{"id":476397,"date":"2023-08-09T07:28:31","date_gmt":"2023-08-09T07:28:31","guid":{"rendered":""},"modified":"2023-09-05T11:12:38","modified_gmt":"2023-09-05T11:12:38","slug":"confidence-interval","status":"publish","type":"wiki","link":"https:\/\/oneproxy.pro\/vn\/wiki\/confidence-interval\/","title":{"rendered":"Kho\u1ea3ng tin c\u1eady"},"content":{"rendered":"

Kho\u1ea3ng tin c\u1eady (CI) l\u00e0 m\u1ed9t kh\u00e1i ni\u1ec7m th\u1ed1ng k\u00ea \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 \u01b0\u1edbc t\u00ednh ph\u1ea1m vi c\u00e1c gi\u00e1 tr\u1ecb c\u00f3 th\u1ec3 c\u00f3 cho m\u1ed9t tham s\u1ed1 t\u1ed5ng th\u1ec3 ch\u01b0a bi\u1ebft d\u1ef1a tr\u00ean m\u1eabu t\u1eeb t\u1ed5ng th\u1ec3 \u0111\u00f3. N\u00f3 cung c\u1ea5p m\u1ed9t ph\u1ea1m vi trong \u0111\u00f3 gi\u00e1 tr\u1ecb th\u1ef1c c\u1ee7a tham s\u1ed1 c\u00f3 th\u1ec3 r\u01a1i v\u00e0o m\u1ed9t m\u1ee9c \u0111\u1ed9 tin c\u1eady nh\u1ea5t \u0111\u1ecbnh. Kho\u1ea3ng tin c\u1eady \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng r\u1ed9ng r\u00e3i trong nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c nhau, bao g\u1ed3m kinh t\u1ebf, khoa h\u1ecdc x\u00e3 h\u1ed9i, y h\u1ecdc v\u00e0 k\u1ef9 thu\u1eadt, \u0111\u1ec3 \u0111\u01b0a ra suy lu\u1eadn v\u1ec1 c\u00e1c th\u00f4ng s\u1ed1 d\u00e2n s\u1ed1 v\u00e0 \u0111\u1ecbnh l\u01b0\u1ee3ng \u0111\u1ed9 kh\u00f4ng ch\u1eafc ch\u1eafn trong \u01b0\u1edbc t\u00ednh th\u1ed1ng k\u00ea.<\/p>\n

L\u1ecbch s\u1eed ngu\u1ed3n g\u1ed1c c\u1ee7a Kho\u1ea3ng tin c\u1eady v\u00e0 l\u1ea7n \u0111\u1ea7u ti\u00ean \u0111\u1ec1 c\u1eadp \u0111\u1ebfn n\u00f3<\/h2>\n

Kh\u00e1i ni\u1ec7m Kho\u1ea3ng tin c\u1eady c\u00f3 th\u1ec3 b\u1eaft ngu\u1ed3n t\u1eeb c\u00f4ng tr\u00ecnh c\u1ee7a Pierre-Simon Laplace, m\u1ed9t nh\u00e0 to\u00e1n h\u1ecdc v\u00e0 thi\u00ean v\u0103n h\u1ecdc ng\u01b0\u1eddi Ph\u00e1p, v\u00e0o cu\u1ed1i th\u1ebf k\u1ef7 18 v\u00e0 \u0111\u1ea7u th\u1ebf k\u1ef7 19. Laplace l\u00e0 m\u1ed9t trong nh\u1eefng ng\u01b0\u1eddi ti\u00ean phong trong l\u0129nh v\u1ef1c l\u00fd thuy\u1ebft x\u00e1c su\u1ea5t v\u00e0 th\u1ed1ng k\u00ea. \u00d4ng \u0111\u01b0a ra \u00fd t\u01b0\u1edfng s\u1eed d\u1ee5ng d\u1eef li\u1ec7u quan s\u00e1t \u0111\u01b0\u1ee3c \u0111\u1ec3 \u01b0\u1edbc t\u00ednh gi\u00e1 tr\u1ecb th\u1ef1c c\u1ee7a m\u1ed9t tham s\u1ed1 v\u00e0 \u0111\u1ec1 xu\u1ea5t ph\u01b0\u01a1ng ph\u00e1p t\u00ednh x\u00e1c su\u1ea5t c\u1ee7a m\u1ed9t tham s\u1ed1 n\u1eb1m trong m\u1ed9t ph\u1ea1m vi gi\u00e1 tr\u1ecb nh\u1ea5t \u0111\u1ecbnh. Tuy nhi\u00ean, b\u1ea3n th\u00e2n thu\u1eadt ng\u1eef \u201cKho\u1ea3ng tin c\u1eady\u201d \u0111\u00e3 \u0111\u01b0\u1ee3c \u0111\u1eb7t ra v\u00e0o cu\u1ed1i th\u1ebf k\u1ef7 20.<\/p>\n

