{"id":476219,"date":"2023-08-09T07:26:52","date_gmt":"2023-08-09T07:26:52","guid":{"rendered":""},"modified":"2023-11-30T03:36:11","modified_gmt":"2023-11-30T03:36:11","slug":"chi-squared-test","status":"publish","type":"wiki","link":"https:\/\/oneproxy.pro\/vn\/wiki\/chi-squared-test\/","title":{"rendered":"Ki\u1ec3m tra chi b\u00ecnh ph\u01b0\u01a1ng"},"content":{"rendered":"<p>Ki\u1ec3m tra Chi-Squared l\u00e0 m\u1ed9t ph\u01b0\u01a1ng ph\u00e1p th\u1ed1ng k\u00ea \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 ph\u00e2n t\u00edch d\u1eef li\u1ec7u ph\u00e2n lo\u1ea1i v\u00e0 x\u00e1c \u0111\u1ecbnh xem li\u1ec7u c\u00f3 m\u1ed1i li\u00ean h\u1ec7 \u0111\u00e1ng k\u1ec3 gi\u1eefa hai ho\u1eb7c nhi\u1ec1u bi\u1ebfn s\u1ed1 hay kh\u00f4ng. \u0110\u00e2y l\u00e0 m\u1ed9t b\u00e0i ki\u1ec3m tra phi tham s\u1ed1, ngh\u0129a l\u00e0 n\u00f3 kh\u00f4ng \u0111\u01b0a ra gi\u1ea3 \u0111\u1ecbnh n\u00e0o v\u1ec1 vi\u1ec7c ph\u00e2n ph\u1ed1i d\u1eef li\u1ec7u v\u00e0 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng r\u1ed9ng r\u00e3i trong nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c nhau, bao g\u1ed3m khoa h\u1ecdc x\u00e3 h\u1ed9i, sinh h\u1ecdc, y h\u1ecdc v\u00e0 ti\u1ebfp th\u1ecb. Th\u1eed nghi\u1ec7m \u0111\u00e1nh gi\u00e1 xem t\u1ea7n su\u1ea5t quan s\u00e1t \u0111\u01b0\u1ee3c c\u1ee7a c\u00e1c danh m\u1ee5c trong d\u1eef li\u1ec7u c\u00f3 kh\u00e1c bi\u1ec7t \u0111\u00e1ng k\u1ec3 so v\u1edbi t\u1ea7n su\u1ea5t d\u1ef1 ki\u1ebfn hay kh\u00f4ng, cung c\u1ea5p nh\u1eefng hi\u1ec3u bi\u1ebft s\u00e2u s\u1eafc c\u00f3 gi\u00e1 tr\u1ecb v\u1ec1 m\u1ed1i quan h\u1ec7 gi\u1eefa c\u00e1c bi\u1ebfn s\u1ed1.<\/p>\n<h2>L\u1ecbch s\u1eed ngu\u1ed3n g\u1ed1c c\u1ee7a b\u00e0i ki\u1ec3m tra Chi-Squared<\/h2>\n<p>B\u00e0i ki\u1ec3m tra Chi-Squared c\u00f3 ngu\u1ed3n g\u1ed1c t\u1eeb c\u00f4ng tr\u00ecnh c\u1ee7a Karl Pearson, m\u1ed9t nh\u00e0 to\u00e1n h\u1ecdc v\u00e0 nh\u00e0 th\u1ed1ng k\u00ea sinh h\u1ecdc ng\u01b0\u1eddi Anh, ng\u01b0\u1eddi \u0111\u00e3 \u0111\u01b0a ra kh\u00e1i ni\u1ec7m n\u00e0y v\u00e0o n\u0103m 1900. C\u00f4ng vi\u1ec7c c\u1ee7a Pearson t\u1eadp trung v\u00e0o vi\u1ec7c ph\u00e1t tri\u1ec3n c\u00e1c ph\u01b0\u01a1ng ph\u00e1p th\u1ed1ng k\u00ea \u0111\u1ec3 hi\u1ec3u m\u1ed1i quan h\u1ec7 gi\u1eefa c\u00e1c bi\u1ebfn trong c\u00e1c t\u1eadp d\u1eef li\u1ec7u l\u1edbn. Ki\u1ec3m \u0111\u1ecbnh Chi-Squared ban \u0111\u1ea7u \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng trong vi\u1ec7c ph\u00e2n t\u00edch c\u00e1c b\u1ea3ng d\u1ef1 ph\u00f2ng, hi\u1ec3n th\u1ecb s\u1ef1 ph\u00e2n b\u1ed1 chung c\u1ee7a hai ho\u1eb7c nhi\u1ec1u bi\u1ebfn ph\u00e2n lo\u1ea1i.