{"id":40,"date":"2026-06-07T00:55:10","date_gmt":"2026-06-07T00:55:10","guid":{"rendered":"https:\/\/blog.phantram.online\/phuong-sai-do-lech-chuan\/"},"modified":"2026-06-07T02:29:25","modified_gmt":"2026-06-07T02:29:25","slug":"phuong-sai-do-lech-chuan","status":"publish","type":"post","link":"https:\/\/1phantram.com\/blog\/phuong-sai-do-lech-chuan\/","title":{"rendered":"Ph\u01b0\u01a1ng Sai V\u00e0 \u0110\u1ed9 L\u1ec7ch Chu\u1ea9n: C\u00f4ng Th\u1ee9c + V\u00ed D\u1ee5 D\u1ec5 Hi\u1ec3u"},"content":{"rendered":"

Ph\u01b0\u01a1ng sai<\/strong> v\u00e0 \u0111\u1ed9 l\u1ec7ch chu\u1ea9n<\/strong> l\u00e0 hai \u0111\u1ea1i l\u01b0\u1ee3ng \u0111o l\u01b0\u1eddng s\u1ef1 ph\u00e2n t\u00e1n c\u1ee7a d\u1eef li\u1ec7u xung quanh gi\u00e1 tr\u1ecb trung t\u00e2m. Trong khi trung b\u00ecnh c\u1ed9ng<\/a>, trung v\u1ecb<\/a> v\u00e0 mode<\/a> cho bi\u1ebft d\u1eef li\u1ec7u “t\u1eadp trung \u1edf \u0111\u00e2u”, ph\u01b0\u01a1ng sai v\u00e0 \u0111\u1ed9 l\u1ec7ch chu\u1ea9n cho bi\u1ebft d\u1eef li\u1ec7u “tr\u1ea3i r\u1ed9ng nh\u01b0 th\u1ebf n\u00e0o”. \u0110\u00e2y l\u00e0 c\u1eb7p \u0111\u00f4i quan tr\u1ecdng nh\u1ea5t trong th\u1ed1ng k\u00ea c\u01a1 b\u1ea3n<\/a>, \u0111\u01b0\u1ee3c \u1ee9ng d\u1ee5ng r\u1ed9ng r\u00e3i t\u1eeb ki\u1ec3m so\u00e1t ch\u1ea5t l\u01b0\u1ee3ng, \u0111\u00e1nh gi\u00e1 r\u1ee7i ro t\u00e0i ch\u00ednh, \u0111\u1ebfn nghi\u00ean c\u1ee9u khoa h\u1ecdc.<\/p>\n

Ph\u01b0\u01a1ng Sai L\u00e0 G\u00ec? \u0110\u1ecbnh Ngh\u0129a Ch\u00ednh X\u00e1c<\/h2>\n
Ph\u01b0\u01a1ng sai (Variance)<\/strong> l\u00e0 trung b\u00ecnh c\u1ee7a b\u00ecnh ph\u01b0\u01a1ng c\u00e1c \u0111\u1ed9 l\u1ec7ch so v\u1edbi gi\u00e1 tr\u1ecb trung b\u00ecnh. N\u00f3 \u0111o l\u01b0\u1eddng m\u1ee9c \u0111\u1ed9 “ph\u00e2n t\u00e1n” hay “lan r\u1ed9ng” c\u1ee7a d\u1eef li\u1ec7u \u2014 ph\u01b0\u01a1ng sai c\u00e0ng l\u1edbn, d\u1eef li\u1ec7u c\u00e0ng ph\u00e2n t\u00e1n.<\/p>\n
T\u1ea1i sao ph\u1ea3i b\u00ecnh ph\u01b0\u01a1ng \u0111\u1ed9 l\u1ec7ch? V\u00ec n\u1ebfu kh\u00f4ng b\u00ecnh ph\u01b0\u01a1ng, c\u00e1c \u0111\u1ed9 l\u1ec7ch d\u01b0\u01a1ng v\u00e0 \u00e2m s\u1ebd tri\u1ec7t ti\u00eau nhau v\u00e0 t\u1ed5ng lu\u00f4n b\u1eb1ng 0 \u2014 kh\u00f4ng mang th\u00f4ng tin g\u00ec v\u1ec1 s\u1ef1 ph\u00e2n t\u00e1n.<\/p>\n