Th\u00f4ng tin chi ti\u1ebft v\u1ec1 Kho\u1ea3ng tin c\u1eady<\/h2>\n

\u0110\u1ec3 hi\u1ec3u r\u00f5 h\u01a1n v\u1ec1 Kho\u1ea3ng tin c\u1eady, \u0111i\u1ec1u c\u1ea7n thi\u1ebft l\u00e0 ph\u1ea3i n\u1eafm \u0111\u01b0\u1ee3c kh\u00e1i ni\u1ec7m v\u1ec1 \u0111\u1ed9 bi\u1ebfn thi\u00ean l\u1ea5y m\u1eabu. Khi ch\u00fang t\u00f4i l\u1ea5y m\u1eabu t\u1eeb m\u1ed9t t\u1ed5ng th\u1ec3 v\u00e0 t\u00ednh to\u00e1n m\u1ed9t th\u1ed1ng k\u00ea (v\u00ed d\u1ee5: gi\u00e1 tr\u1ecb trung b\u00ecnh, t\u1ef7 l\u1ec7, \u0111\u1ed9 l\u1ec7ch chu\u1ea9n) t\u1eeb m\u1eabu \u0111\u00f3, gi\u00e1 tr\u1ecb c\u1ee7a th\u1ed1ng k\u00ea c\u00f3 th\u1ec3 s\u1ebd kh\u00e1c v\u1edbi tham s\u1ed1 th\u1ef1c c\u1ee7a t\u1ed5ng th\u1ec3 do c\u00e1c bi\u1ebfn th\u1ec3 l\u1ea5y m\u1eabu ng\u1eabu nhi\u00ean. Kho\u1ea3ng tin c\u1eady t\u00ednh \u0111\u1ebfn s\u1ef1 thay \u0111\u1ed5i n\u00e0y v\u00e0 cung c\u1ea5p m\u1ed9t ph\u1ea1m vi gi\u00e1 tr\u1ecb c\u00f3 kh\u1ea3 n\u0103ng bao g\u1ed3m tham s\u1ed1 th\u1ef1c.<\/p>\n

C\u00e1ch ti\u00eau chu\u1ea9n \u0111\u1ec3 t\u00ednh Kho\u1ea3ng tin c\u1eady d\u1ef1a tr\u00ean gi\u1ea3 \u0111\u1ecbnh r\u1eb1ng th\u1ed1ng k\u00ea m\u1eabu tu\u00e2n theo ph\u00e2n ph\u1ed1i chu\u1ea9n. V\u00ed d\u1ee5: \u0111\u1ec3 \u01b0\u1edbc t\u00ednh gi\u00e1 tr\u1ecb trung b\u00ecnh c\u1ee7a t\u1ed5ng th\u1ec3 v\u1edbi Kho\u1ea3ng tin c\u1eady, ng\u01b0\u1eddi ta th\u01b0\u1eddng s\u1eed d\u1ee5ng c\u00f4ng th\u1ee9c:<\/p>\n

Kho\u1ea3ng tin c\u1eady<\/mtext>=<\/mo>Trung b\u00ecnh m\u1eabu<\/mtext>\u00b1<\/mo>Bi\u00ean \u0111\u1ed9 l\u1ed7i<\/mtext><\/mrow>v\u0103n b\u1ea3n{Kho\u1ea3ng tin c\u1eady} = v\u0103n b\u1ea3n{Trung b\u00ecnh m\u1eabu} chi\u1ec1u v\u0103n b\u1ea3n{Bi\u00ean \u0111\u1ed9 l\u1ed7i}<\/annotation><\/semantics><\/math><\/span><\/span>Kho\u1ea3ng tin c\u1eady<\/span><\/span><\/span>=<\/span><\/span><\/span><\/span>Trung b\u00ecnh m\u1eabu<\/span><\/span><\/span>\u00b1<\/span><\/span><\/span><\/span>Bi\u00ean \u0111\u1ed9 l\u1ed7i<\/span><\/span><\/span><\/span><\/span><\/span><\/p>\n

Bi\u00ean \u0111\u1ed9 sai s\u1ed1 \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1edfi m\u1ee9c \u0111\u1ed9 tin c\u1eady mong mu\u1ed1n (v\u00ed d\u1ee5: 95%, 99%) v\u00e0 \u0111\u1ed9 l\u1ec7ch chu\u1ea9n c\u1ee7a m\u1eabu ho\u1eb7c c\u00e1c th\u00f4ng s\u1ed1 li\u00ean quan kh\u00e1c.<\/p>\n

C\u1ea5u tr\u00fac b\u00ean trong c\u1ee7a Kho\u1ea3ng tin c\u1eady. Kho\u1ea3ng tin c\u1eady ho\u1ea1t \u0111\u1ed9ng nh\u01b0 th\u1ebf n\u00e0o<\/h2>\n

