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7/24/2019 Statistics for Analytical Chemistry- Vietnamese
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X l thng k
s liu phn tch
Bi gi ng tm t t
PGS.TS.T Th Tho
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Khi nim v Ha phn tch Ha phn tchl ngnh hahcnghi!n c"# v thnh
ph$n c%# to &'nh tnh(v hm l)*ng cc thnh ph$n&'nh l)*ng(t+ong nh,ng m-# ho /t.
Ha phntch 'ng vai t+0 1#an t+ng t+ong hoa hc2 3th#4t2 t+ong nghi!n c"# hoa hc5 'i# t+a c6 7n '8 pht
t+i8n tim n9ng2 hai thc ti ng#:!n hong /n5 'nh gich%t l)*ng /n ph;m< Ha hc phn tch ngnh hoa hc "ng =>ng t?ng h*p
cc thnh t@# cAa cc ngnh hoa hc hcc li!n 1#annh)B ha hc2 v4t lC2 ton hc D tin hc2 /inh hc D mEi
t+)Fng2 v t+>2 hi =)6ng hc2 'a ch%t2 'a lC.v.v...: lmIt ngnh hoa hc c /@ tch h*p cao cAa nhi# ngnhhoa hc t@ nhi!n m m>c 'ch c#Ji cng cAa n l 'Lmli l*i ch tJi 'a cho hoa hc2 'Fi /Jng v /@ pht t+i8ncAa con ng)Fi.
http://vi.wikipedia.org/wiki/H%C3%B3a_h%E1%BB%8Dchttp://vi.wikipedia.org/wiki/H%C3%B3a_h%E1%BB%8Dchttp://vi.wikipedia.org/wiki/H%C3%B3a_h%E1%BB%8Dchttp://vi.wikipedia.org/wiki/H%C3%B3a_h%E1%BB%8Dc7/24/2019 Statistics for Analytical Chemistry- Vietnamese
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WHY TO STUDY ANAL. CHEM.
Moo=
NL=icinL
Pha+ma+c:
OhLmicalin=#/t+:
SpacLin=#/t+:
Hi/to+:aQ
RthL+/
GLolog:
nL+gLtic/
O+iminolog:
Tocicolog:
g+ic#lt#+Lnvi+onmLntal
nal:ticalchLmi/t+:
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Phn tch nh tnh Phn tch nh ln
Phn tch ha h!c Phn tch c"n c#
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$%c%nt t%chn&'(%) *+ Anal,t&cal Ch%-&)t,
OhLmical
mLtho=/
UiochLmi/t+:
Uiolog:
mLtho=/
Ph:/:calmLtho=/
Ph:/icoD chLmicalmLtho=/
NathLmatic
mLtho=/
OhLmomLt+:
nal:tical chLmit+:
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Qu trnh phn tch
1.Xc nh vn nghin cu2.Chn phng php phn tch
3. Ly mu!.Chu"n # mu
$.%ch v& '&m gi&u cht phn tch (n)uc*n+ ,.-hn tch
.X/ '0 thng 'i4u phn tc v& #5 c5 )t 6u7
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Qu trnh phn tch (tip)V. Wc 'nh v%n ' nghi!n c"# phi hi8# +X
O$n Yc 'nh 'i l)*ng noZ
nh tnh ha: 'nh l)*ngZ K[t 1# ')*c =ng lm g\Z i /] /^ =>ng
thEng tin ' v hi no c$n thEng tin 'Z I '_ng v 'I chnh Yc c$n 't ')*c l 7ao
nhi!#Z Gi thnh phn tchZ `g)Fi phn tch c$n h#:!n hch hng '
Y#%t nh,ng ph)6ng php phn tch v cch l%:m-# hi# #.
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Qu trnh phn tch (tip)/. Ch!n ph0n ph1p phn tch c2n c3 45* oi m-# SJ l)*ng v hJi l)*ng m-# c$n l%: '8 phn tch m gi# &n[# hm l)*ng ch%t phn tch 1# nh( Tha mbn 'I chn lc &loi ')*c ch%t g: cn t+( p "ng ')*c 'I '_ng v 'I chnh Yc Thi[t 7 v m: mc /dn c. Ii ng 3 th#4t vi!n v inh nghim Gi c
ThFi gian phn tch e#i t+\nh phn tch t@ 'Ing ha: hEngZ Ph)6ng php phn tch c /dn t+ong ti li# tham ho
ha: hEngZ Oc ph)6ng php ti!# ch#;n c /dn hEngZ
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Qu trnh phn tch (tip)
f. %: m-# Yc 'nh YLm oi m-# no N-# 'i =in ha: m-# ng-# nhi!n Kch th)c m-# &/J l)*ng v l)*ng m-#(
N-# thJng ! ha: m-# t?ng th8 Sai /J hi l%: m-#Z
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Qu trnh phn tch6. Ch(7n 8 -9( phn tch t:, th%* N-# l ch%t +n2 lng ha: ch%t h Oh%t phn tch =ng tan ha: hEng tan t+ong n)c T+o ha hE ha: Y^ lC m-# thLo ph)6ng php )t Tch ch%t 7ng ph)6ng php ha hc ha: chL cc
ch%t cn t+ n[# c$nZ O c$n lm gi# ch%t phn tch hEngZ
O$n ch#:8n =ng ch%t phn tch '8 Yc 'nhhEngZ O$n 'i# chjnh mEi t+)Fng m-# phn tchZ & pH2
th!m th#Jc th^
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Qu trnh phn tch (tip)
k. Tch ch%t 7ng ph)6ng php ha hc hic$n thi[tOh)ng c%tK[t tAaOhi[t 7ng =#ng mEiOhi[t pha +n
Tch /c Cin =i
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Qu trnh phn tch (tip). Phn tch ThLo ph)6ng php ha hcB DPP t+ng l)*ng D PP phn tch th8 tch & 3 th#4t ch#;n 'I( ThLo ph)6ng php phn tch cEng c>
D @ng ')Fng ch#;n &t\m 1#an h gi,a tn hi# phntch v nng 'I ch%t phn tch( D Phn tch m-# ch)a 7i[t D Phn tch m-# hi# chjnhm-# ch#;n i8m t+a v m-#
t+ng.
