{"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\/ar\/wiki\/chi-squared-test\/","title":{"rendered":"\u0627\u062e\u062a\u0628\u0627\u0631 \u0645\u0631\u0628\u0639 \u0643\u0627\u064a"},"content":{"rendered":"<p>\u0627\u062e\u062a\u0628\u0627\u0631 Chi-Squared \u0647\u0648 \u0637\u0631\u064a\u0642\u0629 \u0625\u062d\u0635\u0627\u0626\u064a\u0629 \u062a\u0633\u062a\u062e\u062f\u0645 \u0644\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0641\u0626\u0648\u064a\u0629 \u0648\u062a\u062d\u062f\u064a\u062f \u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646 \u0647\u0646\u0627\u0643 \u0627\u0631\u062a\u0628\u0627\u0637 \u0643\u0628\u064a\u0631 \u0628\u064a\u0646 \u0645\u062a\u063a\u064a\u0631\u064a\u0646 \u0623\u0648 \u0623\u0643\u062b\u0631. \u0648\u0647\u0648 \u0627\u062e\u062a\u0628\u0627\u0631 \u063a\u064a\u0631 \u0645\u0639\u0644\u0645\u064a\u060c \u0645\u0645\u0627 \u064a\u0639\u0646\u064a \u0623\u0646\u0647 \u0644\u0627 \u064a\u0642\u062f\u0645 \u0623\u064a \u0627\u0641\u062a\u0631\u0627\u0636\u0627\u062a \u062d\u0648\u0644 \u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a\u060c \u0648\u064a\u0633\u062a\u062e\u062f\u0645 \u0639\u0644\u0649 \u0646\u0637\u0627\u0642 \u0648\u0627\u0633\u0639 \u0641\u064a \u0645\u062c\u0627\u0644\u0627\u062a \u0645\u062e\u062a\u0644\u0641\u0629\u060c \u0628\u0645\u0627 \u0641\u064a \u0630\u0644\u0643 \u0627\u0644\u0639\u0644\u0648\u0645 \u0627\u0644\u0627\u062c\u062a\u0645\u0627\u0639\u064a\u0629 \u0648\u0639\u0644\u0645 \u0627\u0644\u0623\u062d\u064a\u0627\u0621 \u0648\u0627\u0644\u0637\u0628 \u0648\u0627\u0644\u062a\u0633\u0648\u064a\u0642. \u064a\u0642\u0648\u0645 \u0627\u0644\u0627\u062e\u062a\u0628\u0627\u0631 \u0628\u062a\u0642\u064a\u064a\u0645 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\u0627\u0644\u0643\u0628\u064a\u0631\u0629. \u062a\u0645 \u062a\u0637\u0628\u064a\u0642 \u0627\u062e\u062a\u0628\u0627\u0631 Chi-Squared \u0641\u064a \u0627\u0644\u0628\u062f\u0627\u064a\u0629 \u0641\u064a \u062a\u062d\u0644\u064a\u0644 \u062c\u062f\u0627\u0648\u0644 \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u0627\u062a\u060c \u0648\u0627\u0644\u062a\u064a \u062a\u0639\u0631\u0636 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0645\u0634\u062a\u0631\u0643 \u0644\u0645\u062a\u063a\u064a\u0631\u064a\u0646 \u0641\u0626\u0648\u064a\u064a\u0646 \u0623\u0648 \u0623\u0643\u062b\u0631.<\/p>\n<h2>\u0645\u0639\u0644\u0648\u0645\u0627\u062a \u062a\u0641\u0635\u064a\u0644\u064a\u0629 \u0639\u0646 \u0627\u062e\u062a\u0628\u0627\u0631 \u0643\u0627\u064a \u062a\u0631\u0628\u064a\u0639<\/h2>\n<p>\u064a\u0639\u062a\u0645\u062f \u0627\u062e\u062a\u0628\u0627\u0631 Chi-Squared \u0639\u0644\u0649 \u0645\u0642\u0627\u0631\u0646\u0629 \u0627\u0644\u062a\u0631\u062f\u062f\u0627\u062a \u0627\u0644\u0645\u0631\u0635\u0648\u062f\u0629 (O) \u0641\u064a \u0645\u062c\u0645\u0648\u0639\u0629 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0645\u0639 \u0627\u0644\u062a\u0631\u062f\u062f\u0627\u062a \u0627\u0644\u0645\u062a\u0648\u0642\u0639\u0629 (E) \u0627\u0644\u062a\u064a \u0642\u062f \u062a\u062d\u062f\u062b \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0645\u0633\u062a\u0642\u0644\u0629. \u064a\u062a\u0636\u0645\u0646 \u0627\u0644\u0627\u062e\u062a\u0628\u0627\u0631 \u062d\u0633\u0627\u0628 \u0625\u062d\u0635\u0627\u0626\u064a\u0629 Chi-Squared\u060c \u0627\u0644\u062a\u064a \u062a\u062d\u062f\u062f \u0627\u0644\u0641\u0631\u0642 \u0628\u064a\u0646 \u0627\u0644\u062a\u0631\u062f\u062f\u0627\u062a \u0627\u0644\u0645\u0631\u0635\u0648\u062f\u0629 \u0648\u0627\u0644\u0645\u062a\u0648\u0642\u0639\u0629. \u0635\u064a\u063a\u0629 \u0625\u062d\u0635\u0627\u0626\u064a\u0629 Chi-Squared \u0647\u064a:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/oneproxy.pro\/images\/chi_squared_formula.png\" alt=\"\u0635\u064a\u063a\u0629 \u0645\u0631\u0628\u0639 \u0643\u0627\u064a\" title=\"\"><\/p>\n<p>\u0623\u064a\u0646:<\/p>\n<ul>\n<li>\u03a7\u00b2 \u064a\u0645\u062b\u0644 \u0625\u062d\u0635\u0627\u0626\u064a\u0629 Chi-Squared<\/li>\n<li>O\u1d62 \u0647\u0648 \u0627\u0644\u062a\u0631\u062f\u062f \u0627\u0644\u0645\u0631\u0635\u0648\u062f \u0644\u0644\u0641\u0626\u0629 i<\/li>\n<li>E\u1d62 \u0647\u0648 \u0627\u0644\u062a\u0643\u0631\u0627\u0631 \u0627\u0644\u0645\u062a\u0648\u0642\u0639 \u0644\u0644\u0641\u0626\u0629 i<\/li>\n<li>\u03a3 \u062a\u0634\u064a\u0631 \u0625\u0644\u0649 \u0627\u0644\u0645\u062c\u0645\u0648\u0639 \u0641\u064a \u062c\u0645\u064a\u0639 \u0627\u0644\u0641\u0626\u0627\u062a<\/li>\n<\/ul>\n<p>\u062a\u062a\u0628\u0639 \u0625\u062d\u0635\u0627\u0626\u064a\u0629 Chi-Squared \u062a\u0648\u0632\u064a\u0639 Chi-Squared\u060c \u0648\u064a\u062a\u0645 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 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(\u0627\u0644\u0645\u0639\u0631\u0648\u0641 \u0623\u064a\u0636\u064b\u0627 \u0628\u0627\u0633\u0645 \u0627\u062e\u062a\u0628\u0627\u0631 \u062c\u064a). \u064a\u0633\u062a\u062e\u062f\u0645 \u0643\u0644\u0627 \u0627\u0644\u0627\u062e\u062a\u0628\u0627\u0631\u064a\u0646 \u0646\u0641\u0633 \u0627\u0644\u0635\u064a\u063a\u0629 \u0644\u0625\u062d\u0635\u0627\u0621 \u0643\u0627\u064a \u062a\u0631\u0628\u064a\u0639\u060c \u0644\u0643\u0646\u0647\u0645\u0627 \u064a\u062e\u062a\u0644\u0641\u0627\u0646 \u0641\u064a \u0637\u0631\u064a\u0642\u0629 \u062d\u0633\u0627\u0628 \u0627\u0644\u062a\u0643\u0631\u0627\u0631\u0627\u062a \u0627\u0644\u0645\u062a\u0648\u0642\u0639\u0629.<\/p>\n<ol>\n<li>\u0627\u062e\u062a\u0628\u0627\u0631 \u0628\u064a\u0631\u0633\u0648\u0646 \u0644\u0645\u0631\u0628\u0639 \u0643\u0627\u064a:\n<ul>\n<li>\u064a\u0641\u062a\u0631\u0636 \u0623\u0646 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0644\u0647\u0627 \u062a\u0648\u0632\u064a\u0639 \u0637\u0628\u064a\u0639\u064a \u062a\u0642\u0631\u064a\u0628\u0627.<\/li>\n<li>\u0643\u062b\u064a\u0631\u0627 \u0645\u0627 \u062a\u0633\u062a\u062e\u062f\u0645 \u0639\u0646\u062f\u0645\u0627 \u064a\u0643\u0648\u0646 \u062d\u062c\u0645 \u0627\u0644\u0639\u064a\u0646\u0629 \u0643\u0628\u064a\u0631\u0627.<\/li>\n<\/ul>\n<\/li>\n<li>\u0627\u062e\u062a\u0628\u0627\u0631 \u0646\u0633\u0628\u0629 \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629 \u0644\u0645\u0631\u0628\u0639 \u0643\u0627\u064a (\u0627\u062e\u062a\u0628\u0627\u0631 G):\n<ul>\n<li>\u0628\u0646\u0627\u0621\u064b \u0639\u0644\u0649 \u0646\u0633\u0628\u0629 \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629\u060c \u064a\u062a\u0645 \u0648\u0636\u0639 \u0627\u0641\u062a\u0631\u0627\u0636\u0627\u062a \u0623\u0642\u0644 \u062d\u0648\u0644 \u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a.<\/li>\n<li>\u0645\u0646\u0627\u0633\u0628\u0629 \u0644\u0623\u062d\u062c\u0627\u0645 \u0627\u0644\u0639\u064a\u0646\u0627\u062a \u0627\u0644\u0635\u063a\u064a\u0631\u0629 \u0623\u0648 \u0627\u0644\u062d\u0627\u0644\u0627\u062a \u0630\u0627\u062a \u0627\u0644\u062a\u0643\u0631\u0627\u0631\u0627\u062a \u0627\u0644\u0645\u062a\u0648\u0642\u0639\u0629 \u0623\u0642\u0644 \u0645\u0646 \u062e\u0645\u0633\u0629.