{"id":476219,"date":"2023-08-09T07:26:52","date_gmt":"2023-08-09T07:26:52","guid":{"rendered":""},"modified":"2023-11-30T03:36:11","modified_gmt":"2023-11-30T03:36:11","slug":"chi-squared-test","status":"publish","type":"wiki","link":"https:\/\/oneproxy.pro\/ir\/wiki\/chi-squared-test\/","title":{"rendered":"\u062a\u0633\u062a \u0645\u062c\u0630\u0648\u0631 \u06a9\u0627\u06cc"},"content":{"rendered":"<p>\u0622\u0632\u0645\u0648\u0646 \u06a9\u0627\u06cc \u0627\u0633\u06a9\u0648\u0626\u0631 \u06cc\u06a9 \u0631\u0648\u0634 \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 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0637\u0628\u0642\u0647 \u0628\u0646\u062f\u06cc \u0634\u062f\u0647 \u0648 \u062a\u0639\u06cc\u06cc\u0646 \u0627\u06cc\u0646\u06a9\u0647 \u0622\u06cc\u0627 \u0627\u0631\u062a\u0628\u0627\u0637 \u0645\u0639\u0646\u06cc \u062f\u0627\u0631\u06cc \u0628\u06cc\u0646 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\u0627\u0631\u0632\u0634\u0645\u0646\u062f\u06cc \u0631\u0627 \u062f\u0631 \u0645\u0648\u0631\u062f \u0631\u0648\u0627\u0628\u0637 \u0628\u06cc\u0646 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627 \u0627\u0631\u0627\u0626\u0647 \u0645\u06cc\u200c\u062f\u0647\u062f.<\/p>\n<h2>\u062a\u0627\u0631\u06cc\u062e\u0686\u0647 \u067e\u06cc\u062f\u0627\u06cc\u0634 \u0622\u0632\u0645\u0648\u0646 \u06a9\u0627\u06cc \u062f\u0648<\/h2>\n<p>\u0622\u0632\u0645\u0648\u0646 Chi-Squared \u0631\u06cc\u0634\u0647 \u062f\u0631 \u06a9\u0627\u0631 \u06a9\u0627\u0631\u0644 \u067e\u06cc\u0631\u0633\u0648\u0646\u060c \u0631\u06cc\u0627\u0636\u06cc\u062f\u0627\u0646 \u0648 \u0622\u0645\u0627\u0631\u0634\u0646\u0627\u0633 \u0628\u0631\u06cc\u062a\u0627\u0646\u06cc\u0627\u06cc\u06cc \u062f\u0627\u0631\u062f \u06a9\u0647 \u0627\u06cc\u0646 \u0645\u0641\u0647\u0648\u0645 \u0631\u0627 \u062f\u0631 \u0633\u0627\u0644 1900 \u0645\u0639\u0631\u0641\u06cc \u06a9\u0631\u062f. \u06a9\u0627\u0631 \u067e\u06cc\u0631\u0633\u0648\u0646 \u0628\u0631 \u062a\u0648\u0633\u0639\u0647 \u0631\u0648\u0634 \u0647\u0627\u06cc \u0622\u0645\u0627\u0631\u06cc \u0628\u0631\u0627\u06cc \u062f\u0631\u06a9 \u0631\u0648\u0627\u0628\u0637 \u0628\u06cc\u0646 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627 \u062f\u0631 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0628\u0632\u0631\u06af \u0645\u062a\u0645\u0631\u06a9\u0632 \u0628\u0648\u062f. \u0622\u0632\u0645\u0648\u0646 \u0645\u062c\u0630\u0648\u0631 \u06a9\u0627\u06cc \u062f\u0631 \u0627\u0628\u062a\u062f\u0627 \u062f\u0631 \u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u062c\u062f\u0627\u0648\u0644 \u0627\u0642\u062a\u0636\u0627\u06cc\u06cc \u06a9\u0647 \u062a\u0648\u0632\u06cc\u0639 \u0645\u0634\u062a\u0631\u06a9 \u062f\u0648 \u06cc\u0627 \u0686\u0646\u062f \u0645\u062a\u063a\u06cc\u0631 \u0637\u0628\u0642\u0647\u200c\u0628\u0646\u062f\u06cc \u0631\u0627 \u0646\u0634\u0627\u0646 \u0645\u06cc\u200c\u062f\u0647\u0646\u062f\u060c \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0634\u062f.<\/p>\n<h2>\u0627\u0637\u0644\u0627\u0639\u0627\u062a \u062f\u0642\u06cc\u0642 \u062f\u0631 \u0645\u0648\u0631\u062f \u062a\u0633\u062a Chi-Squared<\/h2>\n<p>\u0622\u0632\u0645\u0648\u0646 Chi-Squared \u0645\u0628\u062a\u0646\u06cc \u0628\u0631 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0641\u0631\u06a9\u0627\u0646\u0633 \u0647\u0627\u06cc \u0645\u0634\u0627\u0647\u062f\u0647 \u0634\u062f\u0647 (O) \u062f\u0631 \u06cc\u06a9 \u0645\u062c\u0645\u0648\u0639\u0647 \u062f\u0627\u062f\u0647 \u0628\u0627 \u0641\u0631\u06a9\u0627\u0646\u0633 \u0647\u0627\u06cc \u0645\u0648\u0631\u062f \u0627\u0646\u062a\u0638\u0627\u0631 (E) \u0627\u0633\u062a \u06a9\u0647 \u062f\u0631 \u0635\u0648\u0631\u062a \u0645\u0633\u062a\u0642\u0644 \u0628\u0648\u062f\u0646 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627 \u0631\u062e \u0645\u06cc \u062f\u0647\u062f. \u0627\u06cc\u0646 \u0622\u0632\u0645\u0648\u0646 \u0634\u0627\u0645\u0644 \u0645\u062d\u0627\u0633\u0628\u0647 \u0622\u0645\u0627\u0631\u0647 Chi-Squared \u0627\u0633\u062a \u06a9\u0647 \u062a\u0641\u0627\u0648\u062a \u0628\u06cc\u0646 \u0641\u0631\u06a9\u0627\u0646\u0633 \u0647\u0627\u06cc \u0645\u0634\u0627\u0647\u062f\u0647 \u0634\u062f\u0647 \u0648 \u0645\u0648\u0631\u062f \u0627\u0646\u062a\u0638\u0627\u0631 \u0631\u0627 \u06a9\u0645\u06cc\u062a \u0645\u06cc \u06a9\u0646\u062f. \u0641\u0631\u0645\u0648\u0644 \u0622\u0645\u0627\u0631\u0647 Chi-Squared \u0628\u0647 \u0635\u0648\u0631\u062a \u0632\u06cc\u0631 \u0627\u0633\u062a:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/oneproxy.pro\/images\/chi_squared_formula.png\" alt=\"\u0641\u0631\u0645\u0648\u0644 Chi-Squared\" title=\"\"><\/p>\n<p>\u062c\u0627\u06cc\u06cc \u06a9\u0647:<\/p>\n<ul>\n<li>\u03a7\u00b2 \u0646\u0634\u0627\u0646 \u062f\u0647\u0646\u062f\u0647 \u0622\u0645\u0627\u0631 Chi-Squared \u0627\u0633\u062a<\/li>\n<li>O\u1d62 \u0641\u0631\u06a9\u0627\u0646\u0633 \u0645\u0634\u0627\u0647\u062f\u0647 \u0634\u062f\u0647 \u0628\u0631\u0627\u06cc \u062f\u0633\u062a\u0647 i \u0627\u0633\u062a<\/li>\n<li>E\u1d62 \u0641\u0631\u06a9\u0627\u0646\u0633 \u0645\u0648\u0631\u062f \u0627\u0646\u062a\u0638\u0627\u0631 \u0628\u0631\u0627\u06cc \u062f\u0633\u062a\u0647 i \u0627\u0633\u062a<\/li>\n<li>\u03a3 \u0646\u0634\u0627\u0646 \u062f\u0647\u0646\u062f\u0647 \u0645\u062c\u0645\u0648\u0639 \u0647\u0645\u0647 \u062f\u0633\u062a\u0647 \u0647\u0627 \u0627\u0633\u062a<\/li>\n<\/ul>\n<p>\u0622\u0645\u0627\u0631\u0647 Chi-Squared \u0627\u0632 \u062a\u0648\u0632\u06cc\u0639 Chi-Squared \u067e\u06cc\u0631\u0648\u06cc \u0645\u06cc \u06a9\u0646\u062f \u0648 \u0645\u0642\u062f\u0627\u0631 \u0622\u0646 \u0628\u0631\u0627\u06cc \u062a\u0639\u06cc\u06cc\u0646 p-value \u0645\u0631\u062a\u0628\u0637 \u0628\u0627 \u0622\u0632\u0645\u0648\u0646 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f. \u0645\u0642\u062f\u0627\u0631 p \u0646\u0634\u0627\u0646 \u062f\u0647\u0646\u062f\u0647 \u0627\u062d\u062a\u0645\u0627\u0644 \u0628\u0647 \u062f\u0633\u062a \u0622\u0648\u0631\u062f\u0646 \u0646\u062a\u0627\u06cc\u062c \u0645\u0634\u0627\u0647\u062f\u0647 \u0634\u062f\u0647 \u0628\u0647 \u062a\u0646\u0647\u0627\u06cc\u06cc \u0627\u0633\u062a. \u0627\u06af\u0631 \u0645\u0642\u062f\u0627\u0631 p \u06a9\u0645\u062a\u0631 \u0627\u0632 \u0633\u0637\u062d \u0645\u0639\u0646\u06cc\u200c\u062f\u0627\u0631\u06cc \u0627\u0632 \u067e\u06cc\u0634 \u062a\u0639\u06cc\u06cc\u0646\u200c\u0634\u062f\u0647 (\u0645\u0639\u0645\u0648\u0644\u0627\u064b 05\/0) \u0628\u0627\u0634\u062f\u060c \u0641\u0631\u0636\u06cc\u0647 \u0635\u0641\u0631 (\u0627\u0633\u062a\u0642\u0644\u0627\u0644 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627) \u0631\u062f \u0645\u06cc\u200c\u0634\u0648\u062f \u06a9\u0647 \u0646\u0634\u0627\u0646\u200c\u062f\u0647\u0646\u062f\u0647 \u0627\u0631\u062a\u0628\u0627\u0637 \u0645\u0639\u0646\u0627\u062f\u0627\u0631 \u0628\u06cc\u0646 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627 \u0627\u0633\u062a.<\/p>\n<h2>\u0633\u0627\u062e\u062a\u0627\u0631 \u062f\u0631\u0648\u0646\u06cc \u0622\u0632\u0645\u0648\u0646 \u06a9\u0627\u06cc \u062f\u0648<\/h2>\n<p>\u0622\u0632\u0645\u0648\u0646 Chi-Squared \u0631\u0627 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0628\u0647 \u062f\u0648 \u0646\u0648\u0639 \u0627\u0635\u0644\u06cc \u062a\u0642\u0633\u06cc\u0645 \u06a9\u0631\u062f: \u0622\u0632\u0645\u0648\u0646 Chi-Squared \u067e\u06cc\u0631\u0633\u0648\u0646 \u0648 \u0622\u0632\u0645\u0648\u0646 Chi-Squared \u0646\u0633\u0628\u062a \u0627\u062d\u062a\u0645\u0627\u0644 (\u0647\u0645\u0686\u0646\u06cc\u0646 \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 G-Test \u0634\u0646\u0627\u062e\u062a\u0647 \u0645\u06cc \u0634\u0648\u062f). \u0647\u0631 \u062f\u0648 \u0622\u0632\u0645\u0648\u0646 \u0627\u0632 \u0641\u0631\u0645\u0648\u0644 \u06cc\u06a9\u0633\u0627\u0646\u06cc \u0628\u0631\u0627\u06cc \u0622\u0645\u0627\u0631\u0647 Chi-Squared \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u06a9\u0646\u0646\u062f\u060c \u0627\u0645\u0627 \u062f\u0631 \u0631\u0648\u0634 \u0645\u062d\u0627\u0633\u0628\u0647 \u0641\u0631\u06a9\u0627\u0646\u0633 \u0647\u0627\u06cc \u0645\u0648\u0631\u062f \u0627\u0646\u062a\u0638\u0627\u0631 \u0645\u062a\u0641\u0627\u0648\u062a \u0647\u0633\u062a\u0646\u062f.<\/p>\n<ol>\n<li>\u062a\u0633\u062a \u06a9\u0627\u06cc \u062f\u0648 \u067e\u06cc\u0631\u0633\u0648\u0646:\n<ul>\n<li>\u0641\u0631\u0636 \u0645\u06cc \u06a9\u0646\u06cc\u0645 \u06a9\u0647 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627 \u062f\u0627\u0631\u0627\u06cc \u062a\u0648\u0632\u06cc\u0639 \u062a\u0642\u0631\u06cc\u0628\u0627 \u0646\u0631\u0645\u0627\u0644 \u0647\u0633\u062a\u0646\u062f.<\/li>\n<li>\u0627\u063a\u0644\u0628 \u0632\u0645\u0627\u0646\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f \u06a9\u0647 \u062d\u062c\u0645 \u0646\u0645\u0648\u0646\u0647 \u0628\u0632\u0631\u06af \u0628\u0627\u0634\u062f.