\u0110\u1ed9 L\u1ec7ch Chu\u1ea9n L\u00e0 G\u00ec? M\u1ed1i Quan H\u1ec7 V\u1edbi Ph\u01b0\u01a1ng Sai<\/h2>\n
\u0110\u1ed9 l\u1ec7ch chu\u1ea9n (Standard Deviation)<\/strong> l\u00e0 c\u0103n b\u1eadc hai c\u1ee7a ph\u01b0\u01a1ng sai. \u0110\u1ed9 l\u1ec7ch chu\u1ea9n “\u0111\u01b0a \u0111\u01a1n v\u1ecb v\u1ec1 l\u1ea1i” \u0111\u01a1n v\u1ecb g\u1ed1c c\u1ee7a d\u1eef li\u1ec7u, gi\u00fap di\u1ec5n gi\u1ea3i d\u1ec5 h\u01a1n ph\u01b0\u01a1ng sai.<\/p>\n
V\u00ed d\u1ee5: N\u1ebfu d\u1eef li\u1ec7u l\u00e0 \u0111i\u1ec3m thi (thang 10), ph\u01b0\u01a1ng sai c\u00f3 \u0111\u01a1n v\u1ecb l\u00e0 “\u0111i\u1ec3m\u00b2” (kh\u00f3 h\u00ecnh dung), c\u00f2n \u0111\u1ed9 l\u1ec7ch chu\u1ea9n c\u00f3 \u0111\u01a1n v\u1ecb l\u00e0 “\u0111i\u1ec3m” \u2014 d\u1ec5 hi\u1ec3u h\u01a1n nhi\u1ec1u.<\/p>\n
C\u00f4ng Th\u1ee9c Ph\u01b0\u01a1ng Sai V\u00e0 \u0110\u1ed9 L\u1ec7ch Chu\u1ea9n<\/h2>\n
C\u00f4ng th\u1ee9c ph\u01b0\u01a1ng sai m\u1eabu (s\u00b2)<\/h3>\n
\ns\u00b2 = \u03a3(x\u1d62 – x\u0304)\u00b2 \/ (n – 1)<\/strong>\n<\/p>\n
Trong \u0111\u00f3:<\/p>\n
\n
x\u1d62<\/strong>: gi\u00e1 tr\u1ecb th\u1ee9 i trong t\u1eadp d\u1eef li\u1ec7u<\/li>\n
x\u0304<\/strong>: trung b\u00ecnh c\u1ed9ng c\u1ee7a m\u1eabu<\/li>\n
n<\/strong>: s\u1ed1 l\u01b0\u1ee3ng ph\u1ea7n t\u1eed<\/li>\n
n – 1<\/strong>: b\u1eadc t\u1ef1 do (d\u00f9ng n-1 thay v\u00ec n \u0111\u1ec3 \u01b0\u1edbc l\u01b0\u1ee3ng kh\u00f4ng ch\u1ec7ch cho t\u1ed5ng th\u1ec3)<\/li>\n<\/ul>\n
C\u00f4ng th\u1ee9c ph\u01b0\u01a1ng sai t\u1ed5ng th\u1ec3 (\u03c3\u00b2)<\/h3>\n
\n\u03c3\u00b2 = \u03a3(x\u1d62 – \u03bc)\u00b2 \/ N<\/strong>\n<\/p>\n
Trong \u0111\u00f3 \u03bc<\/strong> l\u00e0 trung b\u00ecnh t\u1ed5ng th\u1ec3 v\u00e0 N<\/strong> l\u00e0 t\u1ed5ng s\u1ed1 ph\u1ea7n t\u1eed t\u1ed5ng th\u1ec3.<\/p>\n
C\u00f4ng th\u1ee9c \u0111\u1ed9 l\u1ec7ch chu\u1ea9n<\/h3>\n
\n\u0110\u1ed9 l\u1ec7ch chu\u1ea9n m\u1eabu: s = \u221as\u00b2<\/strong>
\n\u0110\u1ed9 l\u1ec7ch chu\u1ea9n t\u1ed5ng th\u1ec3: \u03c3 = \u221a\u03c3\u00b2<\/strong>\n<\/p>\n
H\u01b0\u1edbng D\u1eabn T\u00ednh Tay T\u1eebng B\u01b0\u1edbc \u2014 V\u00ed D\u1ee5 \u0110i\u1ec3m Thi<\/h2>\n
\u0110i\u1ec3m to\u00e1n c\u1ee7a 6 h\u1ecdc sinh: 5, 7, 8, 6, 9, 7<\/strong><\/p>\n
B\u01b0\u1edbc 1: T\u00ednh trung b\u00ecnh c\u1ed9ng (x\u0304)<\/strong>
