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\u0627\u0633\u0627\u0626\u0646\u0645\u0646\u0679 \u0648\u06c1 \u0627\u0646\u062c\u0646 \u06c1\u06d2 \u062c\u0648 A\/B \u0679\u06cc\u0633\u0679\u0646\u06af \u06a9\u0648 \u0627\u06cc\u06a9 \u062f\u0631\u0633\u062a \u06a9\u0627\u0632\u0644 \u0637\u0631\u06cc\u0642\u06c1 \u0628\u0646\u0627\u062a\u0627 \u06c1\u06d2\u06d4 \u0627\u06af\u0631 \u0622\u067e \u06cc\u06c1 \u0641\u06cc\u0635\u0644\u06c1 \u06a9\u0631\u0646\u06d2 \u06a9\u06d2 \u0644\u06cc\u06d2 \u0627\u06cc\u06a9 \u0633\u06a9\u06d2 \u06a9\u0648 \u067e\u0644\u0679\u062a\u06d2 \u06c1\u06cc\u06ba \u06a9\u06c1 \u06a9\u0646 \u0635\u0627\u0631\u0641\u06cc\u0646 \u06a9\u0648 \u062e\u0635\u0648\u0635\u06cc\u062a \u0645\u0644\u06d2 \u06af\u06cc\u060c \u062a\u0648 \u0639\u0644\u0627\u062c \u0627\u0648\u0631 \u06a9\u0646\u0679\u0631\u0648\u0644 \u06af\u0631\u0648\u067e\u0633 \u062a\u0645\u0627\u0645 \u0635\u0627\u0631\u0641\u06cc\u0646 \u06a9\u06cc \u06cc\u06a9\u0633\u0627\u06ba \u062a\u0642\u0633\u06cc\u0645 \u06a9\u06d2 \u0633\u0627\u062a\u06be \u062e\u062a\u0645 \u06c1\u0648\u062a\u06d2 \u06c1\u06cc\u06ba\u06d4 <strong>\u0627\u0644\u062c\u06be\u0627 \u06c1\u0648\u0627 \u0634\u062e\u0635<\/strong> (\u06a9\u0648\u0626\u06cc \u0628\u06be\u06cc \u0645\u062a\u063a\u06cc\u0631 \u062c\u0648 \u0639\u0644\u0627\u062c \u062d\u0627\u0635\u0644 \u06a9\u0631\u0646\u06d2 \u0648\u0627\u0644\u06d2 \u0627\u0648\u0631 \u0646\u0627\u067e\u06d2 \u062c\u0627\u0646\u06d2 \u0648\u0627\u0644\u06d2 \u0646\u062a\u0627\u0626\u062c \u062f\u0648\u0646\u0648\u06ba \u067e\u0631 \u0627\u062b\u0631 \u0627\u0646\u062f\u0627\u0632 \u06c1\u0648\u062a\u0627 \u06c1\u06d2) \u062a\u0641\u0648\u06cc\u0636 \u06a9\u06d2 \u0628\u0639\u062f \u0646\u062a\u0627\u0626\u062c \u0645\u06cc\u06ba \u0641\u0631\u0642 \u0639\u0644\u0627\u062c \u06a9\u0627 \u0633\u0628\u0628 \u0627\u062b\u0631 \u06c1\u06d2\u06d4 \u0645\u06a9\u0645\u0644 \u0633\u0679\u0627\u067e<\/p>\n<p>\u0627\u0646\u0679\u0631\u067e\u0631\u0627\u0626\u0632 \u0648\u0631\u06a9 \u0627\u0633\u067e\u06cc\u0633 \u0645\u06cc\u06ba \u0627\u06cc\u06a9 \u0645\u0631\u062d\u0644\u06c1 \u0648\u0627\u0631 \u0631\u0648\u0644 \u0622\u0624\u0679 \u0627\u0633 \u0627\u0646\u062c\u0646 \u06a9\u0648 \u062a\u06cc\u0646 \u0637\u0631\u06cc\u0642\u0648\u06ba \u0633\u06d2 \u062a\u0648\u0691\u062a\u0627 \u06c1\u06d2:<\/p>\n<h4 id=\"heading-1-the-wave-assignment-isnt-random\">1. \u0644\u06c1\u0631 \u06a9\u06cc \u062a\u0642\u0633\u06cc\u0645 \u0628\u06d2 \u062a\u0631\u062a\u06cc\u0628 \u0646\u06c1\u06cc\u06ba \u06c1\u06d2\u06d4<\/h4>\n<p>\u067e\u0631\u0648\u0688\u06a9\u0679 \u0679\u06cc\u0645\u06cc\u06ba \u0645\u062e\u062a\u0644\u0641 \u0648\u062c\u0648\u06c1\u0627\u062a \u06a9\u06cc \u0628\u0646\u0627 \u067e\u0631 Wave 1 \u0648\u0631\u06a9 \u0627\u0633\u067e\u06cc\u0633 \u06a9\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u06a9\u0631\u062a\u06cc \u06c1\u06cc\u06ba\u06d4 \u0627\u0633 \u06a9\u0627 \u0645\u0637\u0644\u0628 \u06c1\u06d2 \u0633\u0628 \u0633\u06d2 \u0632\u06cc\u0627\u062f\u06c1 \u0645\u0635\u0631\u0648\u0641 \u0645\u06cc\u0646\u06cc\u062c\u0631\u0632\u060c \u0633\u0628 \u0633\u06d2 \u0632\u06cc\u0627\u062f\u06c1 \u0646\u0634\u0633\u062a\u06cc\u06ba\u060c \u06a9\u0633\u0679\u0645\u0631 \u06a9\u06cc \u06a9\u0627\u0645\u06cc\u0627\u0628\u06cc \u06a9\u06d2 \u0633\u0627\u062a\u06be \u0628\u06c1\u062a\u0631\u06cc\u0646 \u062a\u0639\u0644\u0642\u0627\u062a\u060c \u0627\u0648\u0631 \u0628\u06c1\u062a \u06a9\u0686\u06be\u06d4 \u0627\u0646 \u0648\u062c\u0648\u06c1\u0627\u062a \u06a9\u0627 \u0628\u0631\u0627\u06c1 \u0631\u0627\u0633\u062a \u062a\u0639\u0644\u0642 \u0646\u062a\u0627\u0626\u062c \u0633\u06d2 \u06c1\u06d2\u06d4 Wave 1 \u0648\u0631\u06a9 \u0627\u0633\u067e\u06cc\u0633\u0632 \u0632\u06cc\u0627\u062f\u06c1 \u0645\u0635\u0631\u0648\u0641\u06cc\u062a \u062f\u06cc\u06a9\u06be\u06cc\u06ba \u06af\u06d2\u060c \u0642\u0637\u0639 \u0646\u0638\u0631 \u0627\u0633 \u06a9\u06d2 \u06a9\u06c1 \u0627\u0646 \u0645\u06cc\u06ba \u062e\u0635\u0648\u0635\u06cc\u0627\u062a \u06c1\u06cc\u06ba \u06cc\u0627 \u0646\u06c1\u06cc\u06ba\u06d4<\/p>\n<h4 id=\"heading-2-the-calendar-introduces-a-time-trend\">2. \u06a9\u06cc\u0644\u0646\u0688\u0631 \u0648\u0642\u062a \u06a9\u06d2 \u0631\u062c\u062d\u0627\u0646\u0627\u062a \u06a9\u0648 \u0645\u062a\u0639\u0627\u0631\u0641 \u06a9\u0631\u0627\u062a\u0627 \u06c1\u06d2\u06d4<\/h4>\n<p>\u06c1\u0641\u062a\u06c1 20 (\u067e\u06c1\u0644\u06cc \u0644\u0627\u0646\u0686) \u0627\u0648\u0631 \u06c1\u0641\u062a\u06c1 30 (\u062f\u0648\u0633\u0631\u06cc \u0644\u0627\u0646\u0686) \u06a9\u06d2 \u062f\u0631\u0645\u06cc\u0627\u0646\u060c \u0622\u067e \u06a9\u0627 \u067e\u0631\u0648\u0688\u06a9\u0679 \u0628\u06c1\u062a\u0631 \u06c1\u0648 \u062c\u0627\u062a\u0627 \u06c1\u06d2\u060c \u0622\u0646 \u0628\u0648\u0631\u0688\u0646\u06af \u0628\u06c1\u062a\u0631 \u06c1\u0648\u062a\u06cc \u06c1\u06d2\u060c \u0627\u0648\u0631 \u0622\u067e \u06a9\u06cc \u0633\u06cc\u0644\u0632 \u0679\u06cc\u0645 \u0632\u06cc\u0627\u062f\u06c1 \u0633\u06d2 \u0632\u06cc\u0627\u062f\u06c1 \u0635\u0627\u0631\u0641\u06cc\u0646 \u06a9\u0648 \u0631\u0627\u063a\u0628 \u06a9\u0631\u062a\u06cc \u06c1\u06d2\u06d4 \u0627\u06cc\u06a9 \u0633\u0627\u062f\u06c1 &quot;20 \u06c1\u0641\u062a\u0648\u06ba \u06a9\u06d2 \u0628\u0639\u062f \u0645\u0634\u063a\u0648\u0644\u06cc\u062a \u0645\u0627\u0626\u0646\u0633 20 \u06c1\u0641\u062a\u0648\u06ba \u0633\u06d2 \u067e\u06c1\u0644\u06d2 \u0634\u0631\u06a9\u062a&#8221; \u06a9\u0627 \u0645\u0648\u0627\u0632\u0646\u06c1 \u0641\u06cc\u0686\u0631 \u06a9\u06d2 \u0627\u062b\u0631 \u06a9\u06d2 \u0633\u0627\u062a\u06be \u0633\u0627\u062a\u06be \u06c1\u0631 \u0686\u06cc\u0632 \u06a9\u0648 \u0627\u067e\u0646\u06cc \u06af\u0631\u0641\u062a \u0645\u06cc\u06ba \u0644\u06d2 \u0644\u06cc\u062a\u0627 \u06c1\u06d2\u06d4<\/p>\n<h4 id=\"heading-3-adoption-inside-treated-workspaces-is-itself-selective\">3. \u067e\u0631\u0648\u0633\u06cc\u0633 \u0634\u062f\u06c1 \u0648\u0631\u06a9 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\u062a\u06be\u06d2\u06d4<\/p>\n<p>A\/B \u0679\u06cc\u0633\u0679\u0646\u06af \u0645\u0627\u0646\u062a\u06cc \u06c1\u06d2 \u06a9\u06c1 \u0627\u0646 \u062a\u06cc\u0646\u0648\u06ba \u0645\u06cc\u06ba \u0633\u06d2 \u06a9\u0648\u0626\u06cc \u0628\u06be\u06cc \u0645\u0633\u0626\u0644\u06c1 \u0645\u0648\u062c\u0648\u062f \u0646\u06c1\u06cc\u06ba \u06c1\u06d2\u06d4 \u0645\u0631\u062d\u0644\u06c1 \u0648\u0627\u0631 \u0631\u0648\u0644 \u0622\u0624\u0679 \u062a\u06cc\u0646\u0648\u06ba \u06a9\u0648 \u06cc\u0642\u06cc\u0646\u06cc \u0628\u0646\u0627\u062a\u0627 \u06c1\u06d2\u06d4 \u0633\u0627\u062f\u06c1 \u0645\u0648\u0627\u0632\u0646\u06c1 \u0646\u0645\u0628\u0631 \u0641\u0631\u0627\u06c1\u0645 \u06a9\u0631\u062a\u0627 \u06c1\u06d2\u060c \u0627\u0648\u0631 \u0648\u06c1 \u0646\u0645\u0628\u0631 \u0634\u0631\u06cc\u06a9 \u062a\u06be\u06cc\u0626\u0679\u0631\u0632 \u06a9\u06cc \u067e\u06cc\u0645\u0627\u0626\u0634 \u06a9\u0631\u062a\u06d2 \u06c1\u06cc\u06ba\u06d4<\/p>\n<h2 id=\"heading-what-difference-in-differences-does\">\u0641\u0631\u0642 \u0645\u06cc\u06ba \u0641\u0631\u0642 \u06a9\u06cc\u0627 \u06c1\u0648\u062a\u0627 \u06c1\u06d2\u06d4<\/h2>\n<p>\u06a9\u06d2 \u062f\u0631\u0645\u06cc\u0627\u0646 \u0627\u062e\u062a\u0644\u0627\u0641\u0627\u062a \u06a9\u0627 \u0645\u0648\u0627\u0632\u0646\u06c1 \u06a9\u0631\u06cc\u06ba: <em>\u062a\u0628\u062f\u06cc\u0644\u06cc<\/em> \u0639\u0644\u0627\u062c \u0627\u0648\u0631 \u06a9\u0646\u0679\u0631\u0648\u0644 \u06af\u0631\u0648\u067e\u0648\u06ba \u06a9\u06d2 \u062f\u0631\u0645\u06cc\u0627\u0646 \u0648\u0642\u062a \u06a9\u06d2 \u0633\u0627\u062a\u06be \u0646\u062a\u0627\u0626\u062c\u06d4 \u0627\u06cc\u06a9 \u062a\u0628\u062f\u06cc\u0644\u06cc \u06a9\u0648 \u062f\u0648\u0633\u0631\u06d2 \u0633\u06d2 \u06af\u06be\u0679\u0627\u0646\u06d2 \u0633\u06d2 \u0645\u0634\u062a\u0631\u06a9\u06c1 \u0648\u0642\u062a \u06a9\u06d2 \u0631\u062c\u062d\u0627\u0646\u0627\u062a (\u0645\u0635\u0646\u0648\u0639\u0627\u062a \u0645\u06cc\u06ba \u0628\u06c1\u062a\u0631\u06cc\u060c \u0645\u0648\u0633\u0645\u06cc\u060c \u0622\u0646 \u0628\u0648\u0631\u0688\u0646\u06af \u062a\u0628\u062f\u06cc\u0644\u06cc\u0627\u06ba) \u0645\u0646\u0633\u0648\u062e \u06c1\u0648 \u062c\u0627\u062a\u06d2 \u06c1\u06cc\u06ba\u06d4 \u062f\u0648\u0646\u0648\u06ba \u06af\u0631\u0648\u06c1\u0648\u06ba \u06a9\u0627 \u0627\u06cc\u06a9 \u06c1\u06cc \u062a\u062c\u0631\u0628\u06c1 \u06c1\u06d2\u060c \u0644\u06c1\u0630\u0627 \u0635\u0631\u0641 \u0639\u0644\u0627\u062c \u06a9\u0627 \u0627\u062b\u0631 \u0628\u0627\u0642\u06cc \u0631\u06c1\u062a\u0627 \u06c1\u06d2\u06d4<\/p>\n<p>\u06cc\u06c1\u0627\u06ba \u0627\u06cc\u06a9 \u0679\u06be\u0648\u0633 \u0645\u062b\u0627\u0644 \u06c1\u06d2: \u062f\u0648 \u0645\u062d\u0644\u0648\u06ba \u0645\u06cc\u06ba \u06a9\u0627\u0641\u06cc \u0634\u0627\u067e\u0633 \u06a9\u06cc \u0633\u06c1 \u0645\u0627\u06c1\u06cc \u0622\u0645\u062f\u0646\u06cc \u06a9\u0648 \u0679\u0631\u06cc\u06a9 \u06a9\u0631\u0646\u06d2 \u06a9\u0627 \u062a\u0635\u0648\u0631 \u06a9\u0631\u06cc\u06ba\u06d4 \u0627\u06cc\u06a9 \u0645\u062d\u0644\u06d2 \u06a9\u0648 \u062a\u06cc\u0633\u0631\u06cc \u0633\u06c1 \u0645\u0627\u06c1\u06cc \u0645\u06cc\u06ba \u0627\u06cc\u06a9 \u0646\u06cc\u0627 \u0645\u062f\u0645\u0642\u0627\u0628\u0644 \u0645\u0644\u062a\u0627 \u06c1\u06d2\u060c \u0644\u06cc\u06a9\u0646 \u062f\u0648\u0633\u0631\u06d2 \u0645\u062d\u0644\u06d2 \u06a9\u0648 \u0646\u06c1\u06cc\u06ba \u0645\u0644\u062a\u0627\u06d4<\/p>\n<p>\u062f\u0648\u0646\u0648\u06ba \u062e\u0637\u0648\u06ba \u0645\u06cc\u06ba \u0645\u0627\u0631\u06a9\u06cc\u0679 \u06a9\u06d2 \u06cc\u06a9\u0633\u0627\u06ba \u0628\u0646\u06cc\u0627\u062f\u06cc \u0631\u062c\u062d\u0627\u0646\u0627\u062a\u060c \u0645\u0642\u0627\u0645\u06cc \u0627\u0642\u062a\u0635\u0627\u062f\u06cc \u062a\u06cc\u0632\u06cc \u0627\u0648\u0631 \u0686\u06be\u0679\u06cc\u0648\u06ba \u06a9\u06d2 \u0645\u0648\u0633\u0645 \u06a9\u0627 \u062a\u062c\u0631\u0628\u06c1 \u06c1\u0648\u062a\u0627 \u06c1\u06d2\u06d4 DiD \u062f\u0648\u0646\u0648\u06ba \u062e\u0637\u0648\u06ba \u0633\u06d2 \u0622\u0645\u062f\u0646\u06cc \u0645\u06cc\u06ba \u062a\u0628\u062f\u06cc\u0644\u06cc \u06a9\u0648 \u06af\u06be\u0679\u0627 \u06a9\u0631 \u062d\u0631\u06cc\u0641\u0648\u06ba \u06a9\u06d2 \u0627\u062b\u0631\u0627\u062a \u06a9\u0648 \u0627\u0644\u06af \u06a9\u0631\u062a\u0627 \u06c1\u06d2\u06d4<\/p>\n<p>\u0627\u06cc\u06a9 \u0645\u0631\u062d\u0644\u06c1 \u0648\u0627\u0631 \u0631\u0648\u0644 \u0622\u0624\u0679 \u0628\u0627\u0644\u06a9\u0644 \u0648\u06c1\u06cc \u0688\u06be\u0627\u0646\u0686\u06c1 \u062a\u0631\u062a\u06cc\u0628 \u062f\u06cc\u062a\u0627 \u06c1\u06d2\u06d4 Wave 1 \u0648\u0631\u06a9 \u0627\u0633\u067e\u06cc\u0633 \u0627\u06cc\u06a9 \u067e\u0691\u0648\u0633 \u06c1\u06d2 \u062c\u0633 \u0645\u06cc\u06ba \u0646\u0626\u06d2 \u062f\u0627\u062e\u0644\u06d2 \u06c1\u06cc\u06ba \u0627\u0648\u0631 Wave 2 \u0627\u06cc\u06a9 \u0645\u0648\u0627\u0632\u0646\u06c1 \u06c1\u06d2\u06d4<\/p>\n<p>\u0631\u06cc\u0627\u0636\u06cc \u0627\u0633\u06d2 2&#215;2 \u0679\u06cc\u0628\u0644 \u06a9\u06d2 \u0637\u0648\u0631 \u067e\u0631 \u0628\u0627\u0636\u0627\u0628\u0637\u06c1 \u0628\u0646\u0627\u062a\u0627 \u06c1\u06d2\u06d4 \u06cc\u06c1\u0627\u06ba\u060c \u0642\u0637\u0627\u0631\u06cc\u06ba \u06af\u0631\u0648\u067e\u0633 \u06c1\u06cc\u06ba (\u0639\u0644\u0627\u062c\u060c \u06a9\u0646\u0679\u0631\u0648\u0644)\u060c \u06a9\u0627\u0644\u0645 \u067e\u06cc\u0631\u06cc\u0688\u0632 \u06c1\u06cc\u06ba (\u067e\u0631\u06cc\u060c \u067e\u0648\u0633\u0679)\u060c \u0627\u0648\u0631 \u06c1\u0631 \u0633\u06cc\u0644 \u0627\u0633 \u06af\u0631\u0648\u067e \u06a9\u06d2 \u0644\u06cc\u06d2 \u0627\u0633 \u0645\u062f\u062a \u06a9\u06d2 \u0644\u06cc\u06d2 \u0627\u0648\u0633\u0637 \u0646\u062a\u06cc\u062c\u06c1 \u0631\u06a9\u06be\u062a\u0627 \u06c1\u06d2\u06d4<\/p>\n<ul>\n<li>\n<p><strong>\u06a9\u0648\u0626\u06cc \u0631\u0627\u0633\u062a\u06c1 \u0646\u06c1\u06cc\u06ba<\/strong> = \u0648\u06cc\u0648 1 \u06a9\u06d2 \u0635\u0627\u0631\u0641\u06cc\u0646 \u06a9\u06d2 \u0630\u0631\u06cc\u0639\u06c1 \u0645\u06a9\u0645\u0644 \u06a9\u06cc\u0627 \u06af\u06cc\u0627 \u0627\u0648\u0633\u0637 \u06a9\u0627\u0645 <em>\u067e\u06c1\u0644\u06d2<\/em> \u06c1\u0641\u062a\u06c1 20 (\u06a9\u0627\u0641\u06cc \u0634\u0627\u067e: \u062f\u0648\u0633\u0631\u06cc \u0633\u06c1 \u0645\u0627\u06c1\u06cc \u06a9\u06cc \u0641\u0631\u0648\u062e\u062a\u060c \u062d\u0631\u06cc\u0641 \u0648\u0627\u0644\u06d2 \u0639\u0644\u0627\u0642\u06d2)<\/p>\n<\/li>\n<li>\n<p><strong>\u0628\u0627\u0631\u0634<\/strong> = \u0648\u06cc\u0648 1 \u06a9\u06d2 \u0635\u0627\u0631\u0641\u06cc\u0646 \u06a9\u06d2 \u0630\u0631\u06cc\u0639\u06c1 \u0645\u06a9\u0645\u0644 \u06a9\u06cc\u0627 \u06af\u06cc\u0627 \u0627\u0648\u0633\u0637 \u06a9\u0627\u0645 <em>~ \u0628\u0639\u062f<\/em> \u06c1\u0641\u062a\u06c1 20 (\u06a9\u0627\u0641\u06cc \u0634\u0627\u067e: \u062a\u06cc\u0633\u0631\u06cc \u0633\u06c1 \u0645\u0627\u06c1\u06cc \u06a9\u06cc \u0641\u0631\u0648\u062e\u062a\u060c \u0648\u06c1\u06cc \u067e\u0691\u0648\u0633)<\/p>\n<\/li>\n<li>\n<p><strong>aspirate<\/strong> = \u0648\u06cc\u0648 2 \u06a9\u06d2 \u0635\u0627\u0631\u0641\u06cc\u0646 \u06a9\u06cc \u0637\u0631\u0641 \u0633\u06d2 \u06c1\u0641\u062a\u06c1 20 \u0633\u06d2 \u067e\u06c1\u0644\u06d2 \u0645\u06a9\u0645\u0644 \u06a9\u06cc\u06d2 \u06af\u0626\u06d2 \u0627\u0648\u0633\u0637 \u06a9\u0627\u0645 (\u06a9\u0627\u0641\u06cc \u0634\u0627\u067e: Q2 \u0622\u0645\u062f\u0646\u06cc\u060c \u063a\u06cc\u0631 \u0645\u062a\u0627\u062b\u0631\u06c1 \u067e\u0691\u0648\u0633)<\/p>\n<\/li>\n<li>\n<p><strong>d<\/strong> = \u06c1\u0641\u062a\u06c1 20 \u06a9\u06d2 \u0628\u0639\u062f \u0648\u06cc\u0648 2 \u0635\u0627\u0631\u0641\u06cc\u0646 \u06a9\u06d2 \u0630\u0631\u06cc\u0639\u06c1 \u0645\u06a9\u0645\u0644 \u06a9\u06cc\u0627 \u06af\u06cc\u0627 \u0627\u0648\u0633\u0637 \u06a9\u0627\u0645 (\u06a9\u0627\u0641\u06cc \u0634\u0627\u067e: Q3 \u0622\u0645\u062f\u0646\u06cc\u060c \u0648\u06c1\u06cc)<\/p>\n<\/li>\n<\/ul>\n<pre><code class=\"language-text\">                         Pre     Post\nTreated (wave 1):         A       B\nControl (wave 2):         C       D\n\nNaive post-period gap:   B - D     (contaminated by group differences)\nNaive treated change:    B - A     (contaminated by time trend)\nDiD:                 (B - A) - (D - C)   \u2190 the causal effect\n<\/code><\/pre>\n<p><code>B - A<\/code>    \u06cc\u06c1 \u0644\u06c1\u0631 1 \u0633\u06d2 \u062a\u0628\u062f\u06cc\u0644\u06cc \u06c1\u06d2\u060c \u0644\u06cc\u06a9\u0646 \u0627\u0633 \u0645\u06cc\u06ba \u0639\u0644\u0627\u062c \u06a9\u0627 \u0627\u062b\u0631 \u0627\u0648\u0631 \u0648\u0642\u062a \u06a9\u0627 \u0631\u062c\u062d\u0627\u0646 \u062f\u0648\u0646\u0648\u06ba \u0634\u0627\u0645\u0644 \u06c1\u06cc\u06ba \u062c\u0633 \u0646\u06d2 \u06c1\u0631 \u06a9\u0633\u06cc \u06a9\u0648 \u062d\u0631\u06a9\u062a \u0645\u06cc\u06ba \u0644\u0627\u06cc\u0627\u06d4 <code>D - C<\/code> \u06cc\u06c1 \u0627\u06cc\u06a9 \u06c1\u06cc \u0648\u0646\u0688\u0648\u060c \u0627\u06cc\u06a9 \u06c1\u06cc \u0648\u0642\u062a \u06a9\u06d2 \u0631\u062c\u062d\u0627\u0646 \u067e\u0631 \u0644\u06c1\u0631 2 \u0645\u06cc\u06ba \u062a\u0628\u062f\u06cc\u0644\u06cc \u06c1\u06d2\u060c \u0627\u0648\u0631 \u06a9\u0648\u0626\u06cc \u067e\u0631\u0648\u0633\u06cc\u0633\u0646\u06af \u0646\u06c1\u06cc\u06ba \u06c1\u06d2\u06d4 \u0627\u06af\u0631 \u0622\u067e \u0627\u06cc\u06a9 \u06a9\u0648 \u062f\u0648\u0633\u0631\u06d2 \u0633\u06d2 \u06af\u06be\u0679\u0627\u062a\u06d2 \u06c1\u06cc\u06ba \u062a\u0648 \u0635\u0631\u0641 \u0639\u0644\u0627\u062c \u06a9\u0627 \u0627\u062b\u0631 \u0628\u0627\u0642\u06cc \u0631\u06c1\u062a\u0627 \u06c1\u06d2\u06d4<\/p>\n<p>\u06a9\u06c1 <strong>\u0645\u062a\u0636\u0627\u062f<\/strong> \u0639\u0644\u0627\u062c \u06a9\u06d2 \u0628\u063a\u06cc\u0631 \u067e\u06c1\u0644\u06cc \u0644\u06c1\u0631 \u0627\u06cc\u0633\u06cc \u06c1\u06cc \u0646\u0638\u0631 \u0622\u062a\u06cc\u06d4 DiD \u06a9\u0648 \u067e\u06c1\u0646\u0686\u0627\u06cc\u0627 \u062c\u0627\u062a\u0627 \u06c1\u06d2 \u0627\u0648\u0631 \u0644\u06c1\u0631 1 \u06a9\u06cc \u0645\u062a\u0636\u0627\u062f \u0631\u0641\u062a\u0627\u0631 \u06a9\u06cc \u062a\u0634\u06a9\u06cc\u0644 \u06a9\u0631\u062a\u0627 \u06c1\u06d2 = \u0644\u06c1\u0631 1 \u06a9\u06cc \u067e\u0631\u06cc \u067e\u06cc\u0631\u06cc\u0688 \u0644\u06cc\u0648\u0644\u060c \u0644\u06c1\u0631 2 \u06a9\u06d2 \u0628\u0639\u062f \u06a9\u06cc \u0645\u062f\u062a \u06a9\u0627 \u0631\u062c\u062d\u0627\u0646\u06d4 \u0627\u0635\u0644 Wave 1 \u06a9\u06cc \u0631\u0641\u062a\u0627\u0631 \u0627\u0648\u0631 \u062c\u0648\u0627\u0628\u06cc \u0631\u0641\u062a\u0627\u0631 \u06a9\u06d2 \u062f\u0631\u0645\u06cc\u0627\u0646 \u0641\u0631\u0642 DiD \u062a\u062e\u0645\u06cc\u0646\u06c1 \u06c1\u06d2\u06d4<\/p>\n<p><em>\u0634\u06a9\u0644 1: \u0641\u0631\u0642 \u0645\u06cc\u06ba \u0641\u0631\u0642 \u06a9\u0627 \u0627\u0633\u062a\u0639\u0645\u0627\u0644 \u06a9\u0631\u062a\u06d2 \u06c1\u0648\u0626\u06d2 \u0648\u062c\u06c1 \u06a9\u0627 \u0627\u0646\u062f\u0627\u0632\u06c1\u06d4 \u0628\u0644\u06cc\u0648 \u0679\u06be\u0648\u0633: \u0644\u06c1\u0631 1 \u06a9\u06cc \u0627\u0635\u0644 \u0631\u0641\u062a\u0627\u0631\u06d4 \u0627\u0648\u0631\u0646\u062c \u0688\u0627\u0679\u0688 \u0644\u0627\u0626\u0646: \u0644\u06c1\u0631 2 (\u06a9\u0646\u0679\u0631\u0648\u0644\u060c \u0627\u0633 \u0645\u062f\u062a \u06a9\u06d2 \u062f\u0648\u0631\u0627\u0646 \u0639\u0644\u0627\u062c \u0646\u06c1\u06cc\u06ba \u06a9\u06cc\u0627 \u06af\u06cc\u0627)\u06d4 \u0628\u0644\u06cc\u0648 \u0688\u0627\u0679\u0688 \u0644\u0627\u0626\u0646: \u062c\u0648\u0627\u0628\u06cc\u060c \u062c\u06c1\u0627\u06ba \u067e\u06c1\u0644\u06cc \u0644\u06c1\u0631 \u062f\u0648\u0633\u0631\u06cc \u0644\u06c1\u0631 \u06a9\u06cc \u0645\u062f\u062a \u06a9\u06d2 \u0628\u0639\u062f \u0631\u062c\u062d\u0627\u0646 \u06a9\u06cc \u0628\u0646\u06cc\u0627\u062f \u067e\u0631 \u0686\u0644\u06cc 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\u0627\u06cc\u067e\u0644\u06cc \u06a9\u06cc\u0634\u0646\u0632 \u06a9\u06d2 \u0644\u06cc\u06d2 \u06a9\u0627\u0631\u0622\u0645\u062f \u0646\u062a\u0627\u0626\u062c \u06a9\u06d2 \u0644\u06cc\u06d2 \u0627\u06cc\u06a9 \u0642\u0627\u0628\u0644 \u0639\u0645\u0644 Jupyter \u0646\u0648\u0679 \u0628\u06a9 \u0645\u06cc\u06ba \u06c1\u06d2\u06d4<\/p>\n<p>\u0622\u067e \u0627\u0633\u06d2 \u06a9\u0644\u0648\u0646 \u06a9\u0631 \u06a9\u06d2 \u0686\u0644\u0627 \u0633\u06a9\u062a\u06d2 \u06c1\u06cc\u06ba\u06d4 <code>generate_data.py<\/code> \u0627\u0633 \u0645\u0636\u0645\u0648\u0646 \u0633\u06d2 \u062a\u0645\u0627\u0645 \u0622\u0624\u0679 \u067e\u0679 \u0628\u0627\u0644\u06a9\u0644 \u0627\u0633 \u067e\u0631 \u062f\u0648\u0628\u0627\u0631\u06c1 \u062a\u06cc\u0627\u0631 \u06a9\u06cc\u0627 \u06af\u06cc\u0627 \u06c1\u06d2: github.com\/RudrenduPaul\/product-experimentation-causal-inference-genai-llm<\/p>\n<h2 id=\"heading-prerequisites\">\u0634\u0631\u0637\u06cc\u06ba<\/h2>\n<p>\u0622\u067e \u06a9\u0648 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\u06af\u06cc\u06d4<\/p>\n<p>\u0627\u0633 \u0679\u06cc\u0648\u0679\u0648\u0631\u06cc\u0644 \u06a9\u06d2 \u0644\u06cc\u06d2 \u067e\u06cc\u06a9\u062c\u0632 \u0627\u0646\u0633\u0679\u0627\u0644 \u06a9\u0631\u06cc\u06ba\u06d4<\/p>\n<pre><code class=\"language-bash\">pip install numpy pandas statsmodels linearmodels matplotlib\n<\/code><\/pre>\n<p>\u0645\u0635\u0646\u0648\u0639\u06cc \u0688\u06cc\u0679\u0627\u0633\u06cc\u0679 \u062d\u0627\u0635\u0644 \u06a9\u0631\u0646\u06d2 \u06a9\u06d2 \u0644\u06cc\u06d2\u060c \u0633\u0627\u062a\u06be\u06cc \u0631\u06cc\u067e\u0648\u0632\u0679\u0631\u06cc \u06a9\u0648 \u06a9\u0644\u0648\u0646 \u06a9\u0631\u06cc\u06ba\u06d4<\/p>\n<pre><code class=\"language-bash\">git clone https:\/\/github.com\/RudrenduPaul\/product-experimentation-causal-inference-genai-llm.git\ncd product-experimentation-causal-inference-genai-llm\npython data\/generate_data.py --seed 42 --n-users 50000 --out data\/synthetic_llm_logs.csv\n<\/code><\/pre>\n<h2 id=\"heading-setting-up-the-working-example\">\u0648\u0631\u06a9\u0646\u06af \u0645\u062b\u0627\u0644 \u0633\u06cc\u0679 \u0627\u067e<\/h2>\n<p>\u0688\u06cc\u0679\u0627 \u0633\u06cc\u0679 \u062f\u0648 \u0644\u06c1\u0631\u0648\u06ba \u0645\u06cc\u06ba \u062c\u0627\u0631\u06cc \u06a9\u0631\u062f\u06c1 AI \u062e\u0644\u0627\u0635\u06c1 \u062e\u0635\u0648\u0635\u06cc\u0627\u062a \u06a9\u0627 \u0627\u0633\u062a\u0639\u0645\u0627\u0644 \u06a9\u0631\u062a\u06d2 \u06c1\u0648\u0626\u06d2 SaaS \u0645\u0635\u0646\u0648\u0639\u0627\u062a \u06a9\u06cc \u0646\u0642\u0644 \u06a9\u0631\u062a\u0627 \u06c1\u06d2\u06d4 \u0648\u06cc\u0648 1 \u0648\u0631\u06a9 \u0627\u0633\u067e\u06cc\u0633 \u06c1\u0641\u062a\u06c1 20 \u0645\u06cc\u06ba \u062f\u0633\u062a\u06cc\u0627\u0628 \u06c1\u0648\u06af\u0627 \u0627\u0648\u0631 \u0648\u06cc\u0648 2 \u06c1\u0641\u062a\u06c1 30 \u0645\u06cc\u06ba \u062f\u0633\u062a\u06cc\u0627\u0628 \u06c1\u0648\u06af\u0627\u060c \u06c1\u0631 \u0644\u06c1\u0631 \u0645\u06cc\u06ba 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df.groupby(\"wave\").treatment_week.first().to_dict())\n<\/code><\/pre>\n<p><strong>\u0645\u062a\u0648\u0642\u0639 \u067e\u06cc\u062f\u0627\u0648\u0627\u0631:<\/strong><\/p>\n<pre><code class=\"language-text\">(50000, 16)\n   wave  signup_week  workspace_id  task_completed\n0     2           10            36               0\n1     2           51            44               1\n2     2            2            28               1\n3     1           15            20               1\n4     1           29             0               1\nWave sizes: {2: 25063, 1: 24937}\nTreatment weeks per wave: {1: 20, 2: 30}\n<\/code><\/pre>\n<p>\u06cc\u06c1\u0627\u06ba \u06a9\u06cc\u0627 \u06c1\u0648 \u0631\u06c1\u0627 \u06c1\u06d2: 50,000 \u0642\u0637\u0627\u0631\u06cc\u06ba \u0644\u0648\u0688 \u06a9\u0631\u06cc\u06ba\u060c \u0641\u06cc \u0635\u0627\u0631\u0641 \u0627\u06cc\u06a9\u06d4 \u0648\u06cc\u0648 1 \u06a9\u06d2 25 \u0648\u0631\u06a9 \u0627\u0633\u067e\u06cc\u0633 \u0645\u06cc\u06ba \u062a\u0642\u0631\u06cc\u0628\u0627\u064b 24,937 \u0635\u0627\u0631\u0641\u06cc\u0646 \u06c1\u06cc\u06ba\u06d4 \u0648\u06cc\u0648 2 \u06a9\u06d2 25 \u0645\u062e\u062a\u0644\u0641 \u0648\u0631\u06a9 \u0627\u0633\u067e\u06cc\u0633 \u0645\u06cc\u06ba \u062a\u0642\u0631\u06cc\u0628\u0627\u064b 25,063 \u0635\u0627\u0631\u0641\u06cc\u0646 \u06c1\u06cc\u06ba\u06d4 \u06a9\u06c1 <code>treatment_week<\/code> \u06a9\u0627\u0644\u0645 \u0631\u06cc\u06a9\u0627\u0631\u0688 \u06a9\u0631\u062a\u0627 \u06c1\u06d2 \u062c\u0628 \u06c1\u0631 \u0635\u0627\u0631\u0641 \u06a9\u06d2 \u0648\u0631\u06a9 \u0627\u0633\u067e\u06cc\u0633 \u0646\u06d2 AI \u0633\u0645\u0631\u06cc \u06a9\u06cc \u0635\u0644\u0627\u062d\u06cc\u062a\u06cc\u06ba \u062d\u0627\u0635\u0644 \u06a9\u06cc\u06ba (\u0648\u06cc\u0648 1 \u06a9\u06d2 \u0644\u06cc\u06d2 \u06c1\u0641\u062a\u06c1 20 \u0627\u0648\u0631 \u0644\u06c1\u0631 2 \u06a9\u06d2 \u0644\u06cc\u06d2 \u06c1\u0641\u062a\u06c1 30)\u06d4 \u06a9\u06c1 <code>task_completed<\/code> 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\u0645\u0646\u0633\u0644\u06a9 \u0627\u06cc\u06a9 \u0679\u06cc\u0644\u06cc \u0645\u06cc\u0679\u0631\u06cc \u0642\u0637\u0627\u0631 \u06c1\u0648\u062a\u06cc \u06c1\u06d2\u06d4 \u0648\u0642\u062a \u06a9\u06d2 \u0633\u0627\u062a\u06be \u0633\u0627\u062a\u06be \u0641\u06cc \u0635\u0627\u0631\u0641 \u0645\u062a\u0639\u062f\u062f \u0645\u0634\u0627\u06c1\u062f\u0627\u062a \u06a9\u06d2 \u0633\u0627\u062a\u06be \u067e\u06cc\u0646\u0644 \u0688\u06cc\u0679\u0627\u0633\u06cc\u0679\u0633 \u0627\u06cc\u06a9 \u0645\u0634\u0627\u06c1\u062f\u0627\u062a\u06cc \u0679\u0627\u0626\u0645 \u0627\u0633\u0679\u06cc\u0645\u067e \u06a9\u0627\u0644\u0645 \u06a9\u0627 \u0627\u0633\u062a\u0639\u0645\u0627\u0644 \u06a9\u0631\u062a\u06d2 \u06c1\u06cc\u06ba \u062c\u0648 \u06c1\u0631 \u0642\u0637\u0627\u0631 \u06a9\u0648 \u0631\u06cc\u06a9\u0627\u0631\u0688 \u06a9\u0631\u0646\u06d2 \u06a9\u06d2 \u0648\u0642\u062a \u0633\u06d2 \u0648\u0627\u0628\u0633\u062a\u06c1 \u06c1\u0648\u062a\u0627 \u06c1\u06d2\u06d4<\/p>\n<p>\u0627\u067e\u0646\u06d2 \u062a\u062c\u0632\u06cc\u06c1 \u06a9\u0648 \u0635\u0627\u0641 \u0631\u06a9\u06be\u0646\u06d2 \u06a9\u06d2 \u0644\u06cc\u06d2\u060c \u0627\u0633\u06d2 \u0627\u0646 \u0635\u0627\u0631\u0641\u06cc\u0646 \u062a\u06a9 \u0645\u062d\u062f\u0648\u062f \u0631\u06a9\u06be\u06cc\u06ba \u062c\u0646\u06c1\u0648\u06ba \u0646\u06d2 Wave 2 \u06a9\u06d2 \u0622\u063a\u0627\u0632 \u0633\u06d2 \u067e\u06c1\u0644\u06d2 \u0633\u0627\u0626\u0646 \u0627\u067e \u06a9\u06cc\u0627 \u062a\u06be\u0627 (<code>signup_week < 30<\/code>)\u06d4 \u0648\u06cc\u0648 2 \u0646\u06d2 \u0627\u06cc\u06a9 \u0645\u0646\u0627\u0633\u0628 \u06a9\u0646\u0679\u0631\u0648\u0644 \u06af\u0631\u0648\u067e \u06a9\u06d2 \u0637\u0648\u0631 \u067e\u0631 \u06a9\u0627\u0645 \u06a9\u06cc\u0627 \u06a9\u06cc\u0648\u0646\u06a9\u06c1 \u0627\u0646\u06c1\u06cc\u06ba \u0627\u0628\u06be\u06cc \u062a\u06a9 \u0639\u0644\u0627\u062c \u0646\u06c1\u06cc\u06ba \u0645\u0644\u0627 \u062a\u06be\u0627\u060c \u062c\u0628\u06a9\u06c1 \u0648\u06cc\u0648 1 \u0646\u06d2 10 \u06c1\u0641\u062a\u0648\u06ba \u062a\u06a9 \u0639\u0644\u0627\u062c \u062d\u0627\u0635\u0644 \u06a9\u06cc\u0627 \u062a\u06be\u0627\u06d4<\/p>\n<pre><code class=\"language-python\">analysis = df[df.signup_week < 30].copy()\nanalysis[\"post\"] = (analysis.signup_week >= 20).astype(int)\nanalysis[\"treated\"] = (analysis.wave == 1).astype(int)\n\nprint(analysis.groupby([\"treated\", \"post\"])\n              .agg(n=(\"user_id\", \"count\"),\n                   mean_completion=(\"task_completed\", \"mean\"))\n              .round(3))\n<\/code><\/pre>\n<p><strong>\u0645\u062a\u0648\u0642\u0639 \u067e\u06cc\u062f\u0627\u0648\u0627\u0631:<\/strong><\/p>\n<pre><code class=\"language-text\">                 n  mean_completion\ntreated post\n0       0     9590            0.556\n        1     4878            0.555\n1       0     9633            0.592\n        1     4738            0.643\n<\/code><\/pre>\n<p>\u06cc\u06c1\u0627\u06ba \u06a9\u06cc\u0627 \u06c1\u0648 \u0631\u06c1\u0627 \u06c1\u06d2: \u062a\u062c\u0632\u06cc\u06c1 \u0648\u0646\u0688\u0648 (\u06c1\u0641\u062a\u06d2 0 \u0633\u06d2 29) \u06a9\u06d2 \u0630\u0631\u06cc\u0639\u06c1 \u0688\u06cc\u0679\u0627 \u06a9\u0648 \u0641\u0644\u0679\u0631 \u06a9\u0631\u06cc\u06ba \u0627\u0648\u0631 \u062f\u0648 \u0688\u0633\u067e\u0644\u06d2 \u0645\u062a\u063a\u06cc\u0631\u0627\u062a \u0628\u0646\u0627\u0626\u06cc\u06ba\u06d4 <code>post<\/code> 