<\/li>\n<\/ul>\n<\/li>\n<li>\u0646\u0633\u0628\u062a \u0627\u062d\u062a\u0645\u0627\u0644 \u0622\u0632\u0645\u0648\u0646 \u06a9\u0627\u06cc \u062f\u0648 (\u0622\u0632\u0645\u0648\u0646 G):\n<ul>\n<li>\u0628\u0631 \u0627\u0633\u0627\u0633 \u0646\u0633\u0628\u062a \u0627\u062d\u062a\u0645\u0627\u0644\u060c \u0645\u0641\u0631\u0648\u0636\u0627\u062a \u06a9\u0645\u062a\u0631\u06cc \u062f\u0631 \u0645\u0648\u0631\u062f \u062a\u0648\u0632\u06cc\u0639 \u062f\u0627\u062f\u0647 \u0647\u0627 \u0627\u06cc\u062c\u0627\u062f \u0645\u06cc \u0634\u0648\u062f.<\/li>\n<li>\u0645\u0646\u0627\u0633\u0628 \u0628\u0631\u0627\u06cc \u0627\u0646\u062f\u0627\u0632\u0647 \u0647\u0627\u06cc \u0646\u0645\u0648\u0646\u0647 \u06a9\u0648\u0686\u06a9 \u06cc\u0627 \u0645\u0648\u0627\u0631\u062f \u0628\u0627 \u0641\u0631\u06a9\u0627\u0646\u0633 \u0647\u0627\u06cc \u0645\u0648\u0631\u062f \u0627\u0646\u062a\u0638\u0627\u0631 \u06a9\u0645\u062a\u0631 \u0627\u0632 \u067e\u0646\u062c.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<h2>\u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u06a9\u0644\u06cc\u062f\u06cc \u0622\u0632\u0645\u0648\u0646 Chi-Squared<\/h2>\n<p>\u0622\u0632\u0645\u0648\u0646 Chi-Squared \u0686\u0646\u062f\u06cc\u0646 \u0648\u06cc\u0698\u06af\u06cc \u06a9\u0644\u06cc\u062f\u06cc \u062f\u0627\u0631\u062f \u06a9\u0647 \u0622\u0646 \u0631\u0627 \u0628\u0647 \u06cc\u06a9 \u0627\u0628\u0632\u0627\u0631 \u0622\u0645\u0627\u0631\u06cc \u0627\u0631\u0632\u0634\u0645\u0646\u062f \u062a\u0628\u062f\u06cc\u0644 \u0645\u06cc \u06a9\u0646\u062f:<\/p>\n<ul>\n<li><strong>\u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0637\u0628\u0642\u0647 \u0628\u0646\u062f\u06cc \u0634\u062f\u0647:<\/strong> \u0622\u0632\u0645\u0648\u0646 Chi-Squared \u0628\u0647 \u0637\u0648\u0631 \u062e\u0627\u0635 \u0628\u0631\u0627\u06cc \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0637\u0628\u0642\u0647 \u0628\u0646\u062f\u06cc \u0634\u062f\u0647 \u0637\u0631\u0627\u062d\u06cc \u0634\u062f\u0647 \u0627\u0633\u062a \u0648 \u0628\u0647 \u0645\u062d\u0642\u0642\u0627\u0646 \u0627\u06cc\u0646 \u0627\u0645\u06a9\u0627\u0646 \u0631\u0627 \u0645\u06cc \u062f\u0647\u062f \u062a\u0627 \u0627\u0632 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u063a\u06cc\u0631 \u0639\u062f\u062f\u06cc \u0646\u062a\u06cc\u062c\u0647 \u06af\u06cc\u0631\u06cc \u0645\u0639\u0646\u0627\u062f\u0627\u0631\u06cc \u06a9\u0646\u0646\u062f.<\/li>\n<li><strong>\u062a\u0633\u062a \u063a\u06cc\u0631 \u067e\u0627\u0631\u0627\u0645\u062a\u0631\u06cc\u06a9:<\/strong> \u0628\u0647 \u0639\u0646\u0648\u0627\u0646 \u06cc\u06a9 \u0622\u0632\u0645\u0648\u0646 \u0646\u0627\u067e\u0627\u0631\u0627\u0645\u062a\u0631\u06cc\u06a9\u060c \u0622\u0632\u0645\u0648\u0646 Chi-Squared \u0646\u06cc\u0627\u0632\u06cc \u0628\u0647 \u062f\u0646\u0628\u0627\u0644 \u06a9\u0631\u062f\u0646 \u062f\u0627\u062f\u0647 \u0647\u0627 \u0627\u0632 \u06cc\u06a9 \u062a\u0648\u0632\u06cc\u0639 \u062e\u0627\u0635 \u0646\u062f\u0627\u0631\u062f \u0648 \u0622\u0646 \u0631\u0627 \u0647\u0645\u0647 \u06a9\u0627\u0631\u0647 \u0648 \u0642\u0627\u0628\u0644 \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u062f\u0631 \u0633\u0646\u0627\u0631\u06cc\u0648\u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0645\u06cc \u06a9\u0646\u062f.<\/li>\n<li><strong>\u0627\u0631\u0632\u06cc\u0627\u0628\u06cc \u0627\u0633\u062a\u0642\u0644\u0627\u0644:<\/strong> \u0627\u06cc\u0646 \u0622\u0632\u0645\u0648\u0646 \u0628\u0647 \u0634\u0646\u0627\u0633\u0627\u06cc\u06cc \u0631\u0627\u0628\u0637\u0647 \u0628\u06cc\u0646 \u062f\u0648 \u06cc\u0627 \u0686\u0646\u062f \u0645\u062a\u063a\u06cc\u0631 \u0637\u0628\u0642\u0647\u200c\u0628\u0646\u062f\u06cc \u06a9\u0645\u06a9 \u0645\u06cc\u200c\u06a9\u0646\u062f \u0648 \u0628\u0647 \u062f\u0631\u06a9 \u0627\u0644\u06af\u0648\u0647\u0627 \u0648 \u0627\u0631\u062a\u0628\u0627\u0637 \u062f\u0631 \u062f\u0627\u062f\u0647\u200c\u0647\u0627 \u06a9\u0645\u06a9 \u0645\u06cc\u200c\u06a9\u0646\u062f.<\/li>\n<li><strong>\u062a\u0633\u062a \u0627\u0633\u062a\u0646\u062a\u0627\u062c:<\/strong> \u0628\u0627 \u0627\u0631\u0627\u0626\u0647 \u06cc\u06a9 \u0645\u0642\u062f\u0627\u0631 p\u060c \u0622\u0632\u0645\u0648\u0646 Chi-Squared \u0628\u0647 \u0645\u062d\u0642\u0642\u0627\u0646 \u0627\u062c\u0627\u0632\u0647 \u0645\u06cc \u062f\u0647\u062f \u062a\u0627 \u062f\u0631 \u0645\u0648\u0631\u062f \u062f\u0627\u062f\u0647 \u0647\u0627 \u0627\u0633\u062a\u0646\u0628\u0627\u0637 \u0622\u0645\u0627\u0631\u06cc \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u0646\u062f \u0648 \u0628\u0627 \u0633\u0637\u062d \u0627\u0637\u0645\u06cc\u0646\u0627\u0646 \u0646\u062a\u06cc\u062c\u0647 \u06af\u06cc\u0631\u06cc \u06a9\u0646\u0646\u062f.