<\/p>\n<h2>Th\u00f4ng tin chi ti\u1ebft v\u1ec1 Chi-Squared Test<\/h2>\n<p>Ki\u1ec3m tra Chi-Squared d\u1ef1a tr\u00ean vi\u1ec7c so s\u00e1nh t\u1ea7n s\u1ed1 quan s\u00e1t \u0111\u01b0\u1ee3c (O) trong t\u1eadp d\u1eef li\u1ec7u v\u1edbi t\u1ea7n s\u1ed1 d\u1ef1 ki\u1ebfn (E) s\u1ebd x\u1ea3y ra n\u1ebfu c\u00e1c bi\u1ebfn \u0111\u1ed9c l\u1eadp. Th\u1eed nghi\u1ec7m bao g\u1ed3m vi\u1ec7c t\u00ednh to\u00e1n th\u1ed1ng k\u00ea Chi-Squared, \u0111\u1ecbnh l\u01b0\u1ee3ng s\u1ef1 kh\u00e1c bi\u1ec7t gi\u1eefa t\u1ea7n s\u1ed1 \u0111\u01b0\u1ee3c quan s\u00e1t v\u00e0 t\u1ea7n s\u1ed1 d\u1ef1 ki\u1ebfn. C\u00f4ng th\u1ee9c th\u1ed1ng k\u00ea Chi-Squared l\u00e0:<\/p>\n<p><img decoding=\"async\" src=\"https:\/\/oneproxy.pro\/images\/chi_squared_formula.png\" alt=\"C\u00f4ng th\u1ee9c Chi b\u00ecnh ph\u01b0\u01a1ng\" title=\"\"><\/p>\n<p>\u1ede \u0111\u00e2u:<\/p>\n<ul>\n<li>\u03a7\u00b2 \u0111\u1ea1i di\u1ec7n cho th\u1ed1ng k\u00ea Chi-Squared<\/li>\n<li>O\u1d62 l\u00e0 t\u1ea7n s\u1ed1 quan s\u00e1t \u0111\u01b0\u1ee3c \u0111\u1ed1i v\u1edbi lo\u1ea1i i<\/li>\n<li>E\u1d62 l\u00e0 t\u1ea7n su\u1ea5t d\u1ef1 ki\u1ebfn cho lo\u1ea1i i<\/li>\n<li>\u03a3 bi\u1ec3u th\u1ecb t\u1ed5ng c\u1ee7a t\u1ea5t c\u1ea3 c\u00e1c lo\u1ea1i<\/li>\n<\/ul>\n<p>Th\u1ed1ng k\u00ea Chi-Squared tu\u00e2n theo ph\u00e2n ph\u1ed1i Chi-Squared v\u00e0 gi\u00e1 tr\u1ecb c\u1ee7a n\u00f3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh gi\u00e1 tr\u1ecb p li\u00ean quan \u0111\u1ebfn th\u1eed nghi\u1ec7m. Gi\u00e1 tr\u1ecb p bi\u1ec3u th\u1ecb x\u00e1c su\u1ea5t thu \u0111\u01b0\u1ee3c k\u1ebft qu\u1ea3 quan s\u00e1t \u0111\u01b0\u1ee3c m\u1ed9t c\u00e1ch t\u00ecnh c\u1edd. N\u1ebfu gi\u00e1 tr\u1ecb p th\u1ea5p h\u01a1n m\u1ee9c \u00fd ngh\u0129a \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh tr\u01b0\u1edbc (th\u01b0\u1eddng l\u00e0 0,05), th\u00ec gi\u1ea3 thuy\u1ebft kh\u1ed1ng (s\u1ef1 \u0111\u1ed9c l\u1eadp c\u1ee7a c\u00e1c bi\u1ebfn) s\u1ebd b\u1ecb b\u00e1c b\u1ecf, cho th\u1ea5y m\u1ed1i li\u00ean h\u1ec7 \u0111\u00e1ng k\u1ec3 gi\u1eefa c\u00e1c bi\u1ebfn.<\/p>\n<h2>C\u1ea5u tr\u00fac b\u00ean trong c\u1ee7a b\u00e0i ki\u1ec3m tra Chi-Squared<\/h2>\n<p>B\u00e0i ki\u1ec3m tra Chi-Squared c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c ph\u00e2n th\u00e0nh hai lo\u1ea1i ch\u00ednh: b\u00e0i ki\u1ec3m tra Chi-Squared c\u1ee7a Pearson v\u00e0 b\u00e0i ki\u1ec3m tra Chi-Squared T\u1ef7 l\u1ec7 Kh\u1ea3 n\u0103ng (c\u00f2n \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 G-Test). C\u1ea3 hai th\u1eed nghi\u1ec7m \u0111\u1ec1u s\u1eed d\u1ee5ng c\u00f9ng m\u1ed9t c\u00f4ng th\u1ee9c cho th\u1ed1ng k\u00ea Chi-Squared, nh\u01b0ng ch\u00fang kh\u00e1c nhau \u1edf c\u00e1ch t\u00ednh t\u1ea7n s\u1ed1 d\u1ef1 ki\u1ebfn.