{"id":15786,"date":"2024-01-17T03:15:28","date_gmt":"2024-01-16T23:45:28","guid":{"rendered":"https:\/\/rasanegar.com\/blog\/%d8%aa%d8%ac%d8%b2%db%8c%d9%87-%d9%88-%d8%aa%d8%ad%d9%84%db%8c%d9%84-%d9%81%d8%b1%d8%b6%db%8c%d9%87-%d9%87%d8%a7%db%8c-%d8%a2%d9%85%d8%a7%d8%b1%db%8c-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/"},"modified":"2024-01-17T03:15:28","modified_gmt":"2024-01-16T23:45:28","slug":"%d8%aa%d8%ac%d8%b2%db%8c%d9%87-%d9%88-%d8%aa%d8%ad%d9%84%db%8c%d9%84-%d9%81%d8%b1%d8%b6%db%8c%d9%87-%d9%87%d8%a7%db%8c-%d8%a2%d9%85%d8%a7%d8%b1%db%8c-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86","status":"publish","type":"post","link":"https:\/\/rasanegaar.com\/blog\/%d8%aa%d8%ac%d8%b2%db%8c%d9%87-%d9%88-%d8%aa%d8%ad%d9%84%db%8c%d9%84-%d9%81%d8%b1%d8%b6%db%8c%d9%87-%d9%87%d8%a7%db%8c-%d8%a2%d9%85%d8%a7%d8%b1%db%8c-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/","title":{"rendered":"\u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u0641\u0631\u0636\u06cc\u0647 \u0647\u0627\u06cc \u0622\u0645\u0627\u0631\u06cc \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646 \u0628\u0627 ANOVA\u060c \u0645\u062c\u0630\u0648\u0631 \u06a9\u0627\u06cc \u0648 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_85 counter-hierarchy ez-toc-counter ez-toc-custom ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\"><p class=\"ez-toc-title\" style=\"cursor:inherit\">\u0633\u0631\u0641\u0635\u0644\u0647\u0627\u06cc \u0645\u0637\u0644\u0628<\/p>\n<\/div><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%aa%d8%ac%d8%b2%db%8c%d9%87-%d9%88-%d8%aa%d8%ad%d9%84%db%8c%d9%84-%d9%81%d8%b1%d8%b6%db%8c%d9%87-%d9%87%d8%a7%db%8c-%d8%a2%d9%85%d8%a7%d8%b1%db%8c-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d9%85%d8%b9%d8%b1%d9%81%db%8c\" >\u0645\u0639\u0631\u0641\u06cc<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%aa%d8%ac%d8%b2%db%8c%d9%87-%d9%88-%d8%aa%d8%ad%d9%84%db%8c%d9%84-%d9%81%d8%b1%d8%b6%db%8c%d9%87-%d9%87%d8%a7%db%8c-%d8%a2%d9%85%d8%a7%d8%b1%db%8c-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d9%85%d8%b9%d8%b1%d9%81%db%8c_%da%a9%d8%aa%d8%a7%d8%a8%d8%ae%d8%a7%d9%86%d9%87_statsmodels_%d8%af%d8%b1_%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\" >\u0645\u0639\u0631\u0641\u06cc \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 statsmodels \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%aa%d8%ac%d8%b2%db%8c%d9%87-%d9%88-%d8%aa%d8%ad%d9%84%db%8c%d9%84-%d9%81%d8%b1%d8%b6%db%8c%d9%87-%d9%87%d8%a7%db%8c-%d8%a2%d9%85%d8%a7%d8%b1%db%8c-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d8%a7%d9%86%d8%aa%d8%ae%d8%a7%d8%a8_%db%8c%da%a9_%d9%85%d8%ac%d9%85%d9%88%d8%b9%d9%87_%d8%af%d8%a7%d8%af%d9%87\" >\u0627\u0646\u062a\u062e\u0627\u0628 \u06cc\u06a9 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%aa%d8%ac%d8%b2%db%8c%d9%87-%d9%88-%d8%aa%d8%ad%d9%84%db%8c%d9%84-%d9%81%d8%b1%d8%b6%db%8c%d9%87-%d9%87%d8%a7%db%8c-%d8%a2%d9%85%d8%a7%d8%b1%db%8c-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d8%aa%d8%ac%d8%b2%db%8c%d9%87_%d9%88_%d8%aa%d8%ad%d9%84%db%8c%d9%84_%d8%af%d8%a7%d8%af%d9%87_%d9%87%d8%a7%db%8c_%d8%a7%da%a9%d8%aa%d8%b4%d8%a7%d9%81%db%8c_%d9%88_%d9%be%db%8c%d8%b4_%d9%be%d8%b1%d8%af%d8%a7%d8%b2%d8%b4\" >\u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0627\u06a9\u062a\u0634\u0627\u0641\u06cc \u0648 \u067e\u06cc\u0634 \u067e\u0631\u062f\u0627\u0632\u0634<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%aa%d8%ac%d8%b2%db%8c%d9%87-%d9%88-%d8%aa%d8%ad%d9%84%db%8c%d9%84-%d9%81%d8%b1%d8%b6%db%8c%d9%87-%d9%87%d8%a7%db%8c-%d8%a2%d9%85%d8%a7%d8%b1%db%8c-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d8%a7%d9%86%d8%aa%d8%ae%d8%a7%d8%a8_%db%8c%da%a9_%d9%81%d8%b1%d8%b6%db%8c%d9%87_%d9%85%d9%86%d8%a7%d8%b3%d8%a8\" >\u0627\u0646\u062a\u062e\u0627\u0628 \u06cc\u06a9 \u0641\u0631\u0636\u06cc\u0647 \u0645\u0646\u0627\u0633\u0628<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%aa%d8%ac%d8%b2%db%8c%d9%87-%d9%88-%d8%aa%d8%ad%d9%84%db%8c%d9%84-%d9%81%d8%b1%d8%b6%db%8c%d9%87-%d9%87%d8%a7%db%8c-%d8%a2%d9%85%d8%a7%d8%b1%db%8c-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d8%aa%d8%ac%d8%b2%db%8c%d9%87_%d9%88_%d8%aa%d8%ad%d9%84%db%8c%d9%84_%d9%88%d8%a7%d8%b1%db%8c%d8%a7%d9%86%d8%b3_anova\" >\u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u0648\u0627\u0631\u06cc\u0627\u0646\u0633 (ANOVA)<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%aa%d8%ac%d8%b2%db%8c%d9%87-%d9%88-%d8%aa%d8%ad%d9%84%db%8c%d9%84-%d9%81%d8%b1%d8%b6%db%8c%d9%87-%d9%87%d8%a7%db%8c-%d8%a2%d9%85%d8%a7%d8%b1%db%8c-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d8%a2%d8%b2%d9%85%d9%88%d9%86_chi-square_%d8%a7%d8%b3%d8%aa%d9%82%d9%84%d8%a7%d9%84\" >\u0622\u0632\u0645\u0648\u0646 Chi-Square \u0627\u0633\u062a\u0642\u0644\u0627\u0644<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%aa%d8%ac%d8%b2%db%8c%d9%87-%d9%88-%d8%aa%d8%ad%d9%84%db%8c%d9%84-%d9%81%d8%b1%d8%b6%db%8c%d9%87-%d9%87%d8%a7%db%8c-%d8%a2%d9%85%d8%a7%d8%b1%db%8c-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c_%d9%be%db%8c%d8%b1%d8%b3%d9%88%d9%86\" >\u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%aa%d8%ac%d8%b2%db%8c%d9%87-%d9%88-%d8%aa%d8%ad%d9%84%db%8c%d9%84-%d9%81%d8%b1%d8%b6%db%8c%d9%87-%d9%87%d8%a7%db%8c-%d8%a2%d9%85%d8%a7%d8%b1%db%8c-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d9%85%d8%af%db%8c%d8%b1%d8%a7%d9%86_%d9%88_%d8%aa%d8%b9%d8%a7%d9%85%d9%84_%d8%a2%d9%85%d8%a7%d8%b1%db%8c\" >\u0645\u062f\u06cc\u0631\u0627\u0646 \u0648 \u062a\u0639\u0627\u0645\u0644 \u0622\u0645\u0627\u0631\u06cc<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/rasanegaar.com\/blog\/%d8%aa%d8%ac%d8%b2%db%8c%d9%87-%d9%88-%d8%aa%d8%ad%d9%84%db%8c%d9%84-%d9%81%d8%b1%d8%b6%db%8c%d9%87-%d9%87%d8%a7%db%8c-%d8%a2%d9%85%d8%a7%d8%b1%db%8c-%d8%af%d8%b1-%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\/#%d9%86%d8%aa%db%8c%d8%ac%d9%87\" >\u0646\u062a\u06cc\u062c\u0647<\/a><\/li><\/ul><\/nav><\/div>\n<span class=\"span-reading-time rt-reading-time\" style=\"display: block;\"><span class=\"rt-label rt-prefix\">\u0632\u0645\u0627\u0646 \u0644\u0627\u0632\u0645 \u0628\u0631\u0627\u06cc \u0645\u0637\u0627\u0644\u0639\u0647: <\/span> <span class=\"rt-time\"> 15<\/span> <span class=\"rt-label rt-postfix\">\u062f\u0642\u06cc\u0642\u0647<\/span><\/span><p> <br \/>\n<\/p>\n<div><noscript><\/noscript><\/p>\n<h2 id=\"introduction\"><span class=\"ez-toc-section\" id=\"%d9%85%d8%b9%d8%b1%d9%81%db%8c\"><\/span>\u0645\u0639\u0631\u0641\u06cc<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u067e\u0627\u06cc\u062a\u0648\u0646 \u06cc\u06a9 \u0632\u0628\u0627\u0646 \u0641\u0648\u0642 \u0627\u0644\u0639\u0627\u062f\u0647 \u0647\u0645\u0647 \u06a9\u0627\u0631\u0647 \u0627\u0633\u062a \u06a9\u0647 \u0628\u0631\u0627\u06cc \u06a9\u0627\u0631\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u062f\u0631 \u0637\u06cc\u0641 \u0648\u0633\u06cc\u0639\u06cc \u0627\u0632 \u0631\u0634\u062a\u0647 \u0647\u0627 \u0645\u0641\u06cc\u062f \u0627\u0633\u062a.  \u06cc\u06a9\u06cc \u0627\u0632 \u0627\u06cc\u0646 \u0631\u0634\u062a\u0647 \u0647\u0627\u060c \u062a\u062d\u0644\u06cc\u0644 \u0622\u0645\u0627\u0631\u06cc \u0627\u0633\u062a \u0631\u0648\u06cc \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0647\u0627 \u0648 \u062f\u0631 \u06a9\u0646\u0627\u0631 SPSS\u060c \u067e\u0627\u06cc\u062a\u0648\u0646 \u06cc\u06a9\u06cc \u0627\u0632 \u0631\u0627\u06cc\u062c \u062a\u0631\u06cc\u0646 \u0627\u0628\u0632\u0627\u0631\u0647\u0627\u06cc \u0622\u0645\u0627\u0631 \u0627\u0633\u062a.<\/p>\n<p>\u0645\u0627\u0647\u06cc\u062a \u06a9\u0627\u0631\u0628\u0631\u067e\u0633\u0646\u062f \u0648 \u0634\u0647\u0648\u062f\u06cc \u067e\u0627\u06cc\u062a\u0648\u0646 \u0627\u062c\u0631\u0627\u06cc \u062a\u0633\u062a \u0647\u0627\u06cc \u0622\u0645\u0627\u0631\u06cc \u0648 \u067e\u06cc\u0627\u062f\u0647 \u0633\u0627\u0632\u06cc \u062a\u06a9\u0646\u06cc\u06a9 \u0647\u0627\u06cc \u062a\u062d\u0644\u06cc\u0644\u06cc \u0631\u0627 \u0628\u0647 \u0648\u06cc\u0698\u0647 \u0627\u0632 \u0637\u0631\u06cc\u0642 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/www.statsmodels.org\/stable\/index.html\"><code>statsmodels<\/code>  \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647<\/a>.<\/p>\n<h2 id=\"introducingthestatsmodelslibraryinpython\"><span class=\"ez-toc-section\" id=\"%d9%85%d8%b9%d8%b1%d9%81%db%8c_%da%a9%d8%aa%d8%a7%d8%a8%d8%ae%d8%a7%d9%86%d9%87_statsmodels_%d8%af%d8%b1_%d9%be%d8%a7%db%8c%d8%aa%d9%88%d9%86\"><\/span>\u0645\u0639\u0631\u0641\u06cc \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 statsmodels \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0627\u06cc\u0646 <code>statsmodels<\/code> \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 \u06cc\u06a9 \u0645\u0627\u0698\u0648\u0644 \u0628\u0631\u0627\u06cc \u067e\u0627\u06cc\u062a\u0648\u0646 \u0627\u0633\u062a \u06a9\u0647 \u062f\u0633\u062a\u0631\u0633\u06cc \u0622\u0633\u0627\u0646 \u0628\u0647 \u0627\u0646\u0648\u0627\u0639 \u0627\u0628\u0632\u0627\u0631\u0647\u0627\u06cc \u0622\u0645\u0627\u0631\u06cc \u0628\u0631\u0627\u06cc \u0627\u0646\u062c\u0627\u0645 \u062a\u0633\u062a \u0647\u0627\u06cc \u0622\u0645\u0627\u0631\u06cc \u0648 \u06a9\u0627\u0648\u0634 \u062f\u0627\u062f\u0647 \u0647\u0627 \u0631\u0627 \u0645\u06cc \u062f\u0647\u062f.  \u062a\u0639\u062f\u0627\u062f\u06cc \u062a\u0633\u062a \u0648 \u062a\u0648\u0627\u0628\u0639 \u0622\u0645\u0627\u0631\u06cc \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06a9\u0647 \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 \u0628\u0647 \u0622\u0646\u0647\u0627 \u062f\u0633\u062a\u0631\u0633\u06cc \u0645\u06cc \u062f\u0647\u062f\u060c \u0627\u0632 \u062c\u0645\u0644\u0647 \u0631\u06af\u0631\u0633\u06cc\u0648\u0646 \u062d\u062f\u0627\u0642\u0644 \u0645\u0631\u0628\u0639\u0627\u062a \u0645\u0639\u0645\u0648\u0644\u06cc (OLS)\u060c \u0645\u062f\u0644 \u0647\u0627\u06cc \u062e\u0637\u06cc \u062a\u0639\u0645\u06cc\u0645 \u06cc\u0627\u0641\u062a\u0647\u060c \u0645\u062f\u0644 \u0647\u0627\u06cc \u0644\u0627\u062c\u06cc\u062a\u060c <em>\u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u0645\u0624\u0644\u0641\u0647 \u0647\u0627\u06cc \u0627\u0635\u0644\u06cc<\/em> (PCA)\u060c \u0648 <em>\u0645\u06cc\u0627\u0646\u06af\u06cc\u0646 \u0645\u062a\u062d\u0631\u06a9 \u06cc\u06a9\u067e\u0627\u0631\u0686\u0647 \u062e\u0648\u062f\u0631\u06af\u0631\u0633\u06cc\u0648\u0646<\/em> \u0645\u062f\u0644 \u0647\u0627\u06cc (ARIMA).<\/p>\n<p>\u0646\u062a\u0627\u06cc\u062c \u0645\u062f\u0644 \u0647\u0627 \u0628\u0647 \u0637\u0648\u0631 \u0645\u062f\u0627\u0648\u0645 \u062f\u0631 \u0628\u0631\u0627\u0628\u0631 \u0633\u0627\u06cc\u0631 \u0628\u0633\u062a\u0647 \u0647\u0627\u06cc \u0622\u0645\u0627\u0631\u06cc \u0622\u0632\u0645\u0627\u06cc\u0634 \u0645\u06cc \u0634\u0648\u0646\u062f \u062a\u0627 \u0627\u0632 \u062f\u0642\u062a \u0645\u062f\u0644 \u0647\u0627 \u0627\u0637\u0645\u06cc\u0646\u0627\u0646 \u062d\u0627\u0635\u0644 \u0634\u0648\u062f.  \u0647\u0646\u06af\u0627\u0645\u06cc \u06a9\u0647 \u0628\u0627 <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/www.scipy.org\/\">SciPy<\/a> \u0648 <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/pandas.pydata.org\/\">\u067e\u0627\u0646\u062f\u0627\u0647\u0627<\/a>\u060c \u062a\u062c\u0633\u0645 \u062f\u0627\u062f\u0647 \u0647\u0627\u060c \u0627\u062c\u0631\u0627\u06cc \u0622\u0632\u0645\u0627\u06cc\u0634 \u0647\u0627\u06cc \u0622\u0645\u0627\u0631\u06cc \u0648 \u0628\u0631\u0631\u0633\u06cc \u0631\u0648\u0627\u0628\u0637 \u0627\u0632 \u0646\u0638\u0631 \u0627\u0647\u0645\u06cc\u062a \u0628\u0633\u06cc\u0627\u0631 \u0633\u0627\u062f\u0647 \u0627\u0633\u062a.<\/p>\n<h2 id=\"choosingadataset\"><span class=\"ez-toc-section\" id=\"%d8%a7%d9%86%d8%aa%d8%ae%d8%a7%d8%a8_%db%8c%da%a9_%d9%85%d8%ac%d9%85%d9%88%d8%b9%d9%87_%d8%af%d8%a7%d8%af%d9%87\"><\/span>\u0627\u0646\u062a\u062e\u0627\u0628 \u06cc\u06a9 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0642\u0628\u0644 \u0627\u0632 \u0627\u06cc\u0646\u06a9\u0647 \u0628\u062a\u0648\u0627\u0646\u06cc\u0645 \u0622\u0645\u0627\u0631 \u0631\u0627 \u0628\u0627 \u067e\u0627\u06cc\u062a\u0648\u0646 \u062a\u0645\u0631\u06cc\u0646 \u06a9\u0646\u06cc\u0645\u060c \u0628\u0627\u06cc\u062f \u06cc\u06a9 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0631\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u06a9\u0646\u06cc\u0645.  \u0645\u0627 \u0627\u0632 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u06af\u0631\u062f\u0622\u0648\u0631\u06cc \u0634\u062f\u0647 \u062a\u0648\u0633\u0637 \u0628\u0646\u06cc\u0627\u062f Gapminder \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f.<\/p>\n<p><a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/www.kaggle.com\/tklimonova\/gapminder-datacamp-2007?select=gapminder_full.csv\">\u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 Gapminder<\/a> \u0628\u0633\u06cc\u0627\u0631\u06cc \u0627\u0632 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u0645\u0648\u0631\u062f \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0628\u0631\u0627\u06cc \u0627\u0631\u0632\u06cc\u0627\u0628\u06cc \u0633\u0644\u0627\u0645\u062a \u0639\u0645\u0648\u0645\u06cc \u0648 \u062a\u0646\u062f\u0631\u0633\u062a\u06cc \u062c\u0645\u0639\u06cc\u062a \u062f\u0631 \u06a9\u0634\u0648\u0631\u0647\u0627\u06cc \u0633\u0631\u0627\u0633\u0631 \u062c\u0647\u0627\u0646 \u0631\u0627 \u0631\u062f\u06cc\u0627\u0628\u06cc \u0645\u06cc \u06a9\u0646\u062f.  \u0645\u0627 \u0627\u0632 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f \u0632\u06cc\u0631\u0627 \u0628\u0633\u06cc\u0627\u0631 \u0645\u0633\u062a\u0646\u062f\u060c \u0627\u0633\u062a\u0627\u0646\u062f\u0627\u0631\u062f \u0648 \u06a9\u0627\u0645\u0644 \u0627\u0633\u062a.  \u0628\u0631\u0627\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0622\u0646\u060c \u0646\u06cc\u0627\u0632\u06cc \u0628\u0647 \u0627\u0646\u062c\u0627\u0645 \u06a9\u0627\u0631\u0647\u0627\u06cc \u0632\u06cc\u0627\u062f\u06cc \u062f\u0631 \u0632\u0645\u06cc\u0646\u0647 \u067e\u06cc\u0634 \u067e\u0631\u062f\u0627\u0632\u0634 \u0646\u062e\u0648\u0627\u0647\u06cc\u0645 \u062f\u0627\u0634\u062a.