\u00fcven d\u00fczeyine sahip bir <a href=\"https:\/\/statorials.org\/tr\/istatistik-ve-parametre\/\" target=\"_blank\" rel=\"noopener noreferrer\">pop\u00fclasyon parametresini<\/a> i\u00e7ermesi muhtemel bir de\u011fer aral\u0131\u011f\u0131d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki genel form\u00fcle g\u00f6re hesaplan\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>G\u00fcven aral\u0131\u011f\u0131<\/strong> = (nokta tahmini) +\/- (kritik de\u011fer)* (standart hata)<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu form\u00fcl, muhtemelen bir miktar g\u00fcven d\u00fczeyine sahip bir pop\u00fclasyon parametresi i\u00e7eren, alt s\u0131n\u0131r\u0131 ve \u00fcst s\u0131n\u0131r\u0131 olan bir aral\u0131k olu\u015fturur:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>G\u00fcven aral\u0131\u011f\u0131<\/strong> = [alt s\u0131n\u0131r, \u00fcst s\u0131n\u0131r]<\/span><\/p>\n<p> <span style=\"color: #000000;\">Bu e\u011fitimde R&#8217;de a\u015fa\u011f\u0131daki g\u00fcven aral\u0131klar\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131 a\u00e7\u0131klanmaktad\u0131r:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1.<\/strong> Ortalama i\u00e7in g\u00fcven aral\u0131\u011f\u0131<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2.<\/strong> Ortalamalar aras\u0131ndaki fark i\u00e7in g\u00fcven aral\u0131\u011f\u0131<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>3.<\/strong> Bir orant\u0131 i\u00e7in g\u00fcven aral\u0131\u011f\u0131<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>4.<\/strong> Oranlar aras\u0131ndaki fark i\u00e7in g\u00fcven aral\u0131\u011f\u0131<\/span><\/p>\n<p> <span style=\"color: #000000;\">Hadi gidelim!<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 1: Bir ortalama i\u00e7in g\u00fcven aral\u0131\u011f\u0131<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/ortalama-guven-araligi\/\" target=\"_blank\" rel=\"noopener noreferrer\">Bir ortalaman\u0131n g\u00fcven aral\u0131\u011f\u0131n\u0131<\/a> hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullan\u0131r\u0131z:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>G\u00fcven aral\u0131\u011f\u0131 = <span style=\"text-decoration: overline;\">x<\/span> +\/- t <sub>n-1, 1-\u03b1\/2<\/sub> *(s\/\u221an)<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong><span style=\"text-decoration: overline;\">x<\/span> :<\/strong> \u00f6rnek ortalama<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>t:<\/strong> t-kritik de\u011feri<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>s:<\/strong> numune standart sapmas\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>n:<\/strong> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>\u00d6rnek:<\/strong> A\u015fa\u011f\u0131daki bilgileri i\u00e7eren rastgele bir kaplumba\u011fa \u00f6rne\u011fi toplad\u0131\u011f\u0131m\u0131z\u0131 varsayal\u0131m:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc <strong>n = 25<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\">Ortalama numune a\u011f\u0131rl\u0131\u011f\u0131 <strong><span style=\"text-decoration: overline;\">x<\/span> = 300<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\">\u00d6rneklem standart sapmas\u0131 <strong>s = 18,5<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki kod, kaplumba\u011fa pop\u00fclasyonunun ger\u00e7ek ortalama a\u011f\u0131rl\u0131\u011f\u0131 i\u00e7in %95 g\u00fcven aral\u0131\u011f\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131 g\u00f6sterir:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#input sample size, sample mean, and sample standard deviation\n<\/span>n &lt;- 25\nxbar &lt;- 300 \ns &lt;- 18.5\n\n<span style=\"color: #008080;\">#calculate margin of error\n<\/span>margin &lt;- qt(0.975,df=n-1)*s\/sqrt(n)\n\n<span style=\"color: #008080;\">#calculate lower and upper bounds of confidence interval\n<\/span>low &lt;- xbar - margin\nlow\n\n[1] 292.3636\n\nhigh &lt;- xbar + margin\nhigh\n\n[1] 307.6364\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Ger\u00e7ek ortalama kaplumba\u011fa pop\u00fclasyonu a\u011f\u0131rl\u0131\u011f\u0131 i\u00e7in %95 g\u00fcven aral\u0131\u011f\u0131 <strong>[292,36, 307,64]&#8217;<\/strong> t\u00fcr.