\nx\u0304 = (5 + 7 + 8 + 6 + 9 + 7) \/ 6 = 42 \/ 6 = 7<\/strong><\/p>\n
B\u01b0\u1edbc 2: T\u00ednh \u0111\u1ed9 l\u1ec7ch (x\u1d62 – x\u0304) cho t\u1eebng gi\u00e1 tr\u1ecb<\/strong><\/p>\n\n\n\n\n\n\n\n\n\n\n\n
H\u1ecdc sinh (i)<\/th>\n \u0110i\u1ec3m (x\u1d62)<\/th>\n \u0110\u1ed9 l\u1ec7ch (x\u1d62 – x\u0304)<\/th>\n B\u00ecnh ph\u01b0\u01a1ng (x\u1d62 – x\u0304)\u00b2<\/th>\n<\/tr>\n<\/thead>\n
1<\/td>\n 5<\/td>\n 5 – 7 = -2<\/td>\n (-2)\u00b2 = 4<\/td>\n<\/tr>\n
2<\/td>\n 7<\/td>\n 7 – 7 = 0<\/td>\n 0\u00b2 = 0<\/td>\n<\/tr>\n
3<\/td>\n 8<\/td>\n 8 – 7 = 1<\/td>\n 1\u00b2 = 1<\/td>\n<\/tr>\n
4<\/td>\n 6<\/td>\n 6 – 7 = -1<\/td>\n (-1)\u00b2 = 1<\/td>\n<\/tr>\n
5<\/td>\n 9<\/td>\n 9 – 7 = 2<\/td>\n 2\u00b2 = 4<\/td>\n<\/tr>\n
6<\/td>\n 7<\/td>\n 7 – 7 = 0<\/td>\n 0\u00b2 = 0<\/td>\n<\/tr>\n
T\u1ed5ng \u03a3(x\u1d62 – x\u0304)\u00b2<\/strong><\/td>\n 10<\/strong><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
B\u01b0\u1edbc 3: T\u00ednh ph\u01b0\u01a1ng sai m\u1eabu (s\u00b2)<\/strong>
\ns\u00b2 = 10 \/ (6 – 1) = 10 \/ 5 = 2<\/strong><\/p>\n
B\u01b0\u1edbc 4: T\u00ednh \u0111\u1ed9 l\u1ec7ch chu\u1ea9n m\u1eabu (s)<\/strong>
\ns = \u221a2 \u2248 1.41 \u0111i\u1ec3m<\/strong><\/p>\n
Di\u1ec5n gi\u1ea3i:<\/strong> \u0110i\u1ec3m trung b\u00ecnh l\u00e0 7, \u0111\u1ed9 l\u1ec7ch chu\u1ea9n l\u00e0 \u00b11.41. Ngh\u0129a l\u00e0 h\u1ea7u h\u1ebft h\u1ecdc sinh c\u00f3 \u0111i\u1ec3m trong kho\u1ea3ng t\u1eeb 7 – 1.41 = 5.59 \u0111\u1ebfn 7 + 1.41 = 8.41. \u0110i\u1ec1u n\u00e0y ph\u00f9 h\u1ee3p v\u1edbi d\u1eef li\u1ec7u g\u1ed1c (5, 6, 7, 7, 8, 9).<\/p>\n
V\u00ed D\u1ee5 2: So S\u00e1nh Hai Nh\u00f3m H\u1ecdc Sinh<\/h2>\n
L\u1edbp A v\u00e0 l\u1edbp B \u0111\u1ec1u c\u00f3 \u0111i\u1ec3m trung b\u00ecnh = 7, nh\u01b0ng ph\u00e2n ph\u1ed1i r\u1ea5t kh\u00e1c nhau:<\/p>\n\n\n\n\n\n\n\n\n
Ch\u1ec9 s\u1ed1<\/th>\n L\u1edbp A<\/th>\n L\u1edbp B<\/th>\n<\/tr>\n<\/thead>\n
\u0110i\u1ec3m c\u00e1c h\u1ecdc sinh<\/td>\n 6, 7, 7, 7, 8, 7<\/td>\n 3, 5, 7, 9, 10, 8<\/td>\n<\/tr>\n
Trung b\u00ecnh (Mean)<\/td>\n 7<\/td>\n 7<\/td>\n<\/tr>\n
\u0110\u1ed9 l\u1ec7ch chu\u1ea9n<\/td>\n s \u2248 0.63<\/td>\n s \u2248 2.45<\/td>\n<\/tr>\n
