{"id":3228,"date":"2023-07-18T13:59:04","date_gmt":"2023-07-18T13:59:04","guid":{"rendered":"https:\/\/statorials.org\/pl\/test-normalnosci-pythona\/"},"modified":"2023-07-18T13:59:04","modified_gmt":"2023-07-18T13:59:04","slug":"test-normalnosci-pythona","status":"publish","type":"post","link":"https:\/\/statorials.org\/pl\/test-normalnosci-pythona\/","title":{"rendered":"Jak przetestowa\u0107 normalno\u015b\u0107 w pythonie (4 metody)"},"content":{"rendered":"<p><\/p>\n<hr>\n<p><span style=\"color: #000000;\">Wiele test\u00f3w statystycznych <a href=\"https:\/\/statorials.org\/pl\/hipoteza-normalnosci\/\" target=\"_blank\" rel=\"noopener\">zak\u0142ada<\/a> , \u017ce zbiory danych maj\u0105 rozk\u0142ad normalny.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Istniej\u0105 cztery typowe sposoby sprawdzania tej hipotezy w Pythonie:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. (Metoda wizualna) Utw\u00f3rz histogram.<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Je\u017celi histogram ma w przybli\u017ceniu kszta\u0142t dzwonu, zak\u0142ada si\u0119, \u017ce dane maj\u0105 rozk\u0142ad normalny.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>2. (Metoda wizualna) Utw\u00f3rz wykres QQ.<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Je\u017celi punkty na wykresie le\u017c\u0105 w przybli\u017ceniu na prostej uko\u015bnej, w\u00f3wczas zak\u0142ada si\u0119, \u017ce dane maj\u0105 rozk\u0142ad normalny.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>3. (Formalny test statystyczny) Wykonaj test Shapiro-Wilka.<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Je\u017celi warto\u015b\u0107 p testu jest wi\u0119ksza ni\u017c \u03b1 = 0,05, w\u00f3wczas zak\u0142ada si\u0119, \u017ce dane maj\u0105 rozk\u0142ad normalny.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\"><strong>4. (Formalny test statystyczny) Wykonaj test Ko\u0142mogorowa-Smirnowa.<\/strong><\/span><\/p>\n<ul>\n<li> <span style=\"color: #000000;\">Je\u017celi warto\u015b\u0107 p testu jest wi\u0119ksza ni\u017c \u03b1 = 0,05, w\u00f3wczas zak\u0142ada si\u0119, \u017ce dane maj\u0105 rozk\u0142ad normalny.<\/span><\/li>\n<\/ul>\n<p> <span style=\"color: #000000;\">Poni\u017csze przyk\u0142ady pokazuj\u0105, jak zastosowa\u0107 ka\u017cd\u0105 z tych metod w praktyce.<\/span><\/p>\n<h3> <strong><span style=\"color: #000000;\">Metoda 1: Utw\u00f3rz histogram<\/span><\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Poni\u017cszy kod pokazuje, jak utworzy\u0107 histogram dla zbioru danych o <a href=\"https:\/\/statorials.org\/pl\/normalna-dystrybucja-pythona-z-logami\/\" target=\"_blank\" rel=\"noopener\">rozk\u0142adzie logarytmiczno-normalnym<\/a> :<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\"><span style=\"color: #000000;\"><span style=\"color: #008000;\">import<\/span> math\n<span style=\"color: #008000;\">import<\/span> numpy <span style=\"color: #008000;\">as<\/span> np\n<span style=\"color: #008000;\">from<\/span> scipy. <span style=\"color: #3366ff;\">stats<\/span> <span style=\"color: #008000;\">import<\/span> lognorm\n<span style=\"color: #008000;\">import<\/span> matplotlib. <span style=\"color: #3366ff;\">pyplot<\/span> <span style=\"color: #008000;\">as<\/span> plt\n\n<span style=\"color: #008080;\">#make this example reproducible\n<\/span>n.p. <span style=\"color: #3366ff;\">random<\/span> . <span style=\"color: #3366ff;\">seeds<\/span> (1)\n\n<span style=\"color: #008080;\">#generate dataset that contains 1000 log-normal distributed values\n<\/span>lognorm_dataset = lognorm. <span style=\"color: #3366ff;\">rvs<\/span> (s=.5, scale= <span style=\"color: #3366ff;\">math.exp<\/span> (1), size=1000)\n\n<span style=\"color: #008080;\">#create histogram to visualize values in dataset\n<\/span>plt. <span style=\"color: #3366ff;\">hist<\/span> (lognorm_dataset, edgecolor=' <span style=\"color: #ff0000;\">black<\/span> ', bins=20)<\/span><\/span><\/strong> <\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-27387 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/normalitepython1.jpg\" alt=\"\" width=\"559\" height=\"364\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Patrz\u0105c na ten histogram, mo\u017cemy stwierdzi\u0107, \u017ce zbi\u00f3r danych nie ma \u201ekszta\u0142tu dzwonu\u201d i nie ma rozk\u0142adu normalnego.<\/span><\/p>\n<h3> <strong><span style=\"color: #000000;\">Metoda 2: Utw\u00f3rz wykres QQ<\/span><\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Poni\u017cszy kod pokazuje, jak utworzy\u0107 wykres QQ dla zbioru danych o rozk\u0142adzie logarytmiczno-normalnym:<\/span> <\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\"><span style=\"color: #000000;\"><span style=\"color: #008000;\">import<\/span> math\n<span style=\"color: #008000;\">import<\/span> numpy <span style=\"color: #008000;\">as<\/span> np\n<span style=\"color: #008000;\">from<\/span> scipy. <span style=\"color: #3366ff;\">stats<\/span> <span style=\"color: #008000;\">import<\/span> lognorm\n<span style=\"color: #008000;\">import<\/span> statsmodels. <span style=\"color: #3366ff;\">api<\/span> <span style=\"color: #008000;\">as<\/span> sm\n<span style=\"color: #008000;\">import<\/span> matplotlib. <span style=\"color: #3366ff;\">pyplot<\/span> <span style=\"color: #008000;\">as<\/span> plt\n\n<span style=\"color: #008080;\">#make this example reproducible\n<\/span>n.p. <span style=\"color: #3366ff;\">random<\/span> . <span style=\"color: #3366ff;\">seeds<\/span> (1)\n\n<span style=\"color: #008080;\">#generate dataset that contains 1000 log-normal distributed values\n<\/span>lognorm_dataset = lognorm. <span style=\"color: #3366ff;\">rvs<\/span> (s=.5, scale= <span style=\"color: #3366ff;\">math.exp<\/span> (1), size=1000)\n\n<span style=\"color: #008080;\">#create QQ plot with 45-degree line added to plot\n<\/span>fig = sm. <span style=\"color: #3366ff;\">qqplot<\/span> (lognorm_dataset, line=' <span style=\"color: #ff0000;\">45<\/span> ')\n\nplt. <span style=\"color: #3366ff;\">show<\/span> ()\n<\/span><\/span><\/strong><\/pre>\n<p><img decoding=\"async\" loading=\"lazy\" class=\" wp-image-27390 aligncenter\" src=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/normalitepython2.jpg\" alt=\"\" width=\"533\" height=\"359\" srcset=\"\" sizes=\"auto, \"><\/p>\n<p> <span style=\"color: #000000;\">Je\u015bli punkty wykresu le\u017c\u0105 w przybli\u017ceniu na prostej uko\u015bnej, og\u00f3lnie zak\u0142adamy, \u017ce zbi\u00f3r danych ma rozk\u0142ad normalny.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Jednak punkty na tym wykresie wyra\u017anie nie odpowiadaj\u0105 czerwonej linii, wi\u0119c nie mo\u017cemy za\u0142o\u017cy\u0107, \u017ce ten zbi\u00f3r danych ma rozk\u0142ad normalny.