D Phn tch m-#lqp
. W^ lC /J li# phn tch v 7o co [t 1#-hn tch thng 'i4u th8c nghi4m
95 c5 )t 6u7 phn tch
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S&nal ;n)t(-%ntalM%th*?a,@ U@ 4&)&8l%@ %l%ct*n@
A(%B +l(*%)c%nc%@ ph*)ph*%)c%nc%@ an?a,@ U@ an< 4&)&8l%B
7/o+ption or +a=iation Sp%ct*ph*t*-%t, an< ph*t*-%t, =>?a,@ U@ 4&)&8l%@;$B ph*t*ac*()t&c )p%ct*)c*p, n(cl%a -an%t&c%)*nanc% an< %l%ct*n )p&n %)*nanc% )p%ct*)c*p,
ScattL+ing or +a=iation T#+7i=imLt+:5nLphLlomLt+:5 saman /pLct+o/cop:sLr+action or +a=iation sLr+actomLt+:5 intL+rL+omLt+:
irr+action or +a=iation WD+a: an= LlLct+on =irr+action mLtho=/
sotation or +a=iation P*la&-%t, *pt&cal *tat,
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S* )1nh c1c th(Ft phn tch
NLtho= pp+oY.+angL& mol(
pp+oYp+Lci/ion &(
SLlLctivit: SpLL= Oo/t P+inciplL #/L/
G+avimLt+:
Tit+imLt+:
PotLntionmLt+:
lLct+og+avimLt+:2
co#lomLt+:
uoltammLt+:
SpLct+ophotomLt+:
Ml#o+omLt+:tomic /pLct+omLt+:
Oh+omatog+aph:
KinLtic mLtho=/
VDVDVDw
VDVDVD
VDVDVD
VDVDVD
VDfDVDV
VDfDVD
VDDVDxVDfDVDx
VDfDVDx
VDwDVDV
.V
.VDV
w
.VDw
wDk
w
wDk
wDV
wDk
wDV
Poo+D mo=.
Poo+D mo=.
Goo=
No=L+atL
Goo=
Goo=Dmo=.
No=L+atL
Goo=
Goo=
Goo=DNo=.
SloQ
No=.
Ma/t
SloQDmo=.
No=L+atL
Ma/tD mo=.
No=L+atL
Ma/t
Ma/tDNo=.
Ma/tD No=.
oQ
oQ
oQ
No=.
No=.
oQD No=.
No=.
No=.D High
No=.Dhigh
No=.
yno+g.
yno+g.2 R+g.
yno+g.
yno+g.2 o+g.
yno+g.2 o+g.
yno+g.2 o+g.
R+g.
yno+gD N#ltiLlL.
R+g. N#lticom.yno+g.2o+g2Lnz:mL
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S? ghi ch{p t+ong ph0ng th nghim /? ')*c =ng '8 ghi cEng vic phn tch
t+ong PT`2 nh,ng ti li# ha: 7%t c" cEng vicno 7n ti[n hnh.
NIt /J chj =-n chnhB| =ng /? c 7\a c"ng
| 'nh /J t+ang nJi ti[p nha#| chj ghi 7ng 7_t m@c| hEng 7ao giF ')*c ph{p Y{ 'i t+ang no.| ghi +X ng: vo m}i t+ang2 C nh4n v phi c
ch, C Yc nh4n cAa ng)Fi c t+ch nhim| ghi +X t!n cEng vic ti[n hnh2 ti /ao n ')*c
ti[n hnh v ti li# tham ho l g\.| ghi t%t c /J li# m 7n th# ')*c
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S? ghi ch{p t+ong ph0ng th nghim
u => v mIt cch ghi ch{p t+ong /? th nghimB| `g: lm th nghimB| T!n th nghim
| `g#:!n tc ti[n hnh th nghim| Phn "ng =ng '8 'nh l)*ngB| Th nghim pha ch[ =#ng =ch ch#;n2 th#Jc
th^< v nng 'I ch#;n
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Chng 1: Cc dng sai strong Ha phn tch1. :;i
2. :;i tuy4t i v& ;i tng i
3. :;i ngu nhin v& ;i < h4 thng!. :;i th< v& ;i tch '=y$. >? '@p 'Ai v& ? ti 'Bp
,. >? chnh c v& ? chDm. : cE nghF;
G HvIJy mI;uJImInt th;t i m;KI i u#Ict t5 ; num#IJ 5M IJJ5J.