Nh\u1eadn x\u00e9t<\/td>\n T\u1eadp trung, \u0111\u1ed3ng \u0111\u1ec1u<\/td>\n Ph\u00e2n t\u00e1n, ch\u00eanh l\u1ec7ch l\u1edbn<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
C\u00f9ng \u0111i\u1ec3m trung b\u00ecnh 7, nh\u01b0ng l\u1edbp A \u0111\u1ed3ng \u0111\u1ec1u (\u0111\u1ed9 l\u1ec7ch chu\u1ea9n nh\u1ecf), l\u1edbp B c\u00f3 s\u1ef1 ch\u00eanh l\u1ec7ch l\u1edbn gi\u1eefa h\u1ecdc sinh gi\u1ecfi v\u00e0 y\u1ebfu (\u0111\u1ed9 l\u1ec7ch chu\u1ea9n l\u1edbn). \u0110\u00e2y l\u00e0 th\u00f4ng tin quan tr\u1ecdng m\u00e0 ch\u1ec9 nh\u00ecn v\u00e0o mean th\u00f4i s\u1ebd b\u1ecf qua.<\/p>\n
\u00dd Ngh\u0129a Th\u1ef1c T\u1ebf C\u1ee7a Ph\u01b0\u01a1ng Sai V\u00e0 \u0110\u1ed9 L\u1ec7ch Chu\u1ea9n<\/h2>\n
Trong T\u00e0i Ch\u00ednh \u2014 \u0110\u00e1nh Gi\u00e1 R\u1ee7i Ro \u0110\u1ea7u T\u01b0<\/h3>\n
\u0110\u1ed9 l\u1ec7ch chu\u1ea9n c\u1ee7a l\u1ee3i nhu\u1eadn l\u00e0 th\u01b0\u1edbc \u0111o r\u1ee7i ro c\u01a1 b\u1ea3n nh\u1ea5t trong t\u00e0i ch\u00ednh. C\u1ed5 phi\u1ebfu c\u00f3 \u0111\u1ed9 l\u1ec7ch chu\u1ea9n l\u1ee3i nhu\u1eadn cao = r\u1ee7i ro cao (bi\u1ebfn \u0111\u1ed9ng m\u1ea1nh). C\u1ed5 phi\u1ebfu c\u00f3 \u0111\u1ed9 l\u1ec7ch chu\u1ea9n th\u1ea5p = \u1ed5n \u0111\u1ecbnh h\u01a1n.<\/p>\n\n\n\n\n\n\n
C\u1ed5 phi\u1ebfu<\/th>\n L\u1ee3i nhu\u1eadn TB\/n\u0103m<\/th>\n \u0110\u1ed9 l\u1ec7ch chu\u1ea9n<\/th>\n \u0110\u00e1nh gi\u00e1<\/th>\n<\/tr>\n<\/thead>\n
C\u1ed5 phi\u1ebfu A<\/td>\n 12%<\/td>\n 3%<\/td>\n \u1ed4n \u0111\u1ecbnh, \u00edt r\u1ee7i ro<\/td>\n<\/tr>\n
C\u1ed5 phi\u1ebfu B<\/td>\n 12%<\/td>\n 18%<\/td>\n Bi\u1ebfn \u0111\u1ed9ng cao, r\u1ee7i ro l\u1edbn<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
Hai c\u1ed5 phi\u1ebfu c\u00f9ng l\u1ee3i nhu\u1eadn k\u1ef3 v\u1ecdng 12%, nh\u01b0ng c\u1ed5 phi\u1ebfu B c\u00f3 th\u1ec3 cho l\u1ee3i nhu\u1eadn t\u1eeb -6% \u0111\u1ebfn +30% (12\u00b118), trong khi c\u1ed5 phi\u1ebfu A dao \u0111\u1ed9ng trong kho\u1ea3ng 9%-15% (12\u00b13). Nh\u00e0 \u0111\u1ea7u t\u01b0 th\u1eadn tr\u1ecdng s\u1ebd ch\u1ecdn A, nh\u00e0 \u0111\u1ea7u t\u01b0 ch\u1ea5p nh\u1eadn r\u1ee7i ro cao c\u00f3 th\u1ec3 ch\u1ecdn B.<\/p>\n
Trong S\u1ea3n Xu\u1ea5t \u2014 Ki\u1ec3m So\u00e1t Ch\u1ea5t L\u01b0\u1ee3ng (QC)<\/h3>\n