<\/li>\n<\/ul>\n<h2>\u0627\u0646\u0648\u0627\u0639 \u062a\u0633\u062a Chi-Squared<\/h2>\n<p>\u062f\u0648 \u0646\u0648\u0639 \u0627\u0635\u0644\u06cc \u0627\u0632 \u0622\u0632\u0645\u0648\u0646 \u0647\u0627\u06cc \u0645\u062c\u0630\u0648\u0631 \u06a9\u0627\u06cc \u0648\u062c\u0648\u062f \u062f\u0627\u0631\u062f: \u0622\u0632\u0645\u0648\u0646 \u06a9\u0627\u06cc \u0627\u0633\u06a9\u0648\u0626\u0631 \u067e\u06cc\u0631\u0633\u0648\u0646 \u0648 \u0622\u0632\u0645\u0648\u0646 \u06a9\u0627\u06cc \u0627\u0633\u06a9\u0648\u0626\u0631 \u0646\u0633\u0628\u062a \u0627\u062d\u062a\u0645\u0627\u0644. \u062f\u0631 \u0627\u06cc\u0646\u062c\u0627 \u0628\u0647 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u0622\u0646\u0647\u0627 \u0645\u06cc \u067e\u0631\u062f\u0627\u0632\u06cc\u0645:<\/p>\n<table>\n<thead>\n<tr>\n<th>\u0634\u0627\u062e\u0635<\/th>\n<th>\u062a\u0633\u062a \u06a9\u0627\u06cc \u062f\u0648 \u067e\u06cc\u0631\u0633\u0648\u0646<\/th>\n<th>\u0646\u0633\u0628\u062a \u0627\u062d\u062a\u0645\u0627\u0644 \u0622\u0632\u0645\u0648\u0646 \u06a9\u0627\u06cc \u062f\u0648<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u0645\u0641\u0631\u0648\u0636\u0627\u062a<\/td>\n<td>\u062a\u0648\u0632\u06cc\u0639 \u0646\u0631\u0645\u0627\u0644 \u062f\u0627\u062f\u0647 \u0647\u0627 \u0631\u0627 \u0641\u0631\u0636 \u0645\u06cc \u06a9\u0646\u062f<\/td>\n<td>\u0645\u0641\u0631\u0648\u0636\u0627\u062a \u06a9\u0645\u062a\u0631\u06cc \u062f\u0631 \u0645\u0648\u0631\u062f \u062a\u0648\u0632\u06cc\u0639 \u062f\u0627\u062f\u0647 \u0647\u0627 \u0645\u06cc \u06a9\u0646\u062f<\/td>\n<\/tr>\n<tr>\n<td>\u0645\u0646\u0627\u0633\u0628 \u0628\u0631\u0627\u06cc \u0646\u0645\u0648\u0646\u0647 \u0647\u0627\u06cc \u06a9\u0648\u0686\u06a9<\/td>\n<td>\u062e\u06cc\u0631<\/td>\n<td>\u0622\u0631\u0647<\/td>\n<\/tr>\n<tr>\n<td>\u0645\u0648\u0627\u0631\u062f \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u06cc\u062f<\/td>\n<td>\u0627\u0646\u062f\u0627\u0632\u0647 \u0647\u0627\u06cc \u0646\u0645\u0648\u0646\u0647 \u0628\u0632\u0631\u06af<\/td>\n<td>\u0627\u0646\u062f\u0627\u0632\u0647 \u0647\u0627\u06cc \u0646\u0645\u0648\u0646\u0647 \u06a9\u0648\u0686\u06a9<\/td>\n<\/tr>\n<tr>\n<td>\u0641\u0631\u0645\u0648\u0644<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/oneproxy.pro\/images\/pearsons_chi_squared_formula.png\" alt=\"\u0641\u0631\u0645\u0648\u0644 Chi-Squared \u067e\u06cc\u0631\u0633\u0648\u0646\" title=\"\"><\/td>\n<td><img decoding=\"async\" src=\"https:\/\/oneproxy.pro\/images\/likelihood_ratio_chi_squared_formula.png\" alt=\"\u0646\u0633\u0628\u062a \u0627\u062d\u062a\u0645\u0627\u0644 \u0641\u0631\u0645\u0648\u0644 Chi-Squared\" title=\"\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>\u0631\u0627\u0647 \u0647\u0627\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0627\u0632 \u0622\u0632\u0645\u0648\u0646 \u0645\u062c\u0630\u0648\u0631 \u06a9\u0627\u06cc\u060c \u0645\u0633\u0627\u0626\u0644 \u0648 \u0631\u0627\u0647 \u062d\u0644 \u0647\u0627\u06cc \u0622\u0646\u0647\u0627<\/h2>\n<p>\u062a\u0633\u062a Chi-Squared \u06a9\u0627\u0631\u0628\u0631\u062f\u0647\u0627\u06cc\u06cc \u062f\u0631 \u0632\u0645\u06cc\u0646\u0647 \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u067e\u06cc\u062f\u0627 \u0645\u06cc \u06a9\u0646\u062f\u060c \u0627\u0632 \u062c\u0645\u0644\u0647:<\/p>\n<ol>\n<li><strong>\u0628\u0631\u0627\u0632\u0634:<\/strong> \u062a\u0639\u06cc\u06cc\u0646 \u06a9\u0646\u06cc\u062f \u06a9\u0647 \u0622\u06cc\u0627 \u0641\u0631\u06a9\u0627\u0646\u0633 \u0647\u0627\u06cc \u0645\u0634\u0627\u0647\u062f\u0647 \u0634\u062f\u0647 \u0628\u0627 \u062a\u0648\u0632\u06cc\u0639 \u0645\u0648\u0631\u062f \u0627\u0646\u062a\u0638\u0627\u0631 \u0645\u0637\u0627\u0628\u0642\u062a \u062f\u0627\u0631\u0646\u062f \u06cc\u0627 \u062e\u06cc\u0631.<\/li>\n<li><strong>\u062a\u0633\u062a \u0627\u0633\u062a\u0642\u0644\u0627\u0644:<\/strong> \u0627\u0631\u0632\u06cc\u0627\u0628\u06cc \u06a9\u0646\u06cc\u062f \u06a9\u0647 \u0622\u06cc\u0627 \u062f\u0648 \u0645\u062a\u063a\u06cc\u0631 \u0637\u0628\u0642\u0647\u200c\u0628\u0646\u062f\u06cc \u0645\u0631\u062a\u0628\u0637 \u0647\u0633\u062a\u0646\u062f \u06cc\u0627 \u062e\u06cc\u0631.