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<h2>\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0633\u0645\u0627\u062a \u0627\u0644\u0631\u0626\u064a\u0633\u064a\u0629 \u0644\u0627\u062e\u062a\u0628\u0627\u0631 \u0643\u0627\u064a \u062a\u0631\u0628\u064a\u0639<\/h2>\n<p>\u064a\u062d\u062a\u0648\u064a \u0627\u062e\u062a\u0628\u0627\u0631 Chi-Squared \u0639\u0644\u0649 \u0627\u0644\u0639\u062f\u064a\u062f \u0645\u0646 \u0627\u0644\u0645\u064a\u0632\u0627\u062a \u0627\u0644\u0631\u0626\u064a\u0633\u064a\u0629 \u0627\u0644\u062a\u064a \u062a\u062c\u0639\u0644\u0647 \u0623\u062f\u0627\u0629 \u0625\u062d\u0635\u0627\u0626\u064a\u0629 \u0642\u064a\u0645\u0629:<\/p>\n<ul>\n<li><strong>\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0641\u0626\u0648\u064a\u0629:<\/strong> \u062a\u0645 \u062a\u0635\u0645\u064a\u0645 \u0627\u062e\u062a\u0628\u0627\u0631 Chi-Squared \u062e\u0635\u064a\u0635\u064b\u0627 \u0644\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0641\u0626\u0648\u064a\u0629\u060c \u0645\u0645\u0627 \u064a\u0633\u0645\u062d \u0644\u0644\u0628\u0627\u062d\u062b\u064a\u0646 \u0628\u0627\u0633\u062a\u062e\u0644\u0627\u0635 \u0627\u0633\u062a\u0646\u062a\u0627\u062c\u0627\u062a \u0630\u0627\u062a \u0645\u0639\u0646\u0649 \u0645\u0646 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u063a\u064a\u0631 \u0627\u0644\u0631\u0642\u0645\u064a\u0629.<\/li>\n<li><strong>\u0627\u062e\u062a\u0628\u0627\u0631 \u063a\u064a\u0631 \u062d\u062f\u0648\u062f\u064a:<\/strong> \u0643\u0627\u062e\u062a\u0628\u0627\u0631 \u063a\u064a\u0631 \u0645\u0639\u0644\u0645\u064a\u060c \u0644\u0627 \u064a\u062a\u0637\u0644\u0628 \u0627\u062e\u062a\u0628\u0627\u0631 Chi-Squared \u0623\u0646 \u062a\u062a\u0628\u0639 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u062a\u0648\u0632\u064a\u0639\u064b\u0627 \u0645\u062d\u062f\u062f\u064b\u0627\u060c \u0645\u0645\u0627 \u064a\u062c\u0639\u0644\u0647 \u0645\u062a\u0639\u062f\u062f \u0627\u0644\u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0627\u062a \u0648\u0642\u0627\u0628\u0644 \u0644\u0644\u062a\u0637\u0628\u064a\u0642 \u0641\u064a \u0633\u064a\u0646\u0627\u0631\u064a\u0648\u0647\u0627\u062a \u0645\u062e\u062a\u0644\u0641\u0629.<\/li>\n<li><strong>\u062a\u0642\u064a\u064a\u0645 \u0627\u0644\u0627\u0633\u062a\u0642\u0644\u0627\u0644:<\/strong> \u064a\u0633\u0627\u0639\u062f \u0627\u0644\u0627\u062e\u062a\u0628\u0627\u0631 \u0639\u0644\u0649 \u062a\u062d\u062f\u064a\u062f \u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0647\u0646\u0627\u0643 \u0639\u0644\u0627\u0642\u0629 \u0628\u064a\u0646 \u0645\u062a\u063a\u064a\u0631\u064a\u0646 \u0641\u0626\u0648\u064a\u064a\u0646 \u0623\u0648 \u0623\u0643\u062b\u0631\u060c \u0645\u0645\u0627 \u064a\u0633\u0627\u0639\u062f \u0641\u064a \u0641\u0647\u0645 \u0627\u0644\u0623\u0646\u0645\u0627\u0637 \u0648\u0627\u0644\u0627\u0631\u062a\u0628\u0627\u0637\u0627\u062a \u0641\u064a \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a.<\/li>\n<li><strong>\u0627\u062e\u062a\u0628\u0627\u0631 \u0627\u0644\u0627\u0633\u062a\u062f\u0644\u0627\u0644:<\/strong> \u0645\u0646 \u062e\u0644\u0627\u0644 \u062a\u0648\u0641\u064a\u0631 \u0642\u064a\u0645\u0629 p\u060c \u064a\u062a\u064a\u062d \u0627\u062e\u062a\u0628\u0627\u0631 Chi-Squared \u0644\u0644\u0628\u0627\u062d\u062b\u064a\u0646 \u0625\u062c\u0631\u0627\u0621 \u0627\u0633\u062a\u0646\u062a\u0627\u062c\u0627\u062a \u0625\u062d\u0635\u0627\u0626\u064a\u0629 \u062d\u0648\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0648\u0627\u0633\u062a\u062e\u0644\u0627\u0635 \u0627\u0644\u0646\u062a\u0627\u0626\u062c \u0628\u0645\u0633\u062a\u0648\u0649 \u0645\u0646 \u0627\u0644\u062b\u0642\u0629.