Kho\u1ea3ng tin c\u1eady bao g\u1ed3m hai th\u00e0nh ph\u1ea7n ch\u00ednh: \u01b0\u1edbc t\u00ednh \u0111i\u1ec3m (th\u1ed1ng k\u00ea m\u1eabu) v\u00e0 bi\u00ean \u0111\u1ed9 sai s\u1ed1. \u01af\u1edbc t\u00ednh \u0111i\u1ec3m th\u1ec3 hi\u1ec7n gi\u00e1 tr\u1ecb \u0111\u01b0\u1ee3c t\u00ednh to\u00e1n t\u1eeb d\u1eef li\u1ec7u m\u1eabu, trong khi bi\u00ean \u0111\u1ed9 sai s\u1ed1 t\u00ednh \u0111\u1ebfn \u0111\u1ed9 kh\u00f4ng ch\u1eafc ch\u1eafn v\u00e0 \u0111\u1ed9 bi\u1ebfn thi\u00ean li\u00ean quan \u0111\u1ebfn qu\u00e1 tr\u00ecnh \u01b0\u1edbc t\u00ednh.<\/p>\n

V\u00ed d\u1ee5: gi\u1ea3 s\u1eed m\u1ed9t nghi\u00ean c\u1ee9u nh\u1eb1m m\u1ee5c \u0111\u00edch \u01b0\u1edbc t\u00ednh \u0111\u1ed9 tu\u1ed5i trung b\u00ecnh c\u1ee7a kh\u00e1ch h\u00e0ng gh\u00e9 th\u0103m qu\u00e1n c\u00e0 ph\u00ea. M\u1ed9t m\u1eabu g\u1ed3m 100 kh\u00e1ch h\u00e0ng \u0111\u01b0\u1ee3c l\u1ea5y v\u00e0 \u0111\u1ed9 tu\u1ed5i trung b\u00ecnh c\u1ee7a h\u1ecd l\u00e0 35 tu\u1ed5i. B\u00e2y gi\u1edd, c\u00e1c nh\u00e0 nghi\u00ean c\u1ee9u mu\u1ed1n x\u00e1c \u0111\u1ecbnh Kho\u1ea3ng tin c\u1eady 95% cho \u0111\u1ed9 tu\u1ed5i trung b\u00ecnh th\u1ef1c s\u1ef1 c\u1ee7a t\u1ea5t c\u1ea3 kh\u00e1ch h\u00e0ng. N\u1ebfu bi\u00ean \u0111\u1ed9 sai s\u1ed1 \u0111\u01b0\u1ee3c t\u00ednh to\u00e1n l\u00e0 \u00b13 n\u0103m th\u00ec Kho\u1ea3ng tin c\u1eady 95% s\u1ebd l\u00e0 (32, 38) n\u0103m. \u0110i\u1ec1u n\u00e0y c\u00f3 ngh\u0129a l\u00e0 ch\u00fang t\u00f4i c\u00f3 th\u1ec3 tin t\u01b0\u1edfng 95% r\u1eb1ng \u0111\u1ed9 tu\u1ed5i trung b\u00ecnh th\u1ef1c s\u1ef1 c\u1ee7a t\u1ea5t c\u1ea3 kh\u00e1ch h\u00e0ng \u0111\u1ec1u n\u1eb1m trong ph\u1ea1m vi n\u00e0y.<\/p>\n

Ph\u00e2n t\u00edch c\u00e1c t\u00ednh n\u0103ng ch\u00ednh c\u1ee7a Kho\u1ea3ng tin c\u1eady<\/h2>\n

Kho\u1ea3ng tin c\u1eady cung c\u1ea5p m\u1ed9t s\u1ed1 t\u00ednh n\u0103ng ch\u00ednh khi\u1ebfn ch\u00fang tr\u1edf n\u00ean c\u1ea7n thi\u1ebft trong suy lu\u1eadn th\u1ed1ng k\u00ea:<\/p>\n

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  1. \n

    \u0110\u1ecbnh l\u01b0\u1ee3ng \u0111\u1ed9 kh\u00f4ng \u0111\u1ea3m b\u1ea3o<\/strong>: Kho\u1ea3ng tin c\u1eady cung c\u1ea5p th\u01b0\u1edbc \u0111o \u0111\u1ed9 kh\u00f4ng ch\u1eafc ch\u1eafn li\u00ean quan \u0111\u1ebfn \u01b0\u1edbc t\u00ednh m\u1eabu. Ch\u00fang truy\u1ec1n t\u1ea3i ph\u1ea1m vi trong \u0111\u00f3 tham s\u1ed1 t\u1ed5ng th\u1ec3 c\u00f3 kh\u1ea3 n\u0103ng c\u01b0 tr\u00fa.<\/p>\n<\/li>\n