1 \u06c1\u0641\u062a\u06c1 20 \u06cc\u0627 \u0627\u0633 \u06a9\u06d2 \u0628\u0639\u062f \u06a9\u06d2 \u0635\u0627\u0631\u0641\u06cc\u0646 \u06a9\u06d2 \u0644\u06cc\u06d2\u060c \u0628\u0635\u0648\u0631\u062a \u062f\u06cc\u06af\u0631 0\u06d4 <code>treated<\/code> \u0644\u06c1\u0631 1 \u0635\u0627\u0631\u0641\u06cc\u0646 \u06a9\u06d2 \u0644\u06cc\u06d2 1 \u0627\u0648\u0631 \u0644\u06c1\u0631 2 \u0635\u0627\u0631\u0641\u06cc\u0646 \u06a9\u06d2 \u0644\u06cc\u06d2 0 \u06c1\u06d2\u06d4 \u06af\u0631\u0648\u067e \u0628\u0627\u0626\u06cc DiD 2x2 \u0679\u06cc\u0628\u0644 \u0645\u06cc\u06ba \u0686\u0627\u0631 \u0633\u06cc\u0644 \u062f\u06a9\u06be\u0627\u062a\u0627 \u06c1\u06d2: (Process=0, Post=0), (Process=0, Post=1), (Process=1, Post=0), (Process=1, Post=1)\u06d4 \u06cc\u06c1 \u0686\u0627\u0631 \u0630\u0631\u0627\u0626\u0639 \u06c1\u06cc\u06ba \u062c\u0648 \u0622\u067e \u06a9\u0648 \u067e\u06c1\u0644\u06d2 DiD \u062a\u062e\u0645\u06cc\u0646\u06c1 \u06a9\u06d2 \u0644\u06cc\u06d2 \u062f\u0631\u06a9\u0627\u0631 \u06c1\u06cc\u06ba\u06d4<\/p>\n<h2 id=\"heading-step-1-a-simple-2x2-did\">\u0645\u0631\u062d\u0644\u06c1 1: \u0633\u0627\u062f\u06c1 2x2 DiD<\/h2>\n<p>\u0635\u0627\u0641 \u062a\u0631\u06cc\u0646 \u0648\u0631\u0698\u0646 \u06a9\u06d2 \u0633\u0627\u062a\u06be \u0634\u0631\u0648\u0639 \u06a9\u0631\u06cc\u06ba\u06d4 4 \u062e\u0644\u06cc\u0627\u062a \u06a9\u06cc \u0627\u0648\u0633\u0637 \u06a9\u0627 \u0628\u0631\u0627\u06c1 \u0631\u0627\u0633\u062a \u062d\u0633\u0627\u0628 \u0644\u06af\u0627\u0626\u06cc\u06ba \u0627\u0648\u0631 \u067e\u06be\u0631 \u0641\u0631\u0642 \u06a9\u0627 \u0641\u0631\u0642 \u0645\u0639\u0644\u0648\u0645 \u06a9\u0631\u06cc\u06ba\u06d4<\/p>\n<pre><code class=\"language-python\">cells = analysis.groupby([\"treated\", \"post\"]).task_completed.mean()\n\nwave2_pre  = cells.loc[(0, 0)]   # control, pre\nwave2_post = cells.loc[(0, 1)]   # control, post\nwave1_pre  = cells.loc[(1, 0)]   # treated, pre\nwave1_post = cells.loc[(1, 1)]   # treated, post\n\ndid_effect = (wave1_post - wave1_pre) - (wave2_post - wave2_pre)\nprint(f\"Wave 1 change: {wave1_post - wave1_pre:+.4f}\")\nprint(f\"Wave 2 change: {wave2_post - wave2_pre:+.4f}\")\nprint(f\"DiD effect:    {did_effect:+.4f}\")\n<\/code><\/pre>\n<p><strong>\u0645\u062a\u0648\u0642\u0639 \u067e\u06cc\u062f\u0627\u0648\u0627\u0631:<\/strong><\/p>\n<pre><code class=\"language-text\">Wave 1 change: +0.0515\nWave 2 change: -0.0013\nDiD effect:    +0.0527  (ground truth = +0.05)\n<\/code><\/pre>\n<p>\u06cc\u06c1\u0627\u06ba \u06a9\u06cc\u0627 \u06c1\u0648 \u0631\u06c1\u0627 \u06c1\u06d2: 4 \u0633\u06cc\u0644\u0632 \u06a9\u06cc \u0627\u0648\u0633\u0637 \u0644\u06cc\u06ba\u060c \u067e\u06c1\u0644\u06d2 \u0633\u06d2 \u067e\u0648\u0633\u0679 \u062a\u06a9 \u06a9\u0627\u0645 \u06a9\u06cc \u062a\u06a9\u0645\u06cc\u0644 \u06a9\u06d2 \u0644\u06cc\u06d2 \u0644\u06c1\u0631 1 \u0645\u06cc\u06ba \u062a\u0628\u062f\u06cc\u0644\u06cc \u06a9\u0627 \u062d\u0633\u0627\u0628 \u0644\u06af\u0627\u0626\u06cc\u06ba\u060c \u0627\u0633\u06cc \u06a9\u06cc\u0644\u0646\u0688\u0631 \u0648\u0646\u0688\u0648 \u06a9\u06d2 \u0644\u06cc\u06d2 \u0644\u06c1\u0631 2 \u0645\u06cc\u06ba \u062a\u0628\u062f\u06cc\u0644\u06cc \u06a9\u0627 \u062d\u0633\u0627\u0628 \u0644\u06af\u0627\u0626\u06cc\u06ba (\u0648\u06cc\u0648 2 \u067e\u0631 \u0627\u0628\u06be\u06cc \u0639\u0645\u0644 \u0646\u06c1\u06cc\u06ba \u06c1\u0648\u0627 \u06c1\u06d2) \u0627\u0648\u0631 \u0641\u0631\u0642 \u0644\u06cc\u06ba\u06d4 \u0688\u06cc \u0688\u06cc \u06a9\u0627 \u062a\u062e\u0645\u06cc\u0646\u06c1 \u0644\u06c1\u0631 1 \u0645\u06cc\u06ba \u062a\u0628\u062f\u06cc\u0644\u06cc \u06a9\u0627 \u0648\u06c1 \u062d\u0635\u06c1 \u06c1\u06d2 \u062c\u0633 \u06a9\u06cc \u0648\u0636\u0627\u062d\u062a \u06a9\u0633\u06cc \u0628\u06be\u06cc \u0648\u0642\u062a \u06a9\u06d2 \u0631\u062c\u062d\u0627\u0646 \u0633\u06d2 \u0646\u06c1\u06cc\u06ba \u06a9\u06cc \u062c\u0627 \u0633\u06a9\u062a\u06cc \u062c\u0633 \u06a9\u06d2 \u0633\u0627\u062a\u06be \u0644\u06c1\u0631 2 \u0628\u06be\u06cc \u0645\u0646\u062a\u0642\u0644 \u06c1\u0648\u0626\u06cc\u06d4<\/p>\n<p>\u0627\u0633 \u0688\u06cc\u0679\u0627\u0633\u06cc\u0679 \u0645\u06cc\u06ba\u060c \u0627\u06cc\u06a9 \u0633\u0627\u062f\u06c1 2x2 \u062a\u062e\u0645\u06cc\u0646\u06c1 +0.053 \u062a\u06a9 \u067e\u06c1\u0646\u0686\u062a\u0627 \u06c1\u06d2\u060c \u062c\u0648 \u06a9\u06c1 \u0627\u0635\u0644 +0.05 \u06a9\u06d2 \u0628\u06c1\u062a \u0642\u0631\u06cc\u0628 \u06c1\u06d2\u06d4 \u062a\u0627\u06c1\u0645\u060c \u0622\u067e \u0627\u0633 \u0646\u0645\u0628\u0631 \u06a9\u0648 \u067e\u0631\u0648\u0688\u06a9\u0679 \u06a9\u06d2 \u062c\u0627\u0626\u0632\u0648\u06ba \u06a9\u06d2 \u0644\u06cc\u06d2 \u0627\u0633\u062a\u0639\u0645\u0627\u0644 \u0646\u06c1\u06cc\u06ba \u06a9\u0631 \u0633\u06a9\u062a\u06d2\u06d4 \u06a9\u0648\u0626\u06cc \u0645\u0639\u06cc\u0627\u0631\u06cc \u063a\u0644\u0637\u06cc\u0627\u06ba \u0646\u06c1\u06cc\u06ba \u06c1\u06cc\u06ba\u06d4 \u0627\u0633 \u06a9\u0627 \u0645\u0637\u0644\u0628 \u06c1\u06d2 \u06a9\u06c1 \u06c1\u0645 \u06cc\u06c1 \u0646\u06c1\u06cc\u06ba \u0628\u062a\u0627 \u0633\u06a9\u062a\u06d2 \u06a9\u06c1 \u0622\u06cc\u0627 +0.053 \u0627\u0635\u0644 \u0633\u06af\u0646\u0644 \u06c1\u06d2 \u06cc\u0627 \u0633\u06cc\u0645\u067e\u0644\u0646\u06af \u0634\u0648\u0631 \u06a9\u06d2 \u0627\u0646\u062f\u0631\u06d4 \u06a9\u0648\u0626\u06cc \u06a9\u0648\u0648\u0627\u0631\u06cc\u0679 \u0627\u06cc\u0688\u062c\u0633\u0679\u0645\u0646\u0679 \u0646\u06c1\u06cc\u06ba \u06c1\u06d2\u060c \u0644\u06c1\u0630\u0627 \u06a9\u0686\u06be +0.053 \u0634\u0631\u06a9\u062a \u06a9\u06cc \u0633\u0637\u062d \u0628\u0646\u062f\u06cc \u06a9\u06cc \u0648\u062c\u06c1 \u0633\u06d2 \u06c1\u0648 \u0633\u06a9\u062a\u06d2 \u06c1\u06cc\u06ba \u0627\u06af\u0631 \u0644\u06c1\u0631 1 \u0645\u06cc\u06ba \u0627\u0633 \u06af\u0631\u0648\u06c1 \u0645\u06cc\u06ba \u0632\u06cc\u0627\u062f\u06c1 \u0628\u06be\u0627\u0631\u06cc \u0635\u0627\u0631\u0641\u06cc\u0646 \u062a\u06be\u06d2\u06d4 \u0627\u0648\u0631 \u0688\u06cc\u0679\u0627 \u0645\u06cc\u06ba \u0648\u0631\u06a9 \u0627\u0633\u067e\u06cc\u0633 \u0633\u0637\u062d \u06a9\u06d2 \u0627\u0631\u062a\u0628\u0627\u0637 \u06a9\u0648 \u0633\u0646\u0628\u06be\u0627\u0644\u0646\u06d2 \u06a9\u0627 \u06a9\u0648\u0626\u06cc \u0637\u0631\u06cc\u0642\u06c1 \u0646\u06c1\u06cc\u06ba \u06c1\u06d2\u06d4 \u0645\u0631\u062d\u0644\u06c1 2 \u062a\u06cc\u0646\u0648\u06ba \u06a9\u0648 \u0679\u06be\u06cc\u06a9 \u06a9\u0631\u062a\u0627 \u06c1\u06d2\u06d4<\/p>\n<h2 id=\"heading-step-2-regression-did-with-fixed-effects\">\u0645\u0631\u062d\u0644\u06c1 2: \u0645\u0642\u0631\u0631\u06c1 \u0627\u062b\u0631\u0627\u062a \u06a9\u06d2 \u0633\u0627\u062a\u06be \u0631\u06cc\u06af\u0631\u06cc\u0634\u0646 \u0688\u06cc \u0688\u06cc<\/h2>\n<p>DiD \u06a9\u0627 \u0631\u06cc\u06af\u0631\u06cc\u0634\u0646 \u0641\u0627\u0631\u0645\u0648\u0644\u06c1 covariates \u06a9\u06cc \u063a\u06cc\u0631 \u0645\u0648\u062c\u0648\u062f\u06af\u06cc \u0645\u06cc\u06ba 2x2 \u0679\u06cc\u0628\u0644 \u06a9\u06d2 \u0628\u0631\u0627\u0628\u0631 \u067e\u0648\u0627\u0626\u0646\u0679 \u062a\u062e\u0645\u06cc\u0646\u06c1 \u062a\u06cc\u0627\u0631 \u06a9\u0631\u062a\u0627 \u06c1\u06d2\u06d4 \u0644\u06cc\u06a9\u0646 \u06cc\u06c1 \u062a\u06cc\u0646 \u0686\u06cc\u0632\u06cc\u06ba \u0628\u06be\u06cc \u062e\u0631\u06cc\u062f\u062a\u0627 \u06c1\u06d2:<\/p>\n<ul>\n<li>\n<p><strong>\u0645\u0639\u06cc\u0627\u0631\u06cc \u062e\u0631\u0627\u0628\u06cc \u0627\u0648\u0631 \u067e\u06cc \u0648\u06cc\u0644\u06cc\u0648<\/strong> \u0635\u062d\u06cc\u062d \u062d\u0633\u0627\u0628 \u0644\u06af\u0627\u06cc\u0627<\/p>\n<\/li>\n<li>\n<p><strong>Covariate \u0627\u06cc\u0688\u062c\u0633\u0679\u0645\u0646\u0679<\/strong> \u0641\u0631\u0642 \u06a9\u0648 \u06a9\u0645 \u06a9\u0631\u0646\u06d2 \u0627\u0648\u0631 \u062a\u062e\u0645\u06cc\u0646\u0648\u06ba \u06a9\u0648 \u062a\u06cc\u0632 \u06a9\u0631\u0646\u06d2 \u06a9\u06d2 \u0644\u06cc\u06d2<\/p>\n<\/li>\n<li>\n<p><strong>\u06a9\u0644\u0633\u0679\u0631 \u0645\u06cc\u06ba \u0645\u0636\u0628\u0648\u0637 \u0646\u0627\u06a9\u0627\u0645\u06cc\u06d4<\/strong> \u0645\u0631\u062d\u0644\u06c1 \u0648\u0627\u0631 \u0631\u0648\u0644 \u0622\u0624\u0679 \u06c1\u0645\u06cc\u0634\u06c1 \u0648\u0631\u06a9 \u0627\u0633\u067e\u06cc\u0633 \u06a9\u06d2 \u0627\u0646\u062f\u0631 \u0628\u0627\u06c1\u0645\u06cc \u062a\u0639\u0644\u0642 \u06a9\u0648 \u06c1\u06cc\u0646\u0688\u0644 \u06a9\u0631\u062a\u06d2 \u06c1\u06cc\u06ba\u06d4<\/p>\n<\/li>\n<\/ul>\n<p>\u0631\u062c\u0639\u062a \u06cc\u06c1 \u06c1\u06d2: <code>outcome ~ treated + post + treated:post + controls<\/code>. \u06af\u062a\u0627\u0646\u06a9 \u06c1\u06d2\u06d4 <code>treated:post<\/code> \u062a\u0639\u0627\u0645\u0644\u0627\u062a \u0688\u06cc \u0688\u06cc \u062a\u062e\u0645\u06cc\u0646\u06c1 \u06c1\u06cc\u06ba\u06d4<\/p>\n<pre><code class=\"language-python\">import