สูตรและตารางวิชาสถิติวิเคราะห์สำหรับวิทยาศาสตร์ 09121201

สตู รและตารางช่อื วิชา หลกั สถติ ิ รหสั วชิ า 09121015

สูตรวเิ คราะหข์ อ้ มูลทางสถติ ิ หน้าท่ี 1

หน้าท่ี 2 rl'lI).J1,,\).J1EJ ~~(;Ij' Ll.J'1lfL~kI(;I1Y1~~r~).Jl.Jr:;~Ylt rl'll).J LLl.Jj'&rkll.Jj':;'lnm nxr •~).J1.j'J:;~Ylt rl'll).J LLl.Jr&rWll'lmh'l Pr = L + r[---LfjJ/fr 100 Cy = (J C.V. = -x100 Jl s -x100 X

หน้าท่ี 3 n! - (n - k).. n! - k!(n'-k).1. 0 ~ P(EJ~ 12. IP(Ej)= 1p(S) = 1 ; p(¢) = 0 .3. mv \"FI di , v \I) !\II iI4. A r!1::j ~ ua::: B !lJ'U!'Yi~fll·H')'lYIlflYl'lJ'U'j1'.IJfl'U!!'.YIJ1 P (AUB) = P(A) + P(B)nWiJ. ill A !1'J'U!'Yi~fll'ji.UiYl~nWU p( A)=P (A 'il:::'tilnYl) = 1 + P(A)~ i,r A ua::: B !1'J'U!'Yi~fll'jtli4.Y1i~'U s p(A uB) = P(A)+ P(S)- P(A nB) ill A ua::: B !1'JU!'Yi~fll'ji.UiYl~iu S U1;1:B:: ~ A 'il:::'~ P(B) ~ P(A) mmP(AlB) = P(B) P(AIB) = P(A) 'Yi~~P(B/A) = P(B) 'Yi~~P(AB) = P(A)P(B) iI fil.e:t. vv \II v'3. {Il A ua:::-B !lJU~j;1''j:::fluua1 'il:::!Y11l 1. A ua::: B !1'JU8j;1''j:::OU 2. A !m::: B !1'JU8j;1''j:::OU 3. A lla::: B !1'JU8j;1''j:::OU 1. P(AB) = P(A)P(B) 2. P(BC) = P(B)P(C) 3. P(AC) = P(A)P(C) ua::: 4. P(ABC) = P(A). P(B) . P(C)

•O~'1W'lI11U หน้าท่ี 4v .c::I iC ( d.::t ~ .; , v \II !\fI v G ) 0:::9 £'1t111ll't'lIlJOl'HU n l'l'lIlJOl'HU Cl C 2l •• \" Cn hl S 91'1IUhll't'lIlJOl'H,UYlIOVl'llhl':i1110!~hJl !VllVltl~ UCi =5 lll:l~ Cj (lCj =¢;i:;t:j;i,j=l,2, .... ,n t:h Alll'Ul'I'IIlJOl':iW'Vl~ i'U S lVltl~ P(A):;t: 0 i'l111l'l11'il~11l'U~'il~lnVll't'lIlJO~':iu1 C j~0 , \I) V..::t, ~~ V o<!I!VltlOl'l'l'UVl11A !VlIOVl'U'Ulll:l1rHI ~1ll'1.h ~1I1111111'y]jell~ el'l ~1mh ~lIU1111yjell~el'li'l1 X lll'U ~ 1 mh ~1I U11111']yjell~ el'I i'l1 X lll'U~1ll'1.h~lIU1111yjell~el'I1. p(x) ~ 0 1. f(x) ~ 02, LP(x)= 1 2. Jf(x}ix = 13. P(A) = L p(x) lVltl~ A C 5 J3. P(A) = f(x}ix lVltl~ A~S xEA A4. E(x) = Ji = L xp(x)5. Var(x) = (72 = E(x - Ji)2 J4. E(x) = Ji = xf(x)a'x L (X - Ji)2 p(X) 5. Var(x) = (72 = E(x - JiY J(x - Ji)2f(X)a'X P(x) =l/n ;x=xllx2, ••• xiJ L~1b'U~~ = Ji = Xl / n t= =~1bbtl,;t1,;'J'U (72 (Xi - JiY)/ n P(x) = pXql-X ; X = 0,1 ~1b'U~~ = Ji = P ~1bbtl,;t1,;'J'U (72 = pq P(x) p(x) =C)pxqn-x;x=O,l, ....,n , .,j = Ji = np mb'U'6l~ =~1bbtl,;t1,;'J'U (72 npq

หน้าท่ี 5 P(x) = qX-1.p ; X = 1,2,3, ... = J-l =l/p fi1bbtJ-atJ-a'J'U = (Y2 = q / p2 P(x) = (X-1)pr qx-r ; X = r, r + 1, ... r-1 /rn,!1H'H\" J = J-l = r p = =fllUU~lhl'\.t (y 2 rq / p2'IIi'l~'IJ~..:.t~1UU'i Vf..:.t~<U'\.tmlll'l.hil:::I1]'\.t , .,; fllU'lhU'i1'\.t ~i'lvJ~ill --1 ;a<X<b i'\lllHltl b-a a+b (H-,fJY -- 12 .•.., 2uflVi e1 -(x-.ut J-l (Y2 (Y.J2n 20-2 ;-00 < X < 00uflVilllml~l'\.t _Z2 0 1 1i'\l;l'umi 0 --1e 2 ;-00 < Z < 00 2n .J2;rr x~Oe1 --x--1n 2 x2 n ,2(~-1)

หน้าท่ี 6 '\"V\" I [1+-)( n + 1_ 1)' _t n+l 0 n (el\lf11t)1:I''J::: n) 2. 22 ;--<n < t < oc . -- ;n ~3 m'Y'l (~ -1 )~Jrn n n-2(el\lf11t)1:I''J::: u ua::: v) ((U;VJ-l) (UJu V 2v2(u + V - 2) - f2 ~-1 v -- ~ff>O v-2 u(v - 2y (~-1)(~-1)(~-1)(~-1)(1+'IIlii.:JiJ'i~\"ll1D'ii'( 2) '21. normal Ji, (J' 'VI'Jl'IJfll (J' (J'/..Jn -•• X-Ji (, ) Z =i1'j'fl normal \0,1 _X-Ji - normal \I,0,1) - s/..Jn Z = -sX-/-.J.Jin - normal (\0, ,1 ) x - n)normal ~, (J'2 / n )i11el X - normal ~, S2 / li'l'~ml'IJfll (J'2 A P - normal (p, pq / n)

i;Ifl-1Uj:::'lI101 หน้าท่ี 75. X~ normal 0-t1' a 21 ) x - y ~ normal y~ normal (,u2' (21) C~- y ) -(,u1 - ,u2' 0-21 / n1 + 0-22 / n2)f1jlurlJ a21 U~:::a22 (,u1 - ,u2)6. X, Y iimjUllml'il-1U'lJ'lJ1~9 Z = ~ normal (0,1) n1 ~ 30 , LLi,\l~ n2 ~ 30 ~0-21 / n1 + 0-22 / n2 X- Y ~ normala\ )7. X ~ normal ~11f (,u1 - f.12f521 / n1 - 522 / n2) lh11lmlurh a21UfJ::0-22 Y ~ normal 0-t2' a22 )11lml'lJi'h a21 U~:::a22 .Xi UfJ:: Y1 ''.\"IJmjullm!ll-1U'lJ'lJI'lJf~lj\l'~\" n1 LLi,\l~ n2 iii'h'.lJlfl

หน้าท่ี 8·.~1~~lflrjJfli11!llfT!!1l~nti1J1W'1·· .. •·•·~JHf:!l:/jt1!i!1J'iJ~~ll1'ihth:::'lI1m 'fil'rliJ!~~fliW~~ fm·1J1~lJlt1r - ftlm~£J1J'J:::'lIlm ftl-ff~ri1'U 1J'J:::'lIlm ~ X ftl!!1J'J1J'J1'U 1J'J:::'lIlm P 'tHl.:!1J\"i:::'lI1m A ~'t)\liWUtNftl!'Il~£J1J'J:::'lIlm cr2 ~(ll'i WU~~-ff~ ri1'U 1J1:::'lIl m P ~- .S2 ~I .- - PI - P2 XI - X2 1\ /\ PI - P2f11\"ilh:::)J10JA1!fltitlth:::'lI1fl1 (Jl) !!UU'll1.:! cr2 1. 1J'J:::'lIlmijf11'J!!llm!ll~!!'lJ'lJ1Jf)~ !!(l:::'I'l'J1'lJftl 2. 1J'J:::'lIlmijf11mllm!ll~!!'lJ'lJl~ '11l11tJcil~ij'tJln~ l'\1qj (n ~ 30) cr, 2 cr/,[;X ± ZI.a.{2 X S/'fu± ZI.a.{22.1 ml'lJfll X S/'fu± tl.a.{2;n.1cr2.2 'hi'l'lHUftl 23. 1J'J:::'lIlmijfm!!llf)!!ll~!!'lJ'lJ1Jf)~ 1limllJftl cr2!!(l::: n < 30tm1J\"i:::)J1OJATtTvHhl.J1J\"i:::'lI1fl\"i (p) !!UU'll1.:!1. 1J'J:::'lIlmijfm!!llm!M!!'lJlJl~ '1 1l11tJcil~ij'tJ'U1~l'\1qj (n ~ 30) 22 (cr2 (n-I)S ,(n-l)Sf11\"i1J\"i:::)J1OJA1!!th1J\"i1'U1J\"i:::'lI1m ) !!UU'll1~1. 1J'J:::'lIlmijf11mllfl!!ll·mlJlJ1Jf)~ 2 2 X 1·a.{2 X a.{2

\"jtlP~~~*n~~~nJ~~J#~1W~P~~~~ijt;®t~f./ หน้าท่ี 9fnnh ~),I1Wf11Nil,h:n ~'lrh:jf111i)a tIIHI.:j1.h~\" 101d.et 'Q,I' , ~I.Q. Q,IYl),l fl 1~~),I ~ lij tl1.:llTij.:j1~ij tll.:jl uY ij \1'1~flU1. ,.h~'lf1miifmm::ml~.:jIl1J1J,jfl~2. ,j:i~'lf1miifllm~ml~.:jIl1J1Jl~ '1~dtlth.:jjj'IJm~ l'l1tli (nl ~ 30 , nz ~ 30) •z z2.1 '\'I:i11Jfl1 (j 1 II~~ (j z3. ,j:i~'lf1mjjfllm~flll~.:jIl1J1J,jfl~'1 ' 1 2 2 Q,I' ' n < 30 <XI - XZ) ± ,t1.Oo/2Sp\"\"; 1/n1 + 1/nz 1.I'\'1:i11Jfl1(j 1 II~~ (j z 'IJ'U1~llIdtltJ1.:j n Z tl.Oo/2 litl.:jff1fl1;l:i~ nl+nZ-2 Il~~ z zz l S p = (nl-l)S 1+(nZ-l)S Z , ,2 2'13.1 1.I'\'1:i11Jfl1(j I II~~ (j z nl+nZ-2 , ,2 2 1l1ll'\'l:i11Jd1 (j 1 = (j Z '1 ' ,Z z _J Z Z 'is(XI - XZ) ± tl.Oo/23.2 1.1'\'I:i11J1'1 (j I Il~~ (j z /nl + S ,jllZ *-, ,2 2 1l1ll'\'l:i11Jd1 (j 1 (j Z t1.Oo/2litl.:jff1fl1;l:i~ V zz V Sin! + S illz Z ZZ (S /nl ) +(S ,jnz) nl-l nz-2 , r-J;;d ± tl.Oo/2;n.1 Sdfll ~ tJ ~::),I 1Wf11Nil 9iWI ~'ld1.:jf1 11~atl'llij .:jlTij.:j,j~::'111fl'l d; = Xli - X2;1I1.J1.J\l1.J~ d-\"= LJ din , S zd,,=-zLJ (d; - d) /(n-l) ,y liJ'tl,j :i~'lf1m'l1.:j1;ltl.:jjj fllm ~ flll ~.:jIl1J1J,j fl~'I1~tllm1'IfttJ.:jIl1J1J,jfl~ Il~~ n < 30fl1~tJ~ ~),I1Wf11Nil 9i1.:1~~'I111.:jf11i~1f1YU'ij.:jtJ~ ~'111fl~(lll ~ 30 lIil~ 82 ~ 30 )fll'j tJ,. ::),11Wf116 ~ ~ Uf1Y ~ ::'1111.:1f11l11.htJ~ lU'IIij.:jU'tl.:jlh::'111fl'l z Z SI ~I FI.Oo/2;nZ.I,nl.1 \"2 z S2 Sz F1.Oo/2;n1.I,nZ.1 Z Z Sz S 2 F1.Oo/2;nl.I,nZ.1 2\" \"2 SI F1.Oo/2;n2.I,nl.l SI

fll\".i1.h :::mwrilIU~£l1.h :::'lflf1\".i n = [ZI;n af หน้าท่ี 10 1. UJ::;'lIlmlJf11'HI'ilflll'il'lIlUUUf1illlltl::;YlJ1Uftl srn = [ Z,.an a2 £J z n = Z I.an pq 2 £ z n = Z----I.-aorn- 4£ 2 ZZ n = Z I.an (a I + a 2) 2 £ nl=nz=n 2 Z ,.an (Plql + PZq2) 2 £ 1~(J~ n,=n2=n 1I'tl::;PI 1I'tl::;P2 l~'U.ufl~'tll'Ufl~1'l