  2. \n

    M\u1ee9c \u0111\u1ed9 t\u1ef1 tin<\/strong>: Ng\u01b0\u1eddi d\u00f9ng c\u00f3 th\u1ec3 ch\u1ecdn m\u1ee9c \u0111\u1ed9 tin c\u1eady c\u1ea7n thi\u1ebft. C\u00e1c m\u1ee9c th\u01b0\u1eddng \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng l\u00e0 90%, 95% v\u00e0 99%, trong \u0111\u00f3 m\u1ee9c tin c\u1eady cao h\u01a1n h\u00e0m \u00fd kho\u1ea3ng r\u1ed9ng h\u01a1n.<\/p>\n<\/li>\n

  3. \n

    S\u1ef1 ph\u1ee5 thu\u1ed9c c\u1ee1 m\u1eabu<\/strong>: Kho\u1ea3ng tin c\u1eady b\u1ecb \u1ea3nh h\u01b0\u1edfng b\u1edfi c\u1ee1 m\u1eabu; c\u00e1c m\u1eabu l\u1edbn h\u01a1n th\u01b0\u1eddng mang l\u1ea1i kho\u1ea3ng th\u1eddi gian h\u1eb9p h\u01a1n v\u00ec ch\u00fang l\u00e0m gi\u1ea3m \u0111\u1ed9 bi\u1ebfn thi\u00ean c\u1ee7a vi\u1ec7c l\u1ea5y m\u1eabu.<\/p>\n<\/li>\n

  4. \n

    Gi\u1ea3 \u0111\u1ecbnh ph\u00e2n ph\u1ed1i<\/strong>: T\u00ednh to\u00e1n Kho\u1ea3ng tin c\u1eady th\u01b0\u1eddng y\u00eau c\u1ea7u c\u00e1c gi\u1ea3 \u0111\u1ecbnh v\u1ec1 ph\u00e2n b\u1ed1 c\u1ee7a th\u1ed1ng k\u00ea m\u1eabu, th\u01b0\u1eddng gi\u1ea3 \u0111\u1ecbnh ph\u00e2n ph\u1ed1i chu\u1ea9n.<\/p>\n<\/li>\n

  5. \n

    Kh\u1ea3 n\u0103ng gi\u1ea3i th\u00edch<\/strong>: Kho\u1ea3ng tin c\u1eady cung c\u1ea5p c\u00e1ch tr\u00ecnh b\u00e0y d\u1ec5 hi\u1ec3u v\u1ec1 \u0111\u1ed9 kh\u00f4ng ch\u1eafc ch\u1eafn, gi\u00fap nhi\u1ec1u ng\u01b0\u1eddi d\u00f9ng c\u00f3 th\u1ec3 ti\u1ebfp c\u1eadn ch\u00fang.<\/p>\n<\/li>\n<\/ol>\n

    C\u00e1c lo\u1ea1i kho\u1ea3ng tin c\u1eady<\/h2>\n

    Kho\u1ea3ng tin c\u1eady c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c ph\u00e2n lo\u1ea1i d\u1ef1a tr\u00ean lo\u1ea1i tham s\u1ed1 t\u1ed5ng th\u1ec3 \u0111\u01b0\u1ee3c \u01b0\u1edbc t\u00ednh v\u00e0 t\u00ednh ch\u1ea5t c\u1ee7a d\u1eef li\u1ec7u m\u1eabu. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 lo\u1ea1i ph\u1ed5 bi\u1ebfn:<\/p>\n\n\n\n\n\n\n\n\n\n
    Lo\u1ea1i kho\u1ea3ng tin c\u1eady<\/th>\nS\u1ef1 mi\u00eau t\u1ea3<\/th>\n<\/tr>\n<\/thead>\n
    Kho\u1ea3ng tin c\u1eady trung b\u00ecnh<\/strong><\/td>\n\u0110\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 \u01b0\u1edbc t\u00ednh trung b\u00ecnh t\u1ed5ng th\u1ec3 d\u1ef1a tr\u00ean trung b\u00ecnh m\u1eabu.<\/td>\n<\/tr>\n
    Kho\u1ea3ng tin c\u1eady t\u1ef7 l\u1ec7<\/strong><\/td>\n\u01af\u1edbc t\u00ednh t\u1ef7 l\u1ec7 d\u00e2n s\u1ed1 d\u1ef1a tr\u00ean t\u1ef7 l\u1ec7 m\u1eabu, th\u01b0\u1eddng \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng trong d\u1eef li\u1ec7u nh\u1ecb th\u1ee9c.<\/td>\n<\/tr>\n
    Kho\u1ea3ng tin c\u1eady ph\u01b0\u01a1ng sai<\/strong><\/td>\n\u01af\u1edbc t\u00ednh ph\u01b0\u01a1ng sai t\u1ed5ng th\u1ec3 ho\u1eb7c \u0111\u1ed9 l\u1ec7ch chu\u1ea9n.<\/td>\n<\/tr>\n
    S\u1ef1 kh\u00e1c bi\u1ec7t gi\u1eefa c\u00e1c ph\u01b0\u01a1ng ti\u1ec7n<\/strong><\/td>\n\u0110\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 so s\u00e1nh ph\u01b0\u01a1ng ti\u1ec7n c\u1ee7a hai nh\u00f3m ho\u1eb7c qu\u1ea7n th\u1ec3 kh\u00e1c nhau.<\/td>\n<\/tr>\n
    Kho\u1ea3ng tin c\u1eady h\u1ec7 s\u1ed1 h\u1ed3i quy<\/strong><\/td>\n\u01af\u1edbc t\u00ednh c\u00e1c h\u1ec7 s\u1ed1 ch\u01b0a bi\u1ebft trong m\u00f4 h\u00ecnh h\u1ed3i quy.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    C\u00e1ch s\u1eed d\u1ee5ng Kho\u1ea3ng tin c\u1eady, c\u00e1c v\u1ea5n \u0111\u1ec1 v\u00e0 gi\u1ea3i ph\u00e1p li\u00ean quan \u0111\u1ebfn vi\u1ec7c s\u1eed d\u1ee5ng<\/h2>\n