If you cannot measure it you cannot !no" it#
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:;i tuy4t i OX
O gi tJ 5 Pc Q gi tJ th8c XO Q
:;i tng i O xO X R -h*n tJSm ;i tng iO x 1TT
(U+
Sai /J t#:t 'Ji DSai /J
t)6ng 'Ji
S J -
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~ /ai /J hEng Yc 'nh ')*c &ha: hEng i8m /ot')*c2 g: +a =o cc :[# tJ hch 1#an hoqc chA 1#anhEng 7i[t t+)c(
~ Sai /J c th8 c gi t+ m hoqc =)6ng &gi t+ th@cnghim th# ')*c ln h6n hoqc nh h6n gi t+ th@c(
~ Gim /ai /J ng-# nhi!n 7ng cch|ti[n hnh nhi# th nghim|i8m /ot tJt 'i# in th@c nghim &t+ang thi[t
72 ph)6ng php2 +n l#:n ta: ngh phn tchng c>2 thi[t 7 'o lm [t
1# lch v mIt pha
qc 'i8mB DSai /J l#En =)6ng v l#En m
~ O th8 hi# chjnh [t 1#~ O th8 l /ai /J h thJng hEng '?i hoqc 7i[n '?i
8 pht hin /ai /J h thJngB
ng m-# ch#;n ')*c ch"ng nh4n &m-# OsN(
Phn tch m-# t+ng &7lan /amplL(
S^ =>ng ph)6ng php phn tch hc
Tham gia c#Ic thi th^ nghim thnh tho &nhi# ng)Fiphn tch t nhi# PT` hc nha# phn tch cng m-# v/o /nh [t 1#(
J
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P+opo+tional L++o+
inrl#LncL/ thL/lopL.
Oon/tant L++o+ inrl#LncL/ thLintL+cLpt.
Oc loi /ai /J
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Co!put"tion #rror
Addition or Subtraction
Z = A + B C Z = A + B + C
Multiplication or Division
Z = AB / C Z / Z = (A / A) + (B / B) + (C / C)
General function
Z = f (ABC) Z = (df/dA)A+ (df/dB)B+ (df/dC)B
V)u h
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Ph{p cIng v ph{p t+
%ultiplic"tion "n$ $i&ision
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%ultiplic"tion "n$ $i&ision
!"en #ultipl$in% or dividin% #easure#ents t"e rl"ti& rrors "r "$$$&
Conse'uentl$ t"e absolute errors of t"e #easure#ents #ust first be converted to relativ
errors&
#'"!pl 1
A = (&* ,&,-) c# A = ,&,- c# A = ,&,- c# / &* c# = ,&,.*B = (*& ,&.) c#. B = ,&. c#. B = ,&. c#./ *& c#.= ,&,.0
1roduct of A and B AB = (&* c#)(*& c#.) = .-&- c#2= .-& c#2to 2 S3
Addin% relative errors AB = A + B = ,&,.* + ,&,.0 = ,&,22 = ,&,-
4"e 5 relative error in t"e product AB is t"erefore = - 5
Ph{p nhn v chia
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L y m u Chu n b m u"
Phn tch
-M u i di n? A 4-M u ng nh t hay [ khng ng nh t?[
S m t m u8 Nhi m b n\ "
(t bn ngoi] -! nh " ng ch t #hn tch P -$y d ng ng chu n8 ^ "
Sai % do thi t b ) Sai % do dung d ch chu n "
&o' about %am#"ing achoco"at chi# cooki?
I. Sa& )G cG nh /. Sa& )G tha, J&K. Sa& )G th- 45* t*n '(1 tnh phn tch 6. Sa& )G
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DOhj m"c 'I g$n nha# gi,a cc [t 1#+i!ng 7it 't ')*c 7i cng ph)6ng php
vi cng m-# phn tch 'qc t+)ngD`[# ti[n hnh t+ong nh,ng 'i# in nh)
nha# &cng ng)Fi phn tch2 cng t+angthi[t 72 cng PT`2 v t+ong hong thFigian ngn( th\ gi l 'I lqp li &+LpLata7ilit:(.
`[# ti[n hnh t+ong nh,ng 'i# in hcnha# &hc ng)Fi phn tch2 hc t+angthi[t 72 hc PT` v thFi gian hc nha#(
th\ gi l 'I ph>c hi &+Lp+o=#ci7ilit:(.
I lqp li v 'I ph>c hi
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V ch#- 45 V chnh 1c
Gi t+ th@c &t+#L val#L(B~l gi t+ ch#;n2 gi t+'Ji ch"ng hoqc gi t+')*c ch%p nh4n
I chnh Yc &cc#+ac:(~ chj m"c 'I g$n vigi t+ th@c
I ch>m &P+Lci/ion(~ chj'I ph>c hi hoqc 'It+ng nha# cAa cc git+ 'o t+ong cc ph{p 'o
lqp li
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I chnh Yc&cc#+ac:DD P+Lci/ion(I ch>m Ohj 't ')*c hi cc
gi t+ 'o g$n gi t+th@c
O$n gim /ai /J ng-#
nhi!n v /ai /J hthJng '8 t9ng 'I'_ng
#En /^ =>ng m-#ch#;n ')*c ch"ngnh4n &OsN( '8 /o/nh [t 1#
Oho th%: m"c 'I tnmn cAa cc [t 1#'o +i!ng 7it /o vi git+ t+#ng 7\nh
Oho 7i[t 'I ph>c hicAa ph{p 'o
T9ng 'I chnh Yc cAa
ph)6ng php 7ngcch gim /ai /J ng-#nhi!n
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Ch0n /X C1c & ln thGn
m th[ no '8 'nh gi t?ng /ai /J cAa1# t+\nh phn tchZ
D S^ =>ng m-# ch#;n 'Ji ch"ng nh) mItm-# phn tch '8 i8m t+a.