<\/p>\n<p>\u0686\u0646\u062f \u06a9\u0627\u0631 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06a9\u0647 \u0645\u0627 \u0645\u06cc \u062e\u0648\u0627\u0647\u06cc\u0645 \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u0645 \u062a\u0627 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0631\u0627 \u0628\u0631\u0627\u06cc \u0627\u062c\u0631\u0627\u06cc \u0631\u06af\u0631\u0633\u06cc\u0648\u0646 \u0647\u0627\u060c ANOVA \u0647\u0627 \u0648 \u0622\u0632\u0645\u0627\u06cc\u0634 \u0647\u0627\u06cc \u062f\u06cc\u06af\u0631 \u0622\u0645\u0627\u062f\u0647 \u06a9\u0646\u06cc\u0645\u060c \u0627\u0645\u0627 \u0628\u0647 \u0637\u0648\u0631 \u06a9\u0644\u06cc \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0622\u0645\u0627\u062f\u0647 \u06a9\u0627\u0631 \u0627\u0633\u062a.<\/p>\n<p>\u0646\u0642\u0637\u0647 \u0634\u0631\u0648\u0639 \u0628\u0631\u0627\u06cc \u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u0622\u0645\u0627\u0631\u06cc \u0645\u0627 \u0627\u0632 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 Gapminder\u060c \u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0627\u06a9\u062a\u0634\u0627\u0641\u06cc \u0627\u0633\u062a.  \u0645\u0627 \u0627\u0632 \u0628\u0631\u062e\u06cc \u062a\u0648\u0627\u0628\u0639 \u0646\u0645\u0648\u062f\u0627\u0631 \u0648 \u0631\u0633\u0645 \u0627\u0632 Matplotlib \u0648 Seaborn \u0628\u0631\u0627\u06cc \u062a\u062c\u0633\u0645 \u0628\u0631\u062e\u06cc \u0627\u0632 \u0631\u0648\u0627\u0628\u0637 \u062c\u0627\u0644\u0628 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f \u0648 \u0627\u06cc\u062f\u0647 \u0627\u06cc \u0627\u0632 \u0631\u0648\u0627\u0628\u0637 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc\u06cc \u06a9\u0647 \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0628\u062e\u0648\u0627\u0647\u06cc\u0645 \u0628\u0631\u0631\u0633\u06cc \u06a9\u0646\u06cc\u0645 \u0628\u0647 \u062f\u0633\u062a \u0645\u06cc \u0622\u0648\u0631\u06cc\u0645.<\/p>\n<h2 id=\"exploratorydataanalysisandpreprocessing\"><span class=\"ez-toc-section\" id=\"%d8%aa%d8%ac%d8%b2%db%8c%d9%87_%d9%88_%d8%aa%d8%ad%d9%84%db%8c%d9%84_%d8%af%d8%a7%d8%af%d9%87_%d9%87%d8%a7%db%8c_%d8%a7%da%a9%d8%aa%d8%b4%d8%a7%d9%81%db%8c_%d9%88_%d9%be%db%8c%d8%b4_%d9%be%d8%b1%d8%af%d8%a7%d8%b2%d8%b4\"><\/span>\u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0627\u06a9\u062a\u0634\u0627\u0641\u06cc \u0648 \u067e\u06cc\u0634 \u067e\u0631\u062f\u0627\u0632\u0634<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0645\u0627 \u0628\u0627 \u062a\u062c\u0633\u0645 \u0628\u0631\u062e\u06cc \u0627\u0632 \u0631\u0648\u0627\u0628\u0637 \u0645\u0645\u06a9\u0646 \u0634\u0631\u0648\u0639 \u0645\u06cc \u06a9\u0646\u06cc\u0645.  \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 Seaborn \u0648 Pandas \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0631\u06af\u0631\u0633\u06cc\u0648\u0646\u200c\u0647\u0627\u06cc\u06cc \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u0645 \u06a9\u0647 \u0628\u0647 \u0642\u062f\u0631\u062a \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0628\u06cc\u0646 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u0645\u0648\u062c\u0648\u062f \u062f\u0631 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647\u200c\u0645\u0627\u0646 \u0646\u06af\u0627\u0647 \u0645\u06cc\u200c\u06a9\u0646\u062f \u062a\u0627 \u0627\u06cc\u062f\u0647\u200c\u0627\u06cc \u062f\u0631 \u0645\u0648\u0631\u062f \u0627\u06cc\u0646\u06a9\u0647 \u06a9\u062f\u0627\u0645 \u0631\u0648\u0627\u0628\u0637 \u0645\u062a\u063a\u06cc\u0631 \u0627\u0631\u0632\u0634 \u0645\u0637\u0627\u0644\u0639\u0647 \u062f\u0627\u0631\u0646\u062f \u0631\u0627 \u0628\u0647 \u062f\u0633\u062a \u0622\u0648\u0631\u06cc\u0645.<\/p>\n<p>\u062e\u0648\u0628 import \u0622\u0646 \u062f\u0648 \u0648 \u0647\u0631 \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 \u062f\u06cc\u06af\u0631\u06cc \u06a9\u0647 \u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-keyword\">import<\/span> statsmodels.formula.api <span class=\"hljs-keyword\">as<\/span> smf\n<span class=\"hljs-keyword\">import<\/span> statsmodels.stats.multicomp <span class=\"hljs-keyword\">as<\/span> multi\n<span class=\"hljs-keyword\">import<\/span> scipy\n<span class=\"hljs-keyword\">from<\/span> scipy.stats <span class=\"hljs-keyword\">import<\/span> pearsonr\n<span class=\"hljs-keyword\">import<\/span> pandas <span class=\"hljs-keyword\">as<\/span> pd\n<span class=\"hljs-keyword\">from<\/span> seaborn <span class=\"hljs-keyword\">import<\/span> regplot\n<span class=\"hljs-keyword\">import<\/span> matplotlib.pyplot <span class=\"hljs-keyword\">as<\/span> plt\n<span class=\"hljs-keyword\">import<\/span> numpy <span class=\"hljs-keyword\">as<\/span> np\n<span class=\"hljs-keyword\">import<\/span> seaborn <span class=\"hljs-keyword\">as<\/span> sns\n<\/code><\/pre>\n<p>\u067e\u06cc\u0634 \u067e\u0631\u062f\u0627\u0632\u0634 \u0632\u06cc\u0627\u062f\u06cc \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0631\u062f \u06a9\u0647 \u0628\u0627\u06cc\u062f \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u0645\u060c \u0627\u0645\u0627 \u0628\u0627\u06cc\u062f \u0686\u0646\u062f \u06a9\u0627\u0631 \u0631\u0627 \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u0645.  \u0627\u0628\u062a\u062f\u0627\u060c \u0645\u0627 \u06af\u0645 \u0634\u062f\u0646 \u06cc\u0627 \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc \u06a9\u0646\u06cc\u0645 <code>null<\/code> \u062f\u0627\u062f\u0647 \u0648 \u0647\u0631 \u0648\u0631\u0648\u062f\u06cc \u063a\u06cc\u0631 \u0639\u062f\u062f\u06cc \u0631\u0627 \u0628\u0647 \u0639\u062f\u062f\u06cc \u062a\u0628\u062f\u06cc\u0644 \u06a9\u0646\u06cc\u062f.  \u0645\u0627 \u0647\u0645\u0686\u0646\u06cc\u0646 \u06cc\u06a9 \u06a9\u067e\u06cc \u0627\u0632 \u062f\u06cc\u062a\u0627\u0641\u0631\u06cc\u0645 \u062a\u063a\u06cc\u06cc\u0631 \u06cc\u0627\u0641\u062a\u0647 \u06a9\u0647 \u0628\u0627 \u0622\u0646 \u06a9\u0627\u0631 \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f \u062a\u0647\u06cc\u0647 \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f:<\/p>\n<pre><code class=\"hljs\">\n<span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">check_missing_values<\/span>(<span class=\"hljs-params\">df, cols<\/span>):<\/span>\n    <span class=\"hljs-keyword\">for<\/span> col <span class=\"hljs-keyword\">in<\/span> cols:\n        <span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">\"Column {} is missing:\"<\/span>.<span class=\"hljs-built_in\">format<\/span>(col))\n        <span class=\"hljs-built_in\">print<\/span>((df(col).values == <span class=\"hljs-string\">' '<\/span>).<span class=\"hljs-built_in\">sum<\/span>())\n        <span class=\"hljs-built_in\">print<\/span>()\n\n\n<span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">convert_numeric<\/span>(<span class=\"hljs-params\">dataframe, cols<\/span>):<\/span>\n    <span class=\"hljs-keyword\">for<\/span> col <span class=\"hljs-keyword\">in<\/span> cols:\n        dataframe(col) = pd.to_numeric(dataframe(col), errors=<span class=\"hljs-string\">'coerce'<\/span>)\n\ndf = pd.read_csv(<span class=\"hljs-string\">\"gapminder.csv\"<\/span>)\n\n<span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">\"Null values:\"<\/span>)\n<span class=\"hljs-built_in\">print<\/span>(df.isnull().values.<span class=\"hljs-built_in\">any<\/span>())\n\ncols = (<span class=\"hljs-string\">'lifeexpectancy'<\/span>, <span class=\"hljs-string\">'breastcancerper100th'<\/span>, <span class=\"hljs-string\">'suicideper100th'<\/span>)\nnorm_cols = (<span class=\"hljs-string\">'internetuserate'<\/span>, <span class=\"hljs-string\">'employrate'<\/span>)\n\ndf2 = df.copy()\n\ncheck_missing_values(df, cols)\ncheck_missing_values(df, norm_cols)\n\nconvert_numeric(df2, cols)\nconvert_numeric(df2, norm_cols)\n<\/code><\/pre>\n<p>\u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u062e\u0631\u0648\u062c\u06cc \u0647\u0627 \u0622\u0645\u062f\u0647 \u0627\u0633\u062a:<\/p>\n<pre><code class=\"hljs\">Null values:\nColumn lifeexpectancy is missing:\n22\n\nColumn breastcancerper100th is missing:\n40\n\nColumn suicideper100th is missing:\n22\n\nColumn internetuserate is missing:\n21\n\nColumn employrate is missing:\n35\n<\/code><\/pre>\n<p>\u062a\u0639\u062f\u0627\u062f \u0627\u0646\u06af\u0634\u062a \u0634\u0645\u0627\u0631\u06cc \u0627\u0632 \u0645\u0642\u0627\u062f\u06cc\u0631 \u06af\u0645 \u0634\u062f\u0647 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f\u060c \u0627\u0645\u0627 \u062a\u0628\u062f\u06cc\u0644 \u0639\u062f\u062f\u06cc \u0645\u0627 \u0628\u0627\u06cc\u062f \u0622\u0646\u0647\u0627 \u0631\u0627 \u0628\u0647 \u0622\u0646\u0647\u0627 \u062a\u0628\u062f\u06cc\u0644 \u06a9\u0646\u062f <code>NaN<\/code> \u0645\u0642\u0627\u062f\u06cc\u0631\u060c \u0627\u062c\u0627\u0632\u0647 \u0645\u06cc \u062f\u0647\u062f \u062a\u0627 \u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0627\u06a9\u062a\u0634\u0627\u0641\u06cc \u0627\u0646\u062c\u0627\u0645 \u0634\u0648\u062f \u0631\u0648\u06cc \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647<\/p>\n<p>\u0628\u0647 \u0637\u0648\u0631 \u062e\u0627\u0635\u060c \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0631\u0627\u0628\u0637\u0647 \u0628\u06cc\u0646 \u0646\u0631\u062e \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646\u062a\u0631\u0646\u062a \u0648 \u0627\u0645\u06cc\u062f \u0628\u0647 \u0632\u0646\u062f\u06af\u06cc\u060c \u06cc\u0627 \u0628\u06cc\u0646 \u0646\u0631\u062e \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646\u062a\u0631\u0646\u062a \u0648 \u0646\u0631\u062e \u0627\u0634\u062a\u063a\u0627\u0644 \u0631\u0627 \u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u06a9\u0646\u06cc\u0645.  \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0633\u0639\u06cc \u06a9\u0646\u06cc\u0645 \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627\u06cc \u062c\u062f\u0627\u06af\u0627\u0646\u0647 \u0628\u0631\u062e\u06cc \u0627\u0632 \u0627\u06cc\u0646 \u0631\u0648\u0627\u0628\u0637 \u0631\u0627 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 Seaborn \u0648 Matplotlib \u0627\u06cc\u062c\u0627\u062f \u06a9\u0646\u06cc\u0645:<\/p>\n<pre><code class=\"hljs\">sns.lmplot(x=<span class=\"hljs-string\">\"internetuserate\"<\/span>, y=<span class=\"hljs-string\">\"breastcancerper100th\"<\/span>, data=df2, fit_reg=<span class=\"hljs-literal\">False<\/span>)\nplt.title(<span class=\"hljs-string\">\"Internet Use Rate and Breast Cancer Per 100k\"<\/span>)\nplt.show()\n\nsns.lmplot(x=<span class=\"hljs-string\">\"internetuserate\"<\/span>, y=<span class=\"hljs-string\">\"lifeexpectancy\"<\/span>, data=df2, fit_reg=<span class=\"hljs-literal\">False<\/span>)\nplt.title(<span class=\"hljs-string\">\"Internet Use Rate and Life Expectancy\"<\/span>)\nplt.show()\n\nsns.lmplot(x=<span class=\"hljs-string\">\"internetuserate\"<\/span>, y=<span class=\"hljs-string\">\"employrate\"<\/span>, data=df2, fit_reg=<span class=\"hljs-literal\">False<\/span>)\nplt.title(<span class=\"hljs-string\">\"Internet Use Rate and Employment Rate\"<\/span>)\nplt.show()\n<\/code><\/pre>\n<p>\u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u0646\u062a\u0627\u06cc\u062c \u0646\u0645\u0648\u062f\u0627\u0631\u0647\u0627 \u0622\u0645\u062f\u0647 \u0627\u0633\u062a:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/statistical-hypothesis-analysis-with-python-with-anovas-chi-square-and-pearson-correlation-1.png\" alt=\"\u0637\u0631\u062d \u067e\u0631\u0627\u06a9\u0646\u062f\u0647 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646\u062a\u0631\u0646\u062a \u0648 \u0633\u0631\u0637\u0627\u0646 \u0633\u06cc\u0646\u0647\" title=\"\"><br \/>\n<img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/statistical-hypothesis-analysis-with-python-with-anovas-chi-square-and-pearson-correlation-2.png\" alt=\"\u0637\u0631\u062d \u067e\u0631\u0627\u06a9\u0646\u062f\u0647 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646\u062a\u0631\u0646\u062a \u0648 \u0627\u0645\u06cc\u062f \u0628\u0647 \u0632\u0646\u062f\u06af\u06cc\" title=\"\"><br \/>\n<img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/statistical-hypothesis-analysis-with-python-with-anovas-chi-square-and-pearson-correlation-3.png\" alt=\"\u0646\u0645\u0648\u062f\u0627\u0631 \u067e\u0631\u0627\u06a9\u0646\u062f\u06af\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646\u062a\u0631\u0646\u062a \u0648 \u0646\u0631\u062e \u0627\u0634\u062a\u063a\u0627\u0644\" title=\"\"><\/p>\n<p>\u0628\u0647 \u0646\u0638\u0631 \u0645\u06cc \u0631\u0633\u062f \u0631\u0648\u0627\u0628\u0637 \u062c\u0627\u0644\u0628\u06cc \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06a9\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0622\u0646\u0647\u0627 \u0631\u0627 \u0628\u06cc\u0634\u062a\u0631 \u0628\u0631\u0631\u0633\u06cc \u06a9\u0646\u06cc\u0645.  \u062c\u0627\u0644\u0628 \u0627\u06cc\u0646\u062c\u0627\u0633\u062a \u06a9\u0647 \u0628\u0647 \u0646\u0638\u0631 \u0645\u06cc\u200c\u0631\u0633\u062f \u06cc\u06a9 \u0631\u0627\u0628\u0637\u0647 \u0645\u062b\u0628\u062a \u0646\u0633\u0628\u062a\u0627\u064b \u0642\u0648\u06cc \u0628\u06cc\u0646 \u0645\u06cc\u0632\u0627\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646\u062a\u0631\u0646\u062a \u0648 \u0633\u0631\u0637\u0627\u0646 \u0633\u06cc\u0646\u0647 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f\u060c \u0627\u06af\u0631\u0686\u0647 \u0627\u06cc\u0646 \u0627\u062d\u062a\u0645\u0627\u0644\u0627\u064b \u062a\u0646\u0647\u0627 \u0646\u0645\u0648\u0646\u0647\u200c\u0627\u06cc \u0627\u0632 \u0622\u0632\u0645\u0627\u06cc\u0634 \u0628\u0647\u062a\u0631 \u062f\u0631 \u06a9\u0634\u0648\u0631\u0647\u0627\u06cc\u06cc \u0627\u0633\u062a \u06a9\u0647 \u062f\u0633\u062a\u0631\u0633\u06cc \u0628\u06cc\u0634\u062a\u0631\u06cc \u0628\u0647 \u0641\u0646\u0627\u0648\u0631\u06cc \u062f\u0627\u0631\u0646\u062f.<\/p>\n<p>\u0647\u0645\u0686\u0646\u06cc\u0646 \u0628\u0647 \u0646\u0638\u0631 \u0645\u06cc \u0631\u0633\u062f \u06cc\u06a9 \u0631\u0627\u0628\u0637\u0647 \u0646\u0633\u0628\u062a\u0627\u064b \u0642\u0648\u06cc\u060c \u0647\u0631\u0686\u0646\u062f \u062e\u0637\u06cc \u06a9\u0645\u062a\u0631 \u0628\u06cc\u0646 \u0627\u0645\u06cc\u062f \u0628\u0647 \u0632\u0646\u062f\u06af\u06cc \u0648 \u0645\u06cc\u0632\u0627\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646\u062a\u0631\u0646\u062a \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f.