    1. Ki\u1ec3m \u0111\u1ecbnh gi\u1ea3 thuy\u1ebft<\/strong>: Kho\u1ea3ng tin c\u1eady c\u00f3 li\u00ean quan ch\u1eb7t ch\u1ebd \u0111\u1ebfn vi\u1ec7c ki\u1ec3m tra gi\u1ea3 thuy\u1ebft. Ch\u00fang c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 ki\u1ec3m tra c\u00e1c gi\u1ea3 thuy\u1ebft v\u1ec1 c\u00e1c th\u00f4ng s\u1ed1 d\u00e2n s\u1ed1. N\u1ebfu m\u1ed9t gi\u00e1 tr\u1ecb gi\u1ea3 thuy\u1ebft n\u1eb1m ngo\u00e0i Kho\u1ea3ng tin c\u1eady, n\u00f3 c\u00f3 th\u1ec3 g\u1ee3i \u00fd s\u1ef1 kh\u00e1c bi\u1ec7t ho\u1eb7c t\u00e1c \u0111\u1ed9ng \u0111\u00e1ng k\u1ec3.<\/p>\n

    2. X\u00e1c \u0111\u1ecbnh c\u1ee1 m\u1eabu<\/strong>: Kho\u1ea3ng tin c\u1eady c\u00f3 th\u1ec3 gi\u00fap x\u00e1c \u0111\u1ecbnh c\u1ee1 m\u1eabu c\u1ea7n thi\u1ebft cho m\u1ed9t nghi\u00ean c\u1ee9u. Kho\u1ea3ng c\u00e1ch h\u1eb9p h\u01a1n \u0111\u00f2i h\u1ecfi c\u1ee1 m\u1eabu l\u1edbn h\u01a1n \u0111\u1ec3 \u0111\u1ea1t \u0111\u01b0\u1ee3c c\u00f9ng m\u1ee9c \u0111\u1ed9 tin c\u1eady.<\/p>\n

    3. D\u1eef li\u1ec7u ngo\u1ea1i l\u1ec7 v\u00e0 sai l\u1ec7ch<\/strong>: Trong tr\u01b0\u1eddng h\u1ee3p d\u1eef li\u1ec7u kh\u00f4ng \u0111\u01b0\u1ee3c ph\u00e2n ph\u1ed1i b\u00ecnh th\u01b0\u1eddng ho\u1eb7c ch\u1ee9a c\u00e1c gi\u00e1 tr\u1ecb ngo\u1ea1i l\u1ec7, c\u00e1c ph\u01b0\u01a1ng ph\u00e1p thay th\u1ebf, ch\u1eb3ng h\u1ea1n nh\u01b0 kh\u1edfi \u0111\u1ed9ng, c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 t\u00ednh Kho\u1ea3ng tin c\u1eady.<\/p>\n

    4. Gi\u1ea3i th\u00edch c\u00e1c kho\u1ea3ng ch\u1ed3ng ch\u00e9o<\/strong>: Khi so s\u00e1nh nhi\u1ec1u nh\u00f3m ho\u1eb7c \u0111i\u1ec1u ki\u1ec7n, Kho\u1ea3ng tin c\u1eady ch\u1ed3ng ch\u00e9o kh\u00f4ng nh\u1ea5t thi\u1ebft cho th\u1ea5y s\u1ef1 thi\u1ebfu \u00fd ngh\u0129a. Ki\u1ec3m tra gi\u1ea3 thuy\u1ebft ch\u00ednh th\u1ee9c n\u00ean \u0111\u01b0\u1ee3c ti\u1ebfn h\u00e0nh \u0111\u1ec3 so s\u00e1nh th\u00edch h\u1ee3p.<\/p>\n