D N-# ch#;n 'Ji ch"ng phi ')*c phn
tch cng 1# t+\nh nh) m-# phn tch '8Y{t m"c 'I g$n nha# cAa cc [t 1#th@c nghim vi [t 1# cho t+)c t+ong
thnh ph$n m-# ch#;n
N- t? th8 - thJ !
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N-# t?ng th8 v m-# thJng !&pop#lation v/. /amplL(
N-# t?ng th8 l t%t c cc m-# phn tch mIt loi'Ji t)*ng no ' uB c$n phn tch hm l)*ng aYit a/co7ic t+ong vi!n vitamin O
V gam.
Khi ' t%t c cc m-# vitamin O V mg ')*c gi l m-# t?ngth8 N-# thJng ! l mIt ph$n m-# t?ng th8 ')*c l%: '8
phn tch
`[# l%: +a mIt l vitamin O V mg '8 phn tch th\ gi l m-#thJng !.T+ong /J cc m-# thJng ! th\ mItm-# 'Lm vo phn tch ')*cgi l m-# phn tch
Generally only data for samples is available since it is generallyimpossible to obtain data for the whole population
x
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Oc 'i l)*ng thJng !
Gi t+ t+#ng 7\nh &mLan(B
T+#ng v &mL=ian(`[# /p Y[p ` gi t+ lqp li t+ong t4p /J
li# thLo th" t@ t9ng '$n hoqc gim =$n t YV2 Yw2
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V lch ch(7n=Stan
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h: =ivi=L 7: `DV QhLn calc#lating/Z
`DV =Lg+LL/ or r+LL=om &r( or /amplL~ n#m7L+ or in=LpLn=Lnt val#L/ on Qhich a
+L/#lt i/ 7a/L=2 o+ thL n#m7L+ or val#L/ inthL rinal calc#lation or a /tati/tic that a+L +%%
t* 4a,~ ro+ a pop#lation r `
~ ro+ a /amplL r `DV
onL r lo/t QhLn calc#lating thL vL+agL or a/amplL
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No+L on r/4o calculate t"e std& dev& of a rando# sa#ple 6e #ust first calculate
t"e #ean of t"at sa#ple and t"en co#pute t"e su# of t"e severals'uared deviations fro# t"at #ean&
!"ile t"ere 6ill be n suc" s'uared deviations onl$ (n 7 ) of t"e# arein fact free to assu#e an$ value 6"atsoever&
4"is is because t"e final s'uared deviation fro# t"e #ean #ust includet"e one value of 8 suc" t"at t"e su# of all t"e 8s divided b$ n 6ille'ual t"e obtained #ean of t"e sa#ple&
All of t"e ot"er (n 7 ) s'uared deviations fro# t"e #ean cant"eoreticall$ "ave an$ values 6"atsoever&
3or t"ese reasons std& dev& of a sa#ple is said to "ave onl$ (n 7 )de%rees of freedo#&
G 9 J Z
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TFp )G l&( tR -9( tJn thZ[h& )G th nh&- l\n
N ]N ] th xx ] ^] ^ v ) ]) ] __
trung bnh tp hp lch chun tphp.
Khi ti[n hnh th nghim m th# ')*c'I lch ch#;n nh th\ [t 1# /] chnhYc h6n.
Tuy nhin, chnh xc tt !h"ng n#ir$ng %ng tt.
[`t '( thbc nh&- thn c 8&Z(
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I /ai ch# n&Stan=a+= =Lviation or thL mLan(
&/tan=a+= L++o+( Khi tnh 'I lch ch#;n cAa mIt /J gi t+ t+#ng 7\nh th\ t?ng 'I lch gi,a cc gi t+ t+#ng 7\nh /]gim n[# chia 'I l!ch ch#;n cho c9n 74c hai cAa /J th nghim
/ 'I lch ch#;n gi,a cc gi t+ +i!ng +]
/m 'I lch ch#;n gi,a cc gi t+ t+#ng 7\nh
s s
Nm =
= P i i
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cc#+ac: an= P+Lci/ion
Un ch%t 'Ichnh Yc v' lqp li
chnh Yc vch>m Ohj ch>mnh)ng hEngchnh Yc
KhEng chnhYc v hEngch>m
nghathJng !
I lch ch#;n&S( ha: h /J7i[n thi!n &Ou(nhSai /J t)6ng 'Jinh
I lch ch#;n&S( ha: h /J7i[n thi!n &Ou( nhSai /J t)6ng'Ji ln
I lchch#;n &S(ha: h /J 7i[nthi!n &Ou(lnSai /J t)6ng
'Ji ln
,h cnt oth tagt i%th tu /a"u.
+h h
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0 nghathJng !