<\/p>\n<ol>\n<li>Ki\u1ec3m tra Chi b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a Pearson:\n<ul>\n<li>Gi\u1ea3 s\u1eed c\u00e1c bi\u1ebfn c\u00f3 ph\u00e2n ph\u1ed1i x\u1ea5p x\u1ec9 chu\u1ea9n.<\/li>\n<li>Th\u01b0\u1eddng \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng khi c\u1ee1 m\u1eabu l\u1edbn.<\/li>\n<\/ul>\n<\/li>\n<li>T\u1ef7 l\u1ec7 kh\u1ea3 n\u0103ng Ki\u1ec3m tra Chi-Squared (G-Test):\n<ul>\n<li>D\u1ef1a tr\u00ean t\u1ef7 l\u1ec7 kh\u1ea3 n\u0103ng, \u0111\u01b0a ra \u00edt gi\u1ea3 \u0111\u1ecbnh h\u01a1n v\u1ec1 vi\u1ec7c ph\u00e2n ph\u1ed1i d\u1eef li\u1ec7u.<\/li>\n<li>Th\u00edch h\u1ee3p cho c\u1ee1 m\u1eabu nh\u1ecf ho\u1eb7c tr\u01b0\u1eddng h\u1ee3p c\u00f3 t\u1ea7n s\u1ed1 d\u1ef1 ki\u1ebfn d\u01b0\u1edbi 5.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n<h2>Ph\u00e2n t\u00edch c\u00e1c t\u00ednh n\u0103ng ch\u00ednh c\u1ee7a Chi-Squared Test<\/h2>\n<p>B\u00e0i ki\u1ec3m tra Chi-Squared c\u00f3 m\u1ed9t s\u1ed1 t\u00ednh n\u0103ng ch\u00ednh khi\u1ebfn n\u00f3 tr\u1edf th\u00e0nh m\u1ed9t c\u00f4ng c\u1ee5 th\u1ed1ng k\u00ea c\u00f3 gi\u00e1 tr\u1ecb:<\/p>\n<ul>\n<li><strong>Ph\u00e2n t\u00edch d\u1eef li\u1ec7u ph\u00e2n lo\u1ea1i:<\/strong> B\u00e0i ki\u1ec3m tra Chi-Squared \u0111\u01b0\u1ee3c thi\u1ebft k\u1ebf \u0111\u1eb7c bi\u1ec7t cho d\u1eef li\u1ec7u ph\u00e2n lo\u1ea1i, cho ph\u00e9p c\u00e1c nh\u00e0 nghi\u00ean c\u1ee9u r\u00fat ra k\u1ebft lu\u1eadn c\u00f3 \u00fd ngh\u0129a t\u1eeb d\u1eef li\u1ec7u phi s\u1ed1.<\/li>\n<li><strong>Ki\u1ec3m tra phi tham s\u1ed1:<\/strong> L\u00e0 m\u1ed9t th\u1eed nghi\u1ec7m phi tham s\u1ed1, th\u1eed nghi\u1ec7m Chi-Squared kh\u00f4ng y\u00eau c\u1ea7u d\u1eef li\u1ec7u ph\u1ea3i tu\u00e2n theo m\u1ed9t ph\u00e2n ph\u1ed1i c\u1ee5 th\u1ec3, khi\u1ebfn n\u00f3 tr\u1edf n\u00ean linh ho\u1ea1t v\u00e0 c\u00f3 th\u1ec3 \u00e1p d\u1ee5ng trong nhi\u1ec1u t\u00ecnh hu\u1ed1ng kh\u00e1c nhau.<\/li>\n<li><strong>\u0110\u00e1nh gi\u00e1 t\u00ednh \u0111\u1ed9c l\u1eadp:<\/strong> Th\u1eed nghi\u1ec7m gi\u00fap x\u00e1c \u0111\u1ecbnh li\u1ec7u c\u00f3 m\u1ed1i quan h\u1ec7 gi\u1eefa hai ho\u1eb7c nhi\u1ec1u bi\u1ebfn ph\u00e2n lo\u1ea1i hay kh\u00f4ng, gi\u00fap hi\u1ec3u \u0111\u01b0\u1ee3c c\u00e1c m\u1eabu v\u00e0 m\u1ed1i li\u00ean h\u1ec7 trong d\u1eef li\u1ec7u.<\/li>\n<li><strong>Ki\u1ec3m tra suy lu\u1eadn:<\/strong> B\u1eb1ng c\u00e1ch cung c\u1ea5p gi\u00e1 tr\u1ecb p, b\u00e0i ki\u1ec3m tra Chi-Squared cho ph\u00e9p c\u00e1c nh\u00e0 nghi\u00ean c\u1ee9u \u0111\u01b0a ra nh\u1eefng suy lu\u1eadn th\u1ed1ng k\u00ea v\u1ec1 d\u1eef li\u1ec7u v\u00e0 \u0111\u01b0a ra k\u1ebft lu\u1eadn v\u1edbi m\u1ee9c \u0111\u1ed9 tin c\u1eady.