statsmodels.formula.api as smf\n\ndid_model = smf.ols(\n    \"task_completed ~ treated * post + C(engagement_tier)\",\n    data=analysis\n).fit(\n    cov_type=\"cluster\",\n    cov_kwds={\"groups\": analysis.workspace_id}\n)\n\nprint(did_model.summary().tables[1])\n<\/code><\/pre>\n<p><strong>\u0645\u062a\u0648\u0642\u0639 \u067e\u06cc\u062f\u0627\u0648\u0627\u0631:<\/strong><\/p>\n<pre><code class=\"language-text\">================================================================================================\n                                   coef    std err          z      P>|z|      [0.025      0.975]\n------------------------------------------------------------------------------------------------\nIntercept                        0.8301      0.007    126.538      0.000       0.817       0.843\nC(engagement_tier)[T.light]     -0.4027      0.006    -63.168      0.000      -0.415      -0.390\nC(engagement_tier)[T.medium]    -0.1766      0.007    -25.931      0.000      -0.190      -0.163\ntreated                          0.0367      0.005      6.885      0.000       0.026       0.047\npost                            -0.0056      0.008     -0.684      0.494      -0.022       0.011\ntreated:post                     0.0541      0.011      4.981      0.000       0.033       0.075\n================================================================================================\n<\/code><\/pre>\n<p>\u06cc\u06c1 \u06c1\u06d2 \u06a9\u06cc\u0627 \u06c1\u0648 \u0631\u06c1\u0627 \u06c1\u06d2: \u06a9\u0627\u0645 \u06a9\u06cc \u062a\u06a9\u0645\u06cc\u0644 \u06a9\u06d2 \u0644\u06cc\u06d2 \u0639\u0627\u0645 \u06a9\u0645 \u0627\u0632 \u06a9\u0645 \u0645\u0631\u0628\u0639 \u0631\u062c\u0639\u062a <code>treated<\/code> \u062e\u0635\u0648\u0635\u06cc\u062a <code>post<\/code> \u0645\u06cc\u0679\u0631\u06a9\u0633\u060c \u062a\u0639\u0627\u0645\u0644\u0627\u062a\u060c \u0627\u0648\u0631 \u0645\u0634\u063a\u0648\u0644\u06cc\u062a \u06a9\u06cc \u062a\u06c1\u0648\u06ba \u067e\u0631 \u0648\u0627\u0636\u062d \u06a9\u0646\u0679\u0631\u0648\u0644\u06d4<\/p>\n<p>\u06a9\u06c1 <code>treated:post<\/code> \u06af\u062a\u0627\u0646\u06a9 DiD \u062a\u062e\u0645\u06cc\u0646\u06c1 \u06c1\u06cc\u06ba\u06d4 \u0627\u06cc\u06a9 \u06c1\u06cc \u0648\u0631\u06a9 \u0627\u0633\u067e\u06cc\u0633 \u06a9\u06d2 \u0627\u0633\u062a\u0639\u0645\u0627\u0644 \u06a9\u0646\u0646\u062f\u06af\u0627\u0646 \u0627\u06cc\u06a9 \u0645\u0634\u062a\u0631\u06a9\u06c1 \u062c\u0630\u0628\u06d2 \u06a9\u0627 \u0627\u0634\u062a\u0631\u0627\u06a9 \u06a9\u0631\u062a\u06d2 \u06c1\u06cc\u06ba\u060c \u0646\u062a\u0627\u0626\u062c \u06a9\u0648 \u0645\u0631\u0628\u0648\u0637 \u06a9\u0631\u062a\u06d2 \u06c1\u06cc\u06ba\u06d4 \u06a9\u06cc \u0637\u0631\u0641 \u0633\u06d2 \u06af\u0631\u0648\u067e <code>workspace_id<\/code> \u0645\u06cc\u06ba \u0627\u0633 \u067e\u0631 \u0622\u067e \u06a9\u0648 \u062f\u0631\u0633\u062a \u06a9\u0631\u0646\u0627 \u0686\u0627\u06c1\u062a\u0627 \u06c1\u0648\u06ba\u06d4<\/p>\n<p>\u0627\u0633 \u0688\u06cc\u0679\u0627 \u0633\u06cc\u0679 \u0645\u06cc\u06ba <code>treated:post<\/code> \u06af\u062a\u0627\u0646\u06a9 <0.001 \u06a9\u06cc \u06a9\u0644\u0633\u0679\u0631\u0688 p- \u0648\u06cc\u0644\u06cc\u0648 \u06a9\u06d2 \u0633\u0627\u062a\u06be +0.054 \u0645\u0639\u0644\u0648\u0645 \u06c1\u0648\u062a\u0627 \u06c1\u06d2\u06d4 \u0627\u0635\u0644 \u0642\u06cc\u0645\u062a +0.050 \u06c1\u06d2\u06d4 \u06a9\u0627\u0645 \u06a9\u06cc \u062c\u06af\u06c1 \u06a9\u06cc \u0633\u0637\u062d \u06a9\u06d2 \u0627\u0631\u062a\u0628\u0627\u0637 \u06a9\u06d2 \u062d\u0633\u0627\u0628 \u0633\u06d2 \u0645\u0639\u06cc\u0627\u0631\u06cc \u063a\u0644\u0637\u06cc\u0648\u06ba \u06a9\u06d2 \u0633\u0627\u062a\u06be\u060c \u062d\u0642\u06cc\u0642\u06cc \u0627\u062b\u0631 \u0633\u06d2 0.4 \u0641\u06cc\u0635\u062f \u067e\u0648\u0627\u0626\u0646\u0679\u0633 \u0627\u06cc\u06a9 \u0627\u06cc\u0633\u06cc \u062a\u0639\u062f\u0627\u062f \u06c1\u06d2 \u062c\u0633\u06d2 \u067e\u0631\u0648\u0688\u06a9\u0679 \u06a9\u06d2 \u062c\u0627\u0626\u0632\u06d2 \u0645\u06cc\u06ba \u0634\u0627\u0645\u0644 \u06a9\u06cc\u0627 \u062c\u0627 \u0633\u06a9\u062a\u0627 \u06c1\u06d2\u06d4<\/p>\n<p>\u0627\u0633 \u0631\u062c\u0639\u062a \u06a9\u06d2 \u0628\u0627\u0631\u06d2 \u0645\u06cc\u06ba \u0686\u0646\u062f \u0639\u0645\u0644\u06cc \u0646\u0648\u0679:<\/p>\n<ul>\n<li>\n<p><strong>\u06a9\u0646\u0679\u0631\u0648\u0644 \u06a9\u0648 \u0648\u0642\u062a \u06a9\u06d2 \u0633\u0627\u062a\u06be \u062a\u0628\u062f\u06cc\u0644 \u0646\u06c1\u06cc\u06ba \u06c1\u0648\u0646\u0627 \u0686\u0627\u06c1\u0626\u06d2\u06d4<\/strong> (\u0634\u0631\u06a9\u062a \u06a9\u06cc \u06a9\u0644\u0627\u0633\u060c \u0633\u0628\u0633\u06a9\u0631\u067e\u0634\u0646 \u06af\u0631\u0648\u067e)\u06d4 \u0639\u0644\u0627\u062c \u0633\u06d2 \u0645\u062a\u0627\u062b\u0631 \u06c1\u0648\u0646\u06d2 \u0648\u0627\u0644\u06d2 \u0648\u0642\u062a \u06a9\u06d2 \u0645\u062e\u062a\u0644\u0641 \u06a9\u0646\u0679\u0631\u0648\u0644 \u062a\u062e\u0645\u06cc\u0646\u0648\u06ba \u06a9\u06cc \u0637\u0631\u0641\u062f\u0627\u0631\u06cc \u06a9\u0631\u06cc\u06ba \u06af\u06d2\u06d4<\/p>\n<\/li>\n<li>\n<p><strong>\u0635\u0631\u0641 \u062a\u0639\u0627\u0645\u0644\u0627\u062a \u06a9\u06cc \u0648\u062c\u06c1 \u06a9\u06cc \u062a\u0634\u0631\u06cc\u062d \u06c1\u0648\u062a\u06cc \u06c1\u06d2\u06d4<\/strong> \u0645\u062f\u0627\u062e\u0644\u062a \u0627\u0648\u0631 \u0633\u0637\u062d \u06a9\u06cc \u0634\u0631\u0627\u0626\u0637 \u06af\u0631\u0648\u067e\u0648\u06ba \u06a9\u06d2 \u062f\u0631\u0645\u06cc\u0627\u0646 \u0628\u0646\u06cc\u0627\u062f\u06cc \u0641\u0631\u0642 \u06a9\u0648 \u0628\u06cc\u0627\u0646 \u06a9\u0631\u062a\u06cc \u06c1\u06cc\u06ba\u06d4<\/p>\n<\/li>\n<li>\n<p><strong>\u06a9\u0644\u0633\u0679\u0631\u0688 \u063a\u0644\u0637\u06cc\u0627\u06ba \u062f\u0631\u06a9\u0627\u0631 \u06c1\u06cc\u06ba\u06d4<\/strong> \u0627\u06af\u0631 \u0622\u067e \u06a9\u0644\u0633\u0679\u0631\u0646\u06af \u06a9\u0648 \u0686\u06be\u0648\u0691 \u062f\u06cc\u062a\u06d2 \u06c1\u06cc\u06ba\u060c \u062a\u0648 \u0622\u067e \u06a9\u06cc \u0645\u0639\u06cc\u0627\u0631\u06cc \u063a\u0644\u0637\u06cc\u0627\u06ba 3 \u0633\u06d2 10 \u06af\u0646\u0627 \u0628\u06c1\u062a \u0686\u06be\u0648\u0679\u06cc \u06c1\u0648\u06ba \u06af\u06cc \u0627\u0648\u0631 \u0622\u067e \u06a9\u06d2 \u0679\u06cc\u0633\u0679 \u06a9\u06d2 \u0627\u0639\u062f\u0627\u062f\u0648\u0634\u0645\u0627\u0631 \u0645\u0635\u0646\u0648\u0639\u06cc \u0637\u0648\u0631 \u067e\u0631 \u0628\u0691\u06be\u0627\u0626\u06d2 \u062c\u0627\u0626\u06cc\u06ba \u06af\u06d2\u060c \u062c\u0633 \u0633\u06d2 \u0622\u067e \u06a9\u06d2 \u0646\u062a\u0627\u0626\u062c \u0648\u0627\u0642\u0639\u06cc \u0627\u0646 \u0633\u06d2 \u06a9\u06c1\u06cc\u06ba \u0632\u06cc\u0627\u062f\u06c1 \u0627\u06c1\u0645 \u0645\u0639\u0644\u0648\u0645 \u06c1\u0648\u062a\u06d2 \u06c1\u06cc\u06ba\u06d4<\/p>\n<\/li>\n<\/ul>\n<h2 id=\"heading-step-3-checking-the-parallel-trends-assumption\">\u0645\u0631\u062d\u0644\u06c1 3: \u0645\u062a\u0648\u0627\u0632\u06cc \u0631\u062c\u062d\u0627\u0646 \u06a9\u06d2 \u0645\u0641\u0631\u0648\u0636\u0648\u06ba \u06a9\u0648 \u0686\u06cc\u06a9 \u06a9\u0631\u06cc\u06ba\u06d4<\/h2>\n<p>DiD \u0635\u0631\u0641 \u0627\u0633 \u0635\u0648\u0631\u062a \u0645\u06cc\u06ba \u062f\u0631\u0633\u062a \u06c1\u06d2 \u062c\u0628 \u0644\u06c1\u0631 1 \u0627\u0648\u0631 \u0644\u06c1\u0631 2 \u0627\u06cc\u06a9 \u06c1\u06cc \u0633\u0645\u062a \u0627\u0648\u0631 \u0627\u06cc\u06a9 \u06c1\u06cc \u0631\u0641\u062a\u0627\u0631 \u0633\u06d2 \u062d\u0631\u06a9\u062a \u06a9\u0631\u06cc\u06ba\u06d4 <em>\u067e\u06c1\u0644\u06d2<\/em> \u0639\u0644\u0627\u062c \u0634\u0631\u0648\u0639 \u06c1\u0648 \u06af\u06cc\u0627 \u06c1\u06d2\u06d4 \u067e\u0631\u06cc \u067e\u0631\u0648\u0633\u06cc\u0633\u0646\u06af \u0648\u0646\u0688\u0648 \u067e\u0631 \u062f\u0648\u0646\u0648\u06ba \u0644\u06c1\u0631\u0648\u06ba \u06a9\u06d2 \u0644\u0626\u06d2 \u06c1\u0641\u062a\u06c1 \u0648\u0627\u0631 \u0627\u0648\u0633\u0637 \u06a9\u0648 \u067e\u0644\u0627\u0679 (\u06cc\u0627 \u0679\u06cc\u0628\u0644\u0679\u0646\u06af) \u06a9\u0631\u06a9\u06d2 \u0627\u0633\u06d2 \u0686\u06cc\u06a9 \u06a9\u0631\u06cc\u06ba\u06d4<\/p>\n<pre><code class=\"language-python\">import matplotlib.pyplot as plt\nimport numpy as np\n\ndf_plot = df[df.signup_week < 30].copy()\nweekly = (df_plot.groupby([\"signup_week\", \"wave\"])\n             .task_completed.mean()\n             .reset_index()\n             .pivot(index=\"signup_week\", columns=\"wave\", values=\"task_completed\"))\n\n# 3-week rolling average to smooth week-to-week sampling noise\nsmoothed = weekly.rolling(3, center=True, min_periods=2).mean()\n\nTREATMENT_WEEK = 20\npre_idx = smoothed.index[smoothed.index < TREATMENT_WEEK]\npost_idx = smoothed.index[smoothed.index >= TREATMENT_WEEK]\n\n# DiD counterfactual: wave 1 pre-period mean + wave 2's post-period change\nwave1_pre_mean = smoothed.loc[pre_idx, 1].mean()\nwave2_pre_mean = smoothed.loc[pre_idx, 2].mean()\ncounterfactual = wave1_pre_mean + (smoothed.loc[post_idx, 2].values - wave2_pre_mean)\n\nfig, ax = plt.subplots(figsize=(10, 5.5))\nax.axvspan(-0.5, TREATMENT_WEEK, alpha=0.04, color=\"#94A3B8\", zorder=0)\nax.axvspan(TREATMENT_WEEK, 29.5, alpha=0.06, color=\"#3B82F6\", zorder=0)\nax.plot(smoothed.index, smoothed[2], \"s--\", color=\"#F59E0B\", linewidth=2,\n        markersize=4, label=\"Wave 2 \u2014 control (untreated during this window)\", zorder=3)\nax.plot(smoothed.index, smoothed[1], \"o-\", color=\"#2563EB\", linewidth=2.2,\n        markersize=4, label=\"Wave 1 \u2014 treated (AI feature on at week 20)\", zorder=4)\nax.plot(post_idx, counterfactual, \":\", color=\"#2563EB\", linewidth=2.2,\n        label=\"Wave 1 counterfactual (projected without treatment)\", zorder=4)\nax.axvline(TREATMENT_WEEK, color=\"#DC2626\", linestyle=\"--\", linewidth=1.8,\n           label=\"AI feature launched (week 20)\")\n\nax.text(9.5, 0.508, \"Pre-treatment periodn(parallel trends required)\",\n        fontsize=9, ha=\"center\", color=\"#64748B\", style=\"italic\")\nax.text(24, 0.508, \"Post-treatment\",\n        fontsize=9, ha=\"center\", color=\"#64748B\", style=\"italic\")\nax.set_xlabel(\"Week\", fontsize=11)\nax.set_ylabel(\"Mean task completion rate\", fontsize=11)\nax.set_title(\"Figure 2: Data-Driven Parallel-Trends Checkn(3-week rolling average, 50k users)\",\n             fontsize=12, fontweight=\"bold\", pad=14)\nax.legend(loc=\"upper left\", fontsize=9, framealpha=0.92)\nax.set_xlim(-0.5, 29.5)\nax.set_ylim(0.50, 0.72)\nax.grid(True, alpha=0.18, linestyle=\":\")\nax.tick_params(labelsize=10)\nplt.tight_layout()\nplt.savefig(\"parallel_trends.png\", dpi=150, bbox_inches=\"tight\")\nprint(\"Saved parallel_trends.png\")\n<\/code><\/pre>\n<p><strong>\u0645\u062a\u0648\u0642\u0639 \u0646\u062a\u0627\u0626\u062c (\u0634\u06a9\u0644 2\u060c \u0688\u06cc\u0679\u0627 \u0633\u06d2 \u0686\u0644\u0646\u06d2 \u0648\u0627\u0644\u06cc \u062a\u0648\u062b\u06cc\u0642):<\/strong><\/p>\n<pre><code class=\"language-text\">Saved parallel_trends.png\n<\/code><\/pre>\n<p><img decoding=\"async\" src=\"https:\/\/umang.pk\/wp-content\/uploads\/2026\/04\/1776928181_495_AI-\u06a9\u06d2-\u0622\u063a\u0627\u0632-\u06a9\u06d2-\u0644\u06cc\u06d2-\u067e\u0631\u0648\u0688\u06a9\u0679-\u06a9\u0627-\u062a\u062c\u0631\u0628\u06c1-AB-\u0679\u06cc\u0633\u0679\u0646\u06af.png\" alt=\"\u0645\u062a\u0648\u0627\u0632\u06cc \u0631\u062c\u062d\u0627\u0646\u0627\u062a \u06a9\u06cc \u0628\u0635\u0631\u06cc \u062a\u0635\u062f\u06cc\u0642\u060c \u0688\u06cc\u0679\u0627 \u0633\u06d2 \u0686\u0644\u0646\u06d2 \u0648\u0627\u0644\u06cc \u062a\u0635\u062f\u06cc\u0642\" style=\"display:block;margin:0 auto\" width=\"600\" height=\"400\" loading=\"lazy\" title=\"\"><\/p>\n<p><em>\u0634\u06a9\u0644 2 \u062d\u0642\u06cc\u0642\u06cc \u0688\u06cc\u0679\u0627 \u0633\u06cc\u0679 \u06a9\u0627 \u0688\u06cc\u0679\u0627 \u0633\u06d2 \u0686\u0644\u0646\u06d2 \u0648\u0627\u0644\u0627 \u0645\u062a\u0648\u0627\u0632\u06cc \u0679\u0631\u06cc\u0646\u0688 \u0686\u06cc\u06a9 \u06c1\u06d2\u060c \u062c\u0648 \u06c1\u0641\u062a\u06c1 \u0648\u0627\u0631 \u0646\u0645\u0648\u0646\u06d2 \u0644\u06cc\u0646\u06d2 \u06a9\u06d2 \u0634\u0648\u0631 \u06a9\u0648 \u06c1\u0645\u0648\u0627\u0631 \u06a9\u0631\u0646\u06d2 \u06a9\u06d2 \u0644\u06cc\u06d2 \u062a\u06cc\u0646 \u06c1\u0641\u062a\u06d2 \u06a9\u06cc \u0645\u062a\u062d\u0631\u06a9 \u0627\u0648\u0633\u0637 \u06a9\u06d2 \u0637\u0648\u0631 \u067e\u0631 \u067e\u06cc\u0634 \u06a9\u06cc\u0627 \u062c\u0627\u062a\u0627 \u06c1\u06d2\u06d4 \u062f\u0648\u0646\u0648\u06ba \u0644\u06c1\u0631\u06cc\u06ba 20 \u06c1\u0641\u062a\u06d2 \u067e\u06c1\u0644\u06d2 \u0627\u06cc\u06a9 \u062f\u0648\u0633\u0631\u06d2 \u06a9\u0648 \u0642\u0631\u06cc\u0628 \u0633\u06d2 \u0679\u0631\u06cc\u06a9 \u06a9\u0631\u062a\u06cc \u06c1\u06cc\u06ba\u060c \u067e\u0686\u06be\u0644\u06d2 \u062f\u0648\u0631 \u06a9\u06d2 \u0686\u06be\u0648\u0679\u06d2 \u062c\u06be\u0679\u06a9\u0648\u06ba \u06a9\u06d2 \u0633\u0627\u062a\u06be \u0627\u06cc\u06a9 \u06c1\u06cc \u0648\u0642\u062a \u0645\u06cc\u06ba \u062f\u0648\u0646\u0648\u06ba \u06af\u0631\u0648\u06c1\u0648\u06ba \u06a9\u0648 \u0645\u062a\u0627\u062b\u0631 \u06a9\u0631\u062a\u06d2 \u06c1\u06cc\u06ba\u060c \u062c\u0633\u06d2 \u06c1\u0645 \u0645\u062a\u0648\u0627\u0632\u06cc \u0631\u062c\u062d\u0627\u0646\u0627\u062a \u06a9\u06d2 \u0637\u0648\u0631 \u067e\u0631 \u062f\u06cc\u06a9\u06be\u062a\u06d2 \u06c1\u06cc\u06ba\u06d4 \u06c1\u0641\u062a\u06c1 20 \u06a9\u06d2 \u0628\u0639\u062f\u060c \u0644\u06c1\u0631 1 \u0646\u0642\u0637\u06d2 \u0648\u0627\u0644\u06cc \u0644\u0627\u0626\u0646 \u06a9\u06d2 \u0645\u062e\u0627\u0644\u0641 \u0679\u06be\u0648\u0633 \u0644\u0627\u0626\u0646 \u06a9\u06d2 \u0627\u0648\u067e\u0631 \u0635\u0627\u0641 \u0637\u0648\u0631 \u067e\u0631 \u0627\u0644\u06af \u06c1\u0648 \u062c\u0627\u062a\u06cc \u06c1\u06d2\u06d4 \u067e\u0648\u0633\u0679 \u067e\u0631\u0648\u0633\u06cc\u0633\u0646\u06af \u0648\u0646\u0688\u0648 \u0645\u06cc\u06ba \u0646\u06cc\u0644\u06cc \u0679\u06be\u0648\u0633 \u0627\u0648\u0631 \u0688\u06cc\u0634\u0688 \u0644\u0627\u0626\u0646\u0648\u06ba \u06a9\u06d2 \u062f\u0631\u0645\u06cc\u0627\u0646 \u0641\u0631\u0642 \u062d\u0642\u06cc\u0642\u06cc \u0688\u06cc\u0679\u0627 \u0633\u06d2 \u062f\u0648\u0628\u0627\u0631\u06c1 \u062a\u06cc\u0627\u0631 \u06a9\u0631\u062f\u06c1 \u0688\u06cc \u0688\u06cc \u062a\u062e\u0645\u06cc\u0646\u06c1 \u06c1\u06d2\u06d4<\/em><\/p>\n<p>\u06cc\u06c1\u0627\u06ba \u06a9\u06cc\u0627 \u06c1\u0648 \u0631\u06c1\u0627 \u06c1\u06d2: \u0633\u0627\u0626\u0646 \u0627\u067e \u06c1\u0641\u062a\u06c1 \u0627\u0648\u0631 \u0644\u06c1\u0631 \u06a9\u06d2 \u0644\u062d\u0627\u0638 \u0633\u06d2 \u06af\u0631\u0648\u067e \u0628\u0646\u0627\u0626\u06cc\u06ba\u060c \u0641\u06cc \u0633\u06cc\u0644 \u06a9\u0627\u0645 \u06a9\u06cc \u0627\u0648\u0633\u0637 \u062a\u06a9\u0645\u06cc\u0644 \u06a9\u0627 \u062d\u0633\u0627\u0628 \u0644\u06af\u0627\u0626\u06cc\u06ba\u060c \u067e\u06cc\u0648\u0679 \u06a9\u0631\u06cc\u06ba \u062a\u0627\u06a9\u06c1 \u06c1\u0631 \u0644\u06c1\u0631 \u0627\u06cc\u06a9 \u06a9\u0627\u0644\u0645 \u06c1\u0648\u060c \u0627\u0648\u0631 \u062f\u0648\u0646\u0648\u06ba \u0679\u0627\u0626\u0645 \u0633\u06cc\u0631\u06cc\u0632 \u06a9\u0648 \u0627\u06cc\u06a9 \u0633\u0627\u062a\u06be \u062f\u06a9\u06be\u0627\u0626\u06cc\u06ba\u06d4<\/p>\n<p>\u0639\u0645\u0648\u062f\u06cc \u0688\u06cc\u0634\u0688 \u0644\u0627\u0626\u0646 \u06c1\u0641\u062a\u06c1 20 \u06a9\u0648 \u0646\u0634\u0627\u0646 \u0632\u062f \u06a9\u0631\u062a\u06cc \u06c1\u06d2\u060c \u062c\u0628 \u067e\u06c1\u0644\u06cc \u0644\u06c1\u0631 \u06a9\u0627 \u0639\u0644\u0627\u062c \u06c1\u0648\u0627\u06d4 \u0639\u0644\u0627\u062c \u0633\u06d2 \u067e\u06c1\u0644\u06d2 \u06a9\u06cc \u0645\u062f\u062a (0-19 \u06c1\u0641\u062a\u0648\u06ba) \u0645\u06cc\u06ba\u060c \u062f\u0648\u0646\u0648\u06ba \u0633\u06cc\u0631\u06cc\u0632 \u06a9\u0648 \u0627\u06cc\u06a9 \u062f\u0648\u0633\u0631\u06d2 \u06a9\u0648 \u0642\u0631\u06cc\u0628 \u0633\u06d2 \u0679\u0631\u06cc\u06a9 \u06a9\u0631\u0646\u0627 \u0686\u0627\u06c1\u06cc\u06d2\u06d4 \u06c1\u0641\u062a\u06c1 20 \u06a9\u06d2 \u0628\u0639\u062f\u060c Wave 1 \u06a9\u0648 Wave 2 \u06a9\u06cc \u062a\u0642\u0631\u06cc\u0628\u0627\u064b \u0639\u0644\u0627\u062c \u06a9\u06d2 \u0627\u062b\u0631 \u0633\u06d2 \u0631\u06c1\u0646\u0645\u0627\u0626\u06cc \u06a9\u0631\u0646\u06cc \u0686\u0627\u06c1\u06cc\u06d2\u06d4<\/p>\n<p>\u0627\u06af\u0631 \u0622\u067e \u0646\u0645\u0628\u0631\u0648\u06ba \u06a9\u0648 \u06a9\u0645 \u06a9\u0631\u0646\u0627 \u0686\u0627\u06c1\u062a\u06d2 \u06c1\u06cc\u06ba\u060c \u062a\u0648 \u0635\u0631\u0641 \u0639\u0644\u0627\u062c \u0633\u06d2 \u067e\u06c1\u0644\u06d2 \u06a9\u06cc \u0645\u062f\u062a \u06a9\u06d2 \u0644\u06cc\u06d2 \u067e\u0644\u06cc\u0633\u0628\u0648 \u0631\u06cc\u06af\u0631\u06cc\u0634\u0646 \u0686\u0644\u0627\u0626\u06cc\u06ba\u06d4 \u06c1\u0645 \u067e\u0631\u0648\u0633\u06cc\u0633 \u0634\u062f\u06c1 \u0627\u0634\u0627\u0631\u06d2 \u06a9\u06d2 \u0633\u0627\u062a\u06be \u062a\u0639\u0627\u0645\u0644 \u06a9\u0631\u0646\u06d2 \u0648\u0627\u0644\u06d2 \u0644\u06a9\u06cc\u0631\u06cc \u0648\u0642\u062a \u06a9\u06d2 \u0631\u062c\u062d\u0627\u0646 \u06a9\u06d2 \u062e\u0644\u0627\u0641 \u0646\u062a\u0627\u0626\u062c \u06a9\u0648 \u067e\u06cc\u0686\u06be\u06d2 \u0686\u06be\u0648\u0691\u062a\u06d2 \u06c1\u06cc\u06ba\u06d4 \u0627\u06af\u0631 \u062a\u0639\u0627\u0645\u0644 \u06a9\u0627 \u06af\u062a\u0627\u0646\u06a9 0 \u06a9\u06d2 \u0642\u0631\u06cc\u0628 \u062a\u06be\u0627 \u0627\u0648\u0631 \u0627\u06c1\u0645 \u0646\u06c1\u06cc\u06ba \u062a\u06be\u0627\u060c \u062a\u0648 \u062f\u0648\u0646\u0648\u06ba \u06af\u0631\u0648\u067e \u0639\u0644\u0627\u062c \u0633\u06d2 \u067e\u06c1\u0644\u06d2 \u0645\u062a\u0648\u0627\u0632\u06cc \u0637\u0648\u0631 \u067e\u0631 \u0645\u0646\u062a\u0642\u0644 \u06c1\u0648 \u06af\u0626\u06d2 \u062a\u06be\u06d2\u06d4<\/p>\n<pre><code class=\"language-python\">pre_only = analysis[analysis.post == 0].copy()\npre_only[\"weeks_since_start\"] = pre_only.signup_week - 10  # center\n\nplacebo_model = smf.ols(\n    \"task_completed ~ treated * weeks_since_start + C(engagement_tier)\",\n    data=pre_only\n).fit(\n    cov_type=\"cluster\",\n    cov_kwds={\"groups\": pre_only.workspace_id}\n)\n\nprint(\"Pre-trend slope difference:\",\n      placebo_model.params[\"treated:weeks_since_start\"])\nprint(\"p-value:\",\n      placebo_model.pvalues[\"treated:weeks_since_start\"])\n<\/code><\/pre>\n<p><strong>\u0645\u062a\u0648\u0642\u0639 \u067e\u06cc\u062f\u0627\u0648\u0627\u0631:<\/strong><\/p>\n<pre><code class=\"language-text\">Pre-trend slope difference: -0.00095...