หน้าท่ี 11 1. m111~«BtJfhltlaV1h:::'lfJml~£J1..'I\"IB•'ilJvfl~: 1.1 lh:::'lflmiJf115U1JflUMUlllltlfl~ un:::l1)Jllfhutl5tlnlJ 2 crl1){) 1.2 tl5:::'ltJmiJf115U1JflU1J~Ull1l1'1., 'UlJJ\".l1{)ciJ~111qj(n ~ 30) un:::l1)Jll 2 . cr«)J)J9ii]'wh~ Ho: J.l = J.lo 1.,tJ~ J.lo = fiJfl~~«o9il1~«tJtJ Z = L!Lo tiJ'hhmllfiJ cr Hi S U'I1lJ crf\J; ft'lJlJQ\ll!JlJIW\" ~ l'U\lltlOlft''IiHoHI : J.l > J.lo Z>ZI_UH, : J.l < J.loHI : J.l \":f::- J.lo ..Z < -ZI_U Z>ZI_Ufl 115{) Z < -ZI_Ufl 2. m111~«tJtJtillUaV1h:::'lJ1fl11~£J1 ~.~,ytJ~Jtl~: Irl{)tl5:::'ltlmiJf115U1Jflll1J~1l1l1ltlfl'~UlJl.,m{)tJl~ltlfl (n < 30)tf)J)J9ii],lrh~ Ho: J.l = J.lo 1.,tJ~ J.lo = fiJMl1tfo9il1~«tJtJ t = X-J.lo sMH, : J.l > J.lo t> tl_u;n_1H, : J.l < J.lo t < -tl:U;n_1HI : J.l \":f::- J.lo 3. m111~«BtJtil'tJPui1\nh:::'lJlfl1I~£J1 Z>Z,_U ,yB'ihtl~: 'UlJl\".l1{)cil~111qj Z < -Z,_U «)J)J9iiJ'Il~VI Ho : P = Po «o9il1~«tJtJ Z = .1.£\ ..:ElL \"Jpoq./n H, : P > Po HI: P < Po H, : p\":f::- Po'l1)Jl£J1'l1\l'l\IlJJ\".l1{)cil~1J:::111qj01 npo > 5 un::: nqo > 5 4. m111~«tJtJtiJlI1hlln'Ulh:::'lflfl1,ytJ~ltl~ : tl5:::'ltlmiJf11m\lfllI1HUlllltlfl~ 'hjl1)lllfilutlnlnll cr 2 =2 2 1.,tJ~ =2 I ..,;«)J)J9iil'll~l'I Ho: cr cr 0 cr 0 fllfH'I'I«09il1~«BtJ 22 X = (n - 1)S 2 cro ft'lJlJQ\ll!lllIW\"~ 1'\\1lltlOIft''Ii Ho 22 2 > X2 I-U;O-IH, : cr>cro X 22 22HI : cr < cr 0 X <XU;n.lH, : cr 2 \":f::- cr 20 22 22 X X X X> 115{) < Ufl;n-I 1·(1/2;0-1

หน้าท่ี 12 5. fm'YI~tHl1Jfl1)JJIIVlflpjH1::,.rhuhltliimHl.:jlh::'II)fl1v •U _I\" _I ~ ,2 2'Il6'il1fl~: 5.1 u'i::'li1f1':i)Jm'ill~flll~.:jIl'U'UuflVll1'i)'UTI10' , II~:: 0' 2111U 5.2 1J'i::'li1f1':iijfl1'il1~flll~.:jIl'U'Ui'1~ n1 ~ 30 n, ~ 30 .5.3 tf)J1li1Uril.:j~lflll~~:;1J'i:;'li1f1':iUril.:jl1lU6ff'i:;ri'U • ,tl'JJJJ~sndH Ho: J.l, - J.lz = do l~£Jn do = f;,tNntl'ii0J1~tl'61J Z = (XI - )(2) - d.ll._ V,' .2 ...Jo'2 _I V,z/n,+O'22/n2 2 •~ 2 S 2 m)J\"'l~'Ul1)Jl£J1l1\l:jfI1 )Jl1'il'UTI10' , II~:; 0' 2 u'i:;)Jllll~1£J SIll\"':; fflJlJ~!llJU~~ l\",,1JBn1'1i HoH, : J.l1 - J.lz > dOHI : J.l1 - J.l2 < do'*H, : J.l, - J.lz do 6. fl)1'Y1~tl'61Jtl1nUlVlflpjH1:;,.rhuhltliimUl.:jlh::'111fl1 n2 < 30) 'I)J'l1'il'UT,2I10' ,i v..'IVl6;•nflU~: _uI'\"i:;'li1f1':i)Jm111~flll~.:jIl'U.'1Uu~f11\l1••1{)fl\"'lfI£J.:jIl'U_'IUu~f1'\lJl'U)~~\l,ol1S{)£Jl.:jmf(ln, < 30,.II~:; 0'\ 1I~l1'ilUil 0'21 = 0'\ 1\"\":;m'itf)J1li1{)ril.:j~lflll~,,,:;1J'i:;'li1mlrJ'U6ff'i:;ri'U ,'iJJJ2J~S),dH HO: J.l, - J.l2 = dO l~£Jn do = fllMntl'O~11~tl'81J <X, -t = )(2) - dO 1~£J~ =SZp (n, - 1)S2, + (n, - l)S\ Sp\" l/n,+ 1/n2 n,+n2-2 \"ff)J)J~\ll!l'UII£J.:j HI : J.l1 - J.l2 > do H, : J.l, - J.lz < do '*H, : J.l, - J.l2 do,.nmlll1fJ t ij{).:jfl'16ff1:;n, + n2 -2 7. fl)1'Y1~tl'81Jtl1)JJIIVlflpjH1:;ltiH';)ltliit!'iJ6.:jlh:;'111fl1~6;hn~: 1J'i:;'li1f1':iijfl1'il1~flllMll'U'U1JflW111{)ifl~lfi£J.:jll'U'U1Jf'l\WJ'Ul~1li1{)ril.:jl~f(ln, < 30 , '* .ll~l1'il'Ui) 0'\ll\"':; 0'\ 0'22 l\"\":;m'itf)J1li1{)ril.:j~lf11l~,,,:;1J'i:;'lI)f1':ilrJ'U6ff'i:;ri'U ,....tl'JJJJ~inriH HO: J.l, - J.l2 = dO - -l~£Jn do = fllf1.:jntl't1\ll'YI~tl'81J ~V .. I > 11.0.(2 11'i{) I < -1,.0.(2 ff)J)J\ll!l'UII£J.:j V= 2 2 n2 1Z HI : J.l, - J.l2 > do HI : J.l, - J.l2 < do [S / nl + S .j '*H, : J.l, - J.l2 dol1JJlt!1l1fJ I ij{).:jfl'16ff'i:;v l~£Jn 2 22 2 (S / nl) +(S z/ n2) n,-l nz-l

, 'I.et 1.1 •.• , หน้าท่ี 138. m~'I'lmH)'IJmllJll~Jn\l11.:1~Z'I11l'lflllfl\"fHH).:I ~Z'lIln~ll'IJ1H)'IJ~o1ftHJ10Vl: t1'iz'lflmiinml\lnU\l.:lll'I.J'l.Jtln~ 0'\'hhm'I.J~l O'2,11l'l~ ~1J~\"l€lth.:l\l1f1U91m~tl'i~.'Iflm11J1~'\.Jflf('iZn'\.J Ul'lZ n = ~1'\.J1'\.J~ n < 30rrlJlJ~gll,dl.:l Ho: I-l, - 1-l2= do d -do , SJ' -_ L(d, _d)' Sdl..[;; n-\ H,:I-ld>do H,: I-l\" < do H, : I-ld \"# do9. m~'I'lVlrrtl'IJmllJUVl n~h.:l~ Z,..,.il.:lnVltTTWrrtl.:llh Z'lIl n ~o1ftl'iJ10'l: 'U'Wlf1~1tlth.:ll'11~rrlJ)J~2l'I.dl.:1 Ho: P, - P, = Po lf1v~ Po= ~Wl.:l~ O:s Po:s ]rrO~'I'l'lrrtl'IJ Z= (P,-P2)-PO P,-P2 ~ (; 1 ~ I I n, ) + (; 2 ~ 2 I n2 ) ~; ~{(1 I n,) + (1 I n2)} rf1J1J~!l'\.Jll~.:I 1'U~tl5Irfli HO H,: P, - P2 > Po Z < -Z,.U H, : P, : P2 < Po Z> Z,.Un'l11tl Z < -Z,.Un H, : P, - P2 \"# Po\ O. m~'I'l'lrrtl'IJmllJllVl nviN~Zldl.:lflllllhtl~TWrrtl.:ltl~Z'lfln~ ,'Uv tl'i•l•l.n•'l: tI 'i~'Iflm1Jf'\"llm\lnll\l.:lll'I.J'IJ tl~f11\"~ 1JVl'illJf11O' 2 llm~ 0'22 t' I .q' 2 2 ,. rrmJVlgl'W11.:l Ho: 0' I = 0' 2 f(()~Vlflf(eJ'IJ I'UVltl5lrfli Ho F> F,.u Vitl.:lfflflf('i~ ~v _S2, n,-\1ll'l~n2-\ f(lJlJ~~l'WLW.:l F> F,.u Vitl.:lffli1rf'i~ F= n2-\IIl'l~ n,-\H, : 0'2,> 0'2, S22 F > F,. Un Vitl.:lffli1f('i~ n,-]lll'l~ n2-] 22 S2 F > F,. Un Vitl.:lffli1rf'i~H,:O',<O'2 F= 2 n2-\1ll'l~n,-\'*H, : 0'\ 0'\ ~ I F = -S---2.!.- ;m\"s2,>s2 2 S22 ... s; IIS 2 ; lS2>2S, , I 'I1'itlF=-