Trong s\u1ea3n xu\u1ea5t, \u0111\u1ed9 l\u1ec7ch chu\u1ea9n \u0111o l\u01b0\u1eddng t\u00ednh nh\u1ea5t qu\u00e1n c\u1ee7a quy tr\u00ecnh. M\u1ed9t d\u00e2y chuy\u1ec1n s\u1ea3n xu\u1ea5t chai n\u01b0\u1edbc 500ml v\u1edbi \u0111o l\u01b0\u1eddng 5 chai:<\/p>\n
\n
D\u00e2y chuy\u1ec1n A: 499, 500, 501, 500, 499 ml \u2192 \u03c3 \u2248 0.7ml (ch\u1ea5t l\u01b0\u1ee3ng \u0111\u1ec1u)<\/li>\n
D\u00e2y chuy\u1ec1n B: 490, 510, 505, 495, 500 ml \u2192 \u03c3 \u2248 7.1ml (c\u1ea7n hi\u1ec7u ch\u1ec9nh)<\/li>\n<\/ul>\n
Ti\u00eau chu\u1ea9n 6-Sigma trong s\u1ea3n xu\u1ea5t hi\u1ec7n \u0111\u1ea1i y\u00eau c\u1ea7u \u0111\u1ed9 l\u1ec7ch chu\u1ea9n c\u1ef1c nh\u1ecf \u2014 sai s\u1ed1 kh\u00f4ng qu\u00e1 3.4 ph\u1ea7n tri\u1ec7u s\u1ea3n ph\u1ea9m.<\/p>\n
Trong Gi\u00e1o D\u1ee5c \u2014 Ph\u00e2n T\u00edch K\u1ebft Qu\u1ea3 Thi<\/h3>\n
Gi\u00e1o vi\u00ean d\u00f9ng \u0111\u1ed9 l\u1ec7ch chu\u1ea9n \u0111\u1ec3 \u0111\u00e1nh gi\u00e1 \u0111\u1ec1 thi. \u0110\u1ed9 l\u1ec7ch chu\u1ea9n qu\u00e1 nh\u1ecf \u2192 \u0111\u1ec1 qu\u00e1 d\u1ec5 ho\u1eb7c qu\u00e1 kh\u00f3. \u0110\u1ed9 l\u1ec7ch chu\u1ea9n h\u1ee3p l\u00fd (kho\u1ea3ng 10-15% thang \u0111i\u1ec3m) cho th\u1ea5y \u0111\u1ec1 ph\u00e2n h\u00f3a t\u1ed1t h\u1ecdc sinh.<\/p>\n
Quy T\u1eafc 68-95-99.7 (Empirical Rule)<\/h2>\n
V\u1edbi ph\u00e2n ph\u1ed1i chu\u1ea9n (ph\u00e2n ph\u1ed1i h\u00ecnh chu\u00f4ng), quy t\u1eafc th\u1ef1c nghi\u1ec7m n\u1ed5i ti\u1ebfng cho bi\u1ebft:<\/p>\n
\n
68%<\/strong> d\u1eef li\u1ec7u n\u1eb1m trong kho\u1ea3ng (\u03bc – \u03c3, \u03bc + \u03c3) \u2014 t\u1ee9c l\u00e0 trong 1 \u0111\u1ed9 l\u1ec7ch chu\u1ea9n<\/li>\n
95%<\/strong> d\u1eef li\u1ec7u n\u1eb1m trong kho\u1ea3ng (\u03bc – 2\u03c3, \u03bc + 2\u03c3) \u2014 trong 2 \u0111\u1ed9 l\u1ec7ch chu\u1ea9n<\/li>\n
99.7%<\/strong> d\u1eef li\u1ec7u n\u1eb1m trong kho\u1ea3ng (\u03bc – 3\u03c3, \u03bc + 3\u03c3) \u2014 trong 3 \u0111\u1ed9 l\u1ec7ch chu\u1ea9n<\/li>\n<\/ul>\n
V\u00ed d\u1ee5 th\u1ef1c t\u1ebf:<\/strong> Chi\u1ec1u cao nam gi\u1edbi Vi\u1ec7t Nam c\u00f3 \u03bc = 168cm, \u03c3 = 6cm:
\n– 68% nam c\u00f3 chi\u1ec1u cao t\u1eeb 162cm \u0111\u1ebfn 174cm
\n– 95% nam c\u00f3 chi\u1ec1u cao t\u1eeb 156cm \u0111\u1ebfn 180cm
\n– 99.7% nam c\u00f3 chi\u1ec1u cao t\u1eeb 150cm \u0111\u1ebfn 186cm<\/p>\n
Ph\u01b0\u01a1ng Sai V\u00e0 \u0110\u1ed9 L\u1ec7ch Chu\u1ea9n Trong Excel<\/h2>\n\n\n\n\n\n\n\n\n