<\/li>\n<\/ul>\n<h2>C\u00e1c lo\u1ea1i b\u00e0i ki\u1ec3m tra Chi-Squared<\/h2>\n<p>C\u00f3 hai lo\u1ea1i b\u00e0i ki\u1ec3m tra Chi-Squared ch\u00ednh: b\u00e0i ki\u1ec3m tra Chi-Squared c\u1ee7a Pearson v\u00e0 b\u00e0i ki\u1ec3m tra Chi-Squared T\u1ef7 l\u1ec7 Kh\u1ea3 n\u0103ng. D\u01b0\u1edbi \u0111\u00e2y l\u00e0 so s\u00e1nh c\u00e1c \u0111\u1eb7c \u0111i\u1ec3m c\u1ee7a ch\u00fang:<\/p>\n<table>\n<thead>\n<tr>\n<th>Ti\u00eau chu\u1ea9n<\/th>\n<th>Ki\u1ec3m tra Chi b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a Pearson<\/th>\n<th>Ki\u1ec3m tra Chi-Squared T\u1ef7 l\u1ec7 Kh\u1ea3 n\u0103ng<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Gi\u1ea3 \u0111\u1ecbnh<\/td>\n<td>Gi\u1ea3 s\u1eed ph\u00e2n ph\u1ed1i d\u1eef li\u1ec7u b\u00ecnh th\u01b0\u1eddng<\/td>\n<td>\u0110\u01b0a ra \u00edt gi\u1ea3 \u0111\u1ecbnh h\u01a1n v\u1ec1 ph\u00e2n ph\u1ed1i d\u1eef li\u1ec7u<\/td>\n<\/tr>\n<tr>\n<td>Ph\u00f9 h\u1ee3p v\u1edbi c\u1ee1 m\u1eabu nh\u1ecf<\/td>\n<td>KH\u00d4NG<\/td>\n<td>\u0110\u00fang<\/td>\n<\/tr>\n<tr>\n<td>Tr\u01b0\u1eddng h\u1ee3p s\u1eed d\u1ee5ng<\/td>\n<td>C\u1ee1 m\u1eabu l\u1edbn<\/td>\n<td>C\u1ee1 m\u1eabu nh\u1ecf<\/td>\n<\/tr>\n<tr>\n<td>C\u00f4ng th\u1ee9c<\/td>\n<td><img decoding=\"async\" src=\"https:\/\/oneproxy.pro\/images\/pearsons_chi_squared_formula.png\" alt=\"C\u00f4ng th\u1ee9c Chi b\u00ecnh ph\u01b0\u01a1ng c\u1ee7a Pearson\" title=\"\"><\/td>\n<td><img decoding=\"async\" src=\"https:\/\/oneproxy.pro\/images\/likelihood_ratio_chi_squared_formula.png\" alt=\"T\u1ef7 l\u1ec7 kh\u1ea3 n\u0103ng C\u00f4ng th\u1ee9c Chi b\u00ecnh ph\u01b0\u01a1ng\" title=\"\"><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>C\u00e1ch s\u1eed d\u1ee5ng b\u00e0i ki\u1ec3m tra Chi-Squared, c\u00e1c v\u1ea5n \u0111\u1ec1 v\u00e0 gi\u1ea3i ph\u00e1p c\u1ee7a ch\u00fang<\/h2>\n<p>B\u00e0i ki\u1ec3m tra Chi-Squared t\u00ecm th\u1ea5y c\u00e1c \u1ee9ng d\u1ee5ng trong nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c nhau, bao g\u1ed3m:<\/p>\n<ol>\n<li><strong>S\u1ef1 t\u1ed1t l\u00e0nh c\u1ee7a s\u1ef1 ph\u00f9 h\u1ee3p:<\/strong> X\u00e1c \u0111\u1ecbnh xem t\u1ea7n s\u1ed1 quan s\u00e1t \u0111\u01b0\u1ee3c c\u00f3 ph\u00f9 h\u1ee3p v\u1edbi ph\u00e2n b\u1ed1 d\u1ef1 ki\u1ebfn hay kh\u00f4ng.<\/li>\n<li><strong>Ki\u1ec3m tra t\u00ednh \u0111\u1ed9c l\u1eadp:<\/strong> \u0110\u00e1nh gi\u00e1 xem hai bi\u1ebfn ph\u00e2n lo\u1ea1i c\u00f3 li\u00ean quan hay kh\u00f4ng.<\/li>\n<li><strong>Ki\u1ec3m tra t\u00ednh \u0111\u1ed3ng nh\u1ea5t:<\/strong> So s\u00e1nh s\u1ef1 ph\u00e2n b\u1ed1 c\u1ee7a c\u00e1c bi\u1ebfn ph\u00e2n lo\u1ea1i gi\u1eefa c\u00e1c nh\u00f3m kh\u00e1c nhau.