หน้าท่ี 14 '\ ..\" l' 2j'A (x + x') = --Pl~fJl1 11 n, + n2 -+- nn ..• 1: = !(O,-Er'H'HI Ho : Pl = PlO , P2 = P20 , ... , Pk = PkO E,.C). II 2 2 k~3 X > X~ 1 k-l l'lJIll\J{lHTfi : ~ ~1J{)l'!l'fi HO tl1 l = :t(O,-E,)' .e:t. 1 E, Q V2 2 X X1'IJ\l1,1J{ll'!l'fi: ~~1J{)liI'fi HO tl1 > k-l-m , 1~fJn m =~hl.nUrn'ilill\l1e:d'IJ3.:l1J'i~'II1mnIli3.:l 1J'i~1Jltl.lfh LL(O,,-E,,) Eij E\" cJ (rJ( ••• 0 •••• >\"mllfWI 1. Eij _ 5 2. tll r = c , c = 2 lIa~ n < 50 II'l = (10;; - Eul- O.5f ;=\ pI Eu UAUl n ~ 50 'l = LL(O,j-E,Y E

\"111ft nllft '11::,ftll nUl11'1111l'U หน้าท่ี 15 ft1'111 tl'11:: ,ftll nUl11'1111l'UII1J 1.1\1lImft YI HIA t1l . .•. .•..•. f)l'iYlPlff01JfflJlJPl! ll,1 fftlPlflPlffOlJf)l'iflPltlfl'llllJlJ eRD F = MSIr:t.. * .\" . *Ho : JlI = ~ =. . . = Jlit MSEHI : tJ Jli Jlj tltlH'\.Hltl 1 tl ; i j 11{'\"J1ff1i Ho f\"I1 F > F I-a ;k-I,n-kf)l'iflPltlfl'llllJlJ RBD F = MSII.t* *Ho : JlI = ~ =. . . = Jlit MSEHI : ij J..L. Jlj tlVmJtltl 1 ~ ; i j ,j\"{\"J1ff1i Ho f\"I1 F> F I-a ;k-I.(k-I)(b-I)n. l1Jfl;]Oflllvm'illJ'IIfl'l'Wl'l 2 UilUU(Witb Interaction) (m > 1) .•..•. .•. fftlPlflPlfffllJ f)l'iflPlfffllJfflJlJPl! ll,11. Ho : 'l.iijf111tJlIlllfl~H~::'H':iH~::fi'lJ'IItI~i1~~tlYi 1 (A) F=MSA 1 tlVH HI : ijf111tJlIllln~lU::l1iH~::fi'lJ'IItl~'il~~tI~ MSE \"Utltl 1 ~::\P~1'U ,joC\ Ho m\" d~ F > F I-a fltl~ffltlff~:: {Jrff1i (a-I) 11(1::ab(m-l)2. Ho : 'l.iiji'l'l1tJlIllln~H~::l1iH'j::fi''U'IItI~'il~~tlYi 2 {B) F=MSB 2 tlVH H) : iji'l'JltJlIlllfl~lU::l1ilU::fi''U'IItI~'il~~tI~ MSE - \"Utltl 1 1::\P~1'U m,j';:'\" '\" .e:l.o::), {Jlffli Ho F > F l_afltl~fflt1ff1:: (b-l) 11(1::ab(m-I)3. Ho : 'l.iijf111tJlIlllfl~lU::l1iHilfli'Vi(11'ltJ'IIM¥i'~ .. 2'il~~tI F=MSAB ..\" ..HI : iji'l11tJlIlllfl~lU::l1iHill1i'Vi(11'ltJ'IItl~Yi~ 2'il~~tI MSE F > FI_al1dtl~fflt1f\"f\"~':\": \"tltlHUtltI 1 111111tJUIll mtJ\"\"{\" J1ff1i Ho tI (a-l)(b-l) 11(1::ab(m-l)4 , ,q,q,.q\" cv if v ililU(No Interaction) (m = 1)'II.llJfl lJlJfln1fYltl'illJ'IIfl'lfl'l2 .•. .•..•. f)l'iflPlfffl1JfflJlJPl! ll,1 fftlPlflPlfffl1J I'1. Ho : 'l.iiji'l'JltJlIlllfl~lU::l1ilU::fi''U'IItl~'il~~tlYi 1 (A) F=MSA .,;.., 1 tlVH .MSE HI : ijf111tJlIlllfl~H~::l1iH~::fi'lJ'IItl~'il~~tI~ ,j\"'\" m\" .......,. -- {J1ff1i Ho F > F I-a l1t1~fflt1ff~:: \"Utltl 1 ~::\P~1lJ (a-l) 11(1::(a-l)(b-l)2. Ho : 'l.iijf111tJlIlllfl~H~::l1ilU::fi''U'IItIl'il~~tlYi 2 {B) F =MSB 2 tlVH HI : iji'l'lltJlIlllfl~H1::l1iH~::fi''U'IItI~'il~~tI~ MSE \"Utltl 1 1::\P~1'U m1.J\"\"\" \" ....-==to {J1ff1i Ho F > F )_al1t1~fflt1ff~:: (b-l) 11(1::(a-l)(b-l)

fll11mrJmtirJm~.:Ii8U (Multiple Comparisons) หน้าท่ี 16 l'Vlrn1f'lHO:/-Li=~ +LSD = t1 _0,/2; n - k, MSE[~ _1 ]HI: /-Li 7= /-Lj n. n. 1JHO : J.li = /-Lj d* 20, ,S2=MSEHI: J.li 7= J.lj -- Yl a =HO : /-Li = /-Lj k(k -1)HI: J.li 7= J-lj S (-1 +-1) \1 n. n. V1 J I IllBrff1i HO 01 t > t 1. a*12 T = qa(k,n-k) SE -- ~ neHO : /-Li = /-Lj SNK= qa(r,n-k) SEHI : /-Li 7= /-Lj --HO : /-Li = /-Lj ~ neHI: /-Li7= ~ MSE 1 1HO: /-LL = 0 ~-(-+-) SNK = qa(r,n-k) n· n·JHI: J.lL 7=0 I 2 oll~illBl1:1'1iHo -~jl>SNK W=pa(r,n-k) SE -- ~ ne I IllBnY1i HO 01 ~i - ~ j > W VS= .,jV(L) f(k-l)F1_U;k_l,n_k i~t1~ 2 , kC VeL) = S2 L i n. i= 1 1 k- k L C.Xi, L C =0 1 i i= 1 i= 1

pnb~ CBPANOVA หน้าที่ 17 = r reM (Correction lor mton) (rEX, 1n == (1:1; 1n SST,.r.l;X; -eM SSTrI = r.T,2/n, - eM SSE • SST - SSTrt MSI'rl- SSTrt I(k -1) MsE • SSE 1(,,- k) \"l\i\"l~U MSTrr F. MSE- F'-I~. U::EX, rCM (CorreCllon fOr MIQIf) a 111 SST-r,tx; -eM -xYSSTrt:a Ib(T; J = r!L-cM b. SSB- IAJ\B-,-XJ-\1 ct-LB-1CM k lI\tJ~ CM .'(I:LLXykt =!: nn SSBa'•LB--JCM; SSAB-•LL• -(A-B-C~ M-SS. A-SSB J-I am· I-I /-1 m

หน้าท่ี 18 illY1:4+11%\" = SSIt a = f -bXSSxx\",oil SSg =IX' -(L~l}1nSSg eIxy-(rxXLY)/n=S1 I: MSE SSrr -bSSp n-2 . S, = SISSxx S. r:S~1/\"+X1/SS:r~m~\"11Jr.;mN~'N1~\"1\~~m!H y X-xYi±tLAI .s~lIn+(X ISSg • /1,,-1uitrh,,~Y,hl.lt:)l1Nl11J1J't>mH X, Jt ~i ± 'LAL .s 11n + (X, - X Y I SSxx • {'l:Jl-2

ตารางแถว 1-5 6-10 11-15 16-20 21-25 26-30 1 10480 15011 01536 02011 81647 91646 2 22368 46573 25595 85393 30995 89198 3 24130 48360 22527 97265 76393 64809 4 42167 93093 06243 61680 07856 16376 5 37570 39975 81837 16656 06121 91782 6 77921 06907 11008 42751 27756 53498 7 99562 72905 56420 69994 98872 31016 8 96301 91977 05463 07972 18876 20922 9 89579 14342 63661 10281 17453 18103 10 85475 36857 53342 53988 53060 59533 11 28918 69578 88231 33276 70997 79936 12 63553 40961 48235 03427 49626 69445 13 09429 93969 52636 92737 88974 33488 14 10365 61129 87529 85689 48237 52267 15 07119 97336 71048 08178 77233 13916 16 51085 12765 51821 51259 77452 16308 17 02368 21382 52404 60268 89368 19885 18 01011 54092 33362 94904 31273 04146 19 52162 53916 46369 58586 23216 14513 20 07056 97628 33787 09998 42698 06691 21 48663 91245 85828 14346 09172 30168 22 54164 58492 22421 74103 47070 25306 23 32639 32363 05597 24200 13363 38005 24 29334 27001 87637 87308 58731 00256 25 02488 33062 28834 07351 19731 92420

งสถติ ิ1 เลขสมุสดมภ31-35 36-40 41-45 46-50 51-55 56-60 61-65 66-7069179 14194 62590 36207 20969 99570 91291 9070027982 53402 93965 34095 52666 19174 39615 9950515179 24830 49340 32081 30680 19655 63348 5862939440 53537 71341 57004 00849 74917 97758 1637960468 81305 49684 60672 14110 06927 01263 5461318602 70659 90655 15053 21916 81825 44394 4288071194 18738 44013 48840 63213 21069 10634 1295294595 56869 69014 60045 18425 84903 42508 3230757740 84378 25331 12566 58678 44947 05585 5694138867 62300 08158 17983 16439 11458 18593 6495256865 05859 90106 31595 01547 85590 91610 7818818663 72695 52180 20847 12234 90511 33703 9032236320 17617 30015 08272 84115 27156 30613 7495267689 93394 01511 26358 85104 20285 29975 8986847564 81056 97735 85977 29372 74461 28551 9070760756 92144 49442 53900 70960 63990 75601 4071955322 44819 01188 65255 64835 44919 05944 5515718594 29852 71585 85030 51132 01915 92747 6495183149 98736 23495 64350 94738 17752 35156 3574976988 13602 51851 46104 88916 19509 25625 5810490229 04734 59193 22178 30421 61666 99904 3281276468 26384 58151 06646 21524 15227 96909 4459294342 28728 35806 06912 17012 64161 18296 2285145834 15398 46557 41135 10367 07684 36188 1851060952 61280 50001 67658 32586 86679 50720 94953 ผนวก 1