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Powinno to mie\u0107 sens, bior\u0105c pod uwag\u0119, \u017ce dane wygenerowali\u015bmy przy u\u017cyciu funkcji rozk\u0142adu logarytmiczno-normalnego.<\/span><\/p>\n<h3> <strong><span style=\"color: #000000;\">Metoda 3: Wykonaj test Shapiro-Wilka<\/span><\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Poni\u017cszy kod pokazuje, jak wykona\u0107 Shapiro-Wilka dla zbioru danych o rozk\u0142adzie logarytmiczno-normalnym:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\"><span style=\"color: #000000;\"><span style=\"color: #008000;\">import<\/span> math\n<span style=\"color: #008000;\">import<\/span> numpy <span style=\"color: #008000;\">as<\/span> np\n<span style=\"color: #008000;\">from<\/span> scipy.stats <span style=\"color: #008000;\">import<\/span> shapiro \n<span style=\"color: #008000;\">from<\/span> scipy. <span style=\"color: #3366ff;\">stats<\/span> <span style=\"color: #008000;\">import<\/span> lognorm\n\n<span style=\"color: #008080;\">#make this example reproducible\n<\/span>n.p. <span style=\"color: #3366ff;\">random<\/span> . <span style=\"color: #3366ff;\">seeds<\/span> (1)\n\n<span style=\"color: #008080;\">#generate dataset that contains 1000 log-normal distributed values\n<\/span>lognorm_dataset = lognorm. <span style=\"color: #3366ff;\">rvs<\/span> (s=.5, scale= <span style=\"color: #3366ff;\">math.exp<\/span> (1), size=1000)\n\n<span style=\"color: #008080;\">#perform Shapiro-Wilk test for normality\n<\/span>shapiro(lognorm_dataset)\n\nShapiroResult(statistic=0.8573324680328369, pvalue=3.880663073872444e-29)\n<\/span><\/span><\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Z wyniku widzimy, \u017ce statystyka testowa wynosi <strong>0,857<\/strong> , a odpowiadaj\u0105ca jej warto\u015b\u0107 p wynosi <strong>3,88e-29<\/strong> (skrajnie bliska zera).<\/span><\/p>\n<p> <span style=\"color: #000000;\">Poniewa\u017c warto\u015b\u0107 p jest mniejsza ni\u017c 0,05, odrzucamy hipotez\u0119 zerow\u0105 testu Shapiro-Wilka.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Oznacza to, \u017ce mamy wystarczaj\u0105ce dowody, aby stwierdzi\u0107, \u017ce przyk\u0142adowe dane nie pochodz\u0105 z rozk\u0142adu normalnego.<\/span><\/p>\n<h3> <strong><span style=\"color: #000000;\">Metoda 4: Wykonaj test Ko\u0142mogorowa-Smirnowa<\/span><\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Poni\u017cszy kod ilustruje spos\u00f3b przeprowadzenia testu Ko\u0142mogorowa-Smirnowa dla zbioru danych o rozk\u0142adzie logarytmiczno-normalnym:<\/span><\/p>\n<pre style=\"background-color: #ececec; font-size: 15px;\"> <strong><span style=\"color: #008080;\"><span style=\"color: #000000;\"><span style=\"color: #008000;\">import<\/span> math\n<span style=\"color: #008000;\">import<\/span> numpy <span style=\"color: #008000;\">as<\/span> np\n<span style=\"color: #008000;\">from<\/span> scipy.stats <span style=\"color: #008000;\">import<\/span> kstest\n<span style=\"color: #008000;\">from<\/span> scipy. <span style=\"color: #3366ff;\">stats<\/span> <span style=\"color: #008000;\">import<\/span> lognorm\n\n<span style=\"color: #008080;\">#make this example reproducible\n<\/span>n.p. <span style=\"color: #3366ff;\">random<\/span> . <span style=\"color: #3366ff;\">seeds<\/span> (1)\n\n<span style=\"color: #008080;\">#generate dataset that contains 1000 log-normal distributed values\n<\/span>lognorm_dataset = lognorm. <span style=\"color: #3366ff;\">rvs<\/span> (s=.5, scale= <span style=\"color: #3366ff;\">math.exp<\/span> (1), size=1000)\n\n<span style=\"color: #008080;\">#perform Kolmogorov-Smirnov test for normality\n<\/span>kstest(lognorm_dataset, ' <span style=\"color: #ff0000;\">norm<\/span> ')\n\nKstestResult(statistic=0.84125708308077, pvalue=0.0)\n<\/span><\/span><\/strong><\/pre>\n<p> <span style=\"color: #000000;\">Z wyniku widzimy, \u017ce statystyka testowa wynosi <strong>0,841<\/strong> , a odpowiadaj\u0105ca jej warto\u015b\u0107 p wynosi <strong>0,0<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Poniewa\u017c warto\u015b\u0107 p jest mniejsza ni\u017c 0,05, odrzucamy hipotez\u0119 zerow\u0105 testu Ko\u0142mogorowa-Smirnowa.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Oznacza to, \u017ce mamy wystarczaj\u0105ce dowody, aby stwierdzi\u0107, \u017ce przyk\u0142adowe dane nie pochodz\u0105 z rozk\u0142adu normalnego.<\/span><\/p>\n<h3> <strong>Jak post\u0119powa\u0107 z nietypowymi danymi<\/strong><\/h3>\n<p> <span style=\"color: #000000;\">Je\u015bli dany zbi\u00f3r danych <em>nie ma<\/em> rozk\u0142adu normalnego, cz\u0119sto mo\u017cemy wykona\u0107 jedn\u0105 z nast\u0119puj\u0105cych transformacji, aby uzyska\u0107 bardziej normalny rozk\u0142ad:<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>1. Transformacja logu:<\/strong> przekszta\u0142\u0107 warto\u015bci x w <strong>log(x)<\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>2. Transformacja pierwiastka kwadratowego:<\/strong> Przekszta\u0142\u0107 warto\u015bci x na <strong><span style=\"border-top: 1px solid black;\">\u221ax<\/span><\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\"><strong>3. Transformacja pierwiastka sze\u015bciennego:<\/strong> przekszta\u0142\u0107 warto\u015bci x na <strong>x <sup>1\/3<\/sup><\/strong> .<\/span><\/p>\n<p> <span style=\"color: #000000;\">Wykonuj\u0105c te przekszta\u0142cenia, zbi\u00f3r danych og\u00f3lnie ma rozk\u0142ad bardziej normalny.<\/span><\/p>\n<p> <span style=\"color: #000000;\">Przeczytaj <a href=\"https:\/\/statorials.org\/pl\/przekszta\u0142cac-dane-w-pythonie\/\" target=\"_blank\" rel=\"noopener noreferrer\">ten samouczek<\/a> , aby zobaczy\u0107, jak wykona\u0107 te transformacje w Pythonie.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Wiele test\u00f3w statystycznych zak\u0142ada , \u017ce zbiory danych maj\u0105 rozk\u0142ad normalny. Istniej\u0105 cztery typowe sposoby sprawdzania tej hipotezy w Pythonie: 1. (Metoda wizualna) Utw\u00f3rz histogram. Je\u017celi histogram ma w przybli\u017ceniu kszta\u0142t dzwonu, zak\u0142ada si\u0119, \u017ce dane maj\u0105 rozk\u0142ad normalny. 2. (Metoda wizualna) Utw\u00f3rz wykres QQ. Je\u017celi punkty na wykresie le\u017c\u0105 w przybli\u017ceniu na prostej uko\u015bnej, [&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-3228","post","type-post","status-publish","format-standard","hentry","category-przewodnik"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Jak przetestowa\u0107 normalno\u015b\u0107 w Pythonie (4 metody) - Statologia<\/title>\n<meta name=\"description\" content=\"W tym samouczku wyja\u015bniono, jak sprawdzi\u0107 normalno\u015b\u0107 w Pythonie, podaj\u0105c kilka przyk\u0142ad\u00f3w.