<\/li>\n<\/ol>\n<p>C\u00e1c v\u1ea5n \u0111\u1ec1 ti\u1ec1m \u1ea9n v\u1edbi b\u00e0i ki\u1ec3m tra Chi-Squared bao g\u1ed3m:<\/p>\n<ul>\n<li><strong>C\u1ee1 m\u1eabu nh\u1ecf:<\/strong> Ki\u1ec3m tra Chi-Squared c\u00f3 th\u1ec3 cho k\u1ebft qu\u1ea3 kh\u00f4ng ch\u00ednh x\u00e1c v\u1edbi c\u1ee1 m\u1eabu nh\u1ecf ho\u1eb7c \u00f4 c\u00f3 t\u1ea7n s\u1ed1 d\u1ef1 ki\u1ebfn d\u01b0\u1edbi 5. Trong nh\u1eefng tr\u01b0\u1eddng h\u1ee3p nh\u01b0 v\u1eady, th\u1eed nghi\u1ec7m Chi-Squared T\u1ef7 l\u1ec7 Kh\u1ea3 n\u0103ng \u0111\u01b0\u1ee3c \u01b0u ti\u00ean.<\/li>\n<li><strong>D\u1eef li\u1ec7u th\u1ee9 t\u1ef1:<\/strong> Ki\u1ec3m \u0111\u1ecbnh Chi-Squared kh\u00f4ng ph\u00f9 h\u1ee3p v\u1edbi d\u1eef li\u1ec7u th\u1ee9 t\u1ef1 v\u00ec n\u00f3 kh\u00f4ng xem x\u00e9t th\u1ee9 t\u1ef1 c\u1ee7a c\u00e1c danh m\u1ee5c.<\/li>\n<\/ul>\n<p>\u0110\u1ec3 gi\u1ea3i quy\u1ebft nh\u1eefng v\u1ea5n \u0111\u1ec1 n\u00e0y, c\u00e1c nh\u00e0 nghi\u00ean c\u1ee9u c\u00f3 th\u1ec3 s\u1eed d\u1ee5ng c\u00e1c th\u1eed nghi\u1ec7m thay th\u1ebf nh\u01b0 Th\u1eed nghi\u1ec7m ch\u00ednh x\u00e1c c\u1ee7a Fisher cho c\u1ee1 m\u1eabu nh\u1ecf ho\u1eb7c c\u00e1c th\u1eed nghi\u1ec7m phi tham s\u1ed1 kh\u00e1c cho d\u1eef li\u1ec7u th\u1ee9 t\u1ef1.<\/p>\n<h2>C\u00e1c \u0111\u1eb7c \u0111i\u1ec3m ch\u00ednh v\u00e0 so s\u00e1nh v\u1edbi c\u00e1c thu\u1eadt ng\u1eef t\u01b0\u01a1ng t\u1ef1<\/h2>\n<p>B\u00e0i ki\u1ec3m tra Chi-Squared c\u00f3 nh\u1eefng \u0111i\u1ec3m t\u01b0\u01a1ng \u0111\u1ed3ng v\u1edbi c\u00e1c b\u00e0i ki\u1ec3m tra th\u1ed1ng k\u00ea kh\u00e1c, nh\u01b0ng n\u00f3 c\u0169ng s\u1edf h\u1eefu nh\u1eefng \u0111\u1eb7c \u0111i\u1ec3m \u0111\u1ed9c \u0111\u00e1o khi\u1ebfn n\u00f3 tr\u1edf n\u00ean kh\u00e1c bi\u1ec7t:<\/p>\n<table>\n<thead>\n<tr>\n<th>\u0111\u1eb7c tr\u01b0ng<\/th>\n<th>Ki\u1ec3m tra Chi b\u00ecnh ph\u01b0\u01a1ng<\/th>\n<th>Ki\u1ec3m tra T<\/th>\n<th>ANOVA<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>Lo\u1ea1i b\u00e0i ki\u1ec3m tra<\/td>\n<td>Ph\u00e2n t\u00edch d\u1eef li\u1ec7u ph\u00e2n lo\u1ea1i<\/td>\n<td>So s\u00e1nh c\u00e1c ph\u01b0\u01a1ng ti\u1ec7n<\/td>\n<td>So s\u00e1nh c\u00e1c ph\u01b0\u01a1ng ti\u1ec7n<\/td>\n<\/tr>\n<tr>\n<td>S\u1ed1 l\u01b0\u1ee3ng bi\u1ebfn<\/td>\n<td>2 ho\u1eb7c nhi\u1ec1u h\u01a1n<\/td>\n<td>2<\/td>\n<td>3 ho\u1eb7c nhi\u1ec1u h\u01a1n<\/td>\n<\/tr>\n<tr>\n<td>Lo\u1ea1i d\u1eef li\u1ec7u<\/td>\n<td>Ph\u00e2n lo\u1ea1i<\/td>\n<td>Ti\u1ebfp di\u1ec5n<\/td>\n<td>Ti\u1ebfp di\u1ec5n<\/td>\n<\/tr>\n<tr>\n<td>Gi\u1ea3 \u0111\u1ecbnh<\/td>\n<td>Phi tham s\u1ed1<\/td>\n<td>Gi\u1ea3 s\u1eed ph\u00e2n ph\u1ed1i b\u00ecnh th\u01b0\u1eddng<\/td>\n<td>Gi\u1ea3 s\u1eed ph\u00e2n ph\u1ed1i b\u00ecnh th\u01b0\u1eddng<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>Quan \u0111i\u1ec3m v\u00e0 c\u00f4ng ngh\u1ec7 c\u1ee7a