<\/p>\n<p>\u062f\u0631 \u0646\u0647\u0627\u06cc\u062a\u060c \u0628\u0647 \u0646\u0638\u0631 \u0645\u06cc \u0631\u0633\u062f \u06a9\u0647 \u06cc\u06a9 \u0631\u0627\u0628\u0637\u0647 \u0633\u0647\u0645\u0648\u06cc \u0648 \u063a\u06cc\u0631 \u062e\u0637\u06cc \u0628\u06cc\u0646 \u0646\u0631\u062e \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646\u062a\u0631\u0646\u062a \u0648 \u0646\u0631\u062e \u0627\u0634\u062a\u063a\u0627\u0644 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f.<\/p>\n<h2 id=\"selectingasuitablehypothesis\"><span class=\"ez-toc-section\" id=\"%d8%a7%d9%86%d8%aa%d8%ae%d8%a7%d8%a8_%db%8c%da%a9_%d9%81%d8%b1%d8%b6%db%8c%d9%87_%d9%85%d9%86%d8%a7%d8%b3%d8%a8\"><\/span>\u0627\u0646\u062a\u062e\u0627\u0628 \u06cc\u06a9 \u0641\u0631\u0636\u06cc\u0647 \u0645\u0646\u0627\u0633\u0628<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0645\u0627 \u0645\u06cc \u062e\u0648\u0627\u0647\u06cc\u0645 \u0631\u0627\u0628\u0637\u0647 \u0627\u06cc \u0631\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0634\u0627\u06cc\u0633\u062a\u06af\u06cc \u06a9\u0627\u0648\u0634 \u0628\u06cc\u0634\u062a\u0631 \u0631\u0627 \u062f\u0627\u0631\u062f.  \u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u0631\u0648\u0627\u0628\u0637 \u0628\u0627\u0644\u0642\u0648\u0647 \u0632\u06cc\u0627\u062f\u06cc \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06a9\u0647 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u062f\u0631 \u0645\u0648\u0631\u062f \u0622\u0646\u0647\u0627 \u0641\u0631\u0636\u06cc\u0647\u200c\u0627\u06cc \u0627\u06cc\u062c\u0627\u062f \u06a9\u0646\u06cc\u0645 \u0648 \u0628\u0627 \u0622\u0632\u0645\u0648\u0646\u200c\u0647\u0627\u06cc \u0622\u0645\u0627\u0631\u06cc \u0631\u0627\u0628\u0637\u0647 \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u06a9\u0646\u06cc\u0645.  \u0648\u0642\u062a\u06cc \u0641\u0631\u0636\u06cc\u0647 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645 \u0648 \u0628\u06cc\u0646 \u062f\u0648 \u0645\u062a\u063a\u06cc\u0631 \u0622\u0632\u0645\u0648\u0646 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0627\u062c\u0631\u0627 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645\u060c \u0627\u06af\u0631 \u0622\u0632\u0645\u0648\u0646 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0645\u0639\u0646\u0627\u062f\u0627\u0631 \u0627\u0633\u062a\u060c \u0628\u0627\u06cc\u062f \u0622\u0632\u0645\u0648\u0646\u200c\u0647\u0627\u06cc \u0622\u0645\u0627\u0631\u06cc \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u0645 \u062a\u0627 \u0628\u0628\u06cc\u0646\u06cc\u0645 \u0686\u0642\u062f\u0631 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0642\u0648\u06cc \u0627\u0633\u062a \u0648 \u0622\u06cc\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0628\u0647 \u0637\u0648\u0631 \u0642\u0627\u0628\u0644 \u0627\u0639\u062a\u0645\u0627\u062f \u0628\u06af\u0648\u06cc\u06cc\u0645 \u06a9\u0647 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0628\u06cc\u0646 \u062f\u0648 \u0645\u062a\u063a\u06cc\u0631 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06cc\u0627 \u062e\u06cc\u0631. \u0686\u06cc\u0632\u06cc \u0628\u06cc\u0634 \u0627\u0632 \u0634\u0627\u0646\u0633 \u0627\u0633\u062a<\/p>\n<p>\u0646\u0648\u0639 \u0622\u0632\u0645\u0648\u0646 \u0622\u0645\u0627\u0631\u06cc \u0645\u0648\u0631\u062f \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u0627 \u0628\u0633\u062a\u06af\u06cc \u062f\u0627\u0631\u062f \u0631\u0648\u06cc \u0645\u0627\u0647\u06cc\u062a \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u062a\u0648\u0636\u06cc\u062d\u06cc \u0648 \u067e\u0627\u0633\u062e \u0645\u0627\u060c \u0647\u0645\u0686\u0646\u06cc\u0646 \u0634\u0646\u0627\u062e\u062a\u0647 \u0634\u062f\u0647 \u0648 <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/www.thoughtco.com\/independent-and-dependent-variables-differences-606115\">\u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u0645\u0633\u062a\u0642\u0644 \u0648 \u0648\u0627\u0628\u0633\u062a\u0647<\/a>.  \u0645\u0627 \u0628\u0647 \u0631\u0648\u0634 \u0627\u062c\u0631\u0627\u06cc \u0633\u0647 \u0646\u0648\u0639 \u0645\u062e\u062a\u0644\u0641 \u062a\u0633\u062a \u0622\u0645\u0627\u0631\u06cc \u062e\u0648\u0627\u0647\u06cc\u0645 \u067e\u0631\u062f\u0627\u062e\u062a:<\/p>\n<ul>\n<li>ANOVA \u0647\u0627<\/li>\n<li>\u062a\u0633\u062a \u0647\u0627\u06cc \u0645\u0631\u0628\u0639 \u06a9\u0627\u06cc<\/li>\n<li>\u0631\u06af\u0631\u0633\u06cc\u0648\u0646 \u0647\u0627<\/li>\n<\/ul>\n<p>\u0645\u0627 \u0628\u0627 \u0622\u0646\u0686\u0647 \u062f\u0631 \u0628\u0627\u0644\u0627 \u062a\u062c\u0633\u0645 \u06a9\u0631\u062f\u06cc\u0645 \u067e\u06cc\u0634 \u0645\u06cc \u0631\u0648\u06cc\u0645 \u0648 \u0631\u0627\u0628\u0637\u0647 \u0628\u06cc\u0646 \u0646\u0631\u062e \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646\u062a\u0631\u0646\u062a \u0648 \u0627\u0645\u06cc\u062f \u0628\u0647 \u0632\u0646\u062f\u06af\u06cc \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc \u06a9\u0646\u06cc\u0645.<\/p>\n<p>\u0627\u06cc\u0646 <em>\u0641\u0631\u0636\u06cc\u0647 \u0635\u0641\u0631<\/em> \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u0628\u06cc\u0646 \u0645\u06cc\u0632\u0627\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646\u062a\u0631\u0646\u062a \u0648 \u0627\u0645\u06cc\u062f \u0628\u0647 \u0632\u0646\u062f\u06af\u06cc \u0631\u0627\u0628\u0637\u0647 \u0645\u0639\u0646\u0627\u062f\u0627\u0631\u06cc \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0631\u062f\u060c \u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u0641\u0631\u0636\u06cc\u0647 \u0645\u0627 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f <em>\u0627\u0633\u062a<\/em> \u0631\u0627\u0628\u0637\u0647 \u0628\u06cc\u0646 \u062f\u0648 \u0645\u062a\u063a\u06cc\u0631<\/p>\n<p>\u0645\u0627 \u0627\u0646\u0648\u0627\u0639 \u0645\u062e\u062a\u0644\u0641\u06cc \u0627\u0632 \u0622\u0632\u0645\u0648\u0646 \u0647\u0627\u06cc \u0641\u0631\u0636\u06cc\u0647 \u0631\u0627 \u0627\u0646\u062c\u0627\u0645 \u062e\u0648\u0627\u0647\u06cc\u0645 \u062f\u0627\u062f \u0631\u0648\u06cc \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647  \u0646\u0648\u0639 \u0622\u0632\u0645\u0648\u0646 \u0641\u0631\u0636\u06cc\u0647 \u0627\u06cc \u06a9\u0647 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u0648\u0627\u0628\u0633\u062a\u0647 \u0627\u0633\u062a \u0631\u0648\u06cc \u0645\u0627\u0647\u06cc\u062a \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u062a\u0648\u0636\u06cc\u062d\u06cc \u0648 \u067e\u0627\u0633\u062e \u0645\u0627.  \u062a\u0631\u06a9\u06cc\u0628 \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u062a\u0648\u0636\u06cc\u062d\u06cc \u0648 \u067e\u0627\u0633\u062e \u0646\u06cc\u0627\u0632 \u0628\u0647 \u0622\u0632\u0645\u0648\u0646 \u0647\u0627\u06cc \u0622\u0645\u0627\u0631\u06cc \u0645\u062a\u0641\u0627\u0648\u062a\u06cc \u062f\u0627\u0631\u0646\u062f.  \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u062b\u0627\u0644\u060c \u0627\u06af\u0631 \u06cc\u06a9 \u0645\u062a\u063a\u06cc\u0631 \u0645\u0642\u0648\u0644\u0647 \u0627\u06cc \u0648 \u06cc\u06a9 \u0645\u062a\u063a\u06cc\u0631 \u0645\u0627\u0647\u06cc\u062a \u06a9\u0645\u06cc \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f\u060c an <em>\u062a\u062d\u0644\u06cc\u0644 \u0648\u0627\u0631\u06cc\u0627\u0646\u0633<\/em> \u0645\u0648\u0631\u062f \u0646\u06cc\u0627\u0632 \u0627\u0633\u062a.<\/p>\n<h2 id=\"analysisofvarianceanova\"><span class=\"ez-toc-section\" id=\"%d8%aa%d8%ac%d8%b2%db%8c%d9%87_%d9%88_%d8%aa%d8%ad%d9%84%db%8c%d9%84_%d9%88%d8%a7%d8%b1%db%8c%d8%a7%d9%86%d8%b3_anova\"><\/span>\u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u0648\u0627\u0631\u06cc\u0627\u0646\u0633 (ANOVA)<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u06cc\u06a9 <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/www.statsmodels.org\/stable\/anova.html\">\u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u0648\u0627\u0631\u06cc\u0627\u0646\u0633 (ANOVA)<\/a> \u06cc\u06a9 \u0622\u0632\u0645\u0648\u0646 \u0622\u0645\u0627\u0631\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0628\u0631\u0627\u06cc \u0645\u0642\u0627\u06cc\u0633\u0647 \u062f\u0648 \u06cc\u0627 \u0686\u0646\u062f \u0645\u06cc\u0627\u0646\u06af\u06cc\u0646 \u0628\u0627 \u0647\u0645 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f \u06a9\u0647 \u0627\u0632 \u0637\u0631\u06cc\u0642 \u062a\u062d\u0644\u06cc\u0644 \u0648\u0627\u0631\u06cc\u0627\u0646\u0633 \u062a\u0639\u06cc\u06cc\u0646 \u0645\u06cc \u0634\u0648\u062f.  \u0622\u0632\u0645\u0648\u0646 \u0647\u0627\u06cc ANOVA \u06cc\u06a9 \u0637\u0631\u0641\u0647 \u0628\u0631\u0627\u06cc \u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u062a\u0641\u0627\u0648\u062a \u0628\u06cc\u0646 \u06af\u0631\u0648\u0647 \u0647\u0627 \u0648 \u062a\u0639\u06cc\u06cc\u0646 \u0627\u06cc\u0646\u06a9\u0647 \u0622\u06cc\u0627 \u062a\u0641\u0627\u0648\u062a \u0647\u0627 \u0627\u0632 \u0646\u0638\u0631 \u0622\u0645\u0627\u0631\u06cc \u0645\u0639\u0646\u06cc \u062f\u0627\u0631 \u0647\u0633\u062a\u0646\u062f \u06cc\u0627 \u062e\u06cc\u0631\u060c \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f.<\/p>\n<p>ANOVA\u0647\u0627\u06cc \u06cc\u06a9 \u0637\u0631\u0641\u0647 \u062f\u0648 \u06cc\u0627 \u0686\u0646\u062f \u0645\u06cc\u0627\u0646\u06af\u06cc\u0646 \u06af\u0631\u0648\u0647 \u0645\u0633\u062a\u0642\u0644 \u0631\u0627 \u0628\u0627 \u0647\u0645 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0645\u06cc \u06a9\u0646\u0646\u062f\u060c \u0627\u06af\u0631\u0686\u0647 \u062f\u0631 \u0639\u0645\u0644 \u0627\u063a\u0644\u0628 \u0632\u0645\u0627\u0646\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u0646\u062f \u06a9\u0647 \u062d\u062f\u0627\u0642\u0644 \u0633\u0647 \u06af\u0631\u0648\u0647 \u0645\u0633\u062a\u0642\u0644 \u0648\u062c\u0648\u062f \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f.<\/p>\n<p>\u0628\u0647 \u0645\u0646\u0638\u0648\u0631 \u0627\u0646\u062c\u0627\u0645 ANOVA \u0631\u0648\u06cc \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 Gapminder\u060c \u0645\u0627 \u0628\u0627\u06cc\u062f \u0628\u0631\u062e\u06cc \u0627\u0632 \u0648\u06cc\u0698\u06af\u06cc\u200c\u0647\u0627 \u0631\u0627 \u062a\u063a\u06cc\u06cc\u0631 \u062f\u0647\u06cc\u0645\u060c \u0632\u06cc\u0631\u0627 \u0627\u06cc\u0646 \u0645\u0642\u0627\u062f\u06cc\u0631 \u062f\u0631 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u067e\u06cc\u0648\u0633\u062a\u0647 \u0647\u0633\u062a\u0646\u062f\u060c \u0627\u0645\u0627 \u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 ANOVA \u0628\u0631\u0627\u06cc \u0645\u0648\u0642\u0639\u06cc\u062a\u200c\u0647\u0627\u06cc\u06cc \u06a9\u0647 \u06cc\u06a9 \u0645\u062a\u063a\u06cc\u0631 \u0637\u0628\u0642\u0647\u200c\u0628\u0646\u062f\u06cc \u0648 \u06cc\u06a9 \u0645\u062a\u063a\u06cc\u0631 \u06a9\u0645\u06cc \u0627\u0633\u062a \u0645\u0646\u0627\u0633\u0628 \u0627\u0633\u062a.<\/p>\n<p>\u0645\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u062f\u0627\u062f\u0647\u200c\u0647\u0627 \u0631\u0627 \u0627\u0632 \u067e\u06cc\u0648\u0633\u062a\u0647 \u0628\u0647 \u06a9\u0645\u06cc \u0628\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u06cc\u06a9 \u062f\u0633\u062a\u0647 \u0648 \u062a\u0631\u06a9\u06cc\u0628 \u0645\u062a\u063a\u06cc\u0631 \u0645\u0648\u0631\u062f \u0646\u0638\u0631 \u0648 \u062a\u0642\u0633\u06cc\u0645 \u0622\u0646 \u0628\u0647 \u0635\u062f\u06a9 \u062a\u0628\u062f\u06cc\u0644 \u06a9\u0646\u06cc\u0645.  \u0645\u062a\u063a\u06cc\u0631 \u0645\u0633\u062a\u0642\u0644 \u0628\u0647 \u06cc\u06a9 \u0645\u062a\u063a\u06cc\u0631 \u0637\u0628\u0642\u0647 \u0627\u06cc \u062a\u0628\u062f\u06cc\u0644 \u0645\u06cc \u0634\u0648\u062f\u060c \u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u0645\u062a\u063a\u06cc\u0631 \u0648\u0627\u0628\u0633\u062a\u0647 \u067e\u06cc\u0648\u0633\u062a\u0647 \u0645\u06cc \u0645\u0627\u0646\u062f.  \u0645\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u0645 <code>qcut()<\/code> \u062f\u0631 \u067e\u0627\u0646\u062f\u0627\u0647\u0627 \u0628\u0631\u0627\u06cc \u062a\u0642\u0633\u06cc\u0645 \u062f\u06cc\u062a\u0627\u0641\u0631\u06cc\u0645 \u0628\u0647 bin \u0647\u0627 \u0639\u0645\u0644 \u0645\u06cc \u06a9\u0646\u062f:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">bin<\/span>(<span class=\"hljs-params\">dataframe, cols<\/span>):<\/span>\n    \n    <span class=\"hljs-keyword\">for<\/span> col <span class=\"hljs-keyword\">in<\/span> cols:\n        new_col_name = <span class=\"hljs-string\">\"{}_bins\"<\/span>.