    C\u00e1c \u0111\u1eb7c \u0111i\u1ec3m ch\u00ednh v\u00e0 so s\u00e1nh kh\u00e1c v\u1edbi c\u00e1c thu\u1eadt ng\u1eef t\u01b0\u01a1ng t\u1ef1<\/h2>\n\n\n\n\n\n\n\n
    Thu\u1eadt ng\u1eef<\/th>\nS\u1ef1 mi\u00eau t\u1ea3<\/th>\n<\/tr>\n<\/thead>\n
    Kho\u1ea3ng tin c\u1eady<\/td>\nCung c\u1ea5p m\u1ed9t ph\u1ea1m vi gi\u00e1 tr\u1ecb c\u00f3 kh\u1ea3 n\u0103ng bao g\u1ed3m gi\u00e1 tr\u1ecb tham s\u1ed1 th\u1ef1c v\u1edbi m\u1ee9c \u0111\u1ed9 tin c\u1eady \u0111\u01b0\u1ee3c ch\u1ec9 \u0111\u1ecbnh.<\/td>\n<\/tr>\n
    Kho\u1ea3ng th\u1eddi gian d\u1ef1 \u0111o\u00e1n<\/td>\nT\u01b0\u01a1ng t\u1ef1 nh\u01b0 Kho\u1ea3ng tin c\u1eady nh\u01b0ng t\u00ednh \u0111\u1ebfn c\u1ea3 \u0111\u1ed9 bi\u1ebfn thi\u00ean l\u1ea5y m\u1eabu v\u00e0 l\u1ed7i d\u1ef1 \u0111o\u00e1n trong t\u01b0\u01a1ng lai. Kho\u1ea3ng tin c\u1eady r\u1ed9ng h\u01a1n.<\/td>\n<\/tr>\n
    Kho\u1ea3ng dung sai<\/td>\nCh\u1ec9 \u0111\u1ecbnh m\u1ed9t ph\u1ea1m vi gi\u00e1 tr\u1ecb bao g\u1ed3m m\u1ed9t t\u1ef7 l\u1ec7 d\u00e2n s\u1ed1 nh\u1ea5t \u0111\u1ecbnh v\u1edbi m\u1ee9c \u0111\u1ed9 tin c\u1eady nh\u1ea5t \u0111\u1ecbnh. D\u00f9ng \u0111\u1ec3 ki\u1ec3m tra ch\u1ea5t l\u01b0\u1ee3ng.<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

    C\u00e1c quan \u0111i\u1ec3m v\u00e0 c\u00f4ng ngh\u1ec7 c\u1ee7a t\u01b0\u01a1ng lai li\u00ean quan \u0111\u1ebfn Kho\u1ea3ng tin c\u1eady<\/h2>\n

    L\u0129nh v\u1ef1c th\u1ed1ng k\u00ea li\u00ean t\u1ee5c ph\u00e1t tri\u1ec3n v\u00e0 c\u00e1c k\u1ef9 thu\u1eadt Kho\u1ea3ng tin c\u1eady c\u00f3 th\u1ec3 s\u1ebd c\u00f3 nh\u1eefng ti\u1ebfn b\u1ed9 trong t\u01b0\u01a1ng lai. M\u1ed9t s\u1ed1 ph\u00e1t tri\u1ec3n ti\u1ec1m n\u0103ng bao g\u1ed3m:<\/p>\n

      \n
    1. \n

      Ph\u01b0\u01a1ng ph\u00e1p phi tham s\u1ed1<\/strong>: Nh\u1eefng ti\u1ebfn b\u1ed9 trong th\u1ed1ng k\u00ea phi tham s\u1ed1 c\u00f3 th\u1ec3 cung c\u1ea5p nh\u1eefng c\u00e1ch kh\u00e1c \u0111\u1ec3 t\u00ednh Kho\u1ea3ng tin c\u1eady m\u00e0 kh\u00f4ng c\u1ea7n gi\u1ea3 \u0111\u1ecbnh c\u00e1c ph\u00e2n b\u1ed1 d\u1eef li\u1ec7u c\u1ee5 th\u1ec3.<\/p>\n<\/li>\n