Sai /J gi,a
cc ph{p 'o+%t nh
T%t c cc
gi t+ 'o g$ngi t+ th@c
O$n gi t+ch#;n v git+ th@c '8 /o/nh
Oc gi t+
'o ch>mnha# nh)nglch hi git+ th@c
Sai =o')Fng ch#;nhoqc ph{p 'o
ha: =o /ai /Jh thJng
hi# "ng
7n /_ng
O$n lm li
th nghim2tha: '?iph)6ngphp hoqc
ng)Fi hclm thnghim
Ch m / chnh 0*cD Ch ch ma D +hng ch m /Dkhng chnh 0*c
Ui8# =in 'I chnh Yc
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Ui8# =in 'I chnh Yc&acc#+ac:(v 'I ch>m &p+Lci/ion(
Gi t+ t+#ng 7\nh &NLan(&avL+agL( Sai /J t)6ng 'Ji&PL+cLnt L++o+(
Khong 7i[n thi!n
I lch
I lch ch#;n H /J 7i[n thi!n
! ch m? D
!?chnh0*c
&SLL al/o in chaptL+ f(
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Ph0n )a& =a&anc%B
V lch ch(7n t0n G&=$%lat&4% )tan
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) 1o0 and 'hi%k #"ot on Minitab 23
,ung / +ho ng bi n thin7 )
! " ch " n? 4 b! " ch? 4
nh
d&1 t 8it thn
SG c nhja
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SG c nhja /J cc ch, /J t+ong [t 1# phn tch
phn nh 'I '_ng cAa ph{p 'o v 'I chnhYc cAa gi t+ 'o. K[t 1# ')*c 7o co vi /J c ngha t nh%t
&t+ong ph{p nhn v chia( hoqc t /J c nghanh%t /a# =%# th4p phn &t+ong ph{p cIng vt+(
e#i )c /J c ngha
Oc con /J t@ nhi!n nh)V2 2 x< SJ gi,a cc /J c ngha SJ /a# /J t@ nhi!n v 7!n phi /J th4p phn
G
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L5- tkn )G
Oc ch, /J c$n ')*c lm t+0n v /J c nghahi 7o co [t 1# phn tch
`[# 7 cc /J 222x2 th\ t9ng ga t+ t+)c nl!n V '6n v.
`[# loi 7 cc /J V2w2f22 th\ hEng tha: '?i
con /J '"ng t+)c n.`[# loi 7 /J k th\ lm t+0n /J t+)c ' v /J
chdn g$n nh%t.
& d'( ),)* l+m trn th+nh ),)- ),.* th+nh ),/0
Ph0n ph1p 8&Z(
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Ph0n ph1p 8&Z(
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Th
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Oh)6ng fBPhn ph i lC th#: t Ui8# =in [t 1# phn tch 7ng ' th.
&/^ =>ng ph$n mm R+igin2 Ninita72 YcLl
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Hm phn 7J v ch#;n phn 7J
Hm phn 7J l g\Z Oh#;n phn 7J l g\ZHm phn 7J l hm ton hc 7i8# =in 1#i
l#4t phn 7J cAa t4p /J li# v ')*c minhha 7ng ' th
ng =>ngBD cho 7i[t /@ phn 7J cc /J li#D =@ 'on h n9ng Y#%t hin cAa
ch_ng. H5- phn 8G c thZ l&n t#c h*c & c
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Oc loi hm phn 7J
m&n*-&alD&)t&8(t&*n
N*-al D&)t&8(t&*n
P*&))*n D&)t&8(t&*n Ep*n%nt&al
D&)t&8(t&*n
L*&)t&c D&)t&8(t&*n t?D&)t&8(t&*n
Ch&?)'(a%ng ch#;n thJng ! '8 loi
7 /J li# 7%t th)Fng Ti!# ch#;n VB 1#i tc w Ti!# ch#;n wB ch#;n iYon
Oh#;n iYon &ch#;n e( loi gi t+ 7%t
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Oh#;n iYon &ch#;n e( loi gi t+ 7%tth)Fng
Sp Y[p cc /J li# th# ')*c thLo chi# t9nghoqc gim =$n
ng eDtL/t 'nh gi [t 1# nghi ngF hc Ya7ao nhi!# /o vi /J c0n li t+ong t4p /J li#B
DTnh gi t+ e thLo 7i8# th"c
D So /nh vi gi t+ e ch#;n t+a 7ng
e&P2x2 `(
`[# etnh ech#;nth\ ' l /ai /J thE
#in#aJ xx
xx canlanngonghi
Tnh )G th nh&- cn t&`n h5nh lp l&
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gi t+ th@c ha: gi t+ mong m#JnY gi t+ 'o ')*c
n /J m-# c$n lm lqp li
/w
ph)6ng /aiL 'I /ai hc gi,a gi t+ 'o ')*c v gi t+ th@c
t ')*c t+a 7ng hi n
%
n
tsJ= .
..
e
st
n=
Tnh )G th nh&- cn t&`n h5nh lp l&
Ph)6ng php tnh ')*c lqp li '[n hi n hEng tha: '?i
So snh gi tr trung bnh tp
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So snh gi tr trung bnh tphp v gi thc&V (
N>c 'ch B i8m t+a t+#ng 7\nh t4p h*p c hc nha#c ngha vi gi t+ th@c cho t+)c vha: hEng .