<\/li>\n<\/ul>\n<h2>\u0623\u0646\u0648\u0627\u0639 \u0627\u062e\u062a\u0628\u0627\u0631 \u0645\u0631\u0628\u0639 \u0643\u0627\u064a<\/h2>\n<p>\u0647\u0646\u0627\u0643 \u0646\u0648\u0639\u0627\u0646 \u0631\u0626\u064a\u0633\u064a\u0627\u0646 \u0645\u0646 \u0627\u062e\u062a\u0628\u0627\u0631\u0627\u062a \u0645\u0631\u0628\u0639 \u0643\u0627\u064a: \u0627\u062e\u062a\u0628\u0627\u0631 \u0645\u0631\u0628\u0639 \u0643\u0627\u064a \u0628\u064a\u0631\u0633\u0648\u0646 \u0648\u0627\u062e\u062a\u0628\u0627\u0631 \u0646\u0633\u0628\u0629 \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629 \u0644\u0645\u0631\u0628\u0639 \u0643\u0627\u064a. \u0648\u0641\u064a\u0645\u0627 \u064a\u0644\u064a \u0645\u0642\u0627\u0631\u0646\u0629 \u0628\u064a\u0646 \u062e\u0635\u0627\u0626\u0635\u0647\u0627:<\/p>\n<table>\n<thead>\n<tr>\n<th>\u0645\u0639\u0627\u064a\u064a\u0631<\/th>\n<th>\u0627\u062e\u062a\u0628\u0627\u0631 \u0628\u064a\u0631\u0633\u0648\u0646 \u0644\u0645\u0631\u0628\u0639 \u0643\u0627\u064a<\/th>\n<th>\u0627\u062e\u062a\u0628\u0627\u0631 \u0646\u0633\u0628\u0629 \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629 \u0644\u0645\u0631\u0628\u0639 \u0643\u0627\u064a<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u0627\u0644\u0627\u0641\u062a\u0631\u0627\u0636\u0627\u062a<\/td>\n<td>\u064a\u0641\u062a\u0631\u0636 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0637\u0628\u064a\u0639\u064a \u0644\u0644\u0628\u064a\u0627\u0646\u0627\u062a<\/td>\n<td>\u064a\u062c\u0639\u0644 \u0627\u0641\u062a\u0631\u0627\u0636\u0627\u062a \u0623\u0642\u0644 \u062d\u0648\u0644 \u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a<\/td>\n<\/tr>\n<tr>\n<td>\u0645\u0646\u0627\u0633\u0628\u0629 \u0644\u0623\u062d\u062c\u0627\u0645 \u0627\u0644\u0639\u064a\u0646\u0627\u062a \u0627\u0644\u0635\u063a\u064a\u0631\u0629<\/td>\n<td>\u0644\u0627<\/td>\n<td>\u0646\u0639\u0645<\/td>\n<\/tr>\n<tr>\n<td>\u0627\u0633\u062a\u062e\u062f\u0645 \u062d\u0627\u0644\u0627\u062a<\/td>\n<td>\u0623\u062d\u062c\u0627\u0645 \u0627\u0644\u0639\u064a\u0646\u0627\u062a \u0627\u0644\u0643\u0628\u064a\u0631\u0629<\/td>\n<td>\u0623\u062d\u062c\u0627\u0645 \u0627\u0644\u0639\u064a\u0646\u0627\u062a \u0627\u0644\u0635\u063a\u064a\u0631\u0629<\/td>\n<\/tr>\n<tr>\n<td>\u0645\u0639\u0627\u062f\u0644\u0629<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/oneproxy.pro\/images\/pearsons_chi_squared_formula.png\" alt=\"\u0635\u064a\u063a\u0629 \u0628\u064a\u0631\u0633\u0648\u0646 \u0644\u0645\u0631\u0628\u0639 \u0643\u0627\u064a\" title=\"\"><\/td>\n<td><img decoding=\"async\" src=\"https:\/\/oneproxy.pro\/images\/likelihood_ratio_chi_squared_formula.png\" alt=\"\u0635\u064a\u063a\u0629 \u0646\u0633\u0628\u0629 \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629 \u0644\u0645\u0631\u0628\u0639 \u0643\u0627\u064a\" title=\"\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>\u0637\u0631\u0642 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u062e\u062a\u0628\u0627\u0631 \u0643\u0627\u064a \u062a\u0631\u0628\u064a\u0639 \u0648\u0627\u0644\u0645\u0634\u0643\u0644\u0627\u062a \u0648\u062d\u0644\u0648\u0644\u0647\u0627<\/h2>\n<p>\u064a\u062c\u062f \u0627\u062e\u062a\u0628\u0627\u0631 Chi-Squared \u062a\u0637\u0628\u064a\u0642\u0627\u062a \u0641\u064a \u0645\u062c\u0627\u0644\u0627\u062a \u0645\u062e\u062a\u0644\u0641\u0629\u060c \u0628\u0645\u0627 \u0641\u064a \u0630\u0644\u0643:<\/p>\n<ol>\n<li><strong>\u062d\u0633\u0646 \u0627\u0644\u062a\u0644\u0627\u0624\u0645:<\/strong> \u062a\u062d\u062f\u064a\u062f \u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646\u062a \u0627\u0644\u062a\u0631\u062f\u062f\u0627\u062a \u0627\u0644\u0645\u0631\u0635\u0648\u062f\u0629 \u062a\u0646\u0627\u0633\u0628 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0645\u062a\u0648\u0642\u0639.<\/li>\n<li><strong>\u0627\u062e\u062a\u0628\u0627\u0631 \u0627\u0644\u0627\u0633\u062a\u0642\u0644\u0627\u0644:<\/strong> \u062a\u0642\u064a\u064a\u0645 \u0645\u0627 \u0625\u0630\u0627 \u0643\u0627\u0646 \u0647\u0646\u0627\u0643 \u0645\u062a\u063a\u064a\u0631\u064a\u0646 \u0641\u0626\u0648\u064a\u064a\u0646 \u0645\u0631\u062a\u0628\u0637\u064a\u0646.<\/li>\n<li><strong>\u0627\u062e\u062a\u0628\u0627\u0631 \u0627\u0644\u062a\u062c\u0627\u0646\u0633:<\/strong> \u0642\u0627\u0631\u0646 \u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a \u0627\u0644\u0641\u0626\u0648\u064a\u0629 \u0639\u0628\u0631 \u0645\u062c\u0645\u0648\u0639\u0627\u062a \u0645\u062e\u062a\u0644\u0641\u0629.<\/li>\n<\/ol>\n<p>\u062a\u062a\u0636\u0645\u0646 \u0627\u0644\u0645\u0634\u0627\u0643\u0644 \u0627\u0644\u0645\u062d\u062a\u0645\u0644\u0629 \u0641\u064a \u0627\u062e\u062a\u0628\u0627\u0631 Chi-Squared \u0645\u0627 \u064a\u0644\u064a:<\/p>\n<ul>\n<li><strong>\u062d\u062c\u0645 \u0627\u0644\u0639\u064a\u0646\u0629 \u0635\u063a\u064a\u0631:<\/strong> \u0642\u062f \u064a\u0639\u0637\u064a \u0627\u062e\u062a\u0628\u0627\u0631 Chi-Squared \u0646\u062a\u0627\u0626\u062c \u063a\u064a\u0631 \u062f\u0642\u064a\u0642\u0629 \u0645\u0639 \u0623\u062d\u062c\u0627\u0645 \u0639\u064a\u0646\u0627\u062a \u0635\u063a\u064a\u0631\u0629 \u0623\u0648 \u062e\u0644\u0627\u064a\u0627 \u0630\u0627\u062a \u062a\u0631\u062f\u062f\u0627\u062a \u0645\u062a\u0648\u0642\u0639\u0629 \u0623\u0642\u0644 \u0645\u0646 \u062e\u0645\u0633\u0629. \u0641\u064a \u0645\u062b\u0644 \u0647\u0630\u0647 \u0627\u0644\u062d\u0627\u0644\u0627\u062a\u060c \u064a\u0641\u0636\u0644 \u0627\u062e\u062a\u0628\u0627\u0631 \u0646\u0633\u0628\u0629 \u0627\u0644\u0627\u062d\u062a\u0645\u0627\u0644\u064a\u0629 \u0644\u0645\u0631\u0628\u0639 \u0643\u0627\u064a.<\/li>\n<li><strong>\u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u062a\u0631\u062a\u064a\u0628\u064a:<\/strong> \u0627\u062e\u062a\u0628\u0627\u0631 Chi-Squared \u063a\u064a\u0631 \u0645\u0646\u0627\u0633\u0628 \u0644\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u062a\u0631\u062a\u064a\u0628\u064a\u0629\u060c \u0644\u0623\u0646\u0647 \u0644\u0627 \u064a\u0623\u062e\u0630 \u0641\u064a \u0627\u0644\u0627\u0639\u062a\u0628\u0627\u0631 \u062a\u0631\u062a\u064a\u0628 \u0627\u0644\u0641\u0626\u0627\u062a.<\/li>\n<\/ul>\n<p>\u0648\u0644\u0645\u0639\u0627\u0644\u062c\u0629 \u0647\u0630\u0647 \u0627\u0644\u0645\u0634\u0643\u0644\u0627\u062a\u060c \u064a\u0645\u0643\u0646 \u0644\u0644\u0628\u0627\u062d\u062b\u064a\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u062e\u062a\u0628\u0627\u0631\u0627\u062a \u0628\u062f\u064a\u0644\u0629 \u0645\u062b\u0644 \u0627\u062e\u062a\u0628\u0627\u0631 \u0641\u064a\u0634\u0631 \u0627\u0644\u062f\u0642\u064a\u0642 \u0644\u0623\u062d\u062c\u0627\u0645 \u0627\u0644\u0639\u064a\u0646\u0627\u062a \u0627\u0644\u0635\u063a\u064a\u0631\u0629 \u0623\u0648 \u0627\u0644\u0627\u062e\u062a\u0628\u0627\u0631\u0627\u062a \u063a\u064a\u0631 \u0627\u0644\u0645\u0639\u0644\u0645\u064a\u0629 \u0627\u0644\u0623\u062e\u0631\u0649 \u0644\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u062a\u0631\u062a\u064a\u0628\u064a\u0629.