    2. \n

      Suy lu\u1eadn Bayes<\/strong>: C\u00e1c ph\u01b0\u01a1ng ph\u00e1p Bayes, k\u1ebft h\u1ee3p ki\u1ebfn th\u1ee9c tr\u01b0\u1edbc \u0111\u00e2y v\u00e0 ni\u1ec1m tin c\u1eadp nh\u1eadt, c\u00f3 th\u1ec3 \u0111\u01b0a ra nh\u1eefng c\u00e1ch linh ho\u1ea1t v\u00e0 gi\u00e0u th\u00f4ng tin h\u01a1n \u0111\u1ec3 x\u00e2y d\u1ef1ng c\u00e1c kho\u1ea3ng th\u1eddi gian.<\/p>\n<\/li>\n

    3. \n

      \u1ee8ng d\u1ee5ng h\u1ecdc m\u00e1y<\/strong>: V\u1edbi s\u1ef1 ph\u00e1t tri\u1ec3n c\u1ee7a h\u1ecdc m\u00e1y, Kho\u1ea3ng tin c\u1eady c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c t\u00edch h\u1ee3p v\u00e0o c\u00e1c d\u1ef1 \u0111o\u00e1n m\u00f4 h\u00ecnh \u0111\u1ec3 \u01b0\u1edbc t\u00ednh \u0111\u1ed9 kh\u00f4ng ch\u1eafc ch\u1eafn trong c\u00e1c h\u1ec7 th\u1ed1ng ra quy\u1ebft \u0111\u1ecbnh d\u1ef1a tr\u00ean AI.<\/p>\n<\/li>\n<\/ol>\n

      C\u00e1ch s\u1eed d\u1ee5ng ho\u1eb7c li\u00ean k\u1ebft m\u00e1y ch\u1ee7 proxy v\u1edbi Kho\u1ea3ng tin c\u1eady<\/h2>\n

      C\u00e1c m\u00e1y ch\u1ee7 proxy, gi\u1ed1ng nh\u01b0 c\u00e1c m\u00e1y ch\u1ee7 do OneProxy cung c\u1ea5p, c\u00f3 th\u1ec3 \u0111\u00f3ng m\u1ed9t vai tr\u00f2 quan tr\u1ecdng trong vi\u1ec7c thu th\u1eadp d\u1eef li\u1ec7u \u0111\u1ec3 x\u00e2y d\u1ef1ng Kho\u1ea3ng tin c\u1eady. Khi x\u1eed l\u00fd c\u00e1c t\u00e1c v\u1ee5 thu th\u1eadp d\u1eef li\u1ec7u ho\u1eb7c qu\u00e9t web tr\u00ean quy m\u00f4 l\u1edbn, vi\u1ec7c s\u1eed d\u1ee5ng m\u00e1y ch\u1ee7 proxy c\u00f3 th\u1ec3 gi\u00fap tr\u00e1nh ch\u1eb7n IP v\u00e0 ph\u00e2n ph\u1ed1i y\u00eau c\u1ea7u tr\u00ean c\u00e1c \u0111\u1ecba ch\u1ec9 IP kh\u00e1c nhau, gi\u1ea3m nguy c\u01a1 l\u1ea5y m\u1eabu sai l\u1ec7ch. B\u1eb1ng c\u00e1ch lu\u00e2n chuy\u1ec3n IP th\u00f4ng qua c\u00e1c m\u00e1y ch\u1ee7 proxy, c\u00e1c nh\u00e0 nghi\u00ean c\u1ee9u c\u00f3 th\u1ec3 \u0111\u1ea3m b\u1ea3o r\u1eb1ng vi\u1ec7c thu th\u1eadp d\u1eef li\u1ec7u v\u1eabn m\u1ea1nh m\u1ebd v\u00e0 kh\u00f4ng thi\u00ean v\u1ecb, d\u1eabn \u0111\u1ebfn Kho\u1ea3ng tin c\u1eady ch\u00ednh x\u00e1c h\u01a1n.<\/p>\n

      Li\u00ean k\u1ebft li\u00ean quan<\/h2>\n
        \n
      1. Hi\u1ec3u Kho\u1ea3ng Tin C\u1eady \u2013 Khan Academy<\/a><\/li>\n
      2. Kho\u1ea3ng tin c\u1eady \u2013 Wikipedia<\/a><\/li>\n
      3. Gi\u1edbi thi\u1ec7u v\u1ec1 Kho\u1ea3ng tin c\u1eady c\u1ee7a Bootstrap \u2013 H\u01b0\u1edbng t\u1edbi Khoa h\u1ecdc D\u1eef li\u1ec7u<\/a><\/li>\n<\/ol>\n