Gi thi[t thJng ! l HvB v2 n[# hEng tho mbn th\ ha: v m"c tin c4: thEng ! cho t+)c.
e#:[t 'nh m"c C ngha 2 tha: '?i 7c 7 n[# n '_ng=@a t+!n m"c tin c4: thJng ! /^ =>ng t+ong t+)Fng h*pphn phJi ch#;n
Tnh gi t+ v /o /nh vi g t+ ch#;n t+ong 7ng.f.
D`[# DV2x hoqc V2x th\ loi 7 gi thi[t 'o &vi2k(
DT+ong ph$n mm m: tnhB gi thi[t 'o ')*c ch%p nh4nn[# Pval#L 2k( &t"c l giJng nha#(
S* )1nh &1 t t(n 8nh 4\& &1
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S* )1nh &1 t t(n 8nh 4\& &1t thbc =ItB
Tnh gi t+ tB
So /nh ttnhvi tch#;n&tt+a 7ng p2xk v r`DV( `[# ttnh t7ng 1hay 2value34,4*5 th6 hai gi tr7 !hc
nhau c# 8 ngh9a thng !
t
x N
scalc =
( )
=
=
=
x ts
N
x ts
N
x N
st
So /nh hai t4p /J li#
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So /nh hai t4p /J li#So /nh cc gi t t+#ng 7\nh &TDtL/t( &wt(
~Oc /J li# hEng tng cqpN-# /o /nh ')*c l%: cng m-# t?ng th8
~u => /o /nh [t 1# phn tch P7 t+ong n)c ng$m H` cAa hai PT` hcnha#
~SJ li# tng cqpOc m-# hEng cng m-# t?ng th8
~u => /o /nh hm l)*ng cholL/tL+ol t+ong m# cAa nh,ng 7nh nhn hcnha# /^ =>ng hai ph)6ng php phn tch
~So /nh ph)6ng /ai hai t4p /J li# &MDtL/t(
~Ohj /o /nh cc /J li# hEng tng cqp
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So /nh hai ph)6ng /ai &MDtL/t(
DTnh M B
DSo /nh Mtnhvi M7ng&P2xk2 rV2rw(
D`[# Mtnh
M7ng
&ha: Pval#L
2k( th\ SV
an= Swhc nha#c C ngha thJng !
..
.
& >=
S
SFcal
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S* )1nh ha& &1 t t(n 8nh
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S* )1nh ha& &1 t t(n 8nh=(npa&%<
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S* )1nh ha& &1 t t(n 8nh=(npa&%<
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=(npa&%<
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=pa&%<
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ypuI N-# phn tch t
cng mIt ng#n
Oc ph{p /o /nh ccng /J th nghim
Ph)6ng /ai cAa hai ph{p/o /nh c giJng nha# hEng
Oh)6ng kB `Ru &anal:/i/ or va+iancL(
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Oh)6ng kB `Ru &anal:/i/ or va+iancL(
2hCn b tB '8 i8m t+a /@ hc nha# gi,a haigi t+ t+#ng 7\nh.
Oh#;n t hEng ph h*p t+ong mIt /J t+)Fngh*p /a#~ Ohj =@a t+!n mIt ph$n =, li#
~ O 1# nhi# /o /nh nh)ng chj mIt /J t+ong 'c C ngha thJng !
~ KhEng th8 /o /nh nhi# ga t+ t+#ng 7\nh cAa ccnhm t+ong cng mIt m-# t?ng th8
S@ c$n thi[t /^ =>ng `Ru
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S@ c$n thi[t /^ =>ng `Ru
Gi thi[t thJng ! c$n i8m t+a t+ong `RuBcc ga t+ t+#ng 7\nh m-# hc nha#
Phi =ng `Ru v\ c$n i8m t+a ph)6ng /ai
cAa cc gi t+ t+#ng 7\nh c hc nha# c nghaha: hEng
ng =>ng hcB `Ru =ng '8 'nh ga nhh)ng chnh v nh h)ng t)6ng h} cAa mItha: nhi# :[# tJ '[n [t 1# th nghim
Th#4t ton /o /nh cc gi t+ t+#ng\ R
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g g7\nh 7ng `Ru
GTTKB HB V w f
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g g:[# tJ '[n [t 1# th nghim
i# in /^ =>ng `RuB N-# ')*c l%: ng-# nhi!n t m-# t?ng th8
Oc nhm m-# ')*c phn tch 'Ic l4p
nha#. Oc th nghim lqp li cAa m}i m-# ')*c
ti[n hnh 'Ic l4p nha#
T4p /J li# cAa m-# t?ng th8 phi t#nthLo phn 7J ch#;n
TQo So#+cL/ or ua+ia7ilit:
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: #n $%&'$ an )stimat) of *ariabi!it+
b)t,))n groups is compar)d ,ith*ariabi!it+ ,ithin groups-Q .)t,))n/group *ariation is th) *ariation among
th) m)ans of th) di0)r)nt tr)atm)nt conditionsdu) to chanc) (random samp!ing )rror" and
tr)atm)nt )0)cts if an+ )xist-Q 1ithin/group *ariation is th) *ariation du) to
chanc) (random samp!ing )rror" among indi*idua!sgi*)n th) sam) tr)atm)nt-A N O A
W & t h & n ? d . * ( p ) a . & a t & * n
u a + i a t i o n = # L t o c h a n c L .
m % t q % % n ? d . * ( p ) a . & a t & * n
u a + i a t i o n = # L t o c h a n c L
a n = t + L a t m L n t L r r L c t & i r a n : L Y i / t i / ( .