<\/p>\n<h2>\u0627\u0644\u062e\u0635\u0627\u0626\u0635 \u0627\u0644\u0631\u0626\u064a\u0633\u064a\u0629 \u0648\u0627\u0644\u0645\u0642\u0627\u0631\u0646\u0627\u062a \u0645\u0639 \u0627\u0644\u0645\u0635\u0637\u0644\u062d\u0627\u062a \u0627\u0644\u0645\u0645\u0627\u062b\u0644\u0629<\/h2>\n<p>\u064a\u062a\u0634\u0627\u0628\u0647 \u0627\u062e\u062a\u0628\u0627\u0631 Chi-Squared \u0645\u0639 \u0627\u0644\u0627\u062e\u062a\u0628\u0627\u0631\u0627\u062a \u0627\u0644\u0625\u062d\u0635\u0627\u0626\u064a\u0629 \u0627\u0644\u0623\u062e\u0631\u0649\u060c \u0648\u0644\u0643\u0646\u0647 \u064a\u0645\u062a\u0644\u0643 \u0623\u064a\u0636\u064b\u0627 \u062e\u0635\u0627\u0626\u0635 \u0641\u0631\u064a\u062f\u0629 \u062a\u0645\u064a\u0632\u0647:<\/p>\n<table>\n<thead>\n<tr>\n<th>\u0635\u0641\u0629 \u0645\u0645\u064a\u0632\u0629<\/th>\n<th>\u0627\u062e\u062a\u0628\u0627\u0631 \u0645\u0631\u0628\u0639 \u0643\u0627\u064a<\/th>\n<th>\u0627\u062e\u062a\u0628\u0627\u0631 T<\/th>\n<th>\u0623\u0646\u0648\u0641\u0627<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u0646\u0648\u0639 \u0627\u0644\u0627\u062e\u062a\u0628\u0627\u0631<\/td>\n<td>\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0641\u0626\u0648\u064a\u0629<\/td>\n<td>\u0645\u0642\u0627\u0631\u0646\u0629 \u0627\u0644\u0648\u0633\u0627\u0626\u0644<\/td>\n<td>\u0645\u0642\u0627\u0631\u0646\u0629 \u0627\u0644\u0648\u0633\u0627\u0626\u0644<\/td>\n<\/tr>\n<tr>\n<td>\u0639\u062f\u062f \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a<\/td>\n<td>2 \u0623\u0648 \u0623\u0643\u062b\u0631<\/td>\n<td>2<\/td>\n<td>3 \u0623\u0648 \u0623\u0643\u062b\u0631<\/td>\n<\/tr>\n<tr>\n<td>\u0646\u0648\u0639 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a<\/td>\n<td>\u0642\u0627\u0637\u0639<\/td>\n<td>\u0645\u0633\u062a\u0645\u0631<\/td>\n<td>\u0645\u0633\u062a\u0645\u0631<\/td>\n<\/tr>\n<tr>\n<td>\u0627\u0644\u0627\u0641\u062a\u0631\u0627\u0636\u0627\u062a<\/td>\n<td>\u063a\u064a\u0631 \u0645\u0639\u0644\u0645\u064a\u0629<\/td>\n<td>\u064a\u0641\u062a\u0631\u0636 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0637\u0628\u064a\u0639\u064a<\/td>\n<td>\u064a\u0641\u062a\u0631\u0636 \u0627\u0644\u062a\u0648\u0632\u064a\u0639 \u0627\u0644\u0637\u0628\u064a\u0639\u064a<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>\u0648\u062c\u0647\u0627\u062a \u0646\u0638\u0631 \u0648\u062a\u0642\u0646\u064a\u0627\u062a \u0627\u0644\u0645\u0633\u062a\u0642\u0628\u0644 \u0627\u0644\u0645\u062a\u0639\u0644\u0642\u0629 \u0628\u0627\u062e\u062a\u0628\u0627\u0631 \u0643\u0627\u064a \u062a\u0631\u0628\u064a\u0639<\/h2>\n<p>\u0645\u0639 \u0627\u0633\u062a\u0645\u0631\u0627\u0631 \u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0641\u064a \u0644\u0639\u0628 \u062f\u0648\u0631 \u062d\u0627\u0633\u0645 \u0641\u064a \u0645\u062e\u062a\u0644\u0641 \u0627\u0644\u0635\u0646\u0627\u0639\u0627\u062a\u060c \u0633\u064a\u0638\u0644 \u0627\u062e\u062a\u0628\u0627\u0631 Chi-Squared \u0623\u062f\u0627\u0629 \u0623\u0633\u0627\u0633\u064a\u0629 \u0644\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0641\u0626\u0648\u064a\u0629. \u0648\u0645\u0639 \u0630\u0644\u0643\u060c \u0641\u0625\u0646 \u0627\u0644\u062a\u0642\u062f\u0645 \u0641\u064a \u0627\u0644\u0645\u0646\u0647\u062c\u064a\u0627\u062a \u0648\u0627\u0644\u062a\u0642\u0646\u064a\u0627\u062a \u0627\u0644\u0625\u062d\u0635\u0627\u0626\u064a\u0629 \u0642\u062f \u064a\u0624\u062f\u064a \u0625\u0644\u0649 \u0625\u0635\u062f\u0627\u0631\u0627\u062a \u0623\u0648 \u0627\u0645\u062a\u062f\u0627\u062f\u0627\u062a \u0645\u062d\u0633\u0646\u0629 \u0644\u0627\u062e\u062a\u0628\u0627\u0631 Chi-Squared\u060c \u0648\u0645\u0639\u0627\u0644\u062c\u0629 \u062d\u062f\u0648\u062f\u0647 \u0648\u062c\u0639\u0644\u0647 \u0623\u0643\u062b\u0631 \u062a\u0646\u0648\u0639\u064b\u0627 \u0648\u0642\u0648\u0629.<\/p>\n<h2>\u0643\u064a\u0641 \u064a\u0645\u0643\u0646 \u0627\u0633\u062a\u062e\u062f\u0627\u0645 \u0627\u0644\u062e\u0648\u0627\u062f\u0645 \u0627\u0644\u0648\u0643\u064a\u0644\u0629 \u0623\u0648 \u0631\u0628\u0637\u0647\u0627 \u0628\u0627\u062e\u062a\u0628\u0627\u0631 Chi-Squared<\/h2>\n<p>\u064a\u0645\u0643\u0646 \u0644\u0644\u062e\u0648\u0627\u062f\u0645 \u0627\u0644\u0648\u0643\u064a\u0644\u0629 \u0627\u0644\u062a\u064a \u064a\u0642\u062f\u0645\u0647\u0627 \u0645\u0642\u062f\u0645\u0648 \u0627\u0644\u062e\u062f\u0645\u0629 \u0645\u062b\u0644 OneProxy \u062a\u0633\u0647\u064a\u0644 \u062c\u0645\u0639 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0648\u062a\u062d\u0644\u064a\u0644\u0647\u0627 \u0644\u0625\u062c\u0631\u0627\u0621 \u0627\u062e\u062a\u0628\u0627\u0631\u0627\u062a Chi-Squared. \u0641\u0647\u064a \u062a\u0645\u0643\u0646 \u0627\u0644\u0645\u0633\u062a\u062e\u062f\u0645\u064a\u0646 \u0645\u0646 \u0627\u0644\u0648\u0635\u0648\u0644 \u0625\u0644\u0649 \u0645\u0648\u0627\u0642\u0639 \u062c\u063a\u0631\u0627\u0641\u064a\u0629 \u0645\u062e\u062a\u0644\u0641\u0629\u060c \u0648\u0647\u0648 \u0623\u0645\u0631 \u0645\u0641\u064a\u062f \u0628\u0634\u0643\u0644 \u062e\u0627\u0635 \u0639\u0646\u062f \u0627\u0644\u062a\u0639\u0627\u0645\u0644 \u0645\u0639 \u0645\u062c\u0645\u0648\u0639\u0627\u062a \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0630\u0627\u062a \u0627\u0644\u0627\u062e\u062a\u0644\u0627\u0641\u0627\u062a \u0627\u0644\u0625\u0642\u0644\u064a\u0645\u064a\u0629. \u062a\u0636\u0645\u0646 \u0627\u0644\u062e\u0648\u0627\u062f\u0645 \u0627\u0644\u0648\u0643\u064a\u0644\u0629 \u0623\u064a\u0636\u064b\u0627 \u0625\u062e\u0641\u0627\u0621 \u0627\u0644\u0647\u0648\u064a\u0629\u060c \u0645\u0645\u0627 \u064a\u062c\u0639\u0644\u0647\u0627 \u0630\u0627\u062a \u0642\u064a\u0645\u0629 \u0644\u0645\u0647\u0627\u0645 \u0627\u0633\u062a\u062e\u0631\u0627\u062c \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0639\u0644\u0649 \u0627\u0644\u0648\u064a\u0628 \u0648\u062c\u0645\u0639 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a\u060c \u0643\u0644 \u0630\u0644\u0643 \u0645\u0639 \u0645\u0633\u0627\u0639\u062f\u0629 \u0627\u0644\u0628\u0627\u062d\u062b\u064a\u0646 \u0641\u064a \u0627\u0644\u062d\u0641\u0627\u0638 \u0639\u0644\u0649 \u062e\u0635\u0648\u0635\u064a\u0629 \u0648\u0623\u0645\u0627\u0646 \u062a\u062d\u0644\u064a\u0644\u0627\u062a\u0647\u0645.