ผนวก 2ตารางสถติ ิ 2 ความนา จะเปน สะสมทวนิ าม P(X ≤ r) = r ∑ b(x; n,π ) x=0 πn r 0.10 0.15 0.20 0.25 0.30 0.40 0.50 0.60 0.70 0.80 0.905 0 0.5905 0.4437 0.3277 0.2373 0.1681 0.0778 0.0312 0.0102 0.0024 0.0003 0.0000 1 0.9185 0.8352 0.7373 0.6328 0.5282 0.3370 0.1875 0.0870 0.0308 0.0067 0.0005 2 0.9914 0.9734 0.9421 0.8965 0.8369 0.6826 0.5000 0.3174 0.1631 0.0579 0.0086 3 0.9995 0.9978 0.9933 0.9844 0.9692 0.9130 0.8125 0.6630 0.4718 0.2627 0.0815 4 1.0000 0.9999 0.9997 0.9990 0.9976 0.9898 0.9688 0.9222 0.8319 0.6723 0.4095 5 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.000010 0 0.3487 0.1969 0.1074 0.0563 0.0282 0.0060 0.0010 0.0001 0.0000 0.0000 0.0000 1 0.7361 0.5443 0.3758 0.2440 0.1493 0.0464 0.0107 0.0017 0.0001 0.0000 0.0000 2 0.9298 0.8202 0.6778 0.5256 0.3828 0.1673 0.0547 0.0123 0.0016 0.0001 0.0000 3 0.9872 0.9500 0.8791 0.7759 0.6496 0.3823 0.1719 0.0548 0.0106 0.0009 0.0000 4 0.9984 0.9901 0.9672 0.9219 0.8497 0.6331 0.3770 0.1662 0.0473 0.0064 0.0001 5 0.9999 0.9986 0.9936 0.9803 0.9527 0.8338 0.6230 0.3669 0.1503 0.0328 0.0016 6 1.0000 0.9999 0.9991 0.9965 0.9894 0.9452 0.8281 0.6177 0.3504 0.1209 0.0128 7 1.0000 1.0000 0.9999 0.9996 0.9984 0.9877 0.9453 0.8327 0.6172 0.3222 0.0702 8 1.0000 1.0000 1.0000 1.0000 0.9999 0.9983 0.9893 0.9536 0.8507 0.6242 0.2639 9 1.0000 1.0000 1.0000 1.0000 1.0000 0.9999 0.9990 0.9940 0.9718 0.8926 0.6513 10 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.000015 0 0.2059 0.0874 0.0352 0.0134 0.0047 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000 1 0.5490 0.3186 0.1671 0.0802 0.0353 0.0052 0.0005 0.0000 0.0000 0.0000 0.0000 2 0.8159 0.6042 0.3980 0.2361 0.1268 0.0271 0.0037 0.0003 0.0000 0.0000 0.0000 3 0.9444 0.8227 0.6482 0.4613 0.2969 0.0905 0.0176 0.0019 0.0001 0.0000 0.0000 4 0.9873 0.9383 0.8358 0.6865 0.5155 0.2173 0.0592 0.0093 0.0007 0.0000 0.0000 5 0.9978 0.9832 0.9389 0.8516 0.7216 0.4032 0.1509 0.0338 0.0037 0.0001 0.0000 6 0.9997 0.9964 0.9819 0.9434 0.8689 0.6098 0.3036 0.0950 0.0152 0.0008 0.0000 7 1.0000 0.9994 0.9958 0.9827 0.9500 0.7869 0.5000 0.2131 0.0500 0.0042 0.0000 8 1.0000 0.9999 0.9992 0.9958 0.9848 0.9050 0.6964 0.3902 0.1311 0.0181 0.0003 9 1.0000 1.0000 0.9999 0.9992 0.9963 0.9662 0.8491 0.5968 0.2784 0.0611 0.0022 10 1.0000 1.0000 1.0000 0.9999 0.9993 0.9907 0.9408 0.7827 0.4845 0.1642 0.0127 11 1.0000 1.0000 1.0000 1.0000 0.9999 0.9981 0.9824 0.9095 0.7031 0.3518 0.0556 12 1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.9963 0.9729 0.8732 0.6020 0.1841 13 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9995 0.9948 0.9647 0.8329 0.4510 14 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9995 0.9953 0.9648 0.7941 15 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

ตารางสถิติ 2 ความนา จะเปน สะสมทวินาม P(X ≤ r) r (ตอ) ผนวก 3 = ∑ b(x; n,π ) x=0 πn r 0.10 0.15 0.20 0.25 0.30 0.40 0.50 0.60 0.70 0.80 0.9020 0 0.1216 0.0388 0.0115 0.0032 0.0008 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 1 0.3917 0.1756 0.0692 0.0243 0.0076 0.0005 0.0000 0.0000 0.0000 0.0000 0.0000 2 0.6769 0.4049 0.2061 0.0913 0.0355 0.0036 0.0002 0.0000 0.0000 0.0000 0.0000 3 0.8670 0.6477 0.4114 0.2252 0.1071 0.0160 0.0013 0.0000 0.0000 0.0000 0.0000 4 0.9568 0.8298 0.6296 0.4148 0.2375 0.0510 0.0059 0.0003 0.0000 0.0000 0.0000 5 0.9887 0.9327 0.8042 0.6172 0.4164 0.1256 0.0207 0.0016 0.0000 0.0000 0.0000 6 0.9976 0.9781 0.9133 0.7858 0.6080 0.2500 0.0577 0.0065 0.0003 0.0000 0.0000 7 0.9996 0.9941 0.9679 0.8982 0.7723 0.4159 0.1316 0.0210 0.0013 0.0000 0.0000 8 0.9999 0.9987 0.9900 0.9591 0.8867 0.5956 0.2517 0.0565 0.0051 0.0001 0.0000 9 1.0000 0.9998 0.9974 0.9861 0.9520 0.7553 0.4119 0.1275 0.0171 0.0006 0.0000 10 1.0000 1.0000 0.9994 0.9961 0.9829 0.8725 0.5881 0.2447 0.0480 0.0026 0.0000 11 1.0000 1.0000 0.9999 0.9991 0.9949 0.9435 0.7483 0.4044 0.1133 0.0100 0.0001 12 1.0000 1.0000 1.0000 0.9998 0.9987 0.9790 0.8684 0.5841 0.2277 0.0321 0.0004 13 1.0000 1.0000 1.0000 1.0000 0.9997 0.9935 0.9423 0.7500 0.3920 0.0867 0.0024 14 1.0000 1.0000 1.0000 1.0000 1.0000 0.9984 0.9793 0.8744 0.5836 0.1958 0.0113 15 1.0000 1.0000 1.0000 1.0000 1.0000 0.9997 0.9941 0.9490 0.7625 0.3704 0.0432 16 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9987 0.9840 0.8929 0.5886 0.1330 17 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9998 0.9964 0.9645 0.7939 0.3231 18 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9995 0.9924 0.9308 0.6083 19 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 0.9992 0.9885 0.8784 20 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000

ผนวก 4ตารางสถิติ 3 ความนาจะเปน สะสมปว สซอง P(X ≤ r) = r ∑= r e−µ µ x ∑ Pois(x; µ) x=0 x=0 x! µr 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90 0.9048 0.8187 0.7408 0.6703 0.6065 0.5488 0.4966 0.4493 0.40661 0.9953 0.9825 0.9631 0.9384 0.9098 0.8781 0.8442 0.8088 0.77252 0.9998 0.9989 0.9964 0.9921 0.9856 0.9769 0.9659 0.9526 0.93713 1.0000 0.9999 0.9997 0.9992 0.9982 0.9966 0.9942 0.9909 0.98654 1.0000 1.0000 0.9999 0.9998 0.9996 0.9992 0.9986 0.99775 1.0000 1.0000 1.0000 1.0000 0.9999 0.9998 0.99976 1.0000 1.0000 1.0000ตารางสถิติ 3 ความนา จะเปน สะสมปวสซ อง P(X ≤ r) = r ∑= r e−µ µ x (ตอ) ∑ Pois(x; µ) x=0 x=0 x! µr 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.00 0.3679 0.2231 0.1353 0.0821 0.0498 0.0302 0.0183 0.0111 0.00671 0.7358 0.5578 0.4060 0.2873 0.1991 0.1359 0.0916 0.0611 0.04042 0.9197 0.8088 0.6767 0.5438 0.4232 0.3208 0.2381 0.1736 0.12473 0.9810 0.9344 0.8571 0.7576 0.6472 0.5366 0.4335 0.3423 0.26504 0.9963 0.9814 0.9473 0.8912 0.8153 0.7254 0.6288 0.5321 0.44055 0.9994 0.9955 0.9834 0.9580 0.9161 0.8576 0.7851 0.7029 0.61606 0.9999 0.9991 0.9955 0.9858 0.9665 0.9347 0.8893 0.8311 0.76227 1.0000 0.9998 0.9989 0.9958 0.9881 0.9733 0.9489 0.9134 0.86668 1.0000 0.9998 0.9989 0.9962 0.9901 0.9786 0.9597 0.93199 1.0000 0.9997 0.9989 0.9967 0.9919 0.9829 0.968210 0.9999 0.9997 0.9990 0.9972 0.9933 0.986311 1.0000 0.9999 0.9997 0.9991 0.9976 0.994512 1.0000 0.9999 0.9997 0.9992 0.998013 1.0000 0.9999 0.9997 0.999314 1.0000 0.9999 0.999815 1.0000 0.999916 1.0000

ผนวก 5ตารางสถิติ 3 ความนาจะเปน สะสมปว สซ อง P(X ≤ r) = r ∑= r e−µ µ x (ตอ ) ∑ Pois(x; µ) x=0 x=0 x! µr 5.5 6.0 6.5 7.0 7.5 8.0 8.5 9.0 9.50 0.0041 0.0025 0.0015 0.0009 0.0006 0.0003 0.0002 0.0001 0.00011 0.0266 0.0174 0.0113 0.0073 0.0047 0.0030 0.0019 0.0012 0.00082 0.0884 0.0620 0.0430 0.0296 0.0203 0.0138 0.0093 0.0062 0.00423 0.2017 0.1512 0.1118 0.0818 0.0591 0.0424 0.0301 0.0212 0.01494 0.3575 0.2851 0.2237 0.1730 0.1321 0.0996 0.0744 0.0550 0.04035 0.5289 0.4457 0.3690 0.3007 0.2414 0.1912 0.1496 0.1157 0.08856 0.6860 0.6063 0.5265 0.4497 0.3782 0.3134 0.2562 0.2068 0.16497 0.8095 0.7440 0.6728 0.5987 0.5246 0.4530 0.3856 0.3239 0.26878 0.8944 0.8472 0.7916 0.7291 0.6620 0.5925 0.5231 0.4557 0.39189 0.9462 0.9161 0.8774 0.8305 0.7764 0.7166 0.6530 0.5874 0.521810 0.9747 0.9574 0.9332 0.9015 0.8622 0.8159 0.7634 0.7060 0.645311 0.9890 0.9799 0.9661 0.9467 0.9208 0.8881 0.8487 0.8030 0.752012 0.9955 0.9912 0.9840 0.9730 0.9573 0.9362 0.9091 0.8758 0.836413 0.9983 0.9964 0.9929 0.9872 0.9784 0.9658 0.9486 0.9261 0.898114 0.9994 0.9986 0.9970 0.9943 0.9897 0.9827 0.9726 0.9585 0.940015 0.9998 0.9995 0.9988 0.9976 0.9954 0.9918 0.9862 0.9780 0.966516 0.9999 0.9998 0.9996 0.9990 0.9980 0.9963 0.9934 0.9889 0.982317 1.0000 0.9999 0.9998 0.9996 0.9992 0.9984 0.9970 0.9947 0.991118 1.0000 0.9999 0.9999 0.9997 0.9993 0.9987 0.9976 0.995719 1.0000 1.0000 0.9999 0.9997 0.9995 0.9989 0.998020 1.0000 0.9999 0.9998 0.9996 0.999121 1.0000 0.9999 0.9998 0.999622 1.0000 0.9999 0.999923 1.0000 0.999924 1.0000