<\/li>\n<li><strong>\u062a\u0633\u062a \u0647\u0645\u06af\u0646\u06cc:<\/strong> \u062a\u0648\u0632\u06cc\u0639 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627\u06cc \u0637\u0628\u0642\u0647 \u0628\u0646\u062f\u06cc \u0634\u062f\u0647 \u0631\u0627 \u062f\u0631 \u06af\u0631\u0648\u0647 \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641 \u0645\u0642\u0627\u06cc\u0633\u0647 \u06a9\u0646\u06cc\u062f.<\/li>\n<\/ol>\n<p>\u0645\u0634\u06a9\u0644\u0627\u062a \u0627\u062d\u062a\u0645\u0627\u0644\u06cc \u062a\u0633\u062a Chi-Squared \u0639\u0628\u0627\u0631\u062a\u0646\u062f \u0627\u0632:<\/p>\n<ul>\n<li><strong>\u062d\u062c\u0645 \u0646\u0645\u0648\u0646\u0647 \u06a9\u0648\u0686\u06a9:<\/strong> \u062a\u0633\u062a Chi-Squared \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0646\u062a\u0627\u06cc\u062c \u0646\u0627\u062f\u0631\u0633\u062a\u06cc \u0628\u0627 \u0627\u0646\u062f\u0627\u0632\u0647 \u0646\u0645\u0648\u0646\u0647 \u06a9\u0648\u0686\u06a9 \u06cc\u0627 \u0633\u0644\u0648\u0644 \u0647\u0627\u06cc\u06cc \u0628\u0627 \u0641\u0631\u06a9\u0627\u0646\u0633 \u0645\u0648\u0631\u062f \u0627\u0646\u062a\u0638\u0627\u0631 \u06a9\u0645\u062a\u0631 \u0627\u0632 5 \u0627\u0631\u0627\u0626\u0647 \u062f\u0647\u062f. \u062f\u0631 \u0686\u0646\u06cc\u0646 \u0645\u0648\u0627\u0631\u062f\u06cc\u060c \u0622\u0632\u0645\u0648\u0646 Chi-Squared \u0646\u0633\u0628\u062a \u0627\u062d\u062a\u0645\u0627\u0644 \u062a\u0631\u062c\u06cc\u062d \u062f\u0627\u062f\u0647 \u0645\u06cc \u0634\u0648\u062f.<\/li>\n<li><strong>\u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u062a\u0631\u062a\u06cc\u0628\u06cc:<\/strong> \u0622\u0632\u0645\u0648\u0646 Chi-Squared \u0628\u0631\u0627\u06cc \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u062a\u0631\u062a\u06cc\u0628\u06cc \u0645\u0646\u0627\u0633\u0628 \u0646\u06cc\u0633\u062a\u060c \u0632\u06cc\u0631\u0627 \u062a\u0631\u062a\u06cc\u0628 \u062f\u0633\u062a\u0647 \u0647\u0627 \u0631\u0627 \u062f\u0631 \u0646\u0638\u0631 \u0646\u0645\u06cc \u06af\u06cc\u0631\u062f.<\/li>\n<\/ul>\n<p>\u0628\u0631\u0627\u06cc \u0631\u0633\u06cc\u062f\u06af\u06cc \u0628\u0647 \u0627\u06cc\u0646 \u0645\u0633\u0627\u0626\u0644\u060c \u0645\u062d\u0642\u0642\u0627\u0646 \u0645\u06cc\u200c\u062a\u0648\u0627\u0646\u0646\u062f \u0627\u0632 \u0622\u0632\u0645\u0648\u0646\u200c\u0647\u0627\u06cc \u062c\u0627\u06cc\u06af\u0632\u06cc\u0646 \u0645\u0627\u0646\u0646\u062f \u0622\u0632\u0645\u0648\u0646 \u062f\u0642\u06cc\u0642 \u0641\u06cc\u0634\u0631 \u0628\u0631\u0627\u06cc \u0627\u0646\u062f\u0627\u0632\u0647\u200c\u0647\u0627\u06cc \u0646\u0645\u0648\u0646\u0647 \u06a9\u0648\u0686\u06a9 \u06cc\u0627 \u0633\u0627\u06cc\u0631 \u0622\u0632\u0645\u0648\u0646\u200c\u0647\u0627\u06cc \u0646\u0627\u067e\u0627\u0631\u0627\u0645\u062a\u0631\u06cc\u06a9 \u0628\u0631\u0627\u06cc \u062f\u0627\u062f\u0647\u200c\u0647\u0627\u06cc \u062a\u0631\u062a\u06cc\u0628\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0646\u0646\u062f.<\/p>\n<h2>\u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u0627\u0635\u0644\u06cc \u0648 \u0645\u0642\u0627\u06cc\u0633\u0647 \u0628\u0627 \u0627\u0635\u0637\u0644\u0627\u062d\u0627\u062a \u0645\u0634\u0627\u0628\u0647<\/h2>\n<p>\u0622\u0632\u0645\u0648\u0646 Chi-Squared \u0634\u0628\u0627\u0647\u062a \u0647\u0627\u06cc\u06cc \u0628\u0627 \u0633\u0627\u06cc\u0631 \u0622\u0632\u0645\u0648\u0646 \u0647\u0627\u06cc \u0622\u0645\u0627\u0631\u06cc \u062f\u0627\u0631\u062f\u060c \u0627\u0645\u0627 \u0647\u0645\u0686\u0646\u06cc\u0646 \u062f\u0627\u0631\u0627\u06cc \u0648\u06cc\u0698\u06af\u06cc \u0647\u0627\u06cc \u0645\u0646\u062d\u0635\u0631 \u0628\u0647 \u0641\u0631\u062f\u06cc \u0627\u0633\u062a \u06a9\u0647 \u0622\u0646 \u0631\u0627 \u0645\u062a\u0645\u0627\u06cc\u0632 \u0645\u06cc \u06a9\u0646\u062f:<\/p>\n<table>\n<thead>\n<tr>\n<th>\u0645\u0634\u062e\u0635\u0647<\/th>\n<th>\u062a\u0633\u062a Chi-Squared<\/th>\n<th>T-Test<\/th>\n<th>ANOVA<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u0646\u0648\u0639 \u062a\u0633\u062a<\/td>\n<td>\u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0637\u0628\u0642\u0647 \u0628\u0646\u062f\u06cc \u0634\u062f\u0647<\/td>\n<td>\u0645\u0642\u0627\u06cc\u0633\u0647 \u0645\u06cc\u0627\u0646\u06af\u06cc\u0646 \u0647\u0627<\/td>\n<td>\u0645\u0642\u0627\u06cc\u0633\u0647 \u0645\u06cc\u0627\u0646\u06af\u06cc\u0646 \u0647\u0627<\/td>\n<\/tr>\n<tr>\n<td>\u062a\u0639\u062f\u0627\u062f \u0645\u062a\u063a\u06cc\u0631\u0647\u0627<\/td>\n<td>2 \u06cc\u0627 \u0628\u06cc\u0634\u062a\u0631<\/td>\n<td>2<\/td>\n<td>3 \u06cc\u0627 \u0628\u06cc\u0634\u062a\u0631<\/td>\n<\/tr>\n<tr>\n<td>\u0646\u0648\u0639 \u062f\u0627\u062f\u0647<\/td>\n<td>\u062f\u0633\u062a\u0647 \u0628\u0646\u062f\u06cc<\/td>\n<td>\u0645\u062f\u0627\u0648\u0645<\/td>\n<td>\u0645\u062f\u0627\u0648\u0645<\/td>\n<\/tr>\n<tr>\n<td>\u0645\u0641\u0631\u0648\u0636\u0627\u062a<\/td>\n<td>\u0646\u0627\u067e\u0627\u0631\u0627\u0645\u062a\u0631\u06cc\u06a9<\/td>\n<td>\u062a\u0648\u0632\u06cc\u0639 \u0646\u0631\u0645\u0627\u0644 \u0631\u0627 \u0641\u0631\u0636 \u0645\u06cc \u06a9\u0646\u062f<\/td>\n<td>\u062a\u0648\u0632\u06cc\u0639 \u0646\u0631\u0645\u0627\u0644 \u0631\u0627 \u0641\u0631\u0636 \u0645\u06cc \u06a9\u0646\u062f<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>\u062f\u06cc\u062f\u06af\u0627\u0647 \u0647\u0627 \u0648 \u0641\u0646\u0627\u0648\u0631\u06cc \u0647\u0627\u06cc \u0622\u06cc\u0646\u062f\u0647 \u0645\u0631\u062a\u0628\u0637 \u0628\u0627 \u0622\u0632\u0645\u0648\u0646 Chi-Squared<\/h2>\n<p>\u0627\u0632 \u0622\u0646\u062c\u0627\u06cc\u06cc \u06a9\u0647 \u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u062f\u0627\u062f\u0647 \u0647\u0627 \u0647\u0645\u0686\u0646\u0627\u0646 \u0646\u0642\u0634 \u0645\u0647\u0645\u06cc \u062f\u0631 \u0635\u0646\u0627\u06cc\u0639 \u0645\u062e\u062a\u0644\u0641 \u0627\u06cc\u0641\u0627 \u0645\u06cc \u06a9\u0646\u062f\u060c \u0622\u0632\u0645\u0648\u0646 Chi-Squared \u0627\u0628\u0632\u0627\u0631\u06cc \u0627\u0633\u0627\u0633\u06cc \u0628\u0631\u0627\u06cc \u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0637\u0628\u0642\u0647 \u0628\u0646\u062f\u06cc \u0634\u062f\u0647 \u0628\u0627\u0642\u06cc \u062e\u0648\u0627\u0647\u062f \u0645\u0627\u0646\u062f. \u0628\u0627 \u0627\u06cc\u0646 \u062d\u0627\u0644\u060c \u067e\u06cc\u0634\u0631\u0641\u062a\u200c\u0647\u0627 \u062f\u0631 \u0631\u0648\u0634\u200c\u0634\u0646\u0627\u0633\u06cc \u0648 \u0641\u0646\u0627\u0648\u0631\u06cc\u200c\u0647\u0627\u06cc \u0622\u0645\u0627\u0631\u06cc \u0645\u0645\u06a9\u0646 \u0627\u0633\u062a \u0645\u0646\u062c\u0631 \u0628\u0647 \u0646\u0633\u062e\u0647\u200c\u0647\u0627 \u06cc\u0627 \u062a\u0648\u0633\u0639\u0647\u200c\u0647\u0627\u06cc \u0628\u0647\u0628\u0648\u062f \u06cc\u0627\u0641\u062a\u0647 \u0622\u0632\u0645\u0648\u0646 Chi-Squared \u0634\u0648\u062f \u06a9\u0647 \u0645\u062d\u062f\u0648\u062f\u06cc\u062a\u200c\u0647\u0627\u06cc \u0622\u0646 \u0631\u0627 \u0628\u0631\u0637\u0631\u0641 \u0645\u06cc\u200c\u06a9\u0646\u062f \u0648 \u0622\u0646 \u0631\u0627 \u062d\u062a\u06cc \u0647\u0645\u0647\u200c\u06a9\u0627\u0631\u0647\u200c\u062a\u0631 \u0648 \u0642\u062f\u0631\u062a\u0645\u0646\u062f\u062a\u0631 \u0645\u06cc\u200c\u06a9\u0646\u062f.<\/p>\n<h2>\u0686\u06af\u0648\u0646\u0647 \u0645\u06cc \u062a\u0648\u0627\u0646 \u0627\u0632 \u0633\u0631\u0648\u0631\u0647\u0627\u06cc \u067e\u0631\u0648\u06a9\u0633\u06cc \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u06a9\u0631\u062f \u06cc\u0627 \u0628\u0627 \u062a\u0633\u062a Chi-Squared \u0645\u0631\u062a\u0628\u0637 \u0634\u062f<\/h2>\n<p>\u0633\u0631\u0648\u0631\u0647\u0627\u06cc \u067e\u0631\u0627\u06a9\u0633\u06cc \u0627\u0631\u0627\u0626\u0647 \u0634\u062f\u0647 \u062a\u0648\u0633\u0637 \u0627\u0631\u0627\u0626\u0647 \u062f\u0647\u0646\u062f\u06af\u0627\u0646\u06cc \u0645\u0627\u0646\u0646\u062f OneProxy \u0645\u06cc \u062a\u0648\u0627\u0646\u0646\u062f \u062c\u0645\u0639 \u0622\u0648\u0631\u06cc \u0648 \u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u062f\u0627\u062f\u0647 \u0647\u0627 \u0631\u0627 \u0628\u0631\u0627\u06cc \u0627\u0646\u062c\u0627\u0645 \u062a\u0633\u062a \u0647\u0627\u06cc Chi-Squared \u062a\u0633\u0647\u06cc\u0644 \u06a9\u0646\u0646\u062f. \u0622\u0646\u200c\u0647\u0627 \u06a9\u0627\u0631\u0628\u0631\u0627\u0646 \u0631\u0627 \u0642\u0627\u062f\u0631 \u0645\u06cc\u200c\u0633\u0627\u0632\u0646\u062f \u062a\u0627 \u0628\u0647 \u0645\u06a9\u0627\u0646\u200c\u0647\u0627\u06cc \u062c\u063a\u0631\u0627\u0641\u06cc\u0627\u06cc\u06cc \u0645\u062e\u062a\u0644\u0641 \u062f\u0633\u062a\u0631\u0633\u06cc \u062f\u0627\u0634\u062a\u0647 \u0628\u0627\u0634\u0646\u062f\u060c \u06a9\u0647 \u0628\u0647 \u0648\u06cc\u0698\u0647 \u062f\u0631 \u0647\u0646\u06af\u0627\u0645 \u0628\u0631\u062e\u0648\u0631\u062f \u0628\u0627 \u0645\u062c\u0645\u0648\u0639\u0647\u200c\u0647\u0627\u06cc \u062f\u0627\u062f\u0647 \u0628\u0627 \u062a\u063a\u06cc\u06cc\u0631\u0627\u062a \u0645\u0646\u0637\u0642\u0647\u200c\u0627\u06cc \u0645\u0641\u06cc\u062f \u0627\u0633\u062a. \u0633\u0631\u0648\u0631\u0647\u0627\u06cc \u067e\u0631\u0648\u06a9\u0633\u06cc \u0647\u0645\u0686\u0646\u06cc\u0646 \u0646\u0627\u0634\u0646\u0627\u0633 \u0628\u0648\u062f\u0646 \u0631\u0627 \u062a\u0636\u0645\u06cc\u0646 \u0645\u06cc\u200c\u06a9\u0646\u0646\u062f\u060c \u0648 \u0622\u0646\u0647\u0627 \u0631\u0627 \u0628\u0631\u0627\u06cc \u06a9\u0627\u0631\u0647\u0627\u06cc \u062c\u0645\u0639\u200c\u0622\u0648\u0631\u06cc \u062f\u0627\u062f\u0647\u200c\u0647\u0627 \u0648 \u062e\u0631\u0627\u0634\u200c\u0647\u0627\u06cc \u0648\u0628 \u0627\u0631\u0632\u0634\u0645\u0646\u062f \u0645\u06cc\u200c\u0633\u0627\u0632\u062f\u060c \u062f\u0631 \u062d\u0627\u0644\u06cc \u06a9\u0647 \u0628\u0647 \u0645\u062d\u0642\u0642\u0627\u0646 \u06a9\u0645\u06a9 \u0645\u06cc\u200c\u06a9\u0646\u062f \u062d\u0631\u06cc\u0645 \u062e\u0635\u0648\u0635\u06cc \u0648 \u0627\u0645\u0646\u06cc\u062a \u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644\u200c\u0647\u0627\u06cc \u062e\u0648\u062f \u0631\u0627 \u062d\u0641\u0638 \u06a9\u0646\u0646\u062f.<\/p>\n<h2>\u0644\u06cc\u0646\u06a9 \u0647\u0627\u06cc \u0645\u0631\u0628\u0648\u0637\u0647<\/h2>\n<p>\u0628\u0631\u0627\u06cc \u06a9\u0633\u0628 \u0627\u0637\u0644\u0627\u0639\u0627\u062a \u0628\u06cc\u0634\u062a\u0631 \u062f\u0631 \u0645\u0648\u0631\u062f \u0622\u0632\u0645\u0648\u0646 Chi-Squared\u060c \u0645\u06cc \u062a\u0648\u0627\u0646\u06cc\u062f \u0645\u0646\u0627\u0628\u0639 \u0632\u06cc\u0631 \u0631\u0627 \u0628\u0631\u0631\u0633\u06cc \u06a9\u0646\u06cc\u062f:<\/p>\n<ol>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Chi-squared_test\" target=\"_new\" rel=\"noopener nofollow\">\u0648\u06cc\u06a9\u06cc \u067e\u062f\u06cc\u0627 \u2013 \u062a\u0633\u062a Chi-Squared<\/a><\/li>\n<li><a href=\"https:\/\/www.statisticssolutions.com\/non-parametric-analysis-chi-square\/\" target=\"_new\" rel=\"noopener nofollow\">\u0631\u0627\u0647 \u062d\u0644 \u0647\u0627\u06cc \u0622\u0645\u0627\u0631\u06cc \u2013 \u0622\u0632\u0645\u0648\u0646 \u06a9\u0627\u06cc \u0627\u0633\u06a9\u0648\u0626\u0631<\/a><\/li>\n<li><a href=\"https:\/\/www.graphpad.com\/guides\/prism\/8\/statistics\/stat_interpreting_results_chi-square_test.htm\" target=\"_new\" rel=\"noopener nofollow\">GraphPad Prism \u2013 \u062a\u0633\u062a Chi-Squared<\/a><\/li>\n<li><a href=\"https:\/\/ncss-wpengine.netdna-ssl.com\/wp-content\/themes\/ncss\/pdf\/Procedures\/NCSS\/Chi-Square_Test.pdf\" target=\"_new\" rel=\"noopener nofollow\">NCSS - \u062a\u0633\u062a Chi-Square<\/a><\/li>\n<\/ol>\n<p>\u062f\u0631 \u0646\u062a\u06cc\u062c\u0647\u060c \u0622\u0632\u0645\u0648\u0646 \u06a9\u0627\u06cc \u062f\u0648 \u06cc\u06a9 \u0631\u0648\u0634 \u0622\u0645\u0627\u0631\u06cc \u0642\u062f\u0631\u062a\u0645\u0646\u062f \u0628\u0631\u0627\u06cc \u062a\u062c\u0632\u06cc\u0647 \u0648 \u062a\u062d\u0644\u06cc\u0644 \u062f\u0627\u062f\u0647 \u0647\u0627\u06cc \u0637\u0628\u0642\u0647 \u0628\u0646\u062f\u06cc \u0634\u062f\u0647 \u0648 \u0634\u0646\u0627\u0633\u0627\u06cc\u06cc \u0627\u0631\u062a\u0628\u0627\u0637 \u0628\u06cc\u0646 \u0645\u062a\u063a\u06cc\u0631\u0647\u0627 \u0627\u0633\u062a. \u062a\u0637\u0628\u06cc\u0642 \u067e\u0630\u06cc\u0631\u06cc\u060c \u0633\u0647\u0648\u0644\u062a \u0627\u0633\u062a\u0641\u0627\u062f\u0647 \u0648 \u06a9\u0627\u0631\u0628\u0631\u062f\u0647\u0627\u06cc \u0622\u0646 \u062f\u0631 \u062d\u0648\u0632\u0647 \u0647\u0627\u06cc \u0645\u062e\u062a\u0644\u0641\u060c \u0622\u0646 \u0631\u0627 \u0628\u0647 \u0627\u0628\u0632\u0627\u0631\u06cc \u0636\u0631\u0648\u0631\u06cc \u0628\u0631\u0627\u06cc \u0645\u062d\u0642\u0642\u0627\u0646 \u0648 \u062a\u062d\u0644\u06cc\u0644\u06af\u0631\u0627\u0646 \u062f\u0627\u062f\u0647 \u062a\u0628\u062f\u06cc\u0644 \u06a9\u0631\u062f\u0647 \u0627\u0633\u062a. \u0628\u0627 \u067e\u06cc\u0634\u0631\u0641\u062a \u0641\u0646\u0627\u0648\u0631\u06cc\u060c \u0622\u0632\u0645\u0648\u0646 Chi-Squared \u0627\u062d\u062a\u0645\u0627\u0644\u0627\u064b \u0628\u0647 \u062a\u06a9\u0627\u0645\u0644 \u062e\u0648\u062f \u0627\u062f\u0627\u0645\u0647 \u062e\u0648\u0627\u0647\u062f \u062f\u0627\u062f \u0648 \u0628\u0627 \u0631\u0648\u0634\u200c\u0647\u0627 \u0648 \u0627\u0628\u0632\u0627\u0631\u0647\u0627\u06cc \u0646\u0648\u0622\u0648\u0631\u0627\u0646\u0647 \u062a\u06a9\u0645\u06cc\u0644 \u0645\u06cc\u200c\u0634\u0648\u062f \u0648 \u0628\u06cc\u0646\u0634 \u0639\u0645\u06cc\u0642\u200c\u062a\u0631\u06cc \u0631\u0627 \u062f\u0631 \u0645\u0648\u0631\u062f \u0631\u0648\u0627\u0628\u0637 \u062f\u0627\u062f\u0647\u200c\u0647\u0627\u06cc \u0637\u0628\u0642\u0647\u200c\u0628\u0646\u062f\u06cc \u0627\u0631\u0627\u0626\u0647 \u0645\u06cc\u200c\u062f\u0647\u062f.