T * t a l a . & a t & * n A - * n S c * . % )
ua+ia7ilit: ULtQLLn G+o#p/
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ua+ia7ilit: ULtQLLn G+o#p/
Th%% &) a l*t *+ 4a&a8&l&t, +*- *n% -%an t* th% n%t. La%
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`Ru mIt :[# tJ
Tnh cc 'i l)*ngi= trun% bn" c"un% + @n" "]n% can"E# + qi
i= %iM trV ca >Tt 'u@ p"n tLc" t"` itron% n"E# t"` @n" "]n% ca n"E# = s >"Mc n"au %iOa cMc %iM trV
trun% bn" c@u #u t\n% t": t"` v trun% bn"
c"un%qiis l %iM trV n%u n"iNn ca p"n bD c"umn vhi %iM
trV trun% bn" bkn% ,
ThL Dsatio
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A N O A = B
M % a n S ' ( a . % ) W & t h & n
W & t h & n ? d . * ( p ) a . & a t & * n
u a + i a t i o n = # L t o c h a n c L .
M % a n S ' ( a . % ) m % t q % % n
m % t q % % n ? d . * ( p ) a . & a t & * n
u a + i a t i o n = # L t o c h a n c La n = t + L a t m L n t L r r L c t & i r a n : L Y i / t i / ( .
T * t a l a . & a t & * n A - * n S c * . % )
F=
MSbetween
MSwithin
bilit$Grouparia!it"in
bilit$GroupariaBet6een
=F
ThL Dsatio
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F
=
MSbetween
MSwithin
MSbetween= SSbetweendfbetween
MSwithin = SSwithin
dfwithin
SStotal= SSbetween+ SSwithin
ThL DsatioB SS ULtQLLn
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J;nK %5t;' (;KK ;'' 5MthI c5JI t5gIthIJthIn 6u;JI thI t5t;'+
%5t;' num#IJ 5Mu#Ict.
N
%
n
&SS'et(een
..
=
dinK I;ch gJ5up t5t;' 6u;JIit ;nK KiviKI #y thI num#IJ
5M u#Ict in thI gJ5up
.
)( g)andg)oup'et(een **nSS =
ThL DsatioB SS ithin
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:6u;JIK gJ5up t5t;'.
Vum#IJ 5Mu#Ict inI;ch gJ5up.
n
&*SS(ithin
.. =
:6u;JI I;ch inKiviKu;' c5JI;nK thIn ;KK up ;'' 5M thI
6u;JIK c5JI
.
)( g)oup(ithin **SS =
ThL D satioB SS Total
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ThL DsatioB SS Total
)7%roupsofnu#ber='et(eendf
SStotal= X2
G 2
N J;nK %5t;' (;KK ;'' 5MthI c5JI t5gIthIJ
thIn 6u;JI thI t5t;'+
%5t;' num#IJ 5Mu#Ict.
:6u;JI I;chc5JI thIn ;KK;'' 5M thI6u;JIK c5JI
t5gIthIJ.
)()()( . g)oupg)andg)oupg)andtotal
******SS
+==
fIgJII 5M dJIIK5mZfIgJII 5M dJIIK5mZ9IteIInZ9IteIInZ
|ithinZ|ithinZ%roupsofnu#bertotal7subectsofnu#bertotal
&&& 2.
=++=
(ithin
(ithin
df
nnndf
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1
2
3
`Ru hai :[# tJ
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`Ru hai :[# tJ
`Ru /^ =>ng cc 'i l)*ng tnh nh)`Ru mIt :[# tJ
T+#ng 7\nh cAa ph)6ng /ai t+ong mIt cIt
&SSO=rO(
S@ hc nha# gi,a cc cIt SS t l vi m}inh h)ng chnh &=0ng v cIt( v nhh)ng t)6ng h}
SSs2 SSO2 SSsWO
TQoDa: `Ru
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TQo a: `Ru
TQoDa: `Ru
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99/150
TQoDa: `Ru
TQo a: `Ru
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100/150
TQoDa: `Ru
TQoDa: `Ru
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atin /1#a+L
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Lat&n )'(a%) ha) c*(nt%8alanc&n 8(< &n
N *+ *q) %'(al) th% n *+ c*l(-n) Th% l%tt% p%)%nt&n t%at-%nt) app%a) &n%ach c*l(-n an< *q *nl, *nc%
E++%ct) *+ t%at-%nt@ *
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Lat&n S'(a%)
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105/150
Oh)6ng B Phn tch hi 1#i vphn tch t)6ng 1#an
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phn tch t)6ng 1#an
.V. T)6ng 1#an hai 7i[nBDng '8 'o m"c 'I 1#an h t#:[n tnh
gi,a hai 7i[n
D Wc 'nh mJi 1#an h gi,a hai 7i[n
DTnh h /J t)6ng 1#an PLa+/on vt)6ng 1#an th" hng SpLa+mLn.