H\u00e0m Excel<\/th>\n \u00dd ngh\u0129a<\/th>\n Khi n\u00e0o d\u00f9ng<\/th>\n<\/tr>\n<\/thead>\n
=VAR.S(A1:A10)<\/td>\n Ph\u01b0\u01a1ng sai m\u1eabu (s\u00b2)<\/td>\n D\u1eef li\u1ec7u l\u00e0 m\u1eabu c\u1ee7a t\u1ed5ng th\u1ec3<\/td>\n<\/tr>\n
=VAR.P(A1:A10)<\/td>\n Ph\u01b0\u01a1ng sai t\u1ed5ng th\u1ec3 (\u03c3\u00b2)<\/td>\n C\u00f3 \u0111\u1ee7 to\u00e0n b\u1ed9 d\u1eef li\u1ec7u<\/td>\n<\/tr>\n
=STDEV.S(A1:A10)<\/td>\n \u0110\u1ed9 l\u1ec7ch chu\u1ea9n m\u1eabu (s)<\/td>\n D\u1eef li\u1ec7u l\u00e0 m\u1eabu (ph\u1ed5 bi\u1ebfn nh\u1ea5t)<\/td>\n<\/tr>\n
=STDEV.P(A1:A10)<\/td>\n \u0110\u1ed9 l\u1ec7ch chu\u1ea9n t\u1ed5ng th\u1ec3 (\u03c3)<\/td>\n C\u00f3 \u0111\u1ee7 to\u00e0n b\u1ed9 d\u1eef li\u1ec7u<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n
Trong h\u1ea7u h\u1ebft tr\u01b0\u1eddng h\u1ee3p th\u1ef1c t\u1ebf, b\u1ea1n l\u00e0m vi\u1ec7c v\u1edbi m\u1eabu<\/strong> ch\u1ee9 kh\u00f4ng ph\u1ea3i to\u00e0n b\u1ed9 t\u1ed5ng th\u1ec3, v\u00ec v\u1eady d\u00f9ng VAR.S v\u00e0 STDEV.S l\u00e0 \u0111\u00fang.<\/p>\n
C\u00e2u H\u1ecfi Th\u01b0\u1eddng G\u1eb7p (FAQ)<\/h2>\n
Ph\u01b0\u01a1ng sai v\u00e0 \u0111\u1ed9 l\u1ec7ch chu\u1ea9n c\u00e1i n\u00e0o quan tr\u1ecdng h\u01a1n?<\/h3>\n
C\u1ea3 hai \u0111\u1ec1u quan tr\u1ecdng nh\u01b0ng cho m\u1ee5c \u0111\u00edch kh\u00e1c nhau. Ph\u01b0\u01a1ng sai (s\u00b2) \u0111\u01b0\u1ee3c d\u00f9ng trong nhi\u1ec1u c\u00f4ng th\u1ee9c th\u1ed1ng k\u00ea n\u00e2ng cao (ANOVA, h\u1ed3i quy). \u0110\u1ed9 l\u1ec7ch chu\u1ea9n (s) d\u1ec5 di\u1ec5n gi\u1ea3i h\u01a1n v\u00ec c\u00f9ng \u0111\u01a1n v\u1ecb v\u1edbi d\u1eef li\u1ec7u g\u1ed1c. Trong th\u1ef1c t\u1ebf v\u00e0 b\u00e1o c\u00e1o, \u0111\u1ed9 l\u1ec7ch chu\u1ea9n \u0111\u01b0\u1ee3c d\u00f9ng nhi\u1ec1u h\u01a1n.<\/p>\n
T\u1ea1i sao ph\u01b0\u01a1ng sai m\u1eabu chia n-1 thay v\u00ec n?<\/h3>\n
\u0110\u00e2y l\u00e0 “hi\u1ec7u ch\u1ec9nh Bessel” (Bessel’s correction). Khi chia cho n, ph\u01b0\u01a1ng sai m\u1eabu c\u00f3 xu h\u01b0\u1edbng \u01b0\u1edbc l\u01b0\u1ee3ng nh\u1ecf h\u01a1n ph\u01b0\u01a1ng sai th\u1ef1c c\u1ee7a t\u1ed5ng th\u1ec3 (underestimate). Chia cho n-1 t\u1ea1o ra \u01b0\u1edbc l\u01b0\u1ee3ng kh\u00f4ng ch\u1ec7ch (unbiased estimator). \u0110\u00e2y l\u00e0 nguy\u00ean t\u1eafc th\u1ed1ng k\u00ea c\u01a1 b\u1ea3n quan tr\u1ecdng.<\/p>\n