<\/p>","protected":false},"featured_media":497617,"menu_order":0,"template":"","meta":{"_acf_changed":false,"content-type":"","inline_featured_image":false,"footnotes":""},"class_list":["post-476219","wiki","type-wiki","status-publish","has-post-thumbnail","hentry"],"acf":{"faq_title":"Frequently Asked Questions about <mark>Chi-Squared Test: A Comprehensive Overview<\/mark>","faq_items":[{"question":"What is the Chi-Squared test, and how does it work?","answer":"The Chi-Squared test is a statistical method used to analyze categorical data and determine if there is a significant association between two or more variables. It compares observed frequencies with expected frequencies and provides valuable insights into the relationships between variables."},{"question":"Who introduced the Chi-Squared test and when was it first mentioned?","answer":"The Chi-Squared test was introduced by Karl Pearson, a British mathematician and biostatistician, in 1900. He developed this method to analyze the relationships between variables in large datasets."},{"question":"What is the difference between Pearson's Chi-Squared test and the Likelihood Ratio Chi-Squared test?","answer":"Both Pearson's Chi-Squared test and the Likelihood Ratio Chi-Squared test are used to analyze categorical data, but they differ in their assumptions and applications. Pearson's test assumes normal distribution and is suitable for large sample sizes, while the Likelihood Ratio test makes fewer assumptions and is more appropriate for small sample sizes or cases with expected frequencies less than five."},{"question":"In what situations is the Chi-Squared test commonly used?","answer":"The Chi-Squared test finds applications in various scenarios, including goodness of fit testing, independence testing, and homogeneity testing. It is widely used in social sciences, biology, medicine, marketing, and other fields where categorical data analysis is essential."},{"question":"What problems may arise when using the Chi-Squared test?","answer":"The Chi-Squared test may yield inaccurate results with small sample sizes or cells with expected frequencies less than five. In such cases, the Likelihood Ratio Chi-Squared test is preferred. Additionally, the test is not suitable for ordinal data, as it does not consider the order of categories."},{"question":"How can OneProxy's proxy servers be associated with the Chi-Squared test?","answer":"OneProxy's proxy servers facilitate data collection and analysis by offering access to different geographical locations and ensuring anonymity. Researchers can use proxy servers for web scraping and data gathering tasks, enhancing privacy and security while conducting Chi-Squared tests."},{"question":"What are the advantages of using the Chi-Squared test?","answer":"The Chi-Squared test is a non-parametric test, meaning it makes no assumptions about data distribution. It is suitable for categorical data analysis, providing valuable insights into associations between variables. Additionally, it allows researchers to draw statistical inferences and make confident conclusions based on the obtained p-values."},{"question":"Where can I find more information about the Chi-Squared test?","answer":"For further information about the Chi-Squared test, you can explore additional resources, such as Wikipedia's page on Chi-Squared test, Statistics Solutions' guide, and GraphPad Prism's interpretation of results. Visit OneProxy.pro to learn more about proxy servers' benefits and applications."}]},"_links":{"self":[{"href":"https:\/\/oneproxy.pro\/ir\/wp-json\/wp\/v2\/wiki\/476219","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/oneproxy.pro\/ir\/wp-json\/wp\/v2\/wiki"}],"about":[{"href":"https:\/\/oneproxy.pro\/ir\/wp-json\/wp\/v2\/types\/wiki"}],"version-history":[{"count":0,"href":"https:\/\/oneproxy.pro\/ir\/wp-json\/wp\/v2\/wiki\/476219\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/oneproxy.pro\/ir\/wp-json\/wp\/v2\/media\/497617"}],"wp:attachment":[{"href":"https:\/\/oneproxy.pro\/ir\/wp-json\/wp\/v2\/media?parent=476219"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}