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 2: Ortalamalar aras\u0131ndaki fark i\u00e7in g\u00fcven aral\u0131\u011f\u0131<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/ortalamalar-arasindaki-guven-araligi-farki\/\" target=\"_blank\" rel=\"noopener noreferrer\">N\u00fcfus ortalamalar\u0131ndaki farka<\/a> ili\u015fkin g\u00fcven aral\u0131\u011f\u0131n\u0131 hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullan\u0131r\u0131z:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>G\u00fcven aral\u0131\u011f\u0131<\/strong> = ( <span style=\"text-decoration: overline;\">x<\/span> <sub>1<\/sub> \u2013 <span style=\"text-decoration: overline;\">x<\/span> <sub>2<\/sub> ) +\/- t*\u221a((s <sub>p<\/sub> <sup>2<\/sup> \/n <sub>1<\/sub> ) + (s <sub>p<\/sub> <sup>2<\/sup> \/n <sub>2<\/sub> ))<\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><span style=\"text-decoration: overline;\">x<\/span> <sub>1<\/sub> , <span style=\"text-decoration: overline;\">x<\/span> <sub>2<\/sub> : \u00f6rnek 1&#8217;in ortalamas\u0131, \u00f6rnek 2&#8217;nin ortalamas\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\">t: g\u00fcven d\u00fczeyine ve (n <sub>1<\/sub> + n <sub>2<\/sub> -2) serbestlik derecesine dayal\u0131 t-kritik de\u011feri<\/span><\/li>\n<li> <span style=\"color: #000000;\"><sub>sp<\/sub> <sup>2<\/sup> : birle\u015ftirilmi\u015f varyans, \u015fu \u015fekilde hesaplan\u0131r: ((n <sub>1<\/sub> -1)s <sub>1<\/sub> <sup>2<\/sup> + (n <sub>2<\/sub> -1)s <sub>2<\/sub> <sup>2<\/sup> ) \/ (n <sub>1<\/sub> +n <sub>2<\/sub> -2)<\/span><\/li>\n<li> <span style=\"color: #000000;\">t: t-kritik de\u011feri<\/span><\/li>\n<li> <span style=\"color: #000000;\">n <sub>1<\/sub> , n <sub>2<\/sub> : \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc 1, \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc 2<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>\u00d6rnek:<\/strong> \u0130ki farkl\u0131 kaplumba\u011fa t\u00fcr\u00fc aras\u0131ndaki ortalama a\u011f\u0131rl\u0131k fark\u0131n\u0131 tahmin etmek istedi\u011fimizi varsayal\u0131m. Bu nedenle her pop\u00fclasyondan rastgele 15 kaplumba\u011fa \u00f6rne\u011fi topluyoruz. Her numunenin \u00f6zet verileri a\u015fa\u011f\u0131da verilmi\u015ftir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00d6rnek 1:<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><span style=\"text-decoration: overline;\">x1<\/span> = <sub>310<\/sub><\/span><\/li>\n<li> <span style=\"color: #000000;\"><sub>1<\/sub> = 18,5<\/span><\/li>\n<li> <span style=\"color: #000000;\"><sub>n1<\/sub> = 15<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>\u00d6rnek 2:<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><span style=\"text-decoration: overline;\">x2<\/span> <sub>=<\/sub> 300<\/span><\/li>\n<li> <span style=\"color: #000000;\"><sub>s2<\/sub> = 16,4<\/span><\/li>\n<li> <span style=\"color: #000000;\"><sub>n2<\/sub> = 15<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki kod, pop\u00fclasyon ortalamalar\u0131ndaki ger\u00e7ek fark i\u00e7in %95 g\u00fcven aral\u0131\u011f\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131 g\u00f6sterir:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#input sample size, sample mean, and sample standard deviation\n<\/span>n1 &lt;- 15\nxbar1 &lt;- 