\np-value: 0.4435...\n<\/code><\/pre>\n<p>\u06cc\u06c1\u0627\u06ba \u06a9\u06cc\u0627 \u06c1\u0648 \u0631\u06c1\u0627 \u06c1\u06d2: \u0627\u067e\u0646\u06d2 \u0622\u067e \u06a9\u0648 \u0639\u0644\u0627\u062c \u0633\u06d2 \u067e\u06c1\u0644\u06d2 \u06a9\u06d2 \u0645\u0634\u0627\u06c1\u062f\u0627\u062a \u062a\u06a9 \u0645\u062d\u062f\u0648\u062f \u0631\u06a9\u06be\u062a\u06d2 \u06c1\u0648\u0626\u06d2\u060c \u06c1\u0645 \u0627\u06cc\u06a9 \u0631\u062c\u0639\u062a \u06a9\u0648 \u0641\u0679 \u06a9\u0631\u062a\u06d2 \u06c1\u06cc\u06ba \u06a9\u06c1 \u0644\u06c1\u0631 1 \u0627\u0648\u0631 \u0644\u06c1\u0631 2 \u0639\u0644\u0627\u062c \u0633\u06d2 \u067e\u06c1\u0644\u06d2 \u06a9\u06cc \u0645\u062f\u062a \u0645\u06cc\u06ba \u0645\u062e\u062a\u0644\u0641 \u0644\u06a9\u06cc\u0631\u06cc \u0631\u062c\u062d\u0627\u0646\u0627\u062a \u06a9\u06cc \u067e\u06cc\u0631\u0648\u06cc \u06a9\u0631\u062a\u06d2 \u06c1\u06cc\u06ba \u0627\u0648\u0631 \u062a\u0639\u0627\u0645\u0644 \u06a9\u06d2 \u0642\u0627\u0628\u0644\u06cc\u062a \u06a9\u0648 \u067e\u0691\u06be\u062a\u06d2 \u06c1\u06cc\u06ba\u06d4<\/p>\n<p>0 \u06a9\u06d2 \u0642\u0631\u06cc\u0628 \u0627\u06cc\u06a9 \u0639\u062f\u062f\u060c p > 0.05 \u06a9\u06d2 \u0633\u0627\u062a\u06be\u060c \u06a9\u0627 \u0645\u0637\u0644\u0628 \u06c1\u06d2 \u06a9\u06c1 \u0639\u0644\u0627\u062c \u0633\u06d2 \u067e\u06c1\u0644\u06d2 \u062f\u0648\u0646\u0648\u06ba \u0644\u06c1\u0631\u06cc\u06ba \u0645\u062a\u0648\u0627\u0632\u06cc \u062d\u0631\u06a9\u062a \u06a9\u0631\u062a\u06cc \u06c1\u06cc\u06ba\u06d4 \u0627\u06af\u0631 \u06af\u062a\u0627\u0646\u06a9 \u0628\u0691\u0627 \u0627\u0648\u0631 \u0634\u0645\u0627\u0631\u06cc\u0627\u062a\u06cc \u0644\u062d\u0627\u0638 \u0633\u06d2 \u0627\u06c1\u0645 \u06c1\u06d2 \u062a\u0648 \u0645\u062a\u0648\u0627\u0632\u06cc \u0631\u062c\u062d\u0627\u0646\u0627\u062a \u06a9\u0627 \u0645\u0641\u0631\u0648\u0636\u06c1 \u0679\u0648\u0679 \u062c\u0627\u062a\u0627 \u06c1\u06d2\u06d4 \u06cc\u0639\u0646\u06cc\u060c \u0688\u06cc \u0622\u0626\u06cc \u0688\u06cc \u06a9\u0627 \u062a\u062e\u0645\u06cc\u0646\u06c1 \u0627\u0646 \u062a\u0645\u0627\u0645 \u062a\u0641\u0631\u06cc\u0642 \u0631\u062c\u062d\u0627\u0646\u0627\u062a \u06a9\u0648 \u062c\u0630\u0628 \u06a9\u0631\u062a\u0627 \u06c1\u06d2 \u062c\u0646\u06c1\u0648\u06ba \u0646\u06d2 20 \u06c1\u0641\u062a\u06d2 \u0642\u0628\u0644 \u06af\u0631\u0648\u067e\u0648\u06ba \u06a9\u0648 \u0627\u0644\u06af \u06a9\u06cc\u0627 \u062a\u06be\u0627\u06d4<\/p>\n<p>\u0627\u06af\u0631 \u067e\u0644\u06cc\u0633\u0628\u0648 \u0679\u06cc\u0633\u0679 \u0646\u0627\u06a9\u0627\u0645 \u06c1\u0648 \u062c\u0627\u062a\u0627 \u06c1\u06d2 \u062a\u0648 \u0631\u06a9\u06cc\u06ba \u0627\u0648\u0631 \u062f\u0648\u0628\u0627\u0631\u06c1 \u0633\u0648\u0686\u06cc\u06ba\u06d4 \u0627\u062e\u062a\u06cc\u0627\u0631\u0627\u062a \u06cc\u06c1 \u06c1\u06cc\u06ba: \u0645\u062a\u0648\u0627\u0632\u06cc \u0631\u062c\u062d\u0627\u0646\u0627\u062a \u06a9\u06d2 \u0633\u0627\u062a\u06be \u0627\u06cc\u06a9 \u062a\u0646\u06af \u067e\u0631\u0627\u0646\u06cc \u0648\u0646\u0688\u0648 \u062a\u06a9 \u0645\u062d\u062f\u0648\u062f \u0631\u06a9\u06be\u06cc\u06ba\u060c \u06a9\u0646\u0679\u0631\u0648\u0644\u0632 \u06a9\u0627 \u0627\u06cc\u06a9 \u0628\u06c1\u062a\u0631 \u06af\u0631\u0648\u067e \u062a\u0644\u0627\u0634 \u06a9\u0631\u06cc\u06ba\u060c \u06cc\u0627 \u0645\u0635\u0646\u0648\u0639\u06cc \u06a9\u0646\u0679\u0631\u0648\u0644\u0632 \u067e\u0631 \u0633\u0648\u0626\u0686 \u06a9\u0631\u06cc\u06ba \u062c\u0648 \u0645\u062a\u0639\u062f\u062f \u062e\u0627\u0645 \u0627\u06a9\u0627\u0626\u06cc\u0648\u06ba \u0633\u06d2 \u0648\u0632\u0646\u06cc \u062c\u0648\u0627\u0628\u06cc \u062d\u0642\u0627\u0626\u0642 \u0628\u0646\u0627\u062a\u06d2 \u06c1\u06cc\u06ba\u06d4<\/p>\n<p>\u0627\u0633 \u0645\u0635\u0646\u0648\u0639\u06cc \u0688\u06cc\u0679\u0627\u0633\u06cc\u0679 \u067e\u0631 \u067e\u0644\u06cc\u0633\u0628\u0648 \u0679\u06cc\u0633\u0679 \u067e\u0627\u0633 \u06c1\u0648 \u06af\u06cc\u0627\u06d4 \u067e\u0631\u06cc \u0679\u0631\u06cc\u0646\u0688 \u0688\u06be\u0644\u0648\u0627\u0646 \u06a9\u0627 \u0641\u0631\u0642 -0.00095 (p = 0.44) \u06c1\u06d2\u060c \u0627\u0633 \u0644\u06cc\u06d2 \u0645\u062a\u0648\u0627\u0632\u06cc \u0631\u062c\u062d\u0627\u0646\u0627\u062a \u06a9\u0627 \u0642\u06cc\u0627\u0633 \u06c1\u06d2 \u0627\u0648\u0631 \u0645\u0631\u062d\u0644\u06c1 2 \u0633\u06d2 +0.054 \u06a9\u0627 \u062a\u062e\u0645\u06cc\u0646\u06c1 \u0642\u0627\u0628\u0644 \u0627\u0639\u062a\u0645\u0627\u062f \u06c1\u06d2\u06d4<\/p>\n<h2 id=\"heading-when-difference-in-differences-fails\">\u062c\u0628 \u0641\u0631\u0642 \u06a9\u0627 \u0641\u0631\u0642 \u0646\u0627\u06a9\u0627\u0645 \u06c1\u0648\u062c\u0627\u062a\u0627 \u06c1\u06d2\u06d4<\/h2>\n<p>DiD \u0627\u06a9\u0627\u0624\u0646\u0679\u0646\u06af \u06a9\u0627 \u0627\u06cc\u06a9 \u062f\u0631\u0633\u062a \u0637\u0631\u06cc\u0642\u06c1 \u06c1\u06d2\u060c \u0627\u0648\u0631 \u062a\u0645\u0627\u0645 \u062f\u0631\u0633\u062a \u0637\u0631\u06cc\u0642\u0648\u06ba \u0645\u06cc\u06ba \u06a9\u0686\u06be \u0646\u0627\u06a9\u0627\u0645\u06cc \u06a9\u06d2 \u0637\u0631\u06cc\u0642\u06d2 \u06c1\u0648\u062a\u06d2 \u06c1\u06cc\u06ba \u062c\u0646 \u06a9\u06d2 \u0628\u0627\u0631\u06d2 \u0645\u06cc\u06ba \u0622\u067e \u06a9\u0648 \u0646\u062a\u0627\u0626\u062c \u067e\u0631 \u0628\u06be\u0631\u0648\u0633\u06c1 \u06a9\u0631\u0646\u06d2 \u0633\u06d2 \u067e\u06c1\u0644\u06d2 \u0622\u06af\u0627\u06c1 \u06c1\u0648\u0646\u0627 \u0636\u0631\u0648\u0631\u06cc \u06c1\u06d2\u06d4 \u06cc\u06c1\u0627\u06ba \u0686\u0627\u0631 \u0639\u0627\u0645 \u06c1\u06cc\u06ba:<\/p>\n<h3 id=\"heading-1-non-parallel-pre-trends\">1. \u063a\u06cc\u0631 \u0645\u062a\u0648\u0627\u0632\u06cc \u067e\u0631\u06cc \u0631\u062c\u062d\u0627\u0646<\/h3>\n<p>\u0627\u06af\u0631 \u0639\u0644\u0627\u062c \u0627\u0648\u0631 \u06a9\u0646\u0679\u0631\u0648\u0644 \u06af\u0631\u0648\u067e \u0639\u0644\u0627\u062c \u0634\u0631\u0648\u0639 \u06c1\u0648\u0646\u06d2 \u0633\u06d2 \u067e\u06c1\u0644\u06d2 \u06c1\u06cc \u0645\u062e\u062a\u0644\u0641 \u06c1\u0648 \u0631\u06c1\u06d2 \u06c1\u06cc\u06ba\u060c \u062a\u0648 DiD \u0639\u0644\u0627\u062c \u06a9\u06d2 \u0627\u062b\u0631 \u06a9\u06d2 \u0644\u06cc\u06d2 \u0645\u0648\u062c\u0648\u062f\u06c1 \u0628\u06c1\u0627\u0624 \u06a9\u0648 \u063a\u0644\u0637 \u0633\u0645\u062c\u06be\u062a\u0627 \u06c1\u06d2\u06d4<\/p>\n<p>\u062a\u06cc\u0646 \u0645\u0631\u0627\u062d\u0644 \u06a9\u0627 \u067e\u0644\u06cc\u0633\u0628\u0648 \u0679\u06cc\u0633\u0679 \u0645\u062d\u0641\u0648\u0638 \u06c1\u06d2\u06d4 \u0627\u0633\u06d2 \u06c1\u0631 \u0628\u0627\u0631 \u0686\u0644\u0627\u0646\u06d2 \u06a9\u06cc \u06a9\u0648\u0634\u0634 \u06a9\u0631\u06cc\u06ba\u06d4 \u0627\u06af\u0631 \u0622\u067e \u0646\u0627\u06a9\u0627\u0645 \u06c1\u0648 \u062c\u0627\u062a\u06d2 \u06c1\u06cc\u06ba\u060c \u062a\u0648 \u0622\u067e \u06a9\u06d2 \u067e\u0627\u0633 \u062a\u06cc\u0646 \u0627\u062e\u062a\u06cc\u0627\u0631\u0627\u062a \u06c1\u06cc\u06ba:<\/p>\n<ol>\n<li>\n<p>\u0627\u067e\u0646\u06d2 \u062a\u062c\u0632\u06cc\u06d2 \u06a9\u0648 \u067e\u06c1\u0644\u06d2 \u06a9\u06cc \u0645\u062e\u062a\u0635\u0631 \u0645\u062f\u062a \u062a\u06a9 \u0645\u062d\u062f\u0648\u062f \u0631\u06a9\u06be\u06cc\u06ba \u062c\u06c1\u0627\u06ba \u0631\u062c\u062d\u0627\u0646\u0627\u062a \u0627\u06cc\u06a9 \u062c\u06cc\u0633\u06d2 \u06c1\u0648\u06ba \u0627\u0648\u0631 \u067e\u0644\u06cc\u0633\u0628\u0648 \u06a9\u0648 \u062f\u0648\u0628\u0627\u0631\u06c1 \u0686\u0644\u0627\u0626\u06cc\u06ba\u06d4<\/p>\n<\/li>\n<li>\n<p>\u0627\u06cc\u06a9 \u0628\u06c1\u062a\u0631 \u06a9\u0646\u0679\u0631\u0648\u0644 \u06af\u0631\u0648\u067e \u062a\u0644\u0627\u0634 \u06a9\u0631\u06cc\u06ba \u062c\u0633 \u06a9\u06d2 \u0633\u0627\u0628\u0642\u06c1 \u200b\u200b\u0631\u062c\u062d\u0627\u0646\u0627\u062a \u0639\u0644\u0627\u062c \u06a9\u06d2 \u06af\u0631\u0648\u067e \u0633\u06d2 \u0645\u0645\u0627\u062b\u0644 \u06c1\u0648\u06ba\u06d4<\/p>\n<\/li>\n<li>\n<p>\u06c1\u0645 \u0645\u062a\u0639\u062f\u062f \u063a\u06cc\u0631 \u067e\u0631\u0648\u0633\u06cc\u0633 \u0634\u062f\u06c1 \u0627\u06a9\u0627\u0626\u06cc\u0648\u06ba \u0633\u06d2 \u0648\u0632\u0646\u06cc \u062c\u0648\u0627\u0628\u06cc \u062d\u0642\u0627\u0626\u0642 \u0628\u0646\u0627\u062a\u06d2 \u06c1\u06cc\u06ba \u0627\u0648\u0631 \u0645\u0635\u0646\u0648\u0639\u06cc \u06a9\u0646\u0679\u0631\u0648\u0644 \u067e\u0631 \u0633\u0648\u0626\u0686 \u06a9\u0631\u062a\u06d2 \u06c1\u06cc\u06ba\u060c \u062c\u0648 \u0627\u06cc\u0633\u06d2 \u0648\u0632\u0646 \u06a9\u0627 \u0627\u0646\u062a\u062e\u0627\u0628 \u06a9\u0631\u062a\u0627 \u06c1\u06d2 \u062c\u0648 \u0639\u0644\u0627\u062c \u0634\u062f\u06c1 \u06af\u0631\u0648\u067e\u0648\u06ba \u06a9\u06cc \u067e\u0631\u06cc \u067e\u0631\u0648\u0633\u06cc\u0633\u0646\u06af \u0631\u0641\u062a\u0627\u0631 \u0633\u06d2 \u0645\u06cc\u0644 \u06a9\u06be\u0627\u062a\u0627 \u06c1\u06d2\u06d4<\/p>\n<\/li>\n<\/ol>\n<h3 id=\"heading-2-staggered-adoption\">2. \u0644\u0691\u06a9\u06be\u0691\u0627 \u06a9\u0631 \u0627\u067e\u0646\u0627\u0646\u0627<\/h3>\n<p>\u062a\u06cc\u0646 \u06cc\u0627 \u0632\u06cc\u0627\u062f\u06c1 \u0644\u06c1\u0631\u0648\u06ba \u06a9\u06d2 \u0633\u0627\u062a\u06be \u0645\u0631\u062d\u0644\u06c1 \u0648\u0627\u0631 \u0631\u0648\u0644 \u0622\u0624\u0679 \u06a9\u06d2 \u0644\u06cc\u06d2 \u0635\u0627\u0641 2x2 \u0633\u06d2 \u0645\u062e\u062a\u0644\u0641 \u0646\u0642\u0637\u06c1 \u0646\u0638\u0631 \u06a9\u06cc \u0636\u0631\u0648\u0631\u062a \u06c1\u0648\u062a\u06cc \u06c1\u06d2\u06d4 \u0648\u06cc\u0648 1 \u06c1\u0641\u062a\u06c1 20 \u067e\u0631\u060c \u0648\u06cc\u0648 2 \u067e\u0631 \u06c1\u0641\u062a\u06c1 30 \u067e\u0631 \u0627\u0648\u0631 \u0648\u06cc\u0648 3 \u067e\u0631 \u06c1\u0641\u062a\u06c1 40 \u067e\u0631 \u06a9\u0627\u0631\u0631\u0648\u0627\u0626\u06cc \u06a9\u06cc \u062c\u0627\u062a\u06cc \u06c1\u06d2\u06d4 \u0627\u06cc\u06a9 \u0628\u0627\u0631 \u0648\u06cc\u0648 2 \u067e\u0631 \u06a9\u0627\u0631\u0631\u0648\u0627\u0626\u06cc \u06c1\u0648 \u062c\u0627\u0646\u06d2 \u06a9\u06d2 \u0628\u0639\u062f\u060c \u06cc\u06c1 30 \u0627\u0648\u0631 \u0627\u0633 \u06a9\u06d2 \u0628\u0639\u062f \u06a9\u06d2 \u0648\u06cc\u0648 1 \u06a9\u06d2 \u0645\u0648\u0627\u0632\u0646\u06c1 \u06a9\u06d2 \u0644\u06cc\u06d2 \u062f\u0631\u0633\u062a \u06a9\u0646\u0679\u0631\u0648\u0644 \u0646\u06c1\u06cc\u06ba \u0631\u06c1\u062a\u0627 \u06c1\u06d2\u06d4 \u067e\u06c1\u0644\u06d2 \u067e\u0631\u0648\u0633\u06cc\u0633 \u0634\u062f\u06c1 \u06cc\u0648\u0646\u0679\u0633 \u0628\u0639\u062f \u0645\u06cc\u06ba \u067e\u0631\u0648\u0633\u06cc\u0633 \u0634\u062f\u06c1 \u06cc\u0648\u0646\u0679\u0633 \u06a9\u06d2 \u0644\u06cc\u06d2 \u06a9\u0646\u0679\u0631\u0648\u0644 \u06a9\u06d2 \u0637\u0648\u0631 \u067e\u0631 \u06a9\u0627\u0645 \u06a9\u0631\u0646\u0627 \u0634\u0631\u0648\u0639 \u06a9\u0631 \u062f\u06cc\u062a\u06d2 \u06c1\u06cc\u06ba\u060c \u0627\u0646\u062f\u0627\u0632\u0648\u06ba \u06a9\u0648 \u0622\u0644\u0648\u062f\u06c1 \u06a9\u0631\u062a\u06d2 \u06c1\u06cc\u06ba\u06d4<\/p>\n<p>\u06cc\u06c1 \u06af\u0688\u0645\u06cc\u0646 \u0628\u06cc\u06a9\u0646 \u0633\u0691\u0646\u06d2 \u06a9\u0627 \u0645\u0633\u0626\u0644\u06c1 \u06c1\u06d2\u060c \u0627\u0648\u0631 \u0627\u0633\u0679\u06cc\u062c 2 \u0645\u06cc\u06ba \u0645\u0639\u06cc\u0627\u0631\u06cc \u062f\u0648 \u0637\u0631\u0641\u06c1 \u0641\u06a9\u0633\u0688 \u0627\u062b\u0631\u0627\u062a \u06a9\u0627 \u062a\u062e\u0645\u06cc\u0646\u06c1 \u0644\u06af\u0627\u0646\u06d2 \u0648\u0627\u0644\u0627 \u0627\u0633\u06d2 \u062e\u0648\u062f \u0628\u062e\u0648\u062f \u062c\u0630\u0628 \u06a9\u0631 \u0644\u06cc\u062a\u0627 \u06c1\u06d2\u06d4 Callaway-Sant'Anna \u06a9\u0627 \u062a\u062e\u0645\u06cc\u0646\u06c1 \u0644\u06af\u0627\u0646\u06d2 \u0648\u0627\u0644\u0627 (2021 \u067e\u06cc\u067e\u0631 \u062f\u06cc\u06a9\u06be\u06cc\u06ba) \u0627\u0633 \u0645\u0633\u0626\u0644\u06d2 \u06a9\u0648 \u0635\u0631\u0641 \u0635\u0627\u0641 2x2 \u0645\u0648\u0627\u0632\u0646\u06c1 \u06a9\u06cc \u0627\u0648\u0633\u0637 \u0633\u06d2 \u062d\u0644 \u06a9\u0631\u062a\u0627 \u06c1\u06d2 \u0627\u0648\u0631 \u0622\u0644\u0648\u062f\u06c1 \u0645\u0648\u0627\u0632\u0646\u06c1 \u06a9\u0648 \u0645\u0633\u062a\u0631\u062f \u06a9\u0631\u062a\u0627 \u06c1\u06d2\u06d4 \u06a9\u06c1 <code>differences<\/code> \u0627\u0632\u06af\u0631 \u0645\u06cc\u06ba \u0627\u06cc\u06a9 \u067e\u06cc\u06a9\u06cc\u062c \u0627\u0633 \u06a9\u0648 \u0646\u0627\u0641\u0630 \u06a9\u0631\u062a\u0627 \u06c1\u06d2\u06d4<\/p>\n<h3 id=\"heading-3-time-varying-confounders-that-hit-only-the-treated-group\">3. \u0648\u0642\u062a \u06a9\u06d2 \u0644\u062d\u0627\u0638 \u0633\u06d2 \u0645\u062e\u062a\u0644\u0641 \u0627\u0644\u062c\u06be\u0646\u06d2 \u0648\u0627\u0644\u06d2 \u0639\u0648\u0627\u0645\u0644 \u062c\u0648 \u0635\u0631\u0641 \u0639\u0644\u0627\u062c \u0634\u062f\u06c1 \u06af\u0631\u0648\u067e \u06a9\u0648 \u0645\u062a\u0627\u062b\u0631 \u06a9\u0631\u062a\u06d2 \u06c1\u06cc\u06ba\u06d4<\/h3>\n<p>\u0627\u06af\u0631 \u0622\u067e \u06a9\u06cc \u0645\u0627\u0631\u06a9\u06cc\u0679\u0646\u06af \u0679\u06cc\u0645 \u06c1\u0641\u062a\u06c1 22 \u0645\u06cc\u06ba \u0622\u067e \u06a9\u06d2 \u0628\u0646\u06cc\u0627\u062f\u06cc \u0648\u0631\u06a9 \u0627\u0633\u067e\u06cc\u0633 \u0645\u06cc\u06ba \u0627\u06cc\u06a9 \u0679\u0627\u0631\u06af\u0679\u0688 \u0645\u06c1\u0645 \u0686\u0644\u0627\u062a\u06cc \u06c1\u06d2\u060c \u062a\u0648 \u0622\u067e \u06a9\u0648 \u0639\u0644\u0627\u062c \u0633\u06d2 \u0645\u062a\u0639\u0644\u0642 \u0627\u06cc\u06a9 \u062c\u06be\u0679\u06a9\u0627 \u0644\u06af\u06d2 \u06af\u0627 \u062c\u0633\u06d2 DiD \u0628\u0631\u062f\u0627\u0634\u062a \u0646\u06c1\u06cc\u06ba \u06a9\u0631 \u0633\u06a9\u062a\u0627\u06d4<\/p>\n<p>\u0645\u062a\u0648\u0627\u0632\u06cc \u0631\u062c\u062d\u0627\u0646\u0627\u062a \u0639\u0644\u0627\u062c \u0633\u06d2 \u067e\u06c1\u0644\u06d2 \u06a9\u06cc \u0645\u062f\u062a \u06a9\u06cc \u062a\u0635\u062f\u06cc\u0642 \u06a9\u0631\u062a\u06d2 \u06c1\u06cc\u06ba\u060c \u0644\u06cc\u06a9\u0646 \u0639\u0644\u0627\u062c \u06a9\u06d2 \u0628\u0639\u062f \u06a9\u06cc \u0645\u062f\u062a \u0622\u0688\u06cc\u0679\u0646\u06af \u06a9\u06d2 \u0644\u06cc\u06d2 \u0630\u0645\u06c1 \u062f\u0627\u0631 \u06c1\u06d2\u06d4<\/p>\n<p>\u062a\u062c\u0632\u06cc\u06c1 \u0648\u0646\u0688\u0648 \u06a9\u06d2 \u0627\u0646\u062f\u0631 \u062a\u0645\u0627\u0645 \u0645\u0635\u0646\u0648\u0639\u0627\u062a \u06cc\u0627 \u0645\u0627\u0631\u06a9\u06cc\u0679\u0646\u06af \u06a9\u06d2 \u0648\u0627\u0642\u0639\u0627\u062a \u06a9\u0648 \u0686\u06cc\u06a9 \u06a9\u0631\u06cc\u06ba\u06d4 \u0627\u06cc\u06a9 \u0628\u0627\u0631 \u0645\u0644 \u062c\u0627\u0646\u06d2 \u06a9\u06d2 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\u0679\u06cc\u0648\u0679\u0648\u0631\u06cc\u0644 \u06a9\u06d2 \u0644\u06cc\u06d2 \u0633\u0627\u062a\u06be\u06cc \u0646\u0648\u0679 \u0628\u06a9 \u06cc\u06c1\u0627\u06ba \u06c1\u06d2\u06d4 \u0631\u06cc\u067e\u0648\u0632\u0679\u0631\u06cc \u06a9\u0648 \u06a9\u0644\u0648\u0646 \u06a9\u0631\u06cc\u06ba \u0627\u0648\u0631 \u0627\u0633 \u06a9\u0627 \u0627\u0633\u062a\u0639\u0645\u0627\u0644 \u06a9\u0631\u062a\u06d2 \u06c1\u0648\u0626\u06d2 \u0627\u06cc\u06a9 \u0645\u0635\u0646\u0648\u0639\u06cc \u0688\u06cc\u0679\u0627\u0633\u06cc\u0679 \u0628\u0646\u0627\u0626\u06cc\u06ba: <code>generate_data.py<\/code>\u0627\u0648\u0631 \u06a9\u06be\u0648\u0644\u06cc\u06ba <code>did_demo.ipynb<\/code> \u067e\u06c1\u0644\u06d2 \u0633\u06d2 \u0645\u062d\u0641\u0648\u0638 \u0634\u062f\u06c1 \u0622\u0624\u0679 \u067e\u0679 \u06a9\u06d2 \u0633\u0627\u062a\u06be \u06a9\u0633\u06cc \u06a9\u0648\u0688 \u0628\u0644\u0627\u06a9 \u06a9\u0648 \u062f\u0648\u0628\u0627\u0631\u06c1 \u062a\u06cc\u0627\u0631 \u06a9\u0631\u06cc\u06ba\u06d4<\/p>\n<p>\u0627\u06af\u0631 \u0622\u067e AI \u062e\u0635\u0648\u0635\u06cc\u0627\u062a \u06a9\u0648 \u062a\u0631\u062a\u06cc\u0628 \u0648\u0627\u0631 \u0631\u0648\u0644 \u0622\u0624\u0679 \u06a9\u0631 \u0631\u06c1\u06d2 \u06c1\u06cc\u06ba\u060c \u062a\u0648 \u0622\u067e \u06a9\u0627 \u0631\u06cc\u0644\u06cc\u0632 \u0634\u06cc\u0688\u0648\u0644 \u067e\u06c1\u0644\u06d2 \u0633\u06d2 \u06c1\u06cc \u0627\u06cc\u06a9 DiD \u0645\u0637\u0627\u0644\u0639\u06c1 \u06c1\u06d2\u06d4 \u0635\u0631\u0641 \u0633\u0648\u0627\u0644 \u06cc\u06c1 \u06c1\u06d2 \u06a9\u06c1 \u0622\u06cc\u0627 \u0622\u067e \u062a\u062c\u0632\u06cc\u06c1 \u0686\u0644\u0627\u062a\u06d2 \u06c1\u06cc\u06ba \u06cc\u0627 \u0646\u06c1\u06cc\u06ba\u06d4<\/p>\n<\/p><\/div>\n","protected":false},"excerpt":{"rendered":"<p>\u0622\u067e \u06a9\u06cc \u0679\u06cc\u0645 \u0646\u06d2 \u06c1\u0641\u062a\u06c1 20 \u0645\u06cc\u06ba 1 \u0648\u0631\u06a9 \u0627\u0633\u067e\u06cc\u0633 \u06a9\u0648 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