ผนวก 6ตารางสถติ ิ 3 ความนาจะเปน สะสมปว สซ อง P(X ≤ r) = r ∑= r e−µ µ x (ตอ ) ∑ Pois(x; µ) x=0 x=0 x! µr 10.0 11.0 12.0 13.0 14.0 15.0 16.0 17.0 18.01 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.00002 0.0005 0.0002 0.0001 0.0000 0.0000 0.0000 0.0000 0.0000 0.00003 0.0028 0.0012 0.0005 0.0002 0.0001 0.0000 0.0000 0.0000 0.00004 0.0103 0.0049 0.0023 0.0011 0.0005 0.0002 0.0001 0.0000 0.00005 0.0293 0.0151 0.0076 0.0037 0.0018 0.0009 0.0004 0.0002 0.00016 0.0671 0.0375 0.0203 0.0107 0.0055 0.0028 0.0014 0.0007 0.00037 0.1301 0.0786 0.0458 0.0259 0.0142 0.0076 0.0040 0.0021 0.00108 0.2202 0.1432 0.0895 0.0540 0.0316 0.0180 0.0100 0.0054 0.00299 0.3328 0.2320 0.1550 0.0998 0.0621 0.0374 0.0220 0.0126 0.007110 0.4579 0.3405 0.2424 0.1658 0.1094 0.0699 0.0433 0.0261 0.015411 0.5830 0.4599 0.3472 0.2517 0.1757 0.1185 0.0774 0.0491 0.030412 0.6968 0.5793 0.4616 0.3532 0.2600 0.1848 0.1270 0.0847 0.054913 0.7916 0.6887 0.5760 0.4631 0.3585 0.2676 0.1931 0.1350 0.091714 0.8645 0.7813 0.6815 0.5730 0.4644 0.3632 0.2745 0.2009 0.142615 0.9165 0.8540 0.7720 0.6751 0.5704 0.4657 0.3675 0.2808 0.208116 0.9513 0.9074 0.8444 0.7636 0.6694 0.5681 0.4667 0.3715 0.286717 0.9730 0.9441 0.8987 0.8355 0.7559 0.6641 0.5660 0.4677 0.375118 0.9857 0.9678 0.9370 0.8905 0.8272 0.7489 0.6593 0.5640 0.468619 0.9928 0.9823 0.9626 0.9302 0.8826 0.8195 0.7423 0.6550 0.562220 0.9965 0.9907 0.9787 0.9573 0.9235 0.8752 0.8122 0.7363 0.650921 0.9984 0.9953 0.9884 0.9750 0.9521 0.9170 0.8682 0.8055 0.730722 0.9993 0.9977 0.9939 0.9859 0.9712 0.9469 0.9108 0.8615 0.799123 0.9997 0.9990 0.9970 0.9924 0.9833 0.9673 0.9418 0.9047 0.855124 0.9999 0.9995 0.9985 0.9960 0.9907 0.9805 0.9633 0.9367 0.898925 1.0000 0.9998 0.9993 0.9980 0.9950 0.9888 0.9777 0.9594 0.931726 0.9999 0.9997 0.9990 0.9974 0.9938 0.9869 0.9748 0.955427 1.0000 0.9999 0.9995 0.9987 0.9967 0.9925 0.9848 0.971828 0.9999 0.9998 0.9994 0.9983 0.9959 0.9912 0.982729 1.0000 0.9999 0.9997 0.9991 0.9978 0.9950 0.989730 1.0000 0.9999 0.9996 0.9989 0.9973 0.994131 0.9999 0.9998 0.9994 0.9986 0.996732 1.0000 0.9999 0.9997 0.9993 0.998233 1.0000 0.9999 0.9996 0.999034 0.9999 0.9998 0.999535 1.0000 0.9999 0.9998

ผนวก 7under the Standard Normal Curve from 0 to z z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.090.0 0.0000 0.0040 0.0080 0.0120 0.0160 0.0199 0.0239 0.0279 0.0319 0.03590.1 0.0398 0.0438 0.0478 0.0517 0.0557 0.0596 0.0636 0.0675 0.0714 0.07530.2 0.0793 0.0832 0.0871 0.0910 0.0948 0.0987 0.1026 0.10.64 0.1103 0.11410.3 0.1179 0.1217 0.1255 0.1293 0.1331 0.1368 0.1406 0.1443 0.1480 0.15170.4 0.1554 0.1591 0.1628 0.1664 0.1700 0.1736 0.1772 0.1808 0.1844 0.18790.5 0.1915 0.1950 0.1985 0.2019 0.2054 0.2088 0.2123 0.2157 0.2190 0.22240.6 0.2257 0.2291 0.2324 0.2357 0.2389 0.2422 0.2454 0.2486 0.2517 0.25490.7 0.2580 0.2611 0.2642 0.2673 0.27~ 0.2734 0.2764 0.2794 0.2823 0.28520.8 0.2881 0.2910 0.2939 0.2967 0.2995 0.3023 0.3051 0.3078 0.3106 0.31330.9 0.3159 0.318b 0.3212 0.3238 0.3264' 0.3289 0.3315 0.3340 0.3365 0.33891.0 . 0.3413 0.3438 0.3461 0.3485 0.3531 0.3554 0.3577 0.3599 0.36211.1 0.3643 0.3665 0.3686 0.3708 0.3508 0.3749 0.3770 0.3790 0.3810 0.38301.2 0.3849 0.3869 0.3888 0.3907 0.3729 0.3944 0.3962 0.3980 0.3997 0.40151.3 0,4032 0.4049 0.4066 0.4082 0.3925 0.4115 .0.4131 0.4147 0.4162 0.41771.4 0.4192 0.4207 0.4222 0.4099 0.4265, 0.4279 0.4292 0.4306 . 0.43191.5 0.4332 0.4345 0.4357 - 0.4236 0.4251 0.4394 0.4406 0.4418 0.4429 0.44411.6 0.4452 0.4463 0.4474 0.4382 0.4505 0.4515 0.4525 0.4535 0.45451.7 0.4554 0.4564 0.4573 0.4370 0.4495 0.4599 0.4608 0.4616 0.4625 0.46331.8 0.4641 0.4649 0.4656 6.4484 0.4591 0.4678 0.4686 0.4693 0.4699 0.47061.9 0.4713 0.4719 0.4726 0.4582 0.4671 0.4744 0.4750 0.4756 9.4761 0.47672.0 0.4772 0.4778 0.4783 0.4664 0.4738 0.4798 0.4803 0.4808 0.4812 0.48172.1 0.4821 0,4826 0.4830 0.4732 0,4793 0.4842 0.4846 0,4850 0,48572.2 0.4861 0.4864 0.4868 0.4788 0,4838 0.4878 0.4881 0.4884 '4854 0.48902.3 0.4893 0.4896 0.4898 0.483~ 0.4875 0.4906 0.4909 0.4911 0.4887 0.49162.4 0.4918 0.4920 0.4922 0.4871 0.4904 0.4929 0.4931 0.4932 '0.4913 0.49362.5 0.493,8 0.4940 0.4941 0.4901 0.4927 0.4946 0.4948 0.494'} 0.4934 0.49522.6 0.4953 0.4955 0.4956 0.4925 0.4945 0.4960 0.4961 0.4962 0.4951 0.49642.7 0.4965 0.4966 0.4967 0.4943 0.4959 0.4970 0.4971 0.4972 . 0.4963 0.49742.8 0.4974 0.4975 0.4976 0.4957 0.4969 0.4978 0.4979 0.4979 ,0.4973. 0.49812.9 0.4981 0.4982 0.4982 0.4968 0.4977 0,4984 0.4985 0,4985 0.49863.0 0,4987 0.4987 0.4987 0.4977 0.4984 0,4989 0.4989 0,4989 .0.4980 0.49903.1 0.4990 0.4991 0.4991 0.4983 0.4988 0.4992 0.4992 0.4992 0.4986 0.49933.2 0.4993 0.4993 0·'-988 0.4992 0.4994 0.4994 0.4995 0.4990 0.49953.3 0.4995 0.4995 \" 0.4991 0.4994 0.4996 0.4996 0.4996 0.4993 0.49973.4 0.4997 0.4997 0.4994 0.4996 0.4997 0.4997 0.4997 0.4995 0.49983.5 0.4998 0.4998 0.4994 0.4996 0.4!O.~7 0.4998 0.4998 0.4998 0.49983.6 0.4998 0.4998 0.4995 0.4997 0.4998 0.4999 0.4999 0.4999 0.4996 0.4999 0.4997 0.4998 0.49973.7 0.4999 0.4999 0.4998 0.4999 0.4999 0.4999 0.4999 0.4999 0.4998 0.4999 0.49993.8 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.4999 0.49993.9 0.5000 0.5000 0.4999 0.4999 0.5000 0.5000 0.4999 0.4999 0.4999 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000

ผนวก 8 Percentile Values for Student's t Distribution with dregrees of FreedomV t.55 1.60 I I1.70 f.75 I If.80 t.90 I I1.95 1.975 t.99 f.~95 63.661 0.158 0.325 0.727 1.000 1.376 3.08 6.31 12.71 31.82 9.92 0.289 2.92 4.30 6.96 5.842 0.142 0.277 0.617 0.816 1.061 1.89 2.35 3.18 4.54 4.60 0.271 2.13 2.78 3.75 4.033 0.137 0.267 0.584 0.765 0.978 1.64 2.02 2.57 3.36 3.71 0.265 1.94 2.45 3.14 '3.504 0.134 0.263 0.569 0.741 0.941 1.53 1.89 2.36 3.00 3.36 0.262 1.86 2.31 2.90 3.255 0.132 0.261 0.559 0.727 0.920 '1.48 1.83 2.26 2.82 3.17 0.260 1.81 2.23 2.76 3.116 0.131 0.260 0.553 0.718 0.906 1.44 1.80 2.20 2.72 3.057 0.130 0.259 1.78 2.18 2.68 3.018 0.130 0.259 0.549 0.711 0.896 1.41 1.77 2.16 2.65 2.98 0.258 1.76 2.14 2.62 2.95 0.258 0.546 0.706 0.889 1.40 1.75 2.13 2.60 2.92 0.258 1.75 2.12 2.58 2.90I9 0.129 0.257 0.543 0.703 0.883 1.38 1.74 2.11 2.57 2.88 10 0.129 0.257 1.73 2.1(}, 2.55 2.86 0.257 0.542 0.700 0.879 1.37 1.73 2.09 2.54 2.85 0.257 1.72 2.09 2.53 2.8311 0.129 0.257 0.540 - 0.697 0.876 1.36 1.72 2.08 2.52 2.8212 0.128 0.256 0.539 1.72 2.07 2.51 2.8113 0.128 0.256 0.695 0.873 1.36 1.71 2.07 i.50 2.8014 0.128 0.256 1.71 2.06 2.49 2.79 0.256 0.538 0.694 0.870 1.35 1.71 2.06 2.49 2.78 0.256 1.71 2.06 2.48 2.77 0.256 0.537 0.692 0.868 1.35 1.70 2.05 2.47 2.76 0.256 1.70 2.05 2.47 2.7615 0.128 0.256 0.536 0.691 0.866 1.34 1.70 2.05 2.46 2.75 0.256 1.70 2.04 2.46 2.7016 0.128 0.255 0.535 0.690 0.865 1.34 1.68 2.02 2.42 2.66 0.254 1.67 2.00 2.39 2.6217 0.128 0.254 0.534 0.689 0.863 1.33 1.66 1.98 2.36 2.58 0.253 1.64 1.96 2.3318 0.127 0.534 0.688 0.862 1.3319 0.127 0.533 0.688 0.861 1.3320, 0.127 0.533 0.687 0.860 1.3321 0.127 0.532 0.686 0.859 1.3222 0.127 0.532 0.686 0.858 1.3223 0.127 0.532 0.685 0.858 1.3224 0.127 0.531 0.685 0.857 1.3225 0.127 0.531 0.684 0.856 1.3226 0.127 0.531 0.684 0.856 1.31 0.531 0.684 27 0.127 0.855 1.31lG:Jt 0.127 0.530 0.683 0.855 1.31 29 0.127 0.530 0.683 0.854 1.3130 0.127 0.530 0.683 0.854 1.3140 0.126 0.529 0.681 0.851 1.3060 0.126 0.527 0.679 0.848 1.30120 0.126 0.526 0.677 0.845 1.2900 0.126 0.524 0.674 0.842 1.28