\u0110\u1ed9 l\u1ec7ch chu\u1ea9n c\u00f3 th\u1ec3 \u00e2m kh\u00f4ng?<\/h3>\n
Kh\u00f4ng. \u0110\u1ed9 l\u1ec7ch chu\u1ea9n lu\u00f4n \u2265 0. N\u00f3 b\u1eb1ng 0 khi t\u1ea5t c\u1ea3 c\u00e1c gi\u00e1 tr\u1ecb trong t\u1eadp d\u1eef li\u1ec7u \u0111\u1ec1u b\u1eb1ng nhau (kh\u00f4ng c\u00f3 s\u1ef1 ph\u00e2n t\u00e1n). Kh\u00f4ng c\u00f3 \u00fd ngh\u0129a v\u1eadt l\u00fd cho \u0111\u1ed9 l\u1ec7ch chu\u1ea9n \u00e2m.<\/p>\n
Coefficient of Variation (CV) l\u00e0 g\u00ec?<\/h3>\n
CV = (\u0110\u1ed9 l\u1ec7ch chu\u1ea9n \/ Mean) \u00d7 100% \u2014 l\u00e0 t\u1ec9 l\u1ec7 ph\u1ea7n tr\u0103m c\u1ee7a \u0111\u1ed9 l\u1ec7ch chu\u1ea9n so v\u1edbi trung b\u00ecnh. CV cho ph\u00e9p so s\u00e1nh m\u1ee9c \u0111\u1ed9 ph\u00e2n t\u00e1n gi\u1eefa c\u00e1c t\u1eadp d\u1eef li\u1ec7u c\u00f3 \u0111\u01a1n v\u1ecb kh\u00e1c nhau. CV < 15%: \u00edt ph\u00e2n t\u00e1n. CV 15-30%: ph\u00e2n t\u00e1n v\u1eeba. CV > 30%: ph\u00e2n t\u00e1n nhi\u1ec1u.<\/p>\n
Khi n\u00e0o ph\u01b0\u01a1ng sai v\u00e0 \u0111\u1ed9 l\u1ec7ch chu\u1ea9n kh\u00f4ng \u0111\u00e1ng tin c\u1eady?<\/h3>\n
Ch\u00fang k\u00e9m \u0111\u00e1ng tin c\u1eady khi: (1) c\u1ee1 m\u1eabu nh\u1ecf (n < 30), (2) d\u1eef li\u1ec7u c\u00f3 outlier c\u1ef1c \u0111oan, (3) ph\u00e2n ph\u1ed1i kh\u00f4ng chu\u1ea9n. Trong c\u00e1c tr\u01b0\u1eddng h\u1ee3p n\u00e0y, n\u00ean d\u00f9ng IQR (kho\u1ea3ng t\u1ee9 ph\u00e2n v\u1ecb) thay th\u1ebf \u0111\u1ec3 \u0111o ph\u00e2n t\u00e1n.<\/p>\n
K\u1ebft Lu\u1eadn<\/h2>\n
Ph\u01b0\u01a1ng sai v\u00e0 \u0111\u1ed9 l\u1ec7ch chu\u1ea9n l\u00e0 “\u0111\u00f4i b\u1ea1n \u0111\u1ed3ng h\u00e0nh” kh\u00f4ng th\u1ec3 thi\u1ebfu trong ph\u00e2n t\u00edch th\u1ed1ng k\u00ea. Hi\u1ec3u c\u00e1ch t\u00ednh, bi\u1ebft di\u1ec5n gi\u1ea3i, v\u00e0 \u00e1p d\u1ee5ng \u0111\u00fang ng\u1eef c\u1ea3nh \u2014 t\u1eeb t\u00e0i ch\u00ednh \u0111\u1ebfn y t\u1ebf \u0111\u1ebfn ki\u1ec3m so\u00e1t ch\u1ea5t l\u01b0\u1ee3ng \u2014 s\u1ebd n\u00e2ng t\u1ea7m kh\u1ea3 n\u0103ng ph\u00e2n t\u00edch d\u1eef li\u1ec7u c\u1ee7a b\u1ea1n l\u00ean m\u1ed9t m\u1ee9c ho\u00e0n to\u00e0n m\u1edbi.<\/p>\n