t\u01b0\u01a1ng lai li\u00ean quan \u0111\u1ebfn b\u00e0i ki\u1ec3m tra Chi-Squared<\/h2>\n<p>Khi ph\u00e2n t\u00edch d\u1eef li\u1ec7u ti\u1ebfp t\u1ee5c \u0111\u00f3ng m\u1ed9t vai tr\u00f2 quan tr\u1ecdng trong c\u00e1c ng\u00e0nh kh\u00e1c nhau, b\u00e0i ki\u1ec3m tra Chi-Squared s\u1ebd v\u1eabn l\u00e0 c\u00f4ng c\u1ee5 c\u01a1 b\u1ea3n \u0111\u1ec3 ph\u00e2n t\u00edch d\u1eef li\u1ec7u ph\u00e2n lo\u1ea1i. Tuy nhi\u00ean, nh\u1eefng ti\u1ebfn b\u1ed9 trong ph\u01b0\u01a1ng ph\u00e1p v\u00e0 c\u00f4ng ngh\u1ec7 th\u1ed1ng k\u00ea c\u00f3 th\u1ec3 d\u1eabn \u0111\u1ebfn c\u00e1c phi\u00ean b\u1ea3n c\u1ea3i ti\u1ebfn ho\u1eb7c ph\u1ea7n m\u1edf r\u1ed9ng c\u1ee7a b\u00e0i ki\u1ec3m tra Chi-Squared, gi\u1ea3i quy\u1ebft c\u00e1c h\u1ea1n ch\u1ebf c\u1ee7a n\u00f3 v\u00e0 l\u00e0m cho n\u00f3 tr\u1edf n\u00ean linh ho\u1ea1t v\u00e0 m\u1ea1nh m\u1ebd h\u01a1n.<\/p>\n<h2>C\u00e1ch s\u1eed d\u1ee5ng ho\u1eb7c li\u00ean k\u1ebft m\u00e1y ch\u1ee7 proxy v\u1edbi th\u1eed nghi\u1ec7m Chi-Squared<\/h2>\n<p>M\u00e1y ch\u1ee7 proxy do c\u00e1c nh\u00e0 cung c\u1ea5p nh\u01b0 OneProxy cung c\u1ea5p c\u00f3 th\u1ec3 t\u1ea1o \u0111i\u1ec1u ki\u1ec7n thu\u1eadn l\u1ee3i cho vi\u1ec7c thu th\u1eadp v\u00e0 ph\u00e2n t\u00edch d\u1eef li\u1ec7u \u0111\u1ec3 ti\u1ebfn h\u00e0nh ki\u1ec3m tra Chi-Squared. Ch\u00fang cho ph\u00e9p ng\u01b0\u1eddi d\u00f9ng truy c\u1eadp v\u00e0o c\u00e1c v\u1ecb tr\u00ed \u0111\u1ecba l\u00fd kh\u00e1c nhau, \u0111i\u1ec1u n\u00e0y \u0111\u1eb7c bi\u1ec7t h\u1eefu \u00edch khi x\u1eed l\u00fd c\u00e1c t\u1eadp d\u1eef li\u1ec7u c\u00f3 s\u1ef1 kh\u00e1c bi\u1ec7t theo khu v\u1ef1c. C\u00e1c m\u00e1y ch\u1ee7 proxy c\u0169ng \u0111\u1ea3m b\u1ea3o t\u00ednh \u1ea9n danh, khi\u1ebfn ch\u00fang tr\u1edf n\u00ean c\u00f3 gi\u00e1 tr\u1ecb cho c\u00e1c t\u00e1c v\u1ee5 qu\u00e9t web v\u00e0 thu th\u1eadp d\u1eef li\u1ec7u, \u0111\u1ed3ng th\u1eddi gi\u00fap c\u00e1c nh\u00e0 nghi\u00ean c\u1ee9u duy tr\u00ec quy\u1ec1n ri\u00eang t\u01b0 v\u00e0 b\u1ea3o m\u1eadt cho c\u00e1c ph\u00e2n t\u00edch c\u1ee7a h\u1ecd.<\/p>\n<h2>Li\u00ean k\u1ebft li\u00ean quan<\/h2>\n<p>\u0110\u1ec3 bi\u1ebft th\u00eam th\u00f4ng tin v\u1ec1 b\u00e0i ki\u1ec3m tra Chi-Squared, b\u1ea1n c\u00f3 th\u1ec3 kh\u00e1m ph\u00e1 c\u00e1c t\u00e0i nguy\u00ean sau:<\/p>\n<ol>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Chi-squared_test\" target=\"_new\" rel=\"noopener nofollow\">Wikipedia \u2013 Ki\u1ec3m tra Chi b\u00ecnh ph\u01b0\u01a1ng<\/a><\/li>\n<li><a href=\"https:\/\/www.statisticssolutions.com\/non-parametric-analysis-chi-square\/\" target=\"_new\" rel=\"noopener nofollow\">Gi\u1ea3i ph\u00e1p th\u1ed1ng k\u00ea \u2013 Ki\u1ec3m tra Chi-Square<\/a><\/li>\n<li><a