ผนวก 9 Percentile Values' for the Chi - Square Distributionwith V dreegree of FreedomV %.~s %.~1 5 %.io %.;s %;0 %.;s %.~ :i1: %.~7S %.~9 .2 0.102 0.455 1.32 2.711 0.0000 0.0002 0.0010 0.0039 0.015~ 0.575 1.39 4.61 3.84 5.02 6.63 %.995 X.~99 1.21 2.37 2.77 6.25 7.88 10.82 0.0100 0.0201 0.0506 0.103 0.211 1.92 3.36 4.11 7.78 5.99 7.38 9~J 10.6 13:8 2.67 4.35 5.39 9.24 12.8 16.33 0.0717 0.115 0.216 0.352 0.584 3.45 5.35 6.63 10.6 7.81 9.35( 11.3' 14.9 18.5 4.25 6.35 7.84 12'{) 16.7 20.50.207 0.297 0.484 0.711 1.06 5.07 7.34 9.04 13.4 / 18.5 22.5 5.90 8.34 10.2 14.7 20.3 24.3 6.74 9.34 11.4 16.0 9.49 11.1 --13.3 22.0 26.1 7.58 10.3 12.5 17.3 23.6 27,90.412 0.554 0.831 1.15 1.61 8.44 11.3 13.7 18.5 11.1 12.8 15.1 25.2 29.6 9.30 12.3 14.8 19.8 12.6 14.4 16.8 26.8 31.36 0.676 0.872 1.24 1.64 2.20 10.2 13.3 16.0 21.1 14.1 16.0 18.5 28.3 32.9 11.0 14.3 17.1 22.3 15.5 17.5 20.1 29.8 34.50.989 1.24 1.69 2.17 2.83 11.9 15.3 18.2 23.5 16.9 19.0 21.7 31.3 36.1 1.34 1.65 2.18 2.73 3.49 12.8 16.3 19.4 24.8 18.3 20.5 23.2 32.8 37.7 13.7 17.3 20.5 26.0 19.7 21.9 24.7 34.3 39.31.73 2.09 2.70 3.33 4.17 14.6 18.3 21.6 27.2 21.0 23.3 26.2 15.5 19.3 22.7 28.4 22.4 24.7 27.7 35.7 40.82.16 2.56 3.25 3.94 4.87 16.3 20.3 23.8 29.6 37.2 42.3 17.2 21.3 24.9 30.8 38.6 43.811 2.60 3.05 3.82 4.57 5.58 18.1 26.0 32.0 40.0 45.3 22.3 27.1 33.2 41.4 46.812 3.07 3.57 4.40 5.23 6.30 19.0 23.3 28.2 34.4 42.8 48.3 . 19.9 24.3 29.3 35.6 44.2 49.713 3.57 4.11 5.01 5.89 7.04 20.8 25.3 30.4 36.7 23.7 26.1 29.1 45.6 51.2 21.7 26.3 31.5 37.9 25.0 27.5 30.6 46.9 52.6 . 4.07 4.66 5.63 6.57 7.79 22.7 27.3 32.6 39.1 48.3 54.1 23.6 28.3 33.7 40.3 49.6 55.5..., 4.60 5.23 6.26 7.26 8.55 24.5 29.3 34.8 51.8 51.0 56.9 33.7 39.3 45.6 63.2 52.3 58.311: 5.14 5.81 6.91 7.96 9.31 42.9 49.3 56.3 74.4 26.3 28.8 32.0 53:7 59.7 52.3 59.3 67.0 85.5 27.6 30.2 33.4 66.8 73.417 5.70 6.41 7.56 8.67 10.1 61.7 69.3 77.6 96.6 28.9 31.5 34.8 79.5 86.7 71.1 108 36.2 92.0 99.618 6.26 7.01 8.23 9.39 10.9 79.3 88.1 118 30.1 , 32.9 37.6 104 112 80.6 89.3 98.6 116 12519 6.84 7.63 8.91 10.1 11.7 90.1 99.3 109 31.4 34,.2 128 137 140 14920 7.43 8.26 9.59 10.9 12.421 8.03 8.90 10.3 11.6 13.2 32.7 35.5 38.9 33.9 36.8 40.38.64 9.54 11.0 12.3 14.0 35.2 38.1 41.6 36.4 39.4 43.09.26 10.2 11.7 13.1 14.8 37.7 40.6 4;4.3 38.9 41.9 45.624 9.89 10.9 12.4 13.8 15.7 40.1 43.2 47.025 10.5 11.5 13.1 14:6 \"16.$' 41.3 44.5 48.326 11.2 12.2 13.8 15.4 17.327 11.8 12.9 14.6 16.2 18.112.5 13.6 15.3 16.9 18.913.1 14.3 16.0 17.7 19.8 42.6 45.7 49.630 13.8 15.0 16.8 18.5 20.6 43.8 47.0 50.9 40 . 20.7 22.2 24.4 26.5 29.1 55.8 59.3 63.7 67.5 71.4 76.2I 50 28.0 29,7 32.4 34.8 37.760 35.5 37.5 40.5 43.2 46.5 79.1 83.3 88.4 90.5 95.0 100 70 43.3 45.4 48.8 51.7 55.3 102 107 112W 51.2 53.5 57.2 60.4 64.3 113 118 124 90 59.2 61.8 65.6 69.1 73.3100 67.3 70.1 74.2 77.9 82.4 124 130 136

ผนวก 10 ตารางสถติ ิ 7 คา Fα; (ν1,ν2) ณ ระดบั นยั สําคญั α α 0 Fα ; (ν1,ν 2 )ν2 α 1 2 3 ν1 7 8 9 10 456 60.191 0.100 39.86 49.50 53.59 55.83 57.24 58.20 58.91 59.44 59.860.050 161.45 199.50 215.71 224.58 230.16 233.99 236.77 238.88 240.54 241.880.025 647.79 799.50 864.16 899.58 921.85 937.11 948.22 956.66 963.28 968.630.010 4052.18 4999.50 5403.35 5624.58 5763.65 5858.99 5928.36 5981.07 6022.47 6055.850.005 16210.72 19999.50 21614.74 22499.58 23055.80 23437.11 23714.57 23925.41 24091.002 0.100 8.53 9.00 9.16 9.24 9.29 9.33 9.35 9.37 9.38 24224.490.050 18.51 19.00 19.16 19.25 19.30 19.33 19.35 19.37 19.380.025 38.51 39.00 39.17 39.25 39.30 39.33 39.36 39.37 39.39 9.390.010 98.50 99.00 99.17 99.25 99.30 99.33 99.36 99.37 99.39 19.400.005 198.50 199.00 199.17 199.25 199.30 199.33 199.36 199.37 199.39 39.403 0.100 5.54 5.46 5.39 5.34 5.31 5.28 5.27 5.25 5.24 99.400.050 10.13 9.55 9.28 9.12 9.01 8.94 8.89 8.85 8.81 199.400.025 17.44 16.04 15.44 15.10 14.88 14.73 14.62 14.54 14.47 5.230.010 34.12 30.82 29.46 28.71 28.24 27.91 27.67 27.49 27.35 8.790.005 55.55 49.80 47.47 46.19 45.39 44.84 44.43 44.13 43.88 14.424 0.100 4.54 4.32 4.19 4.11 4.05 4.01 3.98 3.95 3.94 27.230.050 7.71 6.94 6.59 6.39 6.26 6.16 6.09 6.04 6.00 43.690.025 12.22 10.65 9.98 9.60 9.36 9.20 9.07 8.98 8.90 3.920.010 21.20 18.00 16.69 15.98 15.52 15.21 14.98 14.80 14.66 5.960.005 31.33 26.28 24.26 23.15 22.46 21.97 21.62 21.35 21.14 8.845 0.100 4.06 3.78 3.62 3.52 3.45 3.40 3.37 3.34 3.32 14.550.050 6.61 5.79 5.41 5.19 5.05 4.95 4.88 4.82 4.77 20.970.025 10.01 8.43 7.76 7.39 7.15 6.98 6.85 6.76 6.68 3.300.010 16.26 13.27 12.06 11.39 10.97 10.67 10.46 10.29 10.16 4.740.005 22.78 18.31 16.53 15.56 14.94 14.51 14.20 13.96 13.77 6.626 0.100 3.78 3.46 3.29 3.18 3.11 3.05 3.01 2.98 2.96 10.050.050 5.99 5.14 4.76 4.53 4.39 4.28 4.21 4.15 4.10 13.620.025 8.81 7.26 6.60 6.23 5.99 5.82 5.70 5.60 5.52 2.940.010 13.75 10.92 9.78 9.15 8.75 8.47 8.26 8.10 7.98 4.060.005 18.63 14.54 12.92 12.03 11.46 11.07 10.79 10.57 10.39 5.467 0.100 3.59 3.26 3.07 2.96 2.88 2.83 2.78 2.75 2.72 7.870.050 5.59 4.74 4.35 4.12 3.97 3.87 3.79 3.73 3.68 10.250.025 8.07 6.54 5.89 5.52 5.29 5.12 4.99 4.90 4.82 2.700.010 12.25 9.55 8.45 7.85 7.46 7.19 6.99 6.84 6.72 3.640.005 16.24 12.40 10.88 10.05 9.52 9.16 8.89 8.68 8.51 4.76 6.62 8.38

ผนวก 11 ตารางสถิติ 7 คา Fα;(ν1,ν2) ณ ระดับนัยสาํ คัญ α (ตอ)ν2 α 1 2 3 ν1 7 8 9 10 4568 0.100 3.46 3.11 2.92 2.81 2.73 2.67 2.62 2.59 2.56 2.540.050 5.32 4.46 4.07 3.84 3.69 3.58 3.50 3.44 3.39 3.350.025 7.57 6.06 5.42 5.05 4.82 4.65 4.53 4.43 4.36 4.300.010 11.26 8.65 7.59 7.01 6.63 6.37 6.18 6.03 5.91 5.810.005 14.69 11.04 9.60 8.81 8.30 7.95 7.69 7.50 7.34 7.219 0.100 3.36 3.01 2.81 2.69 2.61 2.55 2.51 2.47 2.44 2.420.050 5.12 4.26 3.86 3.63 3.48 3.37 3.29 3.23 3.18 3.140.025 7.21 5.71 5.08 4.72 4.48 4.32 4.20 4.10 4.03 3.960.010 10.56 8.02 6.99 6.42 6.06 5.80 5.61 5.47 5.35 5.260.005 13.61 10.11 8.72 7.96 7.47 7.13 6.88 6.69 6.54 6.4210 0.100 3.29 2.92 2.73 2.61 2.52 2.46 2.41 2.38 2.35 2.320.050 4.96 4.10 3.71 3.48 3.33 3.22 3.14 3.07 3.02 2.980.025 6.94 5.46 4.83 4.47 4.24 4.07 3.95 3.85 3.78 3.720.010 10.04 7.56 6.55 5.99 5.64 5.39 5.20 5.06 4.94 4.850.005 12.83 9.43 8.08 7.34 6.87 6.54 6.30 6.12 5.97 5.8511 0.100 3.23 2.86 2.66 2.54 2.45 2.39 2.34 2.30 2.27 2.250.050 4.84 3.98 3.59 3.36 3.20 3.09 3.01 2.95 2.90 2.850.025 6.72 5.26 4.63 4.28 4.04 3.88 3.76 3.66 3.59 3.530.010 9.65 7.21 6.22 5.67 5.32 5.07 4.89 4.74 4.63 4.540.005 12.23 8.91 7.60 6.88 6.42 6.10 5.86 5.68 5.54 5.4212 0.100 3.18 2.81 2.61 2.48 2.39 2.33 2.28 2.24 2.21 2.190.050 4.75 3.89 3.49 3.26 3.11 3.00 2.91 2.85 2.80 2.750.025 6.55 5.10 4.47 4.12 3.89 3.73 3.61 3.51 3.44 3.370.010 9.33 6.93 5.95 5.41 5.06 4.82 4.64 4.50 4.39 4.300.005 11.75 8.51 7.23 6.52 6.07 5.76 5.52 5.35 5.20 5.0913 0.100 3.14 2.76 2.56 2.43 2.35 2.28 2.23 2.20 2.16 2.140.050 4.67 3.81 3.41 3.18 3.03 2.92 2.83 2.77 2.71 2.670.025 6.41 4.97 4.35 4.00 3.77 3.60 3.48 3.39 3.31 3.250.010 9.07 6.70 5.74 5.21 4.86 4.62 4.44 4.30 4.19 4.100.005 11.37 8.19 6.93 6.23 5.79 5.48 5.25 5.08 4.94 4.8214 0.100 3.10 2.73 2.52 2.39 2.31 2.24 2.19 2.15 2.12 2.100.050 4.60 3.74 3.34 3.11 2.96 2.85 2.76 2.70 2.65 2.600.025 6.30 4.86 4.24 3.89 3.66 3.50 3.38 3.29 3.21 3.150.010 8.86 6.51 5.56 5.04 4.69 4.46 4.28 4.14 4.03 3.940.005 11.06 7.92 6.68 6.00 5.56 5.26 5.03 4.86 4.72 4.6015 0.100 3.07 2.70 2.49 2.36 2.27 2.21 2.16 2.12 2.09 2.060.050 4.54 3.68 3.29 3.06 2.90 2.79 2.71 2.64 2.59 2.540.025 6.20 4.77 4.15 3.80 3.58 3.41 3.29 3.20 3.12 3.060.010 8.68 6.36 5.42 4.89 4.56 4.32 4.14 4.00 3.89 3.800.005 10.80 7.70 6.48 5.80 5.37 5.07 4.85 4.67 4.54 4.42