//#mption/
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//#mption/
S#7Lct/ a+L +Lp+L/LntativL or a la+gL+ pop#lation Pai+L= /amplL/ &m#/t havL w va+ia7lL/( a+L
yn=LpLn=Lnt o7/L+vation/
W an= val#L/ m#/t 7L mLa/#+L= in=LpLn=Lntl: W val#L/ a+L mLa/#+L= 7#t not cont+ollL=
`o+mal =i/t+i7#tion &ir not #/L SpLa+man/ +anco++Llation(
ll cova+iation m#/t 7L linLa+
V5tI th;t 5ut'iIJ h;vI ; ';JgI in}uIncI in
ScattL+ iag+am
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ScattL+ iag+am
L/ignatL onL va+ia7lL W an= thL othL+ .~ltho#gh it =oL/ not mattL+ Qhich i/ Qhich2 in ca/L/
QhL+L onL va+ia7lL i/ #/L= to p+L=ict thL othL+2 W i/thL p+L=icto+ va+ia7lL &thL va+ia7lL :o#+L p+L=ictingr+om(.
+aQ aYL/ or L1#al lLngth ro+ :o#+ g+aph. LtL+minL thL +angL or val#L/ ro+ Lach va+ia7lL. PlacL
thL high val#L/ or W to thL +ight on thL ho+izontal aYi/an= thL high val#L/ or toQa+= thL top or thL vL+tical
aYi/. a7Ll convLniLnt point/ along Lach aYi/. Mo+ Lach pai+ or /co+L/2 rin= thL point or intL+/Lction ro+
thL W an= val#L/ an= in=icatL it Qith a =ot.
T)6ng 1#an PLa+/on
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g 1
D Tnh h /J t)6ng 1#an &+( '8 chj +a m"c'I 1#an h t#:[n tnh t+ong m-#
DKi8m t+a thJng ! tnh c nghib cAa &+('8
YLm c mJi 1#an h t#:[n tnh gi,a cc7i[n t+ong t4p /J li# ha: hEng H /J t)6ng 1#an PLa+/on/ r gi= thi;t
r$ng c#
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Ui8# =in mJi t)6ng 1#an hai 7i[n t+!n '
th `h4n Y{t chi# h)ng v m"c 'I t)6ng
1#an gi,a hai 7i[n
Scatt%pl*t) h%lp &ll()tat% th% %lat&*n)h&p) 8%tq%%n 4a&a8l%)
H /J t)6ng 1#an PLa+/on
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Lrinitional ro+m#laB
Oomp#tational ro+m#laB
))()()((
))(()(
....
=
++n**n
+**+n)
r= COVXY
(sx)(sy) n
++**,-.*+
= ))((
separatel$var$and86"ic"tode%ree
t"ervar$ to%eand86"ic"tode%ree=)
N"c 'I t)6ng 1#an
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N"c 'I t)6ng 1#an
Ui8# =in m"c 'I t)6ng 1#an th[ noPLa+/on/ r ( DV+V
%# &D hoqc |( chj +a chi# h)ng mJit)6ng 1#an
Gi t+ t#:t 'Ji + cng g$n V th\ m"c 'It)6ng 1#an cng ln
1 T 1Perfect Relationship No Relationship Perfect Relationship
H /J t)6ng 1#an
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SpLa+man san Oo++Llation
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i/ thL 7L/tDnoQn an= La/iL/t tLchni1#L +/i/ givLn 7: thL L1#ationB
QhL+L = i/ thL =irrL+LncL 7LtQLLn +aning/ in tQo
+aning mLtho=/
hLn ` V2 +/can 7L #/L= to calc#latL a tD/co+L Qith
thL L1#ation an= thL +L/#lting tD/co+L i/ #/L= in
a tQoDtailL= tL/t or /igniricancL
p
#$/N!N
d0
/#")1
1
N
"#is
KLn=all san Oo++Llation
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OoLrriciLnt &(
No+L complicatL= than thL SpLa+man +an Sho#l= 7L #/L= QhLn th+LL o+ mo+L /Lt/ or
+aning/ a+L compa+L=
Oalc#latL= 7: thL p+opo+tion or conco+=ant pai+/min#/ thL p+opo+tion or =i/co+=ant pai+/~ ThL+L LYi/t tQo 7iva+iatL o7/L+vation/2 &Yi2:i( an= &Y2:(
Oonco+=ant pai+/ a+L QhLn &YiDY(&:iD:( a+L po/itivL
i/co+=ant pai+/ a+L QhLn &YiDY(&:iD:( i/ nLgativL
Sco+L/ +angL r+om DV to V
Goo=man an= K+#/al/ am7=a
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&(
i/ #/L= QhLn nominal /calL/ a+L #/L=~ SpLa+man +an an= Qont Qo+ 7Lca#/L thL
o+=L+ing LlLmLnt i/ mi//ing Qith nominal
/calL/ can 7L calc#latL= 7: /tati/tical pacagL/
Pa+tial Oo++Llation/ &+P(
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D To in=icatL thL =Lg+LL or tQo va+ia7lL/ a+L linLa+l:+LlatL= in a /amplL2 pa+tialling o#t thL LrrLct/ oronL o+ mo+L cont+ol va+ia7lL/.
D To intL+p+Lt pa+tial co++Llation 7LtQLLn tQova+ia7lL/ QL m#/t noQ thL 7iva+iatL co++Llation
7LtQLLn thL va+ia7lL/ ri+/t.D To con=#ct a pa+tial co++Llation2 thL+L m#/t 7L atlLa/t th+LL va+ia7lL/.
can 7L #/L= in thL rolloQing Qa:/