href=\"https:\/\/www.graphpad.com\/guides\/prism\/8\/statistics\/stat_interpreting_results_chi-square_test.htm\" target=\"_new\" rel=\"noopener nofollow\">L\u0103ng k\u00ednh GraphPad \u2013 Ki\u1ec3m tra Chi b\u00ecnh ph\u01b0\u01a1ng<\/a><\/li>\n<li><a href=\"https:\/\/ncss-wpengine.netdna-ssl.com\/wp-content\/themes\/ncss\/pdf\/Procedures\/NCSS\/Chi-Square_Test.pdf\" target=\"_new\" rel=\"noopener nofollow\">NCSS \u2013 Ki\u1ec3m tra Chi-Square<\/a><\/li>\n<\/ol>\n<p>T\u00f3m l\u1ea1i, b\u00e0i ki\u1ec3m tra Chi-Squared l\u00e0 m\u1ed9t ph\u01b0\u01a1ng ph\u00e1p th\u1ed1ng k\u00ea m\u1ea1nh m\u1ebd \u0111\u1ec3 ph\u00e2n t\u00edch d\u1eef li\u1ec7u ph\u00e2n lo\u1ea1i v\u00e0 x\u00e1c \u0111\u1ecbnh m\u1ed1i li\u00ean h\u1ec7 gi\u1eefa c\u00e1c bi\u1ebfn. T\u00ednh linh ho\u1ea1t, d\u1ec5 s\u1eed d\u1ee5ng v\u00e0 \u1ee9ng d\u1ee5ng trong nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c nhau khi\u1ebfn n\u00f3 tr\u1edf th\u00e0nh m\u1ed9t c\u00f4ng c\u1ee5 thi\u1ebft y\u1ebfu cho c\u00e1c nh\u00e0 nghi\u00ean c\u1ee9u c\u0169ng nh\u01b0 nh\u00e0 ph\u00e2n t\u00edch d\u1eef li\u1ec7u. Khi c\u00f4ng ngh\u1ec7 ti\u1ebfn b\u1ed9, th\u1eed nghi\u1ec7m Chi-Squared c\u00f3 th\u1ec3 s\u1ebd ti\u1ebfp t\u1ee5c ph\u00e1t tri\u1ec3n, \u0111\u01b0\u1ee3c b\u1ed5 sung b\u1edfi c\u00e1c ph\u01b0\u01a1ng ph\u00e1p v\u00e0 c\u00f4ng c\u1ee5 \u0111\u1ed5i m\u1edbi, cung c\u1ea5p nh\u1eefng hi\u1ec3u bi\u1ebft s\u00e2u s\u1eafc h\u01a1n n\u1eefa v\u1ec1 c\u00e1c m\u1ed1i quan h\u1ec7 d\u1eef li\u1ec7u ph\u00e2n lo\u1ea1i.<\/p>","protected":false},"featured_media":497617,"menu_order":0,"template":"","meta":{"_acf_changed":false,"content-type":"","inline_featured_image":false,"footnotes":""},"class_list":["post-476219","wiki","type-wiki","status-publish","has-post-thumbnail","hentry"],"acf":{"faq_title":"Frequently Asked Questions about <mark>Chi-Squared Test: A Comprehensive Overview<\/mark>","faq_items":[{"question":"What is the Chi-Squared test, and how does it work?","answer":"The Chi-Squared test is a statistical method used to analyze categorical data and determine if there is a significant association between two or more variables. It compares observed frequencies with expected frequencies and provides valuable insights into the relationships between variables."},{"question":"Who introduced the Chi-Squared test and when was it first mentioned?","answer":"The Chi-Squared test was introduced by Karl Pearson, a British mathematician and biostatistician, in 1900. He developed this method to analyze the relationships between variables in large datasets."