ผนวก 12 ตารางสถิติ 7 คา Fα;(ν1,ν2) ณ ระดบั นยั สําคญั α (ตอ)ν2 α 1 2 3 ν1 6 7 8 9 10 4516 0.100 3.05 2.67 2.46 2.33 2.24 2.18 2.13 2.09 2.06 2.03 0.050 4.49 3.63 3.24 3.01 2.85 2.74 2.66 2.59 2.54 2.49 0.025 6.12 4.69 4.08 3.73 3.50 3.34 3.22 3.12 3.05 2.99 0.010 8.53 6.23 5.29 4.77 4.44 4.20 4.03 3.89 3.78 3.69 0.005 10.58 7.51 6.30 5.64 5.21 4.91 4.69 4.52 4.38 4.2717 0.100 3.03 2.64 2.44 2.31 2.22 2.15 2.10 2.06 2.03 2.00 0.050 4.45 3.59 3.20 2.96 2.81 2.70 2.61 2.55 2.49 2.45 0.025 6.04 4.62 4.01 3.66 3.44 3.28 3.16 3.06 2.98 2.92 0.010 8.40 6.11 5.18 4.67 4.34 4.10 3.93 3.79 3.68 3.59 0.005 10.38 7.35 6.16 5.50 5.07 4.78 4.56 4.39 4.25 4.1418 0.100 3.01 2.62 2.42 2.29 2.20 2.13 2.08 2.04 2.00 1.98 0.050 4.41 3.55 3.16 2.93 2.77 2.66 2.58 2.51 2.46 2.41 0.025 5.98 4.56 3.95 3.61 3.38 3.22 3.10 3.01 2.93 2.87 0.010 8.29 6.01 5.09 4.58 4.25 4.01 3.84 3.71 3.60 3.51 0.005 10.22 7.21 6.03 5.37 4.96 4.66 4.44 4.28 4.14 4.0319 0.100 2.99 2.61 2.40 2.27 2.18 2.11 2.06 2.02 1.98 1.96 0.050 4.38 3.52 3.13 2.90 2.74 2.63 2.54 2.48 2.42 2.38 0.025 5.92 4.51 3.90 3.56 3.33 3.17 3.05 2.96 2.88 2.82 0.010 8.18 5.93 5.01 4.50 4.17 3.94 3.77 3.63 3.52 3.43 0.005 10.07 7.09 5.92 5.27 4.85 4.56 4.34 4.18 4.04 3.9320 0.100 2.97 2.59 2.38 2.25 2.16 2.09 2.04 2.00 1.96 1.94 0.050 4.35 3.49 3.10 2.87 2.71 2.60 2.51 2.45 2.39 2.35 0.025 5.87 4.46 3.86 3.51 3.29 3.13 3.01 2.91 2.84 2.77 0.010 8.10 5.85 4.94 4.43 4.10 3.87 3.70 3.56 3.46 3.37 0.005 9.94 6.99 5.82 5.17 4.76 4.47 4.26 4.09 3.96 3.8521 0.100 2.96 2.57 2.36 2.23 2.14 2.08 2.02 1.98 1.95 1.92 0.050 4.32 3.47 3.07 2.84 2.68 2.57 2.49 2.42 2.37 2.32 0.025 5.83 4.42 3.82 3.48 3.25 3.09 2.97 2.87 2.80 2.73 0.010 8.02 5.78 4.87 4.37 4.04 3.81 3.64 3.51 3.40 3.31 0.005 9.83 6.89 5.73 5.09 4.68 4.39 4.18 4.01 3.88 3.7722 0.100 2.95 2.56 2.35 2.22 2.13 2.06 2.01 1.97 1.93 1.90 0.050 4.30 3.44 3.05 2.82 2.66 2.55 2.46 2.40 2.34 2.30 0.025 5.79 4.38 3.78 3.44 3.22 3.05 2.93 2.84 2.76 2.70 0.010 7.95 5.72 4.82 4.31 3.99 3.76 3.59 3.45 3.35 3.26 0.005 9.73 6.81 5.65 5.02 4.61 4.32 4.11 3.94 3.81 3.7023 0.100 2.94 2.55 2.34 2.21 2.11 2.05 1.99 1.95 1.92 1.89 0.050 4.28 3.42 3.03 2.80 2.64 2.53 2.44 2.37 2.32 2.27 0.025 5.75 4.35 3.75 3.41 3.18 3.02 2.90 2.81 2.73 2.67 0.010 7.88 5.66 4.76 4.26 3.94 3.71 3.54 3.41 3.30 3.21 0.005 9.63 6.73 5.58 4.95 4.54 4.26 4.05 3.88 3.75 3.6424 0.100 2.93 2.54 2.33 2.19 2.10 2.04 1.98 1.94 1.91 1.88 0.050 4.26 3.40 3.01 2.78 2.62 2.51 2.42 2.36 2.30 2.25 0.025 5.72 4.32 3.72 3.38 3.15 2.99 2.87 2.78 2.70 2.64 0.010 7.82 5.61 4.72 4.22 3.90 3.67 3.50 3.36 3.26 3.17 0.005 9.55 6.66 5.52 4.89 4.49 4.20 3.99 3.83 3.69 3.5925 0.100 2.92 2.53 2.32 2.18 2.09 2.02 1.97 1.93 1.89 1.87 0.050 4.24 3.39 2.99 2.76 2.60 2.49 2.40 2.34 2.28 2.24 0.025 5.69 4.29 3.69 3.35 3.13 2.97 2.85 2.75 2.68 2.61 0.010 7.77 5.57 4.68 4.18 3.85 3.63 3.46 3.32 3.22 3.13 0.005 9.48 6.60 5.46 4.84 4.43 4.15 3.94 3.78 3.64 3.54

ผนวก 13 ตารางสถติ ิ 7 คา Fα;(ν1,ν2) ณ ระดับนยั สําคญั α (ตอ)ν 2 α 1 2 3 4 ν15 6 7 8 9 1026 0.100 2.91 2.52 2.31 2.17 2.08 2.01 1.96 1.92 1.88 1.86 0.050 4.23 3.37 2.98 2.74 2.59 2.47 2.39 2.32 2.27 2.22 0.025 5.66 4.27 3.67 3.33 3.10 2.94 2.82 2.73 2.65 2.59 0.010 7.72 5.53 4.64 4.14 3.82 3.59 3.42 3.29 3.18 3.09 0.005 9.41 6.54 5.41 4.79 4.38 4.10 3.89 3.73 3.60 3.4927 0.100 2.90 2.51 2.30 2.17 2.07 2.00 1.95 1.91 1.87 1.85 0.050 4.21 3.35 2.96 2.73 2.57 2.46 2.37 2.31 2.25 2.20 0.025 5.63 4.24 3.65 3.31 3.08 2.92 2.80 2.71 2.63 2.57 0.010 7.68 5.49 4.60 4.11 3.78 3.56 3.39 3.26 3.15 3.06 0.005 9.34 6.49 5.36 4.74 4.34 4.06 3.85 3.69 3.56 3.4528 0.100 2.89 2.50 2.29 2.16 2.06 2.00 1.94 1.90 1.87 1.84 0.050 4.20 3.34 2.95 2.71 2.56 2.45 2.36 2.29 2.24 2.19 0.025 5.61 4.22 3.63 3.29 3.06 2.90 2.78 2.69 2.61 2.55 0.010 7.64 5.45 4.57 4.07 3.75 3.53 3.36 3.23 3.12 3.03 0.005 9.28 6.44 5.32 4.70 4.30 4.02 3.81 3.65 3.52 3.4129 0.100 2.89 2.50 2.28 2.15 2.06 1.99 1.93 1.89 1.86 1.83 0.050 4.18 3.33 2.93 2.70 2.55 2.43 2.35 2.28 2.22 2.18 0.025 5.59 4.20 3.61 3.27 3.04 2.88 2.76 2.67 2.59 2.53 0.010 7.60 5.42 4.54 4.04 3.73 3.50 3.33 3.20 3.09 3.00 0.005 9.23 6.40 5.28 4.66 4.26 3.98 3.77 3.61 3.48 3.3830 0.100 2.88 2.49 2.28 2.14 2.05 1.98 1.93 1.88 1.85 1.82 0.050 4.17 3.32 2.92 2.69 2.53 2.42 2.33 2.27 2.21 2.16 0.025 5.57 4.18 3.59 3.25 3.03 2.87 2.75 2.65 2.57 2.51 0.010 7.56 5.39 4.51 4.02 3.70 3.47 3.30 3.17 3.07 2.98 0.005 9.18 6.35 5.24 4.62 4.23 3.95 3.74 3.58 3.45 3.3440 0.100 2.84 2.44 2.23 2.09 2.00 1.93 1.87 1.83 1.79 1.76 0.050 4.08 3.23 2.84 2.61 2.45 2.34 2.25 2.18 2.12 2.08 0.025 5.42 4.05 3.46 3.13 2.90 2.74 2.62 2.53 2.45 2.39 0.010 7.31 5.18 4.31 3.83 3.51 3.29 3.12 2.99 2.89 2.80 0.005 8.83 6.07 4.98 4.37 3.99 3.71 3.51 3.35 3.22 3.1250 0.100 2.81 2.41 2.20 2.06 1.97 1.90 1.84 1.80 1.76 1.73 0.050 4.03 3.18 2.79 2.56 2.40 2.29 2.20 2.13 2.07 2.03 0.025 5.34 3.97 3.39 3.05 2.83 2.67 2.55 2.46 2.38 2.32 0.010 7.17 5.06 4.20 3.72 3.41 3.19 3.02 2.89 2.78 2.70 0.005 8.63 5.90 4.83 4.23 3.85 3.58 3.38 3.22 3.09 2.9960 0.100 2.79 2.39 2.18 2.04 1.95 1.87 1.82 1.77 1.74 1.71 0.050 4.00 3.15 2.76 2.53 2.37 2.25 2.17 2.10 2.04 1.99 0.025 5.29 3.93 3.34 3.01 2.79 2.63 2.51 2.41 2.33 2.27 0.010 7.08 4.98 4.13 3.65 3.34 3.12 2.95 2.82 2.72 2.63 0.005 8.49 5.79 4.73 4.14 3.76 3.49 3.29 3.13 3.01 2.90120 0.100 2.75 2.35 2.13 1.99 1.90 1.82 1.77 1.72 1.68 1.65 0.050 3.92 3.07 2.68 2.45 2.29 2.18 2.09 2.02 1.96 1.91 0.025 5.15 3.80 3.23 2.89 2.67 2.52 2.39 2.30 2.22 2.16 0.010 6.85 4.79 3.95 3.48 3.17 2.96 2.79 2.66 2.56 2.47 0.005 8.18 5.54 4.50 3.92 3.55 3.28 3.09 2.93 2.81 2.71∞ 0.100 2.71 2.30 2.08 1.95 1.85 1.78 1.72 1.67 1.63 1.60 0.050 3.84 3.00 2.61 2.37 2.22 2.10 2.01 1.94 1.88 1.83 0.025 5.03 3.69 3.12 2.79 2.57 2.41 2.29 2.19 2.12 2.05 0.010 6.64 4.61 3.79 3.32 3.02 2.81 2.64 2.51 2.41 2.32 0.005 7.89 5.30 4.28 3.72 3.35 3.10 2.90 2.75 2.63 2.52