<span class=\"hljs-built_in\">format<\/span>(col)\n        dataframe(new_col_name) = pd.qcut(dataframe(col), <span class=\"hljs-number\">10<\/span>, labels=(<span class=\"hljs-string\">\"1=10%\"<\/span>, <span class=\"hljs-string\">\"2=20%\"<\/span>, <span class=\"hljs-string\">\"3=30%\"<\/span>, <span class=\"hljs-string\">\"4=40%\"<\/span>, <span class=\"hljs-string\">\"5=50%\"<\/span>, <span class=\"hljs-string\">\"6=60%\"<\/span>, <span class=\"hljs-string\">\"7=70%\"<\/span>, <span class=\"hljs-string\">\"8=80\"<\/span>, <span class=\"hljs-string\">\"9=90%\"<\/span>, <span class=\"hljs-string\">\"10=100%\"<\/span>))\n\ndf3 = df2.copy()\n\n\n<span class=\"hljs-built_in\">bin<\/span>(df3, cols)\n<span class=\"hljs-built_in\">bin<\/span>(df3, norm_cols)\n<\/code><\/pre>\n<p>\u067e\u0633 \u0627\u0632 \u062a\u0628\u062f\u06cc\u0644 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627 \u0648 \u0622\u0645\u0627\u062f\u0647 \u0634\u062f\u0646 \u0628\u0631\u0627\u06cc \u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644\u060c \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u0627\u0632 \u0622\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u0645 <code>statsmodel<\/code> \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 \u0628\u0631\u0627\u06cc \u0627\u0646\u062c\u0627\u0645 ANOVA \u0631\u0648\u06cc \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u0627\u0646\u062a\u062e\u0627\u0628 \u0634\u062f\u0647  \u062e\u0648\u0628 print \u0646\u062a\u0627\u06cc\u062c ANOVA \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u06a9\u0646\u06cc\u062f \u0648 \u0628\u0631\u0631\u0633\u06cc \u06a9\u0646\u06cc\u062f \u06a9\u0647 \u0622\u06cc\u0627 \u0631\u0627\u0628\u0637\u0647 \u0628\u06cc\u0646 \u062f\u0648 \u0645\u062a\u063a\u06cc\u0631 \u0627\u0632 \u0646\u0638\u0631 \u0622\u0645\u0627\u0631\u06cc \u0645\u0639\u0646\u0627\u062f\u0627\u0631 \u0627\u0633\u062a \u06cc\u0627 \u062e\u06cc\u0631:<\/p>\n<pre><code class=\"hljs\">anova_df = df3((<span class=\"hljs-string\">'lifeexpectancy'<\/span>, <span class=\"hljs-string\">'internetuserate_bins'<\/span>, <span class=\"hljs-string\">'employrate_bins'<\/span>)).dropna()\n\nrelate_df = df3((<span class=\"hljs-string\">'lifeexpectancy'<\/span>, <span class=\"hljs-string\">'internetuserate_bins'<\/span>))\n\nanova = smf.ols(formula=<span class=\"hljs-string\">'lifeexpectancy ~ C(internetuserate_bins)'<\/span>, data=anova_df).fit()\n\n<span class=\"hljs-built_in\">print<\/span>(anova.summary())\n\n\nmean = relate_df.groupby(<span class=\"hljs-string\">\"internetuserate_bins\"<\/span>).mean()\nsd = relate_df.groupby(<span class=\"hljs-string\">\"internetuserate_bins\"<\/span>).std()\n<span class=\"hljs-built_in\">print<\/span>(mean)\n<span class=\"hljs-built_in\">print<\/span>(sd)\n<\/code><\/pre>\n<p>\u0627\u06cc\u0646 \u0647\u0645 \u062e\u0631\u0648\u062c\u06cc \u0645\u062f\u0644:<\/p>\n<pre><code class=\"hljs\">                            OLS Regression Results                            \n==============================================================================\nDep. Variable:         lifeexpectancy   R-squared:                       0.689\nModel:                            OLS   Adj. R-squared:                  0.671\nMethod:                 Least Squares   F-statistic:                     38.65\nDate:                Mon, 11 May 2020   Prob (F-statistic):           1.71e-35\nTime:                        17:49:24   Log-Likelihood:                -521.54\nNo. Observations:                 167   AIC:                             1063.\nDf Residuals:                     157   BIC:                             1094.\nDf Model:                           9                                         \nCovariance Type:            nonrobust                                         \n======================================================================================================\n                                         coef    std err          t      P&gt;|t|      (0.025      0.975)\n------------------------------------------------------------------------------------------------------\nIntercept                             56.6603      1.268     44.700      0.000      54.157      59.164\nC(internetuserate_bins)(T.2=20%)       1.6785      1.870      0.898      0.371      -2.015       5.372\nC(internetuserate_bins)(T.3=30%)       5.5273      1.901      2.907      0.004       1.772       9.283\nC(internetuserate_bins)(T.4=40%)      11.5693      1.842      6.282      0.000       7.932      15.207\nC(internetuserate_bins)(T.5=50%)      14.6991      1.870      7.860      0.000      11.005      18.393\nC(internetuserate_bins)(T.6=60%)      16.7287      1.870      8.946      0.000      13.035      20.422\nC(internetuserate_bins)(T.7=70%)      17.8802      1.975      9.052      0.000      13.978      21.782\nC(internetuserate_bins)(T.8=80)       19.8302      1.901     10.430      0.000      16.075      23.586\nC(internetuserate_bins)(T.9=90%)      23.0723      1.901     12.135      0.000      19.317      26.828\nC(internetuserate_bins)(T.10=100%)    23.3042      1.901     12.257      0.000      19.549      27.060\n==============================================================================\nOmnibus:                       10.625   Durbin-Watson:                   1.920\nProb(Omnibus):                  0.005   Jarque-Bera (JB):               11.911\nSkew:                          -0.484   Prob(JB):                      0.00259\nKurtosis:                       3.879   Cond. No.                         10.0\n==============================================================================\n\nWarnings:\n(1) Standard Errors assume that the covariance matrix of the errors is correctly specified.\n<\/code><\/pre>\n<p>\u0645\u06cc \u0628\u06cc\u0646\u06cc\u0645 \u06a9\u0647 \u0645\u062f\u0644 \u06cc\u06a9 \u0645\u0642\u062f\u0627\u0631 P \u0628\u0633\u06cc\u0627\u0631 \u06a9\u0648\u0686\u06a9 (<em>\u0622\u0645\u0627\u0631\u0647 \u067e\u0631\u0648\u0628 F<\/em>) \u0627\u0632 <em>1.71e-35<\/em>.  \u0627\u06cc\u0646 \u0628\u0633\u06cc\u0627\u0631 \u06a9\u0645\u062a\u0631 \u0627\u0632 \u0622\u0633\u062a\u0627\u0646\u0647 \u0627\u0647\u0645\u06cc\u062a \u0645\u0639\u0645\u0648\u0644 \u0627\u0633\u062a <em>0.05<\/em>\u0628\u0646\u0627\u0628\u0631\u0627\u06cc\u0646 \u0646\u062a\u06cc\u062c\u0647 \u0645\u06cc \u06af\u06cc\u0631\u06cc\u0645 \u06a9\u0647 \u0628\u06cc\u0646 \u0627\u0645\u06cc\u062f \u0628\u0647 \u0632\u0646\u062f\u06af\u06cc \u0648 \u0645\u06cc\u0632\u0627\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646\u062a\u0631\u0646\u062a \u0631\u0627\u0628\u0637\u0647 \u0645\u0639\u0646\u0627\u062f\u0627\u0631\u06cc \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f.<\/p>\n<p>\u0627\u0632 \u0622\u0646\u062c\u0627\u06cc\u06cc \u06a9\u0647 \u0628\u0647 \u0646\u0638\u0631 \u0645\u06cc \u0631\u0633\u062f \u0647\u0645\u0628\u0633\u062a\u06af\u06cc P-value \u0645\u0647\u0645 \u0627\u0633\u062a\u060c \u0648 \u0627\u0632 \u0622\u0646\u062c\u0627\u06cc\u06cc \u06a9\u0647 \u0645\u0627 10 \u062f\u0633\u062a\u0647 \u0645\u062e\u062a\u0644\u0641 \u062f\u0627\u0631\u06cc\u0645\u060c \u0645\u06cc \u062e\u0648\u0627\u0647\u06cc\u0645 \u06cc\u06a9 \u062a\u0633\u062a \u062a\u0639\u0642\u06cc\u0628\u06cc \u0631\u0627 \u0627\u062c\u0631\u0627 \u06a9\u0646\u06cc\u0645 \u062a\u0627 \u0628\u0631\u0631\u0633\u06cc \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u062a\u0641\u0627\u0648\u062a \u0628\u06cc\u0646 \u0645\u06cc\u0627\u0646\u06af\u06cc\u0646 \u0647\u0627 \u0647\u0645\u0686\u0646\u0627\u0646 \u0642\u0627\u0628\u0644 \u062a\u0648\u062c\u0647 \u0627\u0633\u062a \u062d\u062a\u06cc \u067e\u0633 \u0627\u0632 \u0628\u0631\u0631\u0633\u06cc \u0646\u0648\u0639 1. \u062e\u0637\u0627\u0647\u0627  \u0645\u0627 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0622\u0632\u0645\u0627\u06cc\u0634\u200c\u0647\u0627\u06cc \u067e\u0633\u200c\u0647\u06a9 \u0631\u0627 \u0628\u0627 \u06a9\u0645\u06a9 \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u0645 <code>multicomp<\/code> \u0645\u0627\u0698\u0648\u0644\u060c \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 a <em>Tukey \u0635\u0627\u062f\u0642\u0627\u0646\u0647 \u062a\u0641\u0627\u0648\u062a \u0642\u0627\u0628\u0644 \u062a\u0648\u062c\u0647\u06cc<\/em> \u062a\u0633\u062a (Tukey HSD):<\/p>\n<pre><code class=\"hljs\">multi_comparison = multi.MultiComparison(anova_df(<span class=\"hljs-string\">\"lifeexpectancy\"<\/span>), anova_df(<span class=\"hljs-string\">\"internetuserate_bins\"<\/span>))\nresults = multi_comparison.tukeyhsd()\n<span class=\"hljs-built_in\">print<\/span>(results)\n<\/code><\/pre>\n<p>\u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u0646\u062a\u0627\u06cc\u062c \u0622\u0632\u0645\u0627\u06cc\u0634 \u0622\u0645\u062f\u0647 \u0627\u0633\u062a:<\/p>\n<pre><code class=\"hljs\">  Multiple Comparison of Means - Tukey HSD, FWER=0.05  \n=======================================================\n group1 group2 meandiff p-adj   lower    upper   reject\n-------------------------------------------------------\n10=100%  1=10% -23.3042  0.001 -29.4069 -17.2015   True\n10=100%  2=20% -21.6257  0.001 -27.9633 -15.2882   True\n10=100%  3=30% -17.7769  0.001 -24.2097  -11.344   True\n10=100%  4=40% -11.7349  0.001 -17.9865  -5.4833   True\n10=100%  5=50%  -8.6051  0.001 -14.9426  -2.2676   True\n10=100%  6=60%  -6.5755 0.0352  -12.913   -0.238   True\n10=100%  7=70%  -5.4241 0.2199 -12.0827   1.2346  False\n10=100%   8=80  -3.4741 0.7474  -9.9069   2.9588  False\n10=100%  9=90%  -0.2319    0.9  -6.6647    6.201  False\n  1=10%  2=20%   1.6785    0.9  -4.3237   7.6807  False\n  1=10%  3=30%   5.5273 0.1127  -0.5754  11.6301  False\n  1=10%  4=40%  11.5693  0.001   5.6579  17.4807   True\n  1=10%  5=50%  14.6991  0.001   8.6969  20.7013   True\n  1=10%  6=60%  16.7287  0.001  10.7265  22.7309   True\n  1=10%  7=70%  17.8801  0.001  11.5399  24.2204   True\n  1=10%   8=80  19.8301  0.001  13.7274  25.9329   True\n  1=10%  9=90%  23.0723  0.001  16.9696  29.1751   True\n  2=20%  3=30%   3.8489 0.6171  -2.4887  10.1864  False\n  2=20%  4=40%   9.8908  0.001   3.7374  16.0443   True\n  2=20%  5=50%  13.0206  0.001   6.7799  19.2614   True\n  2=20%  6=60%  15.0502  0.001   8.8095   21.291   True\n  2=20%  7=70%  16.2017  0.001   9.6351  22.7683   True\n  2=20%   8=80  18.1517  0.001  11.8141  24.4892   True\n  2=20%  9=90%  21.3939  0.001  15.0563  27.7314   True\n  3=30%  4=40%    6.042 0.0678  -0.2096  12.2936  False\n  3=30%  5=50%   9.1718  0.001   2.8342  15.5093   True\n  3=30%  6=60%  11.2014  0.001   4.8638  17.5389   True\n  3=30%  7=70%  12.3528  0.001   5.6942  19.0114   True\n  3=30%   8=80  14.3028  0.001     7.87  20.7357   True\n  3=30%  9=90%   17.545  0.001  11.1122  23.9778   True\n  4=40%  5=50%   3.1298 0.8083  -3.0237   9.2833  False\n  4=40%  6=60%   5.1594 0.1862  -0.9941  11.3129  False\n  4=40%  7=70%   6.3108 0.0638  -0.1729  12.7945  False\n  4=40%   8=80   8.2608 0.0015   2.0092  14.5124   True\n  4=40%  9=90%   11.503  0.001   5.2514  17.7546   True\n  5=50%  6=60%   2.0296    0.9  -4.2112   8.2704  False\n  5=50%  7=70%    3.181 0.8552  -3.3856   9.7476  False\n  5=50%   8=80    5.131 0.2273  -1.2065  11.4686  False\n  5=50%  9=90%   8.3732 0.0015   2.0357  14.7108   True\n  6=60%  7=70%   1.1514    0.9  -5.4152    7.718  False\n  6=60%   8=80   3.1014 0.8456  -3.2361    9.439  False\n  6=60%  9=90%   6.3436 0.0496   0.0061  12.6812   True\n  7=70%   8=80     1.95    0.9  -4.7086   8.6086  False\n  7=70%  9=90%   5.1922 0.2754  -1.4664  11.8508  False\n   8=80  9=90%   3.2422 0.8173  -3.1907    9.675  False\n-------------------------------------------------------\n<\/code><\/pre>\n<p>\u0627\u06a9\u0646\u0648\u0646 \u0645\u0627 \u0628\u06cc\u0646\u0634 \u0628\u0647\u062a\u0631\u06cc \u062f\u0631 \u0645\u0648\u0631\u062f \u0627\u06cc\u0646\u06a9\u0647 \u06a9\u062f\u0627\u0645 \u06af\u0631\u0648\u0647 \u0647\u0627 \u062f\u0631 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0645\u0627 \u062a\u0641\u0627\u0648\u062a \u0647\u0627\u06cc \u0622\u0645\u0627\u0631\u06cc \u0645\u0639\u0646\u06cc \u062f\u0627\u0631\u06cc \u062f\u0627\u0631\u0646\u062f\u060c \u062f\u0627\u0631\u06cc\u0645.<\/p>\n<p>\u0627\u06af\u0631 <code>reject<\/code> \u0633\u062a\u0648\u0646 \u062f\u0627\u0631\u0627\u06cc \u06cc\u06a9 \u0628\u0631\u0686\u0633\u0628 \u0627\u0632 <code>False<\/code>\u060c \u0645\u06cc \u062f\u0627\u0646\u06cc\u0645 \u06a9\u0647 \u062a\u0648\u0635\u06cc\u0647 \u0645\u06cc \u0634\u0648\u062f \u0627\u06cc\u0646 \u0631\u0627 \u0631\u062f \u06a9\u0646\u06cc\u0645 <em>\u0641\u0631\u0636\u06cc\u0647 \u0635\u0641\u0631<\/em> \u0648 \u0641\u0631\u0636 \u06a9\u0646\u06cc\u062f \u06a9\u0647 \u0628\u06cc\u0646 \u062f\u0648 \u06af\u0631\u0648\u0647 \u0645\u0648\u0631\u062f \u0645\u0642\u0627\u06cc\u0633\u0647 \u062a\u0641\u0627\u0648\u062a \u0645\u0639\u0646\u0627\u062f\u0627\u0631\u06cc \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f.<\/p>\n<h2 id=\"thechisquaretestofindependence\"><span class=\"ez-toc-section\" id=\"%d8%a2%d8%b2%d9%85%d9%88%d9%86_chi-square_%d8%a7%d8%b3%d8%aa%d9%82%d9%84%d8%a7%d9%84\"><\/span>\u0622\u0632\u0645\u0648\u0646 Chi-Square \u0627\u0633\u062a\u0642\u0644\u0627\u0644<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>ANOVA \u0628\u0631\u0627\u06cc \u0645\u0648\u0627\u0631\u062f\u06cc \u0645\u0646\u0627\u0633\u0628 \u0627\u0633\u062a \u06a9\u0647 \u06cc\u06a9 \u0645\u062a\u063a\u06cc\u0631 \u067e\u06cc\u0648\u0633\u062a\u0647 \u0648 \u062f\u06cc\u06af\u0631\u06cc \u0645\u0642\u0648\u0644\u0647 \u0627\u06cc \u0627\u0633\u062a.  \u0627\u06a9\u0646\u0648\u0646 \u0628\u0647 \u0628\u0631\u0631\u0633\u06cc \u0631\u0648\u0634 \u0627\u062c\u0631\u0627\u06cc a \u0645\u06cc \u067e\u0631\u062f\u0627\u0632\u06cc\u0645 <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/www.statsmodels.org\/stable\/contingency_tables.html\">\u0622\u0632\u0645\u0648\u0646 \u06a9\u0627\u06cc \u0627\u0633\u06a9\u0648\u0626\u0631 \u0627\u0633\u062a\u0642\u0644\u0627\u0644<\/a>.<\/p>\n<p>\u0622\u0632\u0645\u0648\u0646 \u06a9\u0627\u06cc \u0627\u0633\u06a9\u0648\u0626\u0631 \u0627\u0633\u062a\u0642\u0644\u0627\u0644 \u0632\u0645\u0627\u0646\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f \u06a9\u0647 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u062a\u0648\u0636\u06cc\u062d\u06cc \u0648 \u067e\u0627\u0633\u062e\u06cc \u0645\u0642\u0648\u0644\u0647 \u0627\u06cc \u0628\u0627\u0634\u0646\u062f.  \u0634\u0645\u0627 \u0628\u0647 \u0627\u062d\u062a\u0645\u0627\u0644 \u0632\u06cc\u0627\u062f \u0645\u06cc \u062e\u0648\u0627\u0647\u06cc\u062f \u0627\u0632 \u062a\u0633\u062a Chi-Square \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u0645\u062a\u063a\u06cc\u0631 \u062a\u0648\u0636\u06cc\u062d\u06cc \u06a9\u0645\u06cc \u0648 \u0645\u062a\u063a\u06cc\u0631 \u067e\u0627\u0633\u062e \u0637\u0628\u0642\u0647 \u0628\u0646\u062f\u06cc \u0645\u06cc \u0634\u0648\u062f \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u062f\u060c \u06a9\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u062f \u0628\u0627 \u062a\u0642\u0633\u06cc\u0645 \u0645\u062a\u063a\u06cc\u0631 \u062a\u0648\u0636\u06cc\u062d\u06cc \u0628\u0647 \u062f\u0633\u062a\u0647 \u0647\u0627 \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u062f.<\/p>\n<p>\u0622\u0632\u0645\u0648\u0646 \u06a9\u0627\u06cc \u0627\u0633\u06a9\u0648\u0626\u0631 \u0627\u0633\u062a\u0642\u0644\u0627\u0644 \u06cc\u06a9 \u0622\u0632\u0645\u0648\u0646 \u0622\u0645\u0627\u0631\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0628\u0631\u0627\u06cc \u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u0645\u06cc\u0632\u0627\u0646 \u0631\u0627\u0628\u0637\u0647 \u0645\u0639\u0646\u0627\u062f\u0627\u0631 \u0628\u06cc\u0646 \u062f\u0648 \u0645\u062a\u063a\u06cc\u0631 \u0637\u0628\u0642\u0647\u200c\u0628\u0646\u062f\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u0634\u0648\u062f.  \u0647\u0646\u06af\u0627\u0645\u06cc \u06a9\u0647 \u0622\u0632\u0645\u0648\u0646 Chi-Square \u0627\u062c\u0631\u0627 \u0645\u06cc \u0634\u0648\u062f\u060c \u0647\u0631 \u062f\u0633\u062a\u0647 \u062f\u0631 \u06cc\u06a9 \u0645\u062a\u063a\u06cc\u0631 \u0628\u0633\u0627\u0645\u062f \u062e\u0648\u062f \u0631\u0627 \u0628\u0627 \u062f\u0633\u062a\u0647 \u0647\u0627\u06cc \u0645\u062a\u063a\u06cc\u0631 \u062f\u0648\u0645 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0645\u06cc \u06a9\u0646\u062f.  \u0627\u06cc\u0646 \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0639\u0646\u06cc \u0627\u0633\u062a \u06a9\u0647 \u062f\u0627\u062f\u0647 \u0647\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646\u0646\u062f \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u06cc\u06a9 \u062c\u062f\u0648\u0644 \u0641\u0631\u06a9\u0627\u0646\u0633 \u0646\u0645\u0627\u06cc\u0634 \u062f\u0627\u062f\u0647 \u0634\u0648\u0646\u062f\u060c \u062c\u0627\u06cc\u06cc \u06a9\u0647 \u0631\u062f\u06cc\u0641 \u0647\u0627 \u0646\u0634\u0627\u0646 \u062f\u0647\u0646\u062f\u0647 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u0645\u0633\u062a\u0642\u0644 \u0648 \u0633\u062a\u0648\u0646 \u0647\u0627 \u0646\u0634\u0627\u0646 \u062f\u0647\u0646\u062f\u0647 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u0648\u0627\u0628\u0633\u062a\u0647 \u0647\u0633\u062a\u0646\u062f.<\/p>\n<p>\u062f\u0631\u0633\u062a \u0645\u0627\u0646\u0646\u062f \u0627\u06cc\u0646\u06a9\u0647 \u0645\u0627 \u0645\u062a\u063a\u06cc\u0631 \u0645\u0633\u062a\u0642\u0644 \u062e\u0648\u062f \u0631\u0627 \u0628\u0647 \u06cc\u06a9 \u0645\u062a\u063a\u06cc\u0631 \u0637\u0628\u0642\u0647 \u0628\u0646\u062f\u06cc \u062a\u0628\u062f\u06cc\u0644 \u06a9\u0631\u062f\u06cc\u0645 (\u0628\u0627 \u0628\u0627\u06cc\u0646\u06cc\u0646\u06af \u06a9\u0631\u062f\u0646 \u0622\u0646)\u060c \u0628\u0631\u0627\u06cc \u0622\u0632\u0645\u0648\u0646 ANOVA\u060c \u0628\u0631\u0627\u06cc \u0627\u0646\u062c\u0627\u0645 \u062a\u0633\u062a Chi-Square \u0628\u0627\u06cc\u062f \u0647\u0631 \u062f\u0648 \u0645\u062a\u063a\u06cc\u0631 \u0631\u0627 \u0637\u0628\u0642\u0647 \u0628\u0646\u062f\u06cc \u06a9\u0646\u06cc\u0645.  \u0641\u0631\u0636\u06cc\u0647 \u0645\u0627 \u0628\u0631\u0627\u06cc \u0627\u06cc\u0646 \u0645\u0634\u06a9\u0644 \u0647\u0645\u0627\u0646\u0646\u062f \u0641\u0631\u0636\u06cc\u0647 \u0645\u0633\u0626\u0644\u0647 \u0642\u0628\u0644\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0628\u06cc\u0646 \u0627\u0645\u06cc\u062f \u0628\u0647 \u0632\u0646\u062f\u06af\u06cc \u0648 \u0645\u06cc\u0632\u0627\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646\u062a\u0631\u0646\u062a \u0631\u0627\u0628\u0637\u0647 \u0645\u0639\u0646\u0627\u062f\u0627\u0631\u06cc \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f.<\/p>\n<p>\u0641\u0639\u0644\u0627\u064b \u0647\u0645\u0647 \u0686\u06cc\u0632 \u0631\u0627 \u0633\u0627\u062f\u0647 \u0646\u06af\u0647 \u0645\u06cc\u200c\u062f\u0627\u0631\u06cc\u0645 \u0648 \u0645\u062a\u063a\u06cc\u0631 \u0646\u0631\u062e \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646\u062a\u0631\u0646\u062a \u062e\u0648\u062f \u0631\u0627 \u0628\u0647 \u062f\u0648 \u062f\u0633\u062a\u0647 \u062a\u0642\u0633\u06cc\u0645 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u0645\u060c \u0627\u06af\u0631\u0686\u0647 \u0628\u0647 \u0631\u0627\u062d\u062a\u06cc \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u06a9\u0627\u0631\u0647\u0627\u06cc \u0628\u06cc\u0634\u062a\u0631\u06cc \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u0645.  \u0645\u0627 \u06cc\u06a9 \u062a\u0627\u0628\u0639 \u0628\u0631\u0627\u06cc \u0631\u0633\u06cc\u062f\u06af\u06cc \u0628\u0647 \u0622\u0646 \u0645\u06cc \u0646\u0648\u06cc\u0633\u06cc\u0645.<\/p>\n<p>\u0645\u0627 \u0628\u0631\u0627\u06cc \u0645\u062d\u0627\u0641\u0638\u062a \u062f\u0631 \u0628\u0631\u0627\u0628\u0631 \u062e\u0637\u0627\u0647\u0627\u06cc \u0646\u0648\u0639 1 (\u0645\u062b\u0628\u062a \u0646\u0627\u062f\u0631\u0633\u062a) \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0631\u0648\u06cc\u06a9\u0631\u062f\u06cc \u0628\u0647 \u0646\u0627\u0645 <em>\u062a\u0646\u0638\u06cc\u0645 \u0628\u0648\u0646\u0641\u0631\u0648\u0646\u06cc<\/em>.  \u0628\u0631\u0627\u06cc \u0627\u0646\u062c\u0627\u0645 \u0627\u06cc\u0646 \u06a9\u0627\u0631\u060c \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u062f \u0645\u0642\u0627\u06cc\u0633\u0647 \u0647\u0627\u06cc\u06cc \u0631\u0627 \u0628\u0631\u0627\u06cc \u062c\u0641\u062a \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0645\u0645\u06a9\u0646 \u0627\u0632 \u0645\u062a\u063a\u06cc\u0631 \u067e\u0627\u0633\u062e \u062e\u0648\u062f \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u062f \u0648 \u0633\u067e\u0633 \u0627\u0647\u0645\u06cc\u062a \u062a\u0646\u0638\u06cc\u0645 \u0634\u062f\u0647 \u0622\u0646\u0647\u0627 \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u06a9\u0646\u06cc\u062f.<\/p>\n<p>\u0645\u0627 \u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u0645\u0642\u0627\u06cc\u0633\u0647\u200c\u0627\u06cc \u0631\u0627 \u0628\u0631\u0627\u06cc \u0647\u0645\u0647 \u062c\u0641\u062a\u200c\u0647\u0627\u06cc \u0645\u0645\u06a9\u0646 \u0645\u062e\u062a\u0644\u0641 \u0627\u0646\u062c\u0627\u0645 \u0646\u0645\u06cc\u200c\u062f\u0647\u06cc\u0645\u060c \u0641\u0642\u0637 \u0646\u0634\u0627\u0646 \u0645\u06cc\u200c\u062f\u0647\u06cc\u0645 \u06a9\u0647 \u0686\u06af\u0648\u0646\u0647 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646 \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u0631\u0627 \u0627\u0646\u062c\u0627\u0645 \u062f\u0627\u062f.  \u0645\u0627 \u0686\u0646\u062f \u0645\u0642\u0627\u06cc\u0633\u0647 \u0645\u062e\u062a\u0644\u0641 \u0628\u0627 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u06cc\u06a9 \u0637\u0631\u062d \u06a9\u062f\u06af\u0630\u0627\u0631\u06cc \u0645\u062c\u062f\u062f \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc \u062f\u0647\u06cc\u0645 \u0648 \u0631\u06a9\u0648\u0631\u062f\u0647\u0627 \u0631\u0627 \u062f\u0631 \u0633\u062a\u0648\u0646 \u0647\u0627\u06cc \u0648\u06cc\u0698\u06af\u06cc \u062c\u062f\u06cc\u062f \u062a\u0631\u0633\u06cc\u0645 \u0645\u06cc \u06a9\u0646\u06cc\u0645.<\/p>\n<p>\u067e\u0633 \u0627\u0632 \u0622\u0646\u060c \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u0645 \u062a\u0639\u062f\u0627\u062f \u0645\u0634\u0627\u0647\u062f\u0647 \u0634\u062f\u0647 \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u06a9\u0646\u06cc\u0645 \u0648 \u062c\u062f\u0627\u0648\u0644 \u0622\u0646 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0647\u0627 \u0631\u0627 \u0627\u06cc\u062c\u0627\u062f \u06a9\u0646\u06cc\u0645:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">half_bin<\/span>(<span class=\"hljs-params\">dataframe, cols<\/span>):<\/span>\n    <span class=\"hljs-keyword\">for<\/span> col <span class=\"hljs-keyword\">in<\/span> cols:\n        new_col_name = <span class=\"hljs-string\">\"{}_bins_2\"<\/span>.<span class=\"hljs-built_in\">format<\/span>(col)\n        dataframe(new_col_name) = pd.qcut(dataframe(col), <span class=\"hljs-number\">2<\/span>, labels=(<span class=\"hljs-string\">\"1=50%\"<\/span>, <span class=\"hljs-string\">\"2=100%\"<\/span>))\n\nhalf_bin(df3, (<span class=\"hljs-string\">'internetuserate'<\/span>))\n\n\nrecode_2 = {<span class=\"hljs-string\">\"3=30%\"<\/span>: <span class=\"hljs-string\">\"3=30%\"<\/span>, <span class=\"hljs-string\">\"7=70%\"<\/span>: <span class=\"hljs-string\">\"7=70%\"<\/span>}\nrecode_3 = {<span class=\"hljs-string\">\"2=20%\"<\/span>: <span class=\"hljs-string\">\"2=20%\"<\/span>, <span class=\"hljs-string\">\"8=80\"<\/span>: <span class=\"hljs-string\">\"8=80\"<\/span>}\nrecode_4 = {<span class=\"hljs-string\">\"6=60%\"<\/span>: <span class=\"hljs-string\">\"6=60%\"<\/span>, <span class=\"hljs-string\">\"9=90%\"<\/span>: <span class=\"hljs-string\">\"9=90%\"<\/span>}\nrecode_5 = {<span class=\"hljs-string\">\"4=40%\"<\/span>: <span class=\"hljs-string\">\"4=40%\"<\/span>, <span class=\"hljs-string\">\"7=70%\"<\/span>: <span class=\"hljs-string\">\"7=70%\"<\/span>}\n\n\ndf3(<span class=\"hljs-string\">'Comp_3v7'<\/span>) = df3(<span class=\"hljs-string\">'lifeexpectancy_bins'<\/span>).<span class=\"hljs-built_in\">map<\/span>(recode_2)\ndf3(<span class=\"hljs-string\">'Comp_2v8'<\/span>) = df3(<span class=\"hljs-string\">'lifeexpectancy_bins'<\/span>).<span class=\"hljs-built_in\">map<\/span>(recode_3)\ndf3(<span class=\"hljs-string\">'Comp_6v9'<\/span>) = df3(<span class=\"hljs-string\">'lifeexpectancy_bins'<\/span>).<span class=\"hljs-built_in\">map<\/span>(recode_4)\ndf3(<span class=\"hljs-string\">'Comp_4v7'<\/span>) = df3(<span class=\"hljs-string\">'lifeexpectancy_bins'<\/span>).<span class=\"hljs-built_in\">map<\/span>(recode_5)\n<\/code><\/pre>\n<p>\u0627\u062c\u0631\u0627\u06cc \u0622\u0632\u0645\u0648\u0646 Chi-Square \u0648 \u0645\u0642\u0627\u06cc\u0633\u0647 \u067e\u0633 \u0627\u0632 \u0622\u0646 \u0627\u0628\u062a\u062f\u0627 \u0634\u0627\u0645\u0644 \u0633\u0627\u062e\u062a \u062c\u062f\u0648\u0644 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0628\u06cc\u0646 \u0632\u0628\u0627\u0646\u0647 \u0647\u0627 \u0645\u06cc \u0634\u0648\u062f.  \u062c\u062f\u0648\u0644 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0632\u0628\u0627\u0646\u0647 \u0647\u0627\u06cc \u0645\u062a\u0642\u0627\u0637\u0639 \u062f\u0631\u0635\u062f \u0648\u0642\u0648\u0639 \u0645\u062a\u063a\u06cc\u0631 \u067e\u0627\u0633\u062e \u0631\u0627 \u0628\u0631\u0627\u06cc \u0633\u0637\u0648\u062d \u0645\u062e\u062a\u0644\u0641 \u0645\u062a\u063a\u06cc\u0631 \u062a\u0648\u0636\u06cc\u062d\u06cc \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u062f.<\/p>\n<p>\u0641\u0642\u0637 \u0628\u0631\u0627\u06cc \u0627\u06cc\u0646\u06a9\u0647 \u0627\u06cc\u062f\u0647 \u0627\u06cc \u0627\u0632 \u0631\u0648\u0634 \u06a9\u0627\u0631 \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u0645\u060c \u0628\u06cc\u0627\u06cc\u06cc\u062f print \u0646\u062a\u0627\u06cc\u062c \u0631\u0627 \u0628\u0631\u0627\u06cc \u0647\u0645\u0647 \u0645\u0642\u0627\u06cc\u0633\u0647\u200c\u0647\u0627\u06cc \u0633\u0637\u0644 \u0627\u0645\u06cc\u062f \u0628\u0647 \u0632\u0646\u062f\u06af\u06cc \u0646\u0634\u0627\u0646 \u062f\u0647\u06cc\u062f:<\/p>\n<pre><code class=\"hljs\">\ncount_table = pd.crosstab(df3(<span class=\"hljs-string\">'internetuserate_bins_2'<\/span>), df3(<span class=\"hljs-string\">'lifeexpectancy_bins'<\/span>))\n<span class=\"hljs-built_in\">print<\/span>(count_table)\n<\/code><\/pre>\n<pre><code class=\"hljs\">lifeexpectancy_bins     1=10%  2=20%  3=30%  4=40%  ...  7=70%  8=80  9=90%  10=100%\ninternetuserate_bins_2                              ...                             \n1=50%                      18     19     16     14  ...      4     4      1        0\n2=100%                      0      0      1      4  ...     15    11     16       19\n<\/code><\/pre>\n<p>\u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0628\u0628\u06cc\u0646\u06cc\u0645 \u06a9\u0647 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0628\u06cc\u0646 \u0632\u0628\u0627\u0646\u0647\u200c\u0647\u0627 \u0641\u0631\u0627\u0648\u0627\u0646\u06cc \u062f\u0633\u062a\u0647\u200c\u0647\u0627\u06cc \u06cc\u06a9 \u0645\u062a\u063a\u06cc\u0631 \u0631\u0627 \u062f\u0631 \u0645\u062a\u063a\u06cc\u0631 \u062f\u0648\u0645 \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc\u200c\u06a9\u0646\u062f.  \u062f\u0631 \u0628\u0627\u0644\u0627\u060c \u062a\u0648\u0632\u06cc\u0639 \u0627\u0645\u06cc\u062f \u0628\u0647 \u0632\u0646\u062f\u06af\u06cc \u0631\u0627 \u062f\u0631 \u0645\u0648\u0642\u0639\u06cc\u062a \u0647\u0627\u06cc\u06cc \u0645\u0634\u0627\u0647\u062f\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u062f\u0631 \u06cc\u06a9\u06cc \u0627\u0632 \u062f\u0648 \u0633\u0637\u0644 \u0632\u0628\u0627\u0644\u0647 \u0627\u06cc \u06a9\u0647 \u0645\u0627 \u0627\u06cc\u062c\u0627\u062f \u06a9\u0631\u062f\u06cc\u0645 \u0642\u0631\u0627\u0631 \u0645\u06cc \u06af\u06cc\u0631\u0646\u062f.<\/p>\n<p>\u0627\u06a9\u0646\u0648\u0646 \u0628\u0627\u06cc\u062f \u0632\u0628\u0627\u0646\u0647 \u0647\u0627\u06cc \u0645\u062a\u0642\u0627\u0637\u0639 \u0631\u0627 \u0628\u0631\u0627\u06cc \u062c\u0641\u062a \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641\u06cc \u06a9\u0647 \u062f\u0631 \u0628\u0627\u0644\u0627 \u0627\u06cc\u062c\u0627\u062f \u06a9\u0631\u062f\u06cc\u0645 \u0645\u062d\u0627\u0633\u0628\u0647 \u06a9\u0646\u06cc\u0645\u060c \u0632\u06cc\u0631\u0627 \u0627\u06cc\u0646 \u0647\u0645\u0627\u0646 \u0686\u06cc\u0632\u06cc \u0627\u0633\u062a \u06a9\u0647 \u062f\u0631 \u0622\u0632\u0645\u0648\u0646 Chi-Square \u0627\u062c\u0631\u0627 \u0645\u06cc \u06a9\u0646\u06cc\u0645:<\/p>\n<pre><code class=\"hljs\">count_table_3 = pd.crosstab(df3(<span class=\"hljs-string\">'internetuserate_bins_2'<\/span>), df3(<span class=\"hljs-string\">'Comp_3v7'<\/span>))\ncount_table_4 = pd.crosstab(df3(<span class=\"hljs-string\">'internetuserate_bins_2'<\/span>), df3(<span class=\"hljs-string\">'Comp_2v8'<\/span>))\ncount_table_5 = pd.crosstab(df3(<span class=\"hljs-string\">'internetuserate_bins_2'<\/span>), df3(<span class=\"hljs-string\">'Comp_6v9'<\/span>))\ncount_table_6 = pd.crosstab(df3(<span class=\"hljs-string\">'internetuserate_bins_2'<\/span>), df3(<span class=\"hljs-string\">'Comp_4v7'<\/span>))\n<\/code><\/pre>\n<p>\u0647\u0646\u06af\u0627\u0645\u06cc \u06a9\u0647 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627 \u0631\u0627 \u0628\u0647 \u06af\u0648\u0646\u0647\u200c\u0627\u06cc \u062a\u0628\u062f\u06cc\u0644 \u06a9\u0631\u062f\u06cc\u0645 \u06a9\u0647 \u062a\u0633\u062a Chi-Square \u0642\u0627\u0628\u0644 \u0627\u0646\u062c\u0627\u0645 \u0628\u0627\u0634\u062f\u060c \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0627\u0632 \u0622\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u0645 <code>chi2_contingency<\/code> \u0639\u0645\u0644\u06a9\u0631\u062f \u062f\u0631 <code>statsmodel<\/code> \u0628\u0631\u0627\u06cc \u0627\u0646\u062c\u0627\u0645 \u0622\u0632\u0645\u0627\u06cc\u0634<\/p>\n<p>\u0645\u0627 \u0645\u06cc \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0647 print \u062f\u0631\u0635\u062f\u0647\u0627\u06cc \u0633\u062a\u0648\u0646 \u0648 \u0647\u0645\u0686\u0646\u06cc\u0646 \u0646\u062a\u0627\u06cc\u062c \u0622\u0632\u0645\u0648\u0646 Chi-Square \u0631\u0627 \u062e\u0627\u0631\u062c \u06a9\u0646\u06cc\u062f\u060c \u0648 \u0645\u0627 \u06cc\u06a9 \u062a\u0627\u0628\u0639 \u0628\u0631\u0627\u06cc \u0627\u0646\u062c\u0627\u0645 \u0627\u06cc\u0646 \u06a9\u0627\u0631 \u0627\u06cc\u062c\u0627\u062f \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f.  \u0633\u067e\u0633 \u0627\u0632 \u062a\u0627\u0628\u0639 \u062e\u0648\u062f \u0628\u0631\u0627\u06cc \u0627\u0646\u062c\u0627\u0645 \u062a\u0633\u062a Chi-Square \u0628\u0631\u0627\u06cc \u0686\u0647\u0627\u0631 \u062c\u062f\u0648\u0644 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0627\u06cc \u06a9\u0647 \u0627\u06cc\u062c\u0627\u062f \u06a9\u0631\u062f\u06cc\u0645 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u0645:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">chi_sq_test<\/span>(<span class=\"hljs-params\">table<\/span>):<\/span>\n    <span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">\"Results for:\"<\/span>)\n    <span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-built_in\">str<\/span>(table))\n\n    \n    col_sum = table.<span class=\"hljs-built_in\">sum<\/span>(axis=<span class=\"hljs-number\">0<\/span>)\n    col_percents = table\/col_sum\n    <span class=\"hljs-built_in\">print<\/span>(col_percents)\n\n    chi_square = scipy.stats.chi2_contingency(table)\n    <span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">\"Chi-square value, p-value, expected_counts\"<\/span>)\n    <span class=\"hljs-built_in\">print<\/span>(chi_square)\n\n    <span class=\"hljs-built_in\">print<\/span>()\n\n<span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">\"Initial Chi-square:\"<\/span>)\nchi_sq_test(count_table)\n<span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">\" \"<\/span>)\n\nchi_sq_test(count_table_3)\nchi_sq_test(count_table_4)\nchi_sq_test(count_table_5)\nchi_sq_test(count_table_6)\n<\/code><\/pre>\n<p>\u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u0646\u062a\u0627\u06cc\u062c \u0622\u0645\u062f\u0647 \u0627\u0633\u062a:<\/p>\n<pre><code class=\"hljs\">Initial Chi-square:\nResults for:\nlifeexpectancy_bins     1=10%  2=20%  3=30%  4=40%  ...  7=70%  8=80  9=90%  10=100%\ninternetuserate_bins_2                              ...                             \n1=50%                      18     19     16     14  ...      4     4      1        0\n2=100%                      0      0      1      4  ...     15    11     16       19\n\n(2 rows x 10 columns)\nlifeexpectancy_bins     1=10%  2=20%     3=30%  ...      8=80     9=90%  10=100%\ninternetuserate_bins_2                          ...                             \n1=50%                     1.0    1.0  0.941176  ...  0.266667  0.058824      0.0\n2=100%                    0.0    0.0  0.058824  ...  0.733333  0.941176      1.0\n\n(2 rows x 10 columns)\nChi-square value, p-value, expected_counts\n(102.04563740451277, 6.064860600653971e-18, 9, array(((9.45251397, 9.97765363, 8.9273743 , 9.45251397, 9.45251397,\n        9.97765363, 9.97765363, 7.87709497, 8.9273743 , 9.97765363),\n       (8.54748603, 9.02234637, 8.0726257 , 8.54748603, 8.54748603,\n        9.02234637, 9.02234637, 7.12290503, 8.0726257 , 9.02234637))))\n-----\n \nResults for:\nComp_3v7                3=30%  7=70%\ninternetuserate_bins_2              \n1=50%                      16      4\n2=100%                      1     15\nComp_3v7                   3=30%     7=70%\ninternetuserate_bins_2                    \n1=50%                   0.941176  0.210526\n2=100%                  0.058824  0.789474\nChi-square value, p-value, expected_counts\n(16.55247678018576, 4.7322137795376575e-05, 1, array((( 9.44444444, 10.55555556),\n       ( 7.55555556,  8.44444444))))\n-----\nResults for:\nComp_2v8                2=20%  8=80\ninternetuserate_bins_2             \n1=50%                      19     4\n2=100%                      0    11\nComp_2v8                2=20%      8=80\ninternetuserate_bins_2                 \n1=50%                     1.0  0.266667\n2=100%                    0.0  0.733333\nChi-square value, p-value, expected_counts\n(17.382650301643437, 3.0560286589975315e-05, 1, array(((12.85294118, 10.14705882),\n       ( 6.14705882,  4.85294118))))\n-----\nResults for:\nComp_6v9                6=60%  9=90%\ninternetuserate_bins_2              \n1=50%                       6      1\n2=100%                     13     16\nComp_6v9                   6=60%     9=90%\ninternetuserate_bins_2                    \n1=50%                   0.315789  0.058824\n2=100%                  0.684211  0.941176\nChi-square value, p-value, expected_counts\n(2.319693757720874, 0.12774517376836148, 1, array((( 3.69444444,  3.30555556),\n       (15.30555556, 13.69444444))))\n-----\nResults for:\nComp_4v7                4=40%  7=70%\ninternetuserate_bins_2              \n1=50%                      14      4\n2=100%                      4     15\nComp_4v7                   4=40%     7=70%\ninternetuserate_bins_2                    \n1=50%                   0.777778  0.210526\n2=100%                  0.222222  0.789474\nChi-square value, p-value, expected_counts\n(9.743247922437677, 0.0017998260000241526, 1, array(((8.75675676, 9.24324324),\n       (9.24324324, 9.75675676))))\n-----\n<\/code><\/pre>\n<p>\u0627\u06af\u0631 \u0645\u0627 \u0641\u0642\u0637 \u0628\u0647 \u0646\u062a\u0627\u06cc\u062c \u062c\u062f\u0648\u0644 \u0634\u0645\u0627\u0631\u0634 \u06a9\u0627\u0645\u0644 \u0646\u06af\u0627\u0647 \u06a9\u0646\u06cc\u0645\u060c \u0628\u0647 \u0646\u0638\u0631 \u0645\u06cc \u0631\u0633\u062f \u06a9\u0647 \u06cc\u06a9 \u0645\u0642\u062f\u0627\u0631 P \u0627\u0632 <em>6.064860600653971e-18<\/em>.<\/p>\n<p>\u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644\u060c \u0628\u0631\u0627\u06cc \u0627\u0637\u0645\u06cc\u0646\u0627\u0646 \u0627\u0632 \u0627\u06cc\u0646\u06a9\u0647 \u0686\u06af\u0648\u0646\u0647 \u06af\u0631\u0648\u0647\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0627\u0632 \u06cc\u06a9\u062f\u06cc\u06af\u0631 \u062c\u062f\u0627 \u0645\u06cc\u200c\u0634\u0648\u0646\u062f\u060c \u0628\u0627\u06cc\u062f \u0622\u0632\u0645\u0648\u0646 Chi-Square \u0631\u0627 \u0628\u0631\u0627\u06cc \u062c\u0641\u062a\u200c\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u062f\u0631 \u0686\u0627\u0631\u0686\u0648\u0628 \u062f\u0627\u062f\u0647\u200c\u0645\u0627\u0646 \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u0645.  \u0645\u0627 \u0628\u0631\u0631\u0633\u06cc \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0622\u06cc\u0627 \u062a\u0641\u0627\u0648\u062a \u0622\u0645\u0627\u0631\u06cc \u0645\u0639\u0646\u06cc \u062f\u0627\u0631\u06cc \u0628\u0631\u0627\u06cc \u0647\u0631 \u06cc\u06a9 \u0627\u0632 \u062c\u0641\u062a \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0627\u0646\u062a\u062e\u0627\u0628 \u0634\u062f\u0647 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06cc\u0627 \u062e\u06cc\u0631.  \u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f \u06a9\u0647 \u0645\u0642\u062f\u0627\u0631 P \u06a9\u0647 \u06cc\u06a9 \u0646\u062a\u06cc\u062c\u0647 \u0642\u0627\u0628\u0644 \u062a\u0648\u062c\u0647 \u0631\u0627 \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u062f \u0628\u0633\u062a\u0647 \u0628\u0647 \u0622\u0646 \u062a\u063a\u06cc\u06cc\u0631 \u0645\u06cc \u06a9\u0646\u062f \u0631\u0648\u06cc \u0686\u0642\u062f\u0631 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0645\u06cc \u06a9\u0646\u06cc\u062f\u060c \u0648 \u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u0645\u0627 \u062f\u0631 \u0627\u06cc\u0646 \u0622\u0645\u0648\u0632\u0634 \u0628\u0647 \u0622\u0646 \u0646\u0645\u06cc \u067e\u0631\u062f\u0627\u0632\u06cc\u0645\u060c \u0628\u0627\u06cc\u062f \u0628\u0647 \u0622\u0646 \u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f.<\/p>\n<p>\u0645\u0642\u0627\u06cc\u0633\u0647 6 \u062f\u0631 \u0645\u0642\u0627\u0628\u0644 9 \u0645\u0642\u062f\u0627\u0631 P \u0631\u0627 \u0628\u0647 \u0645\u0627 \u0645\u06cc \u062f\u0647\u062f <code>0.127<\/code>\u060c \u06a9\u0647 \u0628\u0627\u0644\u0627\u062a\u0631 \u0627\u0632 <code>0.05<\/code> \u0622\u0633\u062a\u0627\u0646\u0647\u060c \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u062f \u06a9\u0647 \u062a\u0641\u0627\u0648\u062a \u0628\u0631\u0627\u06cc \u0622\u0646 \u062f\u0633\u062a\u0647 \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u063a\u06cc\u0631 \u0642\u0627\u0628\u0644 \u062a\u0648\u062c\u0647 \u0628\u0627\u0634\u062f.  \u062f\u06cc\u062f\u0646 \u062a\u0641\u0627\u0648\u062a\u200c\u0647\u0627\u06cc \u0645\u0642\u0627\u06cc\u0633\u0647\u200c\u0647\u0627 \u0628\u0647 \u0645\u0627 \u06a9\u0645\u06a9 \u0645\u06cc\u200c\u06a9\u0646\u062f \u0628\u0641\u0647\u0645\u06cc\u0645 \u0686\u0631\u0627 \u0628\u0627\u06cc\u062f \u0633\u0637\u0648\u062d \u0645\u062e\u062a\u0644\u0641 \u0631\u0627 \u0628\u0627 \u06cc\u06a9\u062f\u06cc\u06af\u0631 \u0645\u0642\u0627\u06cc\u0633\u0647 \u06a9\u0646\u06cc\u0645.<\/p>\n<h2 id=\"pearsoncorrelation\"><span class=\"ez-toc-section\" id=\"%d9%87%d9%85%d8%a8%d8%b3%d8%aa%da%af%db%8c_%d9%be%db%8c%d8%b1%d8%b3%d9%88%d9%86\"><\/span>\u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0645\u0627 \u062a\u0633\u062a\u06cc \u0631\u0627 \u06a9\u0647 \u0628\u0627\u06cc\u062f \u062f\u0631 \u0647\u0646\u06af\u0627\u0645 \u062f\u0627\u0634\u062a\u0646 \u06cc\u06a9 \u0645\u062a\u063a\u06cc\u0631 \u062a\u0648\u0636\u06cc\u062d\u06cc \u0637\u0628\u0642\u0647\u200c\u0627\u06cc \u0648 \u06cc\u06a9 \u0645\u062a\u063a\u06cc\u0631 \u067e\u0627\u0633\u062e \u06a9\u0645\u06cc (ANOVA) \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u062f\u060c \u0648 \u0647\u0645\u0686\u0646\u06cc\u0646 \u062a\u0633\u062a\u06cc \u0631\u0627 \u06a9\u0647 \u062f\u0631 \u0635\u0648\u0631\u062a \u062f\u0627\u0634\u062a\u0646 \u062f\u0648 \u0645\u062a\u063a\u06cc\u0631 \u0637\u0628\u0642\u0647\u200c\u0628\u0646\u062f\u06cc (Chi-Squared) \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u062f\u060c \u067e\u0648\u0634\u0634 \u062f\u0627\u062f\u0647\u200c\u0627\u06cc\u0645.<\/p>\n<p>\u0627\u06a9\u0646\u0648\u0646 \u0646\u06af\u0627\u0647\u06cc \u062e\u0648\u0627\u0647\u06cc\u0645 \u062f\u0627\u0634\u062a \u0628\u0647 \u0646\u0648\u0639 \u0622\u0632\u0645\u0648\u0646 \u0645\u0646\u0627\u0633\u0628 \u0628\u0631\u0627\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0632\u0645\u0627\u0646\u06cc \u06a9\u0647 \u06cc\u06a9 \u0645\u062a\u063a\u06cc\u0631 \u062a\u0648\u0636\u06cc\u062d\u06cc \u06a9\u0645\u06cc \u0648 \u06cc\u06a9 \u0645\u062a\u063a\u06cc\u0631 \u067e\u0627\u0633\u062e \u06a9\u0645\u06cc \u062f\u0627\u0631\u06cc\u062f &#8211; <em>\u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646<\/em>.<\/p>\n<p><a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/docs.scipy.org\/doc\/scipy-0.14.0\/reference\/generated\/scipy.stats.pearsonr.html\">\u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646<\/a> \u0622\u0632\u0645\u0648\u0646 \u0628\u0631\u0627\u06cc \u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u0642\u062f\u0631\u062a \u0631\u0627\u0628\u0637\u0647 \u0628\u06cc\u0646 \u062f\u0648 \u0645\u062a\u063a\u06cc\u0631 \u0627\u0631\u0627\u0626\u0647 \u0634\u062f\u0647\u060c \u0647\u0631 \u062f\u0648 \u0627\u0632 \u0646\u0638\u0631 \u0645\u0627\u0647\u06cc\u062a \u06a9\u0645\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f.  \u0645\u0642\u062f\u0627\u0631\u060c \u06cc\u0627 \u0642\u062f\u0631\u062a \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646\u060c \u0628\u06cc\u0646 \u062e\u0648\u0627\u0647\u062f \u0628\u0648\u062f <em>+1<\/em> \u0648 <em>-1<\/em>.<\/p>\n<p>\u0647\u0645\u0628\u0633\u062a\u06af\u06cc 1 \u0646\u0634\u0627\u0646 \u062f\u0647\u0646\u062f\u0647 \u0627\u0631\u062a\u0628\u0627\u0637 \u06a9\u0627\u0645\u0644 \u0628\u06cc\u0646 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627 \u0627\u0633\u062a \u0648 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0645\u062b\u0628\u062a \u06cc\u0627 \u0645\u0646\u0641\u06cc \u0627\u0633\u062a.  \u0636\u0631\u0627\u06cc\u0628 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0646\u0632\u062f\u06cc\u06a9 \u0628\u0647 0 \u0646\u0634\u0627\u0646 \u062f\u0647\u0646\u062f\u0647 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0647\u0627\u06cc \u0628\u0633\u06cc\u0627\u0631 \u0636\u0639\u06cc\u0641\u060c \u062a\u0642\u0631\u06cc\u0628\u0627\u064b \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0631\u062f.  \u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u0631\u0648\u0634 \u0647\u0627\u06cc \u062f\u06cc\u06af\u0631\u06cc \u0628\u0631\u0627\u06cc \u0627\u0646\u062f\u0627\u0632\u0647 \u06af\u06cc\u0631\u06cc \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0628\u06cc\u0646 \u062f\u0648 \u0645\u062a\u063a\u06cc\u0631 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f\u060c \u0645\u0627\u0646\u0646\u062f <em>\u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0627\u0633\u067e\u06cc\u0631\u0645\u0646<\/em> \u06cc\u0627 <em>\u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0631\u062a\u0628\u0647 \u06a9\u0646\u062f\u0627\u0644<\/em>\u060c \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646 \u0627\u062d\u062a\u0645\u0627\u0644\u0627\u064b \u0631\u0627\u06cc\u062c \u062a\u0631\u06cc\u0646 \u0622\u0632\u0645\u0648\u0646 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0627\u0633\u062a.<\/p>\n<p>\u0627\u0632 \u0622\u0646\u062c\u0627\u06cc\u06cc \u06a9\u0647 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 Gapminder \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u062e\u0648\u062f \u0631\u0627 \u0628\u0627 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u06a9\u0645\u06cc \u0646\u0634\u0627\u0646 \u0645\u06cc \u062f\u0647\u062f\u060c \u0642\u0628\u0644 \u0627\u0632 \u0627\u062c\u0631\u0627\u06cc \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646 \u0646\u06cc\u0627\u0632\u06cc \u0628\u0647 \u062a\u063a\u06cc\u06cc\u0631 \u062f\u0633\u062a\u0647 \u0628\u0646\u062f\u06cc \u062f\u0627\u062f\u0647 \u0647\u0627 \u0646\u062f\u0627\u0631\u06cc\u0645. \u0631\u0648\u06cc \u0622\u06cc \u062a\u06cc.  \u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f \u06a9\u0647 \u0641\u0631\u0636 \u0628\u0631 \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u0647\u0631 \u062f\u0648 \u0645\u062a\u063a\u06cc\u0631 \u0628\u0647 \u0637\u0648\u0631 \u0645\u0639\u0645\u0648\u0644 \u062a\u0648\u0632\u06cc\u0639 \u0634\u062f\u0647 \u0627\u0646\u062f \u0648 \u0645\u0642\u0627\u062f\u06cc\u0631 \u067e\u0631\u062a \u0642\u0627\u0628\u0644 \u062a\u0648\u062c\u0647\u06cc \u062f\u0631 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0648\u062c\u0648\u062f \u0646\u062f\u0627\u0631\u062f.  \u0628\u0631\u0627\u06cc \u0627\u0646\u062c\u0627\u0645 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646 \u0628\u0647 SciPy \u0646\u06cc\u0627\u0632 \u062f\u0627\u0631\u06cc\u0645.<\/p>\n<p>\u0645\u0627 \u0631\u0627\u0628\u0637\u0647 \u0628\u06cc\u0646 \u0627\u0645\u06cc\u062f \u0628\u0647 \u0632\u0646\u062f\u06af\u06cc \u0648 \u0646\u0631\u062e \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646\u062a\u0631\u0646\u062a \u0648 \u0647\u0645\u0686\u0646\u06cc\u0646 \u0646\u0631\u062e \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646\u062a\u0631\u0646\u062a \u0648 \u0646\u0631\u062e \u0627\u0634\u062a\u063a\u0627\u0644 \u0631\u0627 \u0646\u0645\u0648\u062f\u0627\u0631 \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f \u062a\u0627 \u0628\u0628\u06cc\u0646\u06cc\u0645 \u0646\u0645\u0648\u062f\u0627\u0631 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u062f\u06cc\u06af\u0631\u06cc \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0686\u06af\u0648\u0646\u0647 \u0628\u0627\u0634\u062f.  \u067e\u0633 \u0627\u0632 \u0627\u06cc\u062c\u0627\u062f \u06cc\u06a9 \u062a\u0627\u0628\u0639 \u0646\u0645\u0648\u062f\u0627\u0631\u06cc\u060c \u0627\u0632 \u0622\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f <code>pearsonr()<\/code> \u062a\u0627\u0628\u0639 SciPy \u0628\u0631\u0627\u06cc \u0627\u0646\u062c\u0627\u0645 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0648 \u0628\u0631\u0631\u0633\u06cc \u0646\u062a\u0627\u06cc\u062c:<\/p>\n<pre><code class=\"hljs\">df_clean = df2.dropna()\ndf_clean(<span class=\"hljs-string\">'incomeperperson'<\/span>) = df_clean(<span class=\"hljs-string\">'incomeperperson'<\/span>).replace(<span class=\"hljs-string\">''<\/span>, np.nan)\n\n<span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">plt_regression<\/span>(<span class=\"hljs-params\">x, y, data, label_1, label_2<\/span>):<\/span>\n    reg_plot = regplot(x=x, y=y, fit_reg=<span class=\"hljs-literal\">True<\/span>, data=data)\n    plt.xlabel(label_1)\n    plt.ylabel(label_2)\n    plt.show()\n\nplt_regression(<span class=\"hljs-string\">'lifeexpectancy'<\/span>, <span class=\"hljs-string\">'internetuserate'<\/span>, df_clean, <span class=\"hljs-string\">'Life Expectancy'<\/span>, <span class=\"hljs-string\">'Internet Use Rate'<\/span>)\nplt_regression(<span class=\"hljs-string\">'employrate'<\/span>, <span class=\"hljs-string\">'internetuserate'<\/span>, df_clean, <span class=\"hljs-string\">'Employment Rate'<\/span>, <span class=\"hljs-string\">'Internet Use Rate'<\/span>)\n\n<span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">'Assoc. - life expectancy and internet use rate'<\/span>)\n<span class=\"hljs-built_in\">print<\/span>(pearsonr(df_clean(<span class=\"hljs-string\">'lifeexpectancy'<\/span>), df_clean(<span class=\"hljs-string\">'internetuserate'<\/span>)))\n\n<span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">'Assoc. - between employment rate and internet use rate'<\/span>)\n<span class=\"hljs-built_in\">print<\/span>(pearsonr(df_clean(<span class=\"hljs-string\">'employrate'<\/span>), df_clean(<span class=\"hljs-string\">'internetuserate'<\/span>)))\n<\/code><\/pre>\n<p>\u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u062e\u0631\u0648\u062c\u06cc \u0647\u0627 \u0622\u0645\u062f\u0647 \u0627\u0633\u062a:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/statistical-hypothesis-analysis-with-python-with-anovas-chi-square-and-pearson-correlation-4.png\" alt=\"\u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0628\u06cc\u0646 \u0645\u06cc\u0632\u0627\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646\u062a\u0631\u0646\u062a \u0648 \u0627\u0645\u06cc\u062f \u0628\u0647 \u0632\u0646\u062f\u06af\u06cc\" title=\"\"><br \/>\n<img decoding=\"async\" src=\"https:\/\/rasanegar.com\/blog\/wp-content\/uploads\/2024\/01\/statistical-hypothesis-analysis-with-python-with-anovas-chi-square-and-pearson-correlation-5.png\" alt=\"\u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0628\u06cc\u0646 \u0646\u0631\u062e \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646\u062a\u0631\u0646\u062a \u0648 \u0646\u0631\u062e \u0627\u0634\u062a\u063a\u0627\u0644\" title=\"\"><\/p>\n<pre><code class=\"hljs\">Assoc. - life expectancy and internet use rate\n(0.77081050888289, 5.983388253650836e-33)\nAssoc. - between employment rate and internet use rate\n(-0.1950109538173115, 0.013175901971555317)\n<\/code><\/pre>\n<p>\u0627\u0648\u0644\u06cc\u0646 \u0645\u0642\u062f\u0627\u0631 \u062c\u0647\u062a \u0648 \u0642\u062f\u0631\u062a \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0627\u0633\u062a\u060c \u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u062f\u0648\u0645\u06cc\u0646 \u0645\u0642\u062f\u0627\u0631 P-value \u0627\u0633\u062a.  \u0627\u0639\u062f\u0627\u062f \u0646\u0634\u0627\u0646 \u0645\u06cc\u200c\u062f\u0647\u0646\u062f \u06a9\u0647 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0646\u0633\u0628\u062a\u0627\u064b \u0642\u0648\u06cc \u0628\u06cc\u0646 \u0627\u0645\u06cc\u062f \u0628\u0647 \u0632\u0646\u062f\u06af\u06cc \u0648 \u0645\u06cc\u0632\u0627\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646\u062a\u0631\u0646\u062a \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06a9\u0647 \u0628\u0647 \u062f\u0644\u06cc\u0644 \u0634\u0627\u0646\u0633 \u0646\u06cc\u0633\u062a.  \u062f\u0631 \u0647\u0645\u06cc\u0646 \u062d\u0627\u0644\u060c \u0628\u06cc\u0646 \u0646\u0631\u062e \u0627\u0634\u062a\u063a\u0627\u0644 \u0648 \u0645\u06cc\u0632\u0627\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0627\u06cc\u0646\u062a\u0631\u0646\u062a \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0636\u0639\u06cc\u0641\u200c\u062a\u0631\u060c \u0647\u0631\u0686\u0646\u062f \u0647\u0646\u0648\u0632 \u0645\u0639\u0646\u06cc\u200c\u062f\u0627\u0631 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f.<\/p>\n<p>\u062a\u0648\u062c\u0647 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u06cc\u062f \u06a9\u0647 \u0627\u0645\u06a9\u0627\u0646 \u0627\u062c\u0631\u0627\u06cc \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646 \u0646\u06cc\u0632 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u0631\u0648\u06cc \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0637\u0628\u0642\u0647 \u0628\u0646\u062f\u06cc \u0634\u062f\u0647\u060c \u0627\u06af\u0631\u0686\u0647 \u0646\u062a\u0627\u06cc\u062c \u062a\u0627 \u062d\u062f\u0648\u062f\u06cc \u0645\u062a\u0641\u0627\u0648\u062a \u0628\u0647 \u0646\u0638\u0631 \u0645\u06cc \u0631\u0633\u062f.  \u0627\u06af\u0631 \u0628\u062e\u0648\u0627\u0647\u06cc\u0645 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u0645 \u0633\u0637\u0648\u062d \u062f\u0631\u0622\u0645\u062f \u0631\u0627 \u06af\u0631\u0648\u0647\u200c\u0628\u0646\u062f\u06cc \u06a9\u0646\u06cc\u0645 \u0648 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646 \u0631\u0627 \u0627\u062c\u0631\u0627 \u06a9\u0646\u06cc\u0645 \u0631\u0648\u06cc \u0622\u0646\u0647\u0627 \u0631\u0627  \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u062f \u0627\u0632 \u0622\u0646 \u0628\u0631\u0627\u06cc \u0628\u0631\u0631\u0633\u06cc \u0648\u062c\u0648\u062f \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u062a\u0639\u062f\u06cc\u0644 \u06a9\u0646\u0646\u062f\u0647 \u06a9\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646\u0646\u062f \u062a\u0623\u062b\u06cc\u0631\u06af\u0630\u0627\u0631 \u0628\u0627\u0634\u0646\u062f \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u062f \u0631\u0648\u06cc \u0627\u0646\u062c\u0645\u0646 \u0645\u0648\u0631\u062f \u0639\u0644\u0627\u0642\u0647 \u0634\u0645\u0627<\/p>\n<h2 id=\"moderatorsandstatisticalinteraction\"><span class=\"ez-toc-section\" id=\"%d9%85%d8%af%db%8c%d8%b1%d8%a7%d9%86_%d9%88_%d8%aa%d8%b9%d8%a7%d9%85%d9%84_%d8%a2%d9%85%d8%a7%d8%b1%db%8c\"><\/span>\u0645\u062f\u06cc\u0631\u0627\u0646 \u0648 \u062a\u0639\u0627\u0645\u0644 \u0622\u0645\u0627\u0631\u06cc<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0631\u0648\u0634 \u0645\u062d\u0627\u0633\u0628\u0647 \u062a\u0639\u0627\u0645\u0644 \u0622\u0645\u0627\u0631\u06cc \u0628\u06cc\u0646 \u0686\u0646\u062f\u06cc\u0646 \u0645\u062a\u063a\u06cc\u0631 \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u06a9\u0646\u06cc\u0645\u060c AKA moderation.<\/p>\n<p>\u062a\u0639\u062f\u06cc\u0644 \u0632\u0645\u0627\u0646\u06cc \u0627\u0633\u062a \u06a9\u0647 \u06cc\u06a9 \u0645\u062a\u063a\u06cc\u0631 \u0633\u0648\u0645 (\u06cc\u0627 \u0628\u06cc\u0634\u062a\u0631) \u0628\u0631 \u0642\u062f\u0631\u062a \u0627\u0631\u062a\u0628\u0627\u0637 \u0628\u06cc\u0646 \u0645\u062a\u063a\u06cc\u0631 \u0645\u0633\u062a\u0642\u0644 \u0648 \u0645\u062a\u063a\u06cc\u0631 \u0648\u0627\u0628\u0633\u062a\u0647 \u062a\u0623\u062b\u06cc\u0631 \u0645\u06cc \u06af\u0630\u0627\u0631\u062f.<\/p>\n<p>\u0631\u0648\u0634 \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641\u06cc \u0628\u0631\u0627\u06cc \u062a\u0633\u062a \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f <a rel=\"nofollow noopener\" target=\"_blank\" href=\"https:\/\/www.statisticssolutions.com\/free-resources\/directory-of-statistical-analyses\/moderator-variable\/\">\u0627\u0639\u062a\u062f\u0627\u0644 \/ \u062a\u0639\u0627\u0645\u0644 \u0622\u0645\u0627\u0631\u06cc<\/a> \u0628\u06cc\u0646 \u0645\u062a\u063a\u06cc\u0631 \u0633\u0648\u0645 \u0648 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u0645\u0633\u062a\u0642\u0644\/\u0648\u0627\u0628\u0633\u062a\u0647.  \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u062b\u0627\u0644\u060c \u0627\u06af\u0631 \u0634\u0645\u0627 \u06cc\u06a9 \u062a\u0633\u062a ANOVA \u0627\u0646\u062c\u0627\u0645 \u062f\u0627\u062f\u0647 \u0627\u06cc\u062f\u060c \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u062f \u0628\u0627 \u0627\u0646\u062c\u0627\u0645 \u06cc\u06a9 \u062a\u0633\u062a ANOVA \u062f\u0648 \u0637\u0631\u0641\u0647 \u0628\u0631\u0627\u06cc \u0628\u0631\u0631\u0633\u06cc \u062a\u0639\u062f\u06cc\u0644 \u0627\u062d\u062a\u0645\u0627\u0644\u06cc \u0622\u0646 \u0631\u0627 \u062a\u0633\u062a \u06a9\u0646\u06cc\u062f.<\/p>\n<p>\u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644\u060c \u06cc\u06a9 \u0631\u0648\u0634 \u0642\u0627\u0628\u0644 \u0627\u0639\u062a\u0645\u0627\u062f \u0628\u0631\u0627\u06cc \u062a\u0633\u062a \u062a\u0639\u062f\u06cc\u0644\u060c \u0635\u0631\u0641 \u0646\u0638\u0631 \u0627\u0632 \u0646\u0648\u0639 \u0622\u0632\u0645\u0648\u0646 \u0622\u0645\u0627\u0631\u06cc \u06a9\u0647 \u0627\u062c\u0631\u0627 \u06a9\u0631\u062f\u0647 \u0627\u06cc\u062f (ANOVA\u060c Chi-Square\u060c Pearson Correlation) \u0627\u06cc\u0646 \u0627\u0633\u062a \u06a9\u0647 \u0628\u0631\u0631\u0633\u06cc \u06a9\u0646\u06cc\u062f \u0622\u06cc\u0627 \u0627\u0631\u062a\u0628\u0627\u0637\u06cc \u0628\u06cc\u0646 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u062a\u0648\u0636\u06cc\u062d\u06cc \u0648 \u067e\u0627\u0633\u062e \u0628\u0631\u0627\u06cc \u0647\u0631 \u0632\u06cc\u0631\u06af\u0631\u0648\u0647\/\u0633\u0637\u062d \u0633\u0648\u0645 \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f \u06cc\u0627 \u062e\u06cc\u0631. \u0645\u062a\u063a\u06cc\u0631.<\/p>\n<p>\u0628\u0631\u0627\u06cc \u062f\u0642\u06cc\u0642\u200c\u062a\u0631 \u0628\u0648\u062f\u0646\u060c \u0627\u06af\u0631 \u0622\u0632\u0645\u0627\u06cc\u0634\u200c\u0647\u0627\u06cc ANOVA \u0631\u0627 \u0627\u0646\u062c\u0627\u0645 \u0645\u06cc\u200c\u062f\u0627\u062f\u06cc\u062f\u060c \u0641\u0642\u0637 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u062f \u06cc\u06a9 ANOVA \u0631\u0627 \u0628\u0631\u0627\u06cc \u0647\u0631 \u062f\u0633\u062a\u0647 \u062f\u0631 \u0645\u062a\u063a\u06cc\u0631 \u0633\u0648\u0645 \u0627\u062c\u0631\u0627 \u06a9\u0646\u06cc\u062f (\u0645\u062a\u063a\u06cc\u0631\u06cc \u06a9\u0647 \u06af\u0645\u0627\u0646 \u0645\u06cc\u200c\u06a9\u0646\u06cc\u062f \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0627\u062b\u0631 \u062a\u0639\u062f\u06cc\u0644\u200c\u06a9\u0646\u0646\u062f\u0647 \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u062f. \u0631\u0648\u06cc \u0631\u0627\u0628\u0637\u0647 \u0627\u06cc \u06a9\u0647 \u062f\u0631 \u062d\u0627\u0644 \u0645\u0637\u0627\u0644\u0639\u0647 \u0622\u0646 \u0647\u0633\u062a\u06cc\u062f).<\/p>\n<p>\u0627\u06af\u0631 \u0627\u0632 \u062a\u0633\u062a Chi-Square \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u06a9\u0631\u062f\u06cc\u062f\u060c \u0641\u0642\u0637 \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u062f \u062a\u0633\u062a Chi-Square \u0631\u0627 \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u062f \u0631\u0648\u06cc \u0641\u0631\u06cc\u0645 \u0647\u0627\u06cc \u062f\u0627\u062f\u0647 \u062c\u062f\u06cc\u062f \u06a9\u0647 \u062a\u0645\u0627\u0645 \u0646\u0642\u0627\u0637 \u062f\u0627\u062f\u0647 \u0645\u0648\u062c\u0648\u062f \u062f\u0631 \u062f\u0633\u062a\u0647 \u0647\u0627\u06cc \u0645\u062a\u063a\u06cc\u0631 \u062a\u0639\u062f\u06cc\u0644 \u06a9\u0646\u0646\u062f\u0647 \u0634\u0645\u0627 \u0631\u0627 \u062f\u0631 \u062e\u0648\u062f \u0646\u06af\u0647 \u0645\u06cc \u062f\u0627\u0631\u062f.