},{"question":"What is the difference between Pearson's Chi-Squared test and the Likelihood Ratio Chi-Squared test?","answer":"Both Pearson's Chi-Squared test and the Likelihood Ratio Chi-Squared test are used to analyze categorical data, but they differ in their assumptions and applications. Pearson's test assumes normal distribution and is suitable for large sample sizes, while the Likelihood Ratio test makes fewer assumptions and is more appropriate for small sample sizes or cases with expected frequencies less than five."},{"question":"In what situations is the Chi-Squared test commonly used?","answer":"The Chi-Squared test finds applications in various scenarios, including goodness of fit testing, independence testing, and homogeneity testing. It is widely used in social sciences, biology, medicine, marketing, and other fields where categorical data analysis is essential."},{"question":"What problems may arise when using the Chi-Squared test?","answer":"The Chi-Squared test may yield inaccurate results with small sample sizes or cells with expected frequencies less than five. In such cases, the Likelihood Ratio Chi-Squared test is preferred. Additionally, the test is not suitable for ordinal data, as it does not consider the order of categories."},{"question":"How can OneProxy's proxy servers be associated with the Chi-Squared test?","answer":"OneProxy's proxy servers facilitate data collection and analysis by offering access to different geographical locations and ensuring anonymity. Researchers can use proxy servers for web scraping and data gathering tasks, enhancing privacy and security while conducting Chi-Squared tests."},{"question":"What are the advantages of using the Chi-Squared test?","answer":"The Chi-Squared test is a non-parametric test, meaning it makes no assumptions about data distribution. It is suitable for categorical data analysis, providing valuable insights into associations between variables. Additionally, it allows researchers to draw statistical inferences and make confident conclusions based on the obtained p-values."},{"question":"Where can I find more information about the Chi-Squared test?","answer":"For further information about the Chi-Squared test, you can explore additional resources, such as Wikipedia's page on Chi-Squared test, Statistics Solutions' guide, and GraphPad Prism's interpretation of results. Visit OneProxy.pro to learn more about proxy servers' benefits and applications."}]},"_links":{"self":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/wiki\/476219","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\/476219\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/media\/497617"}],"wp:attachment":[{"href":"https:\/\/oneproxy.pro\/vn\/wp-json\/wp\/v2\/media?parent=476219"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}