\" \/>\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\/pl\/test-normalnosci-pythona\/\" \/>\n<meta property=\"og:locale\" content=\"pl_PL\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Jak przetestowa\u0107 normalno\u015b\u0107 w Pythonie (4 metody) - Statologia\" \/>\n<meta property=\"og:description\" content=\"W tym samouczku wyja\u015bniono, jak sprawdzi\u0107 normalno\u015b\u0107 w Pythonie, podaj\u0105c kilka przyk\u0142ad\u00f3w.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/statorials.org\/pl\/test-normalnosci-pythona\/\" \/>\n<meta property=\"og:site_name\" content=\"Statorials\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-18T13:59:04+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/statorials.org\/wp-content\/uploads\/2023\/08\/normalitepython1.jpg\" \/>\n<meta name=\"author\" content=\"Benjamin Anderson\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Napisane przez\" \/>\n\t<meta name=\"twitter:data1\" content=\"Benjamin Anderson\" \/>\n\t<meta name=\"twitter:label2\" content=\"Szacowany czas czytania\" \/>\n\t<meta name=\"twitter:data2\" content=\"4 minuty\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/statorials.org\/pl\/test-normalnosci-pythona\/\",\"url\":\"https:\/\/statorials.org\/pl\/test-normalnosci-pythona\/\",\"name\":\"Jak przetestowa\u0107 normalno\u015b\u0107 w Pythonie (4 metody) - Statologia\",\"isPartOf\":{\"@id\":\"https:\/\/statorials.org\/pl\/#website\"},\"datePublished\":\"2023-07-18T13:59:04+00:00\",\"dateModified\":\"2023-07-18T13:59:04+00:00\",\"author\":{\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\"},\"description\":\"W tym samouczku wyja\u015bniono, jak sprawdzi\u0107 normalno\u015b\u0107 w Pythonie, podaj\u0105c kilka przyk\u0142ad\u00f3w.\",\"breadcrumb\":{\"@id\":\"https:\/\/statorials.org\/pl\/test-normalnosci-pythona\/#breadcrumb\"},\"inLanguage\":\"pl-PL\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/statorials.org\/pl\/test-normalnosci-pythona\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/statorials.org\/pl\/test-normalnosci-pythona\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Dom\",\"item\":\"https:\/\/statorials.org\/pl\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Jak przetestowa\u0107 normalno\u015b\u0107 w pythonie (4 metody)\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/statorials.org\/pl\/#website\",\"url\":\"https:\/\/statorials.org\/pl\/\",\"name\":\"Statorials\",\"description\":\"Tw\u00f3j przewodnik po kompetencjach statystycznych!\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/statorials.org\/pl\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"pl-PL\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/6484727a4612df3e69f016c3129c6965\",\"name\":\"Benjamin Anderson\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"pl-PL\",\"@id\":\"https:\/\/statorials.org\/pl\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/statorials.org\/pl\/wp-content\/uploads\/2023\/11\/Benjamin-Anderson-96x96.jpg\",\"contentUrl\":\"https:\/\/statorials.org\/pl\/wp-content\/uploads\/2023\/11\/Benjamin-Anderson-96x96.jpg\",\"caption\":\"Benjamin Anderson\"},\"description\":\"Cze\u015b\u0107, jestem Benjamin i jestem emerytowanym profesorem statystyki, kt\u00f3ry zosta\u0142 oddanym nauczycielem Statorials. 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