310 \ns1 &lt;- 18.5\n\nn2 &lt;- 15\nxbar2 &lt;- 300\ns2 &lt;- 16.4\n\n<span style=\"color: #008080;\">#calculate pooled variance\n<span style=\"color: #000000;\">sp = ((n1-1)*s1^2 + (n2-1)*s2^2) \/ (n1+n2-2)<\/span>\n\n#calculate margin of error\n<\/span>margin &lt;- qt(0.975,df=n1+n2-1)*sqrt(sp\/n1 + sp\/n2)\n\n<span style=\"color: #008080;\">#calculate lower and upper bounds of confidence interval\n<\/span>low &lt;- (xbar1-xbar2) - margin\nlow\n\n[1] -3.055445\n\nhigh &lt;- (xbar1-xbar2) + margin\nhigh\n\n[1] 23.05544\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Pop\u00fclasyon ortalamalar\u0131 aras\u0131ndaki ger\u00e7ek fark i\u00e7in %95 g\u00fcven aral\u0131\u011f\u0131 <strong>[-3,06, 23,06]&#8217;<\/strong> d\u0131r.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 3: Bir orant\u0131 i\u00e7in g\u00fcven aral\u0131\u011f\u0131<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/guven-araligi-orani\/\" target=\"_blank\" rel=\"noopener noreferrer\">Bir orana ili\u015fkin g\u00fcven aral\u0131\u011f\u0131n\u0131<\/a> hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullan\u0131r\u0131z:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>G\u00fcven aral\u0131\u011f\u0131 = p<\/strong> <strong>+\/- z*(\u221a <span style=\"text-decoration: overline;\">p(1-p) \/ n<\/span> )<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><strong>p:<\/strong> \u00f6rnek oran\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>z:<\/strong> se\u00e7ilen z de\u011feri<\/span><\/li>\n<li> <span style=\"color: #000000;\"><strong>n:<\/strong> \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>\u00d6rnek:<\/strong> Bir il\u00e7ede belirli bir yasay\u0131 destekleyen sakinlerin oran\u0131n\u0131 tahmin etmek istedi\u011fimizi varsayal\u0131m. 100 sakinden rastgele bir \u00f6rnek se\u00e7iyoruz ve onlara yasadaki konumlar\u0131n\u0131n ne oldu\u011funu soruyoruz. Sonu\u00e7lar burada:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">\u00d6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc <strong>n = 100<\/strong><\/span><\/li>\n<li> <span style=\"color: #000000;\">Kanun lehine oran <strong>p = 0,56<\/strong><\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki kod, yasay\u0131 destekleyen \u00fclke \u00e7ap\u0131nda sakinlerin ger\u00e7ek oran\u0131 i\u00e7in %95 g\u00fcven aral\u0131\u011f\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131 g\u00f6sterir:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#input sample size and sample proportion\n<\/span>n &lt;- 100\np &lt;- .56<span style=\"color: #008080;\">\n\n#calculate margin of error\n<\/span>margin &lt;- qnorm(0.975)*sqrt(p*(1-p)\/n)\n\n<span style=\"color: #008080;\">#calculate lower and upper bounds of confidence interval\n<\/span>low &lt;- p - margin\nlow\n\n[1] 0.4627099\n\nhigh &lt;- p + margin\nhigh\n\n[1] 0.6572901\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Eyalet genelinde yasay\u0131 destekleyen sakinlerin ger\u00e7ek oran\u0131 i\u00e7in %95 g\u00fcven aral\u0131\u011f\u0131 <strong>[0,463, 0,657]&#8217;<\/strong> dir.<\/span><\/p>\n<h3> <span style=\"color: #000000;\"><strong>\u00d6rnek 4: Oranlardaki fark i\u00e7in g\u00fcven aral\u0131\u011f\u0131<\/strong><\/span><\/h3>\n<p> <span style=\"color: #000000;\"><a href=\"https:\/\/statorials.org\/tr\/orantilarin-guven-araligi-farki\/\" target=\"_blank\" rel=\"noopener noreferrer\">Oranlardaki farka ili\u015fkin g\u00fcven aral\u0131\u011f\u0131n\u0131<\/a> hesaplamak i\u00e7in a\u015fa\u011f\u0131daki form\u00fcl\u00fc kullan\u0131r\u0131z:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>G\u00fcven aral\u0131\u011f\u0131 = (p <sub>1<\/sub> \u2013p <sub>2<\/sub> ) +\/- z*\u221a(p <sub>1<\/sub> (1-p <sub>1<\/sub> )\/n <sub>1<\/sub> + p <sub>2<\/sub> (1-p <sub>2<\/sub> )\/n <sub>2<\/sub> )<\/strong><\/span><\/p>\n<p> <span style=\"color: #000000;\">Alt\u0131n:<\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">p <sub>1<\/sub> , p <sub>2<\/sub> : 1. numunenin oran\u0131, 2. numunenin oran\u0131<\/span><\/li>\n<li> <span style=\"color: #000000;\">z: g\u00fcven d\u00fczeyine dayal\u0131 z-kritik de\u011feri<\/span><\/li>\n<li> <span style=\"color: #000000;\">n <sub>1<\/sub> , n <sub>2<\/sub> : \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc 1, \u00f6rneklem b\u00fcy\u00fckl\u00fc\u011f\u00fc 2<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>\u00d6rnek:<\/strong> A \u0130l\u00e7esinde belirli bir yasay\u0131 destekleyen sakinlerin oran\u0131 ile B \u0130l\u00e7esinde yasay\u0131 destekleyen sakinlerin oran\u0131 aras\u0131ndaki fark\u0131 tahmin etmek istedi\u011fimizi varsayal\u0131m. Her \u00f6rnek i\u00e7in \u00f6zet veriler a\u015fa\u011f\u0131da verilmi\u015ftir:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>\u00d6rnek 1:<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><sub>n1<\/sub> = 100<\/span><\/li>\n<li> <span style=\"color: #000000;\">p <sub>1<\/sub> = 0,62 (yani 100 ki\u015fiden 62&#8217;si yasay\u0131 destekliyor)<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>\u00d6rnek 2:<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\"><sub>n2<\/sub> = 100<\/span><\/li>\n<li> <span style=\"color: #000000;\">p <sub>2<\/sub> = 0,46 (yani 100 ki\u015fiden 46&#8217;s\u0131 yasay\u0131 destekliyor)<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">A\u015fa\u011f\u0131daki kod, il\u00e7eler aras\u0131nda yasay\u0131 destekleyen sakinlerin oran\u0131ndaki ger\u00e7ek fark i\u00e7in %95 g\u00fcven aral\u0131\u011f\u0131n\u0131n nas\u0131l hesaplanaca\u011f\u0131n\u0131 g\u00f6sterir:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\">#input sample sizes and sample proportions\n<\/span>n1 &lt;- 100\np1 &lt;- .62\n\nn2 &lt;- 100\np2 &lt;- .46<span style=\"color: #008080;\">\n\n#calculate margin of error\n<\/span>margin &lt;- qnorm(0.975)*sqrt(p1*(1-p1)\/n1 + p2*(1-p2)\/n2)\n\n<span style=\"color: #008080;\">#calculate lower and upper bounds of confidence interval\n<\/span>low &lt;- (p1-p2) - margin\nlow\n\n[1] 0.02364509\n\n\nhigh &lt;- (p1-p2) + margin\nhigh\n\n[1] 0.2963549\n<\/strong><\/pre>\n<p> <span style=\"color: #000000;\">\u0130l\u00e7eler aras\u0131nda yasay\u0131 destekleyen sakinlerin oran\u0131ndaki ger\u00e7ek fark i\u00e7in %95 g\u00fcven aral\u0131\u011f\u0131 <strong>[0,024, 0,296]&#8217;<\/strong> d\u0131r.<\/span><\/p>\n<p> <span style=\"color: #000000;\"><em>Daha fazla R e\u011fitimini burada bulabilirsiniz.<\/em><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>G\u00fcven aral\u0131\u011f\u0131, belirli bir g\u00fcven d\u00fczeyine sahip bir pop\u00fclasyon parametresini i\u00e7ermesi muhtemel bir de\u011fer aral\u0131\u011f\u0131d\u0131r. A\u015fa\u011f\u0131daki genel form\u00fcle g\u00f6re hesaplan\u0131r: G\u00fcven aral\u0131\u011f\u0131 = (nokta tahmini) +\/- (kritik de\u011fer)* (standart hata) Bu form\u00fcl, muhtemelen bir miktar g\u00fcven d\u00fczeyine sahip bir pop\u00fclasyon parametresi i\u00e7eren, alt s\u0131n\u0131r\u0131 ve \u00fcst s\u0131n\u0131r\u0131 olan bir aral\u0131k olu\u015fturur: G\u00fcven aral\u0131\u011f\u0131 = [alt [&hellip;]<\/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-1229","post","type-post","status-publish","format-standard","hentry","category-rehber"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.3 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>R&#039;de G\u00fcven Aral\u0131klar\u0131 Nas\u0131l Bulunur (\u00d6rneklerle)<\/title>\n<meta name=\"description\" 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