ผนวก 14 ตารางสถติ ิ 7 คา Fα;(ν1,ν2) ณ ระดบั นัยสําคญั α (ตอ)ν2 α ν1 11 12 13 14 15 20 25 30 35 40 50 608 0.100 2.52 2.50 2.49 2.48 2.46 2.42 2.40 2.38 2.37 2.36 2.35 2.340.050 3.31 3.28 3.26 3.24 3.22 3.15 3.11 3.08 3.06 3.04 3.02 3.010.025 4.24 4.20 4.16 4.13 4.10 4.00 3.94 3.89 3.86 3.84 3.81 3.780.010 5.73 5.67 5.61 5.56 5.52 5.36 5.26 5.20 5.15 5.12 5.07 5.030.005 7.10 7.01 6.94 6.87 6.81 6.61 6.48 6.40 6.33 6.29 6.22 6.189 0.100 2.40 2.38 2.36 2.35 2.34 2.30 2.27 2.25 2.24 2.23 2.22 2.210.050 3.10 3.07 3.05 3.03 3.01 2.94 2.89 2.86 2.84 2.83 2.80 2.790.025 3.91 3.87 3.83 3.80 3.77 3.67 3.60 3.56 3.53 3.51 3.47 3.450.010 5.18 5.11 5.05 5.01 4.96 4.81 4.71 4.65 4.60 4.57 4.52 4.480.005 6.31 6.23 6.15 6.09 6.03 5.83 5.71 5.62 5.56 5.52 5.45 5.4110 0.100 2.30 2.28 2.27 2.26 2.24 2.20 2.17 2.16 2.14 2.13 2.12 2.110.050 2.94 2.91 2.89 2.86 2.85 2.77 2.73 2.70 2.68 2.66 2.64 2.620.025 3.66 3.62 3.58 3.55 3.52 3.42 3.35 3.31 3.28 3.26 3.22 3.200.010 4.77 4.71 4.65 4.60 4.56 4.41 4.31 4.25 4.20 4.17 4.12 4.080.005 5.75 5.66 5.59 5.53 5.47 5.27 5.15 5.07 5.01 4.97 4.90 4.8611 0.100 2.23 2.21 2.19 2.18 2.17 2.12 2.10 2.08 2.06 2.05 2.04 2.030.050 2.82 2.79 2.76 2.74 2.72 2.65 2.60 2.57 2.55 2.53 2.51 2.490.025 3.47 3.43 3.39 3.36 3.33 3.23 3.16 3.12 3.09 3.06 3.03 3.000.010 4.46 4.40 4.34 4.29 4.25 4.10 4.01 3.94 3.89 3.86 3.81 3.780.005 5.32 5.24 5.16 5.10 5.05 4.86 4.74 4.65 4.60 4.55 4.49 4.4512 0.100 2.17 2.15 2.13 2.12 2.10 2.06 2.03 2.01 2.00 1.99 1.97 1.960.050 2.72 2.69 2.66 2.64 2.62 2.54 2.50 2.47 2.44 2.43 2.40 2.380.025 3.32 3.28 3.24 3.21 3.18 3.07 3.01 2.96 2.93 2.91 2.87 2.850.010 4.22 4.16 4.10 4.05 4.01 3.86 3.76 3.70 3.65 3.62 3.57 3.540.005 4.99 4.91 4.84 4.77 4.72 4.53 4.41 4.33 4.27 4.23 4.17 4.1213 0.100 2.12 2.10 2.08 2.07 2.05 2.01 1.98 1.96 1.94 1.93 1.92 1.900.050 2.63 2.60 2.58 2.55 2.53 2.46 2.41 2.38 2.36 2.34 2.31 2.300.025 3.20 3.15 3.12 3.08 3.05 2.95 2.88 2.84 2.80 2.78 2.74 2.720.010 4.02 3.96 3.91 3.86 3.82 3.66 3.57 3.51 3.46 3.43 3.38 3.340.005 4.72 4.64 4.57 4.51 4.46 4.27 4.15 4.07 4.01 3.97 3.91 3.8714 0.100 2.07 2.05 2.04 2.02 2.01 1.96 1.93 1.91 1.90 1.89 1.87 1.860.050 2.57 2.53 2.51 2.48 2.46 2.39 2.34 2.31 2.28 2.27 2.24 2.220.025 3.09 3.05 3.01 2.98 2.95 2.84 2.78 2.73 2.70 2.67 2.64 2.610.010 3.86 3.80 3.75 3.70 3.66 3.51 3.41 3.35 3.30 3.27 3.22 3.180.005 4.51 4.43 4.36 4.30 4.25 4.06 3.94 3.86 3.80 3.76 3.70 3.6615 0.100 2.04 2.02 2.00 1.99 1.97 1.92 1.89 1.87 1.86 1.85 1.83 1.820.050 2.51 2.48 2.45 2.42 2.40 2.33 2.28 2.25 2.22 2.20 2.18 2.160.025 3.01 2.96 2.92 2.89 2.86 2.76 2.69 2.64 2.61 2.59 2.55 2.520.010 3.73 3.67 3.61 3.56 3.52 3.37 3.28 3.21 3.17 3.13 3.08 3.050.005 4.33 4.25 4.18 4.12 4.07 3.88 3.77 3.69 3.63 3.58 3.52 3.48

ผนวก 15 ตารางสถิติ 7 คา Fα;(ν1,ν2) ณ ระดับนัยสาํ คัญ α (ตอ)ν2 α ν1 11 12 13 14 15 20 25 30 35 40 50 6016 0000....100002510005 24322.....1946086321 43221.....1854929509 23421.....4058950307 22331.....9843925775 32321.....3974912594 23231.....2627836889 33221.....2661826136 32231.....5115890474 32321.....1450858732 33221.....1450812541 22231.....1394777279 23221.....9143715338 0.00517 00000.....100000051200055 43221.....5804912758 22331.....4893972866 23321.....9473900954 22331.....7833955343 32321.....7373919211 22331.....6612862136 22331.....4051885793 22331.....0451800151 23221.....1349772569 23221.....4193714028 22321.....4028757186 22321.....283076831518 000...100052050 22331.....8439931475 33221.....7833967743 32231.....7373929312 32231.....2772909370 23321.....6226878739 22331.....1055860894 32221.....3419898840 32221.....1349741208 32221.....4208717587 32221.....2083706845 23221.....3170748544 22321.....7031722502 00..00105019 0.100 22331.....3738946643 22331.....7733921061 23321.....2672848089 32231.....6612896548 32321.....5612829356 32231.....4015860101 22231.....1249791418 32221.....2308747916 22321.....8130756504 23221.....0371733163 22231.....7003710041 21231.....9206707780 0000....00000215505020 00000.....100000501205005 22331.....7237996211 32321.....6262883889 32321.....6261848517 32231.....1526850236 32231.....0255800794 22321.....1493762429 32221.....0482770406 23221.....7310748524 32221.....7030711732 23211.....9206729991 21221.....2699676459 22121.....296962125821 0000....100005210500 33221.....6622984880 33221.....6216857407 23231.....6125820246 32321.....5402806784 32321.....5014838333 23221.....1248724808 23221.....7310765394 32221.....3007725112 22121.....6992787790 22121.....9962654659 22121.....9258618847 12221.....1589624586 0.00522 00000.....100000025100505 33221.....1626868518 22331.....5126832046 23321.....2054867074 33221.....4015837123 23221.....5391880651 22231.....1038779836 22321.....3070722363 22121.....9296777880 22121.....6299662248 22121.....5298684187 22211.....5891671325 21221.....517867049423 000...100025050 32321.....2651845247 23231.....5402870774 23231.....5104838123 23221.....1593857051 22321.....9413837300 32221.....1037768524 22321.....0260709901 22121.....2699624269 21221.....8592606737 21221.....8519684126 22121.....7481648864 22211.....8147615162 00..00100524 0.100 32231.....5250802995 23231.....0154842383 32221.....3951805581 23221.....1439807330 22321.....2418795148 23221.....0370764333 22121.....2996776450 21221.....9258617487 21221.....9185613715 22121.....8174659974 21221.....8417661042 12221.....4608660841 0000....00001250050525 00000.....100000205105050 22331.....2045866054 22231.....9315867192 22231.....3419884040 22321.....2814794519 22231.....8042750917 23221.....3070701012 12221.....6299600638 21221.....9518622846 12221.....7148695694 22211.....1487622753 21221.....6804650841 22121.....8063565219

ผนวก16 ตารางสถิติ 7 คา Fα;(ν1,ν2) ณ ระดบั นัยสําคญั α (ตอ )ν2 α 11 12 13 14 15 ν 1 25 30 35 40 50 60 2026 000...100052005 212...185834 212...184519 212...174295 212...074972 212...073769 112...972918 112...962471 112...961056 112...861732 112...860519 112...850295 112...850083 00..001005 33..4020 32..9363 23..2960 32..2860 32..8115 22..6976 22..8575 22..5707 22..4725 22..4672 22..3616 22..356327 00000.....100000051200055 32221.....9135891672 23221.....1924838370 22231.....2184723708 32221.....3801768926 32221.....0371768615 21221.....9692737350 22211.....8915621846 12221.....4817637384 12221.....4861607262 12221.....0386638740 21221.....5083537138 22121.....702552909728 0000....100005210500 22321.....4193895621 23221.....9412750259 32221.....1084789147 23221.....3701796275 32221.....0730744574 12221.....6298630969 21221.....1975661715 22121.....8146691473 22211.....3680648941 12221.....0358595529 21221.....0753503917 21121.....9742576886 0.00529 00000.....100000520100505 22231.....4912889430 23221.....1428713078 22231.....8031751986 23221.....0037779565 32221.....3007724333 12221.....8295616748 12221.....8714644984 21221.....4680669512 12221.....0863630660 12221.....8350513368 21211.....4792577996 22111.....429756355530 00000.....100000215000550 22231.....2914731569 32221.....1480714987 32221.....0173791675 23221.....0073746444 22321.....0037711012 12221.....5892625307 22121.....7418651823 12221.....0863693471 12221.....0835547419 12221.....3705521097 12121.....2749566755 21121.....924754214440 0.100 22321.....3700743334 22221.....9620769501 22211.....8296775190 12221.....5289651368 22121.....1579628286 22121.....8603674701 21211.....7942597887 21211.....2479544004 11221.....7391524052 21121.....1368589101 22111.....0682466338 12121.....6801482047 0000....00005012055050 00000.....100000150200505 21221.....6299703960 21221.....2589662258 22121.....1579661286 12221.....4871604694 22211.....8146652173 12121.....7429579877 12121.....9173537253 12211.....8261509770 21121.....6028453168 12211.....1806406316 11211.....6197450054 21111.....950748512260 0000....100002510050 22121.....8259662258 12221.....7519627046 22121.....6418639484 12221.....3608669922 21221.....5308656470 11221.....9273549054 22111.....2186597700 12211.....8160453298 11211.....6917483285 11121.....9075448494 11121.....5870406811 11111.....9865437460 0.005120 00000.....100000251005050 21221.....1648602703 21221.....8053634540 22211.....4208588108 11221.....2974583826 12121.....7931547595 21121.....6018462398 12111.....0769407354 11111.....6859486951 11111.....6985322519 11111.....7658307167 11111.....7458360064 11111.....7654333652∞ 00000.....100000250100550 11222.....5742070954 11212.....5913755956 11221.....5391730231 12112.....5082619947 12121.....4081694479 12111.....4087528071 11111.....3758688381 11111.....3745747960 11111.....3465722334 11111.....3646400079 11111.....2543575933 11111.....2353448429