<\/p>\n<p>\u0627\u06af\u0631 \u0622\u0632\u0645\u0648\u0646 \u0622\u0645\u0627\u0631\u06cc \u0634\u0645\u0627 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646 \u0627\u0633\u062a\u060c \u0628\u0627\u06cc\u062f \u0628\u0631\u0627\u06cc \u0645\u062a\u063a\u06cc\u0631 \u062a\u0639\u062f\u06cc\u0644 \u06a9\u0646\u0646\u062f\u0647 \u062f\u0633\u062a\u0647 \u0647\u0627 \u06cc\u0627 \u0628\u0646 \u0647\u0627 \u0627\u06cc\u062c\u0627\u062f \u06a9\u0646\u06cc\u062f \u0648 \u0633\u067e\u0633 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646 \u0631\u0627 \u0628\u0631\u0627\u06cc \u0647\u0631 \u0633\u0647 \u0622\u0646 \u0628\u0646 \u0647\u0627 \u0627\u062c\u0631\u0627 \u06a9\u0646\u06cc\u062f.<\/p>\n<p>\u0628\u06cc\u0627\u06cc\u06cc\u062f \u0646\u06af\u0627\u0647\u06cc \u06af\u0630\u0631\u0627 \u0628\u0647 \u0631\u0648\u0634 \u0627\u0646\u062c\u0627\u0645 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646 \u0628\u0631\u0627\u06cc \u062a\u0639\u062f\u06cc\u0644 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627 \u0628\u06cc\u0646\u062f\u0627\u0632\u06cc\u0645.  \u0645\u0627 \u062f\u0633\u062a\u0647\u200c\u0647\u0627\/\u0633\u0637\u0648\u062d \u0645\u0635\u0646\u0648\u0639\u06cc \u0631\u0627 \u0627\u0632 \u0648\u06cc\u0698\u06af\u06cc\u200c\u0647\u0627\u06cc \u067e\u06cc\u0648\u0633\u062a\u0647 \u062e\u0648\u062f \u0627\u06cc\u062c\u0627\u062f \u062e\u0648\u0627\u0647\u06cc\u0645 \u06a9\u0631\u062f.  \u0627\u06cc\u0646 process \u0628\u0631\u0627\u06cc \u062a\u0633\u062a \u0627\u0639\u062a\u062f\u0627\u0644 \u0628\u0631\u0627\u06cc \u062f\u0648 \u0646\u0648\u0639 \u062a\u0633\u062a \u062f\u06cc\u06af\u0631 (Chi-Square \u0648 ANOVA) \u0628\u0633\u06cc\u0627\u0631 \u0634\u0628\u06cc\u0647 \u0627\u0633\u062a\u060c \u0627\u0645\u0627 \u062f\u0631 \u0639\u0648\u0636 \u0634\u0645\u0627 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u0637\u0628\u0642\u0647\u200c\u0628\u0646\u062f\u06cc \u0627\u0632 \u0642\u0628\u0644 \u0645\u0648\u062c\u0648\u062f \u0631\u0627 \u0628\u0631\u0627\u06cc \u06a9\u0627\u0631 \u0628\u0627 \u0622\u0646\u0647\u0627 \u062e\u0648\u0627\u0647\u06cc\u062f \u062f\u0627\u0634\u062a.<\/p>\n<p>\u0645\u0627 \u0645\u06cc \u062e\u0648\u0627\u0647\u06cc\u0645 \u06cc\u06a9 \u0645\u062a\u063a\u06cc\u0631 \u0645\u0646\u0627\u0633\u0628 \u0631\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u06a9\u0646\u06cc\u0645 \u062a\u0627 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u0645\u062a\u063a\u06cc\u0631 \u062a\u0639\u062f\u06cc\u0644 \u06a9\u0646\u0646\u062f\u0647 \u0645\u0627 \u0639\u0645\u0644 \u06a9\u0646\u062f.  \u0628\u06cc\u0627\u06cc\u06cc\u062f \u0633\u0637\u062d \u062f\u0631\u0622\u0645\u062f \u0631\u0627 \u0628\u0631\u0627\u06cc \u0647\u0631 \u0646\u0641\u0631 \u0627\u0645\u062a\u062d\u0627\u0646 \u06a9\u0646\u06cc\u0645 \u0648 \u0622\u0646 \u0631\u0627 \u0628\u0647 \u0633\u0647 \u06af\u0631\u0648\u0647 \u0645\u062e\u062a\u0644\u0641 \u062a\u0642\u0633\u06cc\u0645 \u06a9\u0646\u06cc\u0645:<\/p>\n<pre><code class=\"hljs\"><span class=\"hljs-function\"><span class=\"hljs-keyword\">def<\/span> <span class=\"hljs-title\">income_groups<\/span>(<span class=\"hljs-params\">row<\/span>):<\/span>\n    <span class=\"hljs-keyword\">if<\/span> row(<span class=\"hljs-string\">'incomeperperson'<\/span>) &lt;= <span class=\"hljs-number\">744.23<\/span>:\n        <span class=\"hljs-keyword\">return<\/span> <span class=\"hljs-number\">1<\/span>\n    <span class=\"hljs-keyword\">elif<\/span> row(<span class=\"hljs-string\">'incomeperperson'<\/span>) &lt;= <span class=\"hljs-number\">942.32<\/span>:\n        <span class=\"hljs-keyword\">return<\/span> <span class=\"hljs-number\">2<\/span>\n    <span class=\"hljs-keyword\">else<\/span>:\n        <span class=\"hljs-keyword\">return<\/span> <span class=\"hljs-number\">3<\/span>\n\n\n\ndf_clean(<span class=\"hljs-string\">'income_group'<\/span>) = df_clean.apply(<span class=\"hljs-keyword\">lambda<\/span> row: income_groups(row), axis=<span class=\"hljs-number\">1<\/span>)\n\n\nsubframe_1 = df_clean((df_clean(<span class=\"hljs-string\">'income_group'<\/span>) == <span class=\"hljs-number\">1<\/span>))\nsubframe_2 = df_clean((df_clean(<span class=\"hljs-string\">'income_group'<\/span>) == <span class=\"hljs-number\">2<\/span>))\nsubframe_3 = df_clean((df_clean(<span class=\"hljs-string\">'income_group'<\/span>) == <span class=\"hljs-number\">3<\/span>))\n\n<span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">'Assoc. - life expectancy and internet use rate for low income countries'<\/span>)\n\n<span class=\"hljs-built_in\">print<\/span>(pearsonr(subframe_1(<span class=\"hljs-string\">'lifeexpectancy'<\/span>), subframe_1(<span class=\"hljs-string\">'internetuserate'<\/span>)))\n\n<span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">'Assoc. - life expectancy and internet use rate for medium income countries'<\/span>)\n\n<span class=\"hljs-built_in\">print<\/span>(pearsonr(subframe_2(<span class=\"hljs-string\">'lifeexpectancy'<\/span>), subframe_2(<span class=\"hljs-string\">'internetuserate'<\/span>)))\n\n<span class=\"hljs-built_in\">print<\/span>(<span class=\"hljs-string\">'Assoc. - life expectancy and internet use rate for high income countries'<\/span>)\n\n<span class=\"hljs-built_in\">print<\/span>(pearsonr(subframe_3(<span class=\"hljs-string\">'lifeexpectancy'<\/span>), subframe_3(<span class=\"hljs-string\">'internetuserate'<\/span>)))\n<\/code><\/pre>\n<p>\u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u062e\u0631\u0648\u062c\u06cc \u0647\u0627 \u0622\u0645\u062f\u0647 \u0627\u0633\u062a:<\/p>\n<pre><code class=\"hljs\">Assoc. - life expectancy and internet use rate for low income countries\n(0.38386370068495235, 0.010101223355274047)\n\nAssoc. - life expectancy and internet use rate for medium income countries\n(0.9966009508278395, 0.05250454954743393)\n\nAssoc. - life expectancy and internet use rate for high income countries\n(0.7019997488251704, 6.526819886007788e-18)\n<\/code><\/pre>\n<p>\u06cc\u06a9 \u0628\u0627\u0631 \u062f\u06cc\u06af\u0631\u060c \u0627\u0648\u0644\u06cc\u0646 \u0645\u0642\u062f\u0627\u0631 \u062c\u0647\u062a \u0648 \u0642\u062f\u0631\u062a \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u0627\u0633\u062a\u060c \u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u062f\u0648\u0645\u06cc\u0646 \u0645\u0642\u062f\u0627\u0631 P-value \u0627\u0633\u062a.<\/p>\n<h2 id=\"conclusion\"><span class=\"ez-toc-section\" id=\"%d9%86%d8%aa%db%8c%d8%ac%d9%87\"><\/span>\u0646\u062a\u06cc\u062c\u0647<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><code>statsmodels<\/code>  \u06cc\u06a9 \u06a9\u062a\u0627\u0628\u062e\u0627\u0646\u0647 \u0628\u0633\u06cc\u0627\u0631 \u0645\u0641\u06cc\u062f \u0627\u0633\u062a \u06a9\u0647 \u0628\u0647 \u06a9\u0627\u0631\u0628\u0631\u0627\u0646 \u067e\u0627\u06cc\u062a\u0648\u0646 \u0627\u0645\u06a9\u0627\u0646 \u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u062f\u0627\u062f\u0647 \u0647\u0627 \u0648 \u0627\u062c\u0631\u0627\u06cc \u062a\u0633\u062a \u0647\u0627\u06cc \u0622\u0645\u0627\u0631\u06cc \u0631\u0627 \u0645\u06cc \u062f\u0647\u062f \u0631\u0648\u06cc \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0647\u0627  \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u06cc\u062f ANOVA\u060c \u062a\u0633\u062a\u200c\u0647\u0627\u06cc Chi-Square\u060c \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646 \u0648 \u062a\u0633\u062a\u200c\u0647\u0627\u06cc\u06cc \u0631\u0627 \u0628\u0631\u0627\u06cc \u062a\u0639\u062f\u06cc\u0644 \u0627\u0646\u062c\u0627\u0645 \u062f\u0647\u06cc\u062f.<\/p>\n<p>\u0647\u0646\u06af\u0627\u0645\u06cc \u06a9\u0647 \u0628\u0627 \u0631\u0648\u0634 \u0627\u0646\u062c\u0627\u0645 \u0627\u06cc\u0646 \u0622\u0632\u0645\u0648\u0646 \u0647\u0627 \u0622\u0634\u0646\u0627 \u0634\u062f\u06cc\u062f\u060c \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u062f \u0631\u0648\u0627\u0628\u0637 \u0645\u0639\u0646\u0627\u062f\u0627\u0631 \u0628\u06cc\u0646 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u0648\u0627\u0628\u0633\u062a\u0647 \u0648 \u0645\u0633\u062a\u0642\u0644 \u0631\u0627 \u0622\u0632\u0645\u0627\u06cc\u0634 \u06a9\u0646\u06cc\u062f \u0648 \u0628\u0627 \u0645\u0627\u0647\u06cc\u062a \u0637\u0628\u0642\u0647 \u0628\u0646\u062f\u06cc \u06cc\u0627 \u067e\u06cc\u0648\u0633\u062a\u0647 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627 \u0633\u0627\u0632\u06af\u0627\u0631 \u0634\u0648\u06cc\u062f.<\/p>\n<\/div>\n<p><script>\n                        !function(f,b,e,v,n,t,s)\n                        {if(f.fbq)return;n=f.fbq=function(){n.callMethod?\n                        n.callMethod.apply(n,arguments):n.queue.push(arguments)};\n                        if(!f._fbq)f._fbq=n;n.push=n;n.loaded=!0;n.version='2.0';\n                        n.queue=();t=b.createElement(e);t.async=!0;\n                        t.src=v;s=b.getElementsByTagName(e)(0);\n                        s.parentNode.insertBefore(t,s)}(window, document,'script',\n                        'https:\/\/connect.facebook.net\/en_US\/fbevents.js');\n                        fbq('init', '525232124909042');\n                        fbq('track', 'PageView');\n                    <\/script>    (\u0628\u0631\u0686\u0633\u0628\u200c\u0647\u0627 \u0628\u0647 \u062a\u0631\u062c\u0645\u0647)# python<br \/>\n<br \/><br \/>\n<br \/>\u0645\u0646\u062a\u0634\u0631 \u0634\u062f\u0647 \u062f\u0631 1403-01-17 03:15:05<br \/>\n<\/p>\n\n\n<div class=\"kk-star-ratings kksr-auto kksr-align-center kksr-valign-bottom\"\n    data-payload='{&quot;align&quot;:&quot;center&quot;,&quot;id&quot;:&quot;15786&quot;,&quot;slug&quot;:&quot;default&quot;,&quot;valign&quot;:&quot;bottom&quot;,&quot;ignore&quot;:&quot;&quot;,&quot;reference&quot;:&quot;auto&quot;,&quot;class&quot;:&quot;&quot;,&quot;count&quot;:&quot;0&quot;,&quot;legendonly&quot;:&quot;&quot;,&quot;readonly&quot;:&quot;&quot;,&quot;score&quot;:&quot;0&quot;,&quot;starsonly&quot;:&quot;&quot;,&quot;best&quot;:&quot;5&quot;,&quot;gap&quot;:&quot;5&quot;,&quot;greet&quot;:&quot;\u0627\u0645\u062a\u06cc\u0627\u0632 \u0634\u0645\u0627 \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0637\u0644\u0628&quot;,&quot;legend&quot;:&quot;0\\\/5 (0 \u0631\u0627\u06cc)&quot;,&quot;size&quot;:&quot;30&quot;,&quot;title&quot;:&quot;\u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u0641\u0631\u0636\u06cc\u0647 \u0647\u0627\u06cc \u0622\u0645\u0627\u0631\u06cc \u062f\u0631 \u067e\u0627\u06cc\u062a\u0648\u0646 \u0628\u0627 ANOVA\u060c \u0645\u062c\u0630\u0648\u0631 \u06a9\u0627\u06cc \u0648 \u0647\u0645\u0628\u0633\u062a\u06af\u06cc \u067e\u06cc\u0631\u0633\u0648\u0646&quot;,&quot;width&quot;:&quot;0&quot;,&quot;_legend&quot;:&quot;{score}\\\/{best} ({count} \u0631\u0627\u06cc)&quot;,&quot;font_factor&quot;:&quot;1.25&quot;}'>\n            \n<div class=\"kksr-stars\">\n    \n<div class=\"kksr-stars-inactive\">\n            <div class=\"kksr-star\" data-star=\"1\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"2\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"3\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"4\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" data-star=\"5\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n    <\/div>\n    \n<div class=\"kksr-stars-active\" style=\"width: 0px;\">\n            <div class=\"kksr-star\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n            <div class=\"kksr-star\" style=\"padding-left: 5px\">\n            \n\n<div class=\"kksr-icon\" style=\"width: 30px; height: 30px;\"><\/div>\n        <\/div>\n    <\/div>\n<\/div>\n                \n\n<div class=\"kksr-legend\" style=\"font-size: 24px;\">\n            <span class=\"kksr-muted\">\u0627\u0645\u062a\u06cc\u0627\u0632 \u0634\u0645\u0627 \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0637\u0644\u0628<\/span>\n    <\/div>\n    <\/div>\n","protected":false},"excerpt":{"rendered":"<p><span class=\"span-reading-time rt-reading-time\" style=\"display: block;\"><span class=\"rt-label rt-prefix\">\u0632\u0645\u0627\u0646 \u0644\u0627\u0632\u0645 \u0628\u0631\u0627\u06cc \u0645\u0637\u0627\u0644\u0639\u0647: <\/span> <span class=\"rt-time\"> 15<\/span> <span class=\"rt-label rt-postfix\">\u062f\u0642\u06cc\u0642\u0647<\/span><\/span>\u0645\u0639\u0631\u0641\u06cc \u067e\u0627\u06cc\u062a\u0648\u0646 \u06cc\u06a9 \u0632\u0628\u0627\u0646 \u0641\u0648\u0642 \u0627\u0644\u0639\u0627\u062f\u0647 \u0647\u0645\u0647 \u06a9\u0627\u0631\u0647 \u0627\u0633\u062a \u06a9\u0647 \u0628\u0631\u0627\u06cc \u06a9\u0627\u0631\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u062f\u0631 \u0637\u06cc\u0641 \u0648\u0633\u06cc\u0639\u06cc \u0627\u0632 \u0631\u0634\u062a\u0647 \u0647\u0627 \u0645\u0641\u06cc\u062f \u0627\u0633\u062a. \u06cc\u06a9\u06cc \u0627\u0632 \u0627\u06cc\u0646 \u0631\u0634\u062a\u0647 \u0647\u0627\u060c \u062a\u062d\u0644\u06cc\u0644 \u0622\u0645\u0627\u0631\u06cc \u0627\u0633\u062a \u0631\u0648\u06cc \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0647\u0627 \u0648 \u062f\u0631 \u06a9\u0646\u0627\u0631 SPSS\u060c \u067e\u0627\u06cc\u062a\u0648\u0646 \u06cc\u06a9\u06cc \u0627\u0632 \u0631\u0627\u06cc\u062c \u062a\u0631\u06cc\u0646 \u0627\u0628\u0632\u0627\u0631\u0647\u0627\u06cc \u0622\u0645\u0627\u0631 \u0627\u0633\u062a. \u0645\u0627\u0647\u06cc\u062a \u06a9\u0627\u0631\u0628\u0631\u067e\u0633\u0646\u062f \u0648 \u0634\u0647\u0648\u062f\u06cc \u067e\u0627\u06cc\u062a\u0648\u0646 \u0627\u062c\u0631\u0627\u06cc \u062a\u0633\u062a \u0647\u0627\u06cc \u0622\u0645\u0627\u0631\u06cc \u0648 [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":15787,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1743,620],"tags":[],"class_list":["post-15786","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-python","category-programming"],"acf":[],"_links":{"self":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/posts\/15786","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/comments?post=15786"}],"version-history":[{"count":0,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/posts\/15786\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/media\/15787"}],"wp:attachment":[{"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/media?parent=15786"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/categories?post=15786"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/rasanegaar.com\/blog\/wp-json\/wp\/v2\/tags?post=15786"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}