        T\u00f3m l\u1ea1i, Kho\u1ea3ng tin c\u1eady l\u00e0 m\u1ed9t c\u00f4ng c\u1ee5 c\u01a1 b\u1ea3n trong suy lu\u1eadn th\u1ed1ng k\u00ea, cung c\u1ea5p cho c\u00e1c nh\u00e0 nghi\u00ean c\u1ee9u v\u00e0 ng\u01b0\u1eddi ra quy\u1ebft \u0111\u1ecbnh th\u00f4ng tin c\u00f3 gi\u00e1 tr\u1ecb v\u1ec1 \u0111\u1ed9 kh\u00f4ng ch\u1eafc ch\u1eafn li\u00ean quan \u0111\u1ebfn \u01b0\u1edbc t\u00ednh c\u1ee7a h\u1ecd. H\u1ecd \u0111\u00f3ng vai tr\u00f2 quan tr\u1ecdng trong nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c nhau, t\u1eeb nghi\u00ean c\u1ee9u h\u1ecdc thu\u1eadt \u0111\u1ebfn ph\u00e2n t\u00edch kinh doanh v\u00e0 s\u1ef1 hi\u1ec3u bi\u1ebft \u0111\u00fang \u0111\u1eafn c\u1ee7a h\u1ecd l\u00e0 \u0111i\u1ec1u c\u1ea7n thi\u1ebft \u0111\u1ec3 \u0111\u01b0a ra quy\u1ebft \u0111\u1ecbnh s\u00e1ng su\u1ed1t d\u1ef1a tr\u00ean d\u1eef li\u1ec7u m\u1eabu. V\u1edbi nh\u1eefng ti\u1ebfn b\u1ed9 kh\u00f4ng ng\u1eebng v\u1ec1 ph\u01b0\u01a1ng ph\u00e1p v\u00e0 c\u00f4ng ngh\u1ec7 th\u1ed1ng k\u00ea, Kho\u1ea3ng tin c\u1eady s\u1ebd ti\u1ebfp t\u1ee5c l\u00e0 n\u1ec1n t\u1ea3ng c\u1ee7a qu\u00e1 tr\u00ecnh ph\u00e2n t\u00edch d\u1eef li\u1ec7u v\u00e0 ra quy\u1ebft \u0111\u1ecbnh hi\u1ec7n \u0111\u1ea1i.<\/p>","protected":false},"featured_media":467989,"menu_order":0,"template":"","meta":{"_acf_changed":false,"content-type":"","inline_featured_image":false,"footnotes":""},"class_list":["post-476397","wiki","type-wiki","status-publish","has-post-thumbnail","hentry"],"acf":{"faq_title":"Frequently Asked Questions about Confidence Interval<\/mark>","faq_items":[{"question":"What is a Confidence Interval?","answer":"

        A Confidence Interval (CI) is a statistical concept used to estimate the range of possible values for an unknown population parameter based on a sample from that population. It provides a level of confidence that the true value of the parameter lies within the calculated interval.<\/p>"},{"question":"Who introduced the concept of Confidence Interval?","answer":"

        The concept of Confidence Interval can be traced back to Pierre-Simon Laplace, a French mathematician and astronomer, in the late 18th and early 19th centuries. He laid the groundwork for using observed data to estimate population parameters and proposed a method to calculate the probability of a parameter falling within a certain range of values.<\/p>"},{"question":"How do Confidence Intervals work?","answer":"

        Confidence Intervals consist of a point estimate (sample statistic) and a margin of error. The point estimate represents the calculated value from the sample data, while the margin of error accounts for the uncertainty associated with the estimation process. The interval is determined by the desired level of confidence and the sample's standard deviation or other relevant parameters.<\/p>"},{"question":"What are the main types of Confidence Intervals?","answer":"

        There are several types of Confidence Intervals, depending on the parameter being estimated and the nature of the sample data. Common types include Mean, Proportion, Variance, Difference between Means, and Regression Coefficient Confidence Intervals.<\/p>"},{"question":"How are Confidence Intervals used in practice?","answer":"

        Confidence Intervals have numerous applications in statistics and data analysis. They are used for hypothesis testing, sample size determination, and making inferences about population parameters with a known level of confidence. They also help address problems related to skewed data or outliers and facilitate proper comparisons between multiple groups.<\/p>"},{"question":"How can proxy servers be associated with Confidence Intervals?","answer":"

        Proxy servers, like those provided by OneProxy, are valuable tools for data collection when constructing Confidence Intervals. They help prevent IP blocking during large-scale data gathering or web scraping tasks, ensuring unbiased samples and accurate interval estimations. By rotating IPs through proxy servers, researchers can enhance the robustness of their data collection process.<\/p>"},{"question":"What are the future perspectives of Confidence Intervals?","answer":"

        The field of statistics is continuously evolving, and Confidence Interval techniques are likely to see advancements in the future. Potential developments may include non-parametric methods, Bayesian inference, and integration with machine learning applications to estimate uncertainty in AI-based decision-making systems.<\/p>"}]},"_links":{"self":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/wiki\/476397","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/wiki"}],"about":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/types\/wiki"}],"version-history":[{"count":0,"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/wiki\/476397\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/media\/467989"}],"wp:attachment":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/media?parent=476397"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}