<\/p>\n<h2>\u0631\u0648\u0627\u0628\u0637 \u0630\u0627\u062a \u0639\u0644\u0627\u0642\u0629<\/h2>\n<p>\u0644\u0645\u0632\u064a\u062f \u0645\u0646 \u0627\u0644\u0645\u0639\u0644\u0648\u0645\u0627\u062a \u062d\u0648\u0644 \u0627\u062e\u062a\u0628\u0627\u0631 \u0643\u0627\u064a \u062a\u0631\u0628\u064a\u0639\u060c \u064a\u0645\u0643\u0646\u0643 \u0627\u0633\u062a\u0643\u0634\u0627\u0641 \u0627\u0644\u0645\u0648\u0627\u0631\u062f \u0627\u0644\u062a\u0627\u0644\u064a\u0629:<\/p>\n<ol>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Chi-squared_test\" target=\"_new\" rel=\"noopener nofollow\">\u0648\u064a\u0643\u064a\u0628\u064a\u062f\u064a\u0627 \u2013 \u0627\u062e\u062a\u0628\u0627\u0631 \u0643\u0627\u064a \u062a\u0631\u0628\u064a\u0639<\/a><\/li>\n<li><a href=\"https:\/\/www.statisticssolutions.com\/non-parametric-analysis-chi-square\/\" target=\"_new\" rel=\"noopener nofollow\">\u0627\u0644\u062d\u0644\u0648\u0644 \u0627\u0644\u0625\u062d\u0635\u0627\u0626\u064a\u0629 \u2013 \u0627\u062e\u062a\u0628\u0627\u0631 \u0643\u0627\u064a \u0633\u0643\u0648\u064a\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\">\u0645\u0646\u0634\u0648\u0631 GraphPad \u2013 \u0627\u062e\u062a\u0628\u0627\u0631 \u0645\u0631\u0628\u0639 \u0643\u0627\u064a<\/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 \u2013 \u0627\u062e\u062a\u0628\u0627\u0631 \u0645\u0631\u0628\u0639 \u0643\u0627\u064a<\/a><\/li>\n<\/ol>\n<p>\u0641\u064a \u0627\u0644\u062e\u062a\u0627\u0645\u060c \u064a\u0639\u062f \u0627\u062e\u062a\u0628\u0627\u0631 Chi-Squared \u0637\u0631\u064a\u0642\u0629 \u0625\u062d\u0635\u0627\u0626\u064a\u0629 \u0642\u0648\u064a\u0629 \u0644\u062a\u062d\u0644\u064a\u0644 \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0641\u0626\u0648\u064a\u0629 \u0648\u062a\u062d\u062f\u064a\u062f \u0627\u0644\u0627\u0631\u062a\u0628\u0627\u0637\u0627\u062a \u0628\u064a\u0646 \u0627\u0644\u0645\u062a\u063a\u064a\u0631\u0627\u062a. \u0625\u0646 \u062a\u0639\u062f\u062f \u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0627\u062a\u0647 \u0648\u0633\u0647\u0648\u0644\u0629 \u0627\u0633\u062a\u062e\u062f\u0627\u0645\u0647 \u0648\u062a\u0637\u0628\u064a\u0642\u0627\u062a\u0647 \u0641\u064a \u0645\u062e\u062a\u0644\u0641 \u0627\u0644\u0645\u062c\u0627\u0644\u0627\u062a \u064a\u062c\u0639\u0644\u0647 \u0623\u062f\u0627\u0629 \u0623\u0633\u0627\u0633\u064a\u0629 \u0644\u0644\u0628\u0627\u062d\u062b\u064a\u0646 \u0648\u0645\u062d\u0644\u0644\u064a \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0639\u0644\u0649 \u062d\u062f\u064d \u0633\u0648\u0627\u0621. \u0645\u0639 \u062a\u0642\u062f\u0645 \u0627\u0644\u062a\u0643\u0646\u0648\u0644\u0648\u062c\u064a\u0627\u060c \u0645\u0646 \u0627\u0644\u0645\u0631\u062c\u062d \u0623\u0646 \u064a\u0633\u062a\u0645\u0631 \u0627\u062e\u062a\u0628\u0627\u0631 Chi-Squared \u0641\u064a \u0627\u0644\u062a\u0637\u0648\u0631\u060c \u0645\u0639 \u0627\u0633\u062a\u0643\u0645\u0627\u0644\u0647 \u0628\u0645\u0646\u0647\u062c\u064a\u0627\u062a \u0648\u0623\u062f\u0648\u0627\u062a \u0645\u0628\u062a\u0643\u0631\u0629\u060c \u0645\u0645\u0627 \u064a\u0648\u0641\u0631 \u0631\u0624\u0649 \u0623\u0639\u0645\u0642 \u062d\u0648\u0644 \u0639\u0644\u0627\u0642\u0627\u062a \u0627\u0644\u0628\u064a\u0627\u0646\u0627\u062a \u0627\u0644\u0641\u0626\u0648\u064a\u0629.<\/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\/ar\/wp-json\/wp\/v2\/wiki\/476219","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/oneproxy.pro\/ar\/wp-json\/wp\/v2\/wiki"}],"about":[{"href":"https:\/\/oneproxy.pro\/ar\/wp-json\/wp\/v2\/types\/wiki"}],"version-history":[{"count":0,"href":"https:\/\/oneproxy.pro\/ar\/wp-json\/wp\/v2\/wiki\/476219\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/oneproxy.pro\/ar\/wp-json\/wp\/v2\/media\/497617"}],"wp:attachment":[{"href":"https:\/\/oneproxy.pro\/ar\/wp-json\/wp\/v2\/media?parent=476219"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}