\u0110\u1ec3 ho\u00e0n thi\u1ec7n b\u1ed9 k\u1ef9 n\u0103ng th\u1ed1ng k\u00ea, \u0111\u1ecdc th\u00eam v\u1ec1 t\u1ea7n su\u1ea5t v\u00e0 b\u1ea3ng t\u1ea7n s\u1ed1<\/a> \u2014 c\u00f4ng c\u1ee5 t\u1ed5ng h\u1ee3p d\u1eef li\u1ec7u tr\u01b0\u1edbc khi t\u00ednh ph\u01b0\u01a1ng sai. Xem t\u1ed5ng quan \u0111\u1ea7y \u0111\u1ee7 t\u1ea1i h\u01b0\u1edbng d\u1eabn th\u1ed1ng k\u00ea c\u01a1 b\u1ea3n<\/a>.<\/p>\n
\ud83d\udd22 D\u00f9ng ngay c\u00f4ng c\u1ee5 t\u00ednh % t\u1ea1i 1phantram.com<\/a><\/strong> \u2014 T\u00ednh Coefficient of Variation (CV = \u03c3\/\u03bc \u00d7 100%) v\u00e0 c\u00e1c t\u1ec9 l\u1ec7 ph\u1ea7n tr\u0103m th\u1ed1ng k\u00ea nhanh ch\u00f3ng!<\/p>\n","protected":false},"excerpt":{"rendered":"
Ph\u01b0\u01a1ng sai v\u00e0 \u0111\u1ed9 l\u1ec7ch chu\u1ea9n l\u00e0 hai \u0111\u1ea1i l\u01b0\u1ee3ng \u0111o l\u01b0\u1eddng s\u1ef1 ph\u00e2n t\u00e1n c\u1ee7a d\u1eef li\u1ec7u xung quanh gi\u00e1 tr\u1ecb trung t\u00e2m. Trong…<\/p>\n","protected":false},"author":1,"featured_media":1050,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"rank_math_title":"","rank_math_description":"","rank_math_focus_keyword":"","footnotes":""},"categories":[1],"tags":[],"class_list":["post-40","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-huong-dan"],"_links":{"self":[{"href":"https:\/\/1phantram.com\/blog\/wp-json\/wp\/v2\/posts\/40","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/1phantram.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/1phantram.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/1phantram.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/1phantram.com\/blog\/wp-json\/wp\/v2\/comments?post=40"}],"version-history":[{"count":1,"href":"https:\/\/1phantram.com\/blog\/wp-json\/wp\/v2\/posts\/40\/revisions"}],"predecessor-version":[{"id":52,"href":"https:\/\/1phantram.com\/blog\/wp-json\/wp\/v2\/posts\/40\/revisions\/52"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/1phantram.com\/blog\/wp-json\/wp\/v2\/media\/1050"}],"wp:attachment":[{"href":"https:\/\/1phantram.com\/blog\/wp-json\/wp\/v2\/media?parent=40"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/1phantram.com\/blog\/wp-json\/wp\/v2\/categories?post=40"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/1phantram.com\/blog\/wp-json\/wp\/v2\/tags?post=40"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}