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-Jr i-A ~ ~f 1[*On Sampling Method of Food
Consumption Survey in Taiwan
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( 11 )
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( 16 )
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(t~}JtfTM!~0-M)
ffor Jjlj t:f" m llcJ~thlZ.1?Kj.:~ttz.:ZJt!~. {is if!' ~ iff il'~ i t {,ifI
SI1 158 98.19 I 6.732.91 I 6.53 15.04I
S12 23 78.70 3,399.49 12.33 6.38
S13 23 127.70 13,320.13 24.07 5.31
S21 33 118.63 8,504.79 16.05 7.39
S22 31 104.16 8.009.26 16.07 6.48
S23 28 117.70 14,954.39 23.11 4.83
S31 44 87.07 3,373.82 8.76 9.94
S32 56 105.09 6,622.54 10.87 9.67
S33 58 108.47 9.940.23 13.09 14.41
So 47 96.54 5,108.72 10.43 9.26
S42 12 107.87 6,749.65 23.72 4.53
Sl3 128 104.77 7,251.91 7.53 13.91
S51 62 120.97 10,293.71 12.89 i 9.38
S52 25 96.58 5,662.15 15.05 6.42
S53 53 123.66 16,842.48 17.83 6.94
S61 8 lOB .31 3,554.70 21.08 5.14
S62 3 11.22 84.28 5.30 2.12
S63 8 105.29 1,558.98 13.96 7.54
~i1!tik&;' 800 104.79 8,292.85I
3.22I
32.54
i~:M*iW( : .fEHIl.l:f;IlA+l\.:IF=JJ {51~il!Hiitil'ittitl/Htl, 600?.f**itHirl·WDrJ1~' 0
itt : SIJ = TiiJjIj
11~U",2=~f£ f 1 =Ur]l-. 3 =If$~ j = 2 =!l{~1= 4=.m~3=~H
5=~!lE&;,6=J¥..~
( 20 )
-137-
["3~;ffffi.:>i-;::t~1tpri'll%!!lttffiiJfIIIf*'fH'£0 4-~ffl~~~~ (Nested Design)
.~~~~fi'~~M~~A~~.~*MR*~~••&Z~.~.'~~~-ffl~~~~#~r'~~~~;::t.*~R*M;::t.*~~~o
H .~z~ft
(4-1)
AIft:Yi j k 1 = ~ i fij;![ , ~ j :tIlrlJf~)ff::X ' ~ k ttl!Vg' ~ I P;::tZjS-j!;j~A tf];:
a*mft:l:i = "A1ij;
-138-
dfB(A) ('$rlHt.II?kr",'E1!b~) =~(L-l)=6 x 2=12;
dfC (B) (tJ"lI!.r",'E1 Fi3/t) =~~ (rn, i-I) =~~(~2il.- 1)1 J i i \
=SST-SSA-SSB(A) -SSC(B)
dfE (Fir"" 13 !bit) = ~~2: (n , j k - 1 )j j k
MSA U!H",'~~lt:Z.t!~~) =SSA/dfA
MSB (A) (fimfl:lI?kr",'lf~lt:Z.t!~~) =SSB (A) /dfB (A)
MSC (B) (ftlI!.r",'lf~~zl!~~) =SSC (B) /dfC (B)
MSE (Fir""zW~.) =SSE/dfE
!b~m:fffllltiz*1IftlI!..~~, mj;.)'~*~JG~ (Unequal Sample Size
) ztJlfi£~Hz 0 f:!!. H. C. Fryer (ltl:+=) ml±l*"R*f':l:rd]~~~zJtJl":
fi (Expected Mean Square Errors) ~:
E (MSE) =a;'A;9": f i = (l/ni -lin) I ( I - 1 )
•f ii = (lIn; j -lind /2: (J - 1)
j =1
f j j k= (l/ni jk-l/nj il /2:2: (M; j - 1); J
tt+= : H.C. Fryer, "Concepts and Methods of Experimental StatisticsModels." Richard D. Irwin, Inc. 1974, PP. 509-514.
( 22 )
-139-
~
a = E { (Y i j k 1 - u) 2}Y ,
2 2 ::! .2
=E{aj+fJjj+'Yjjk+ejjU+Cross Products}
2 2 2 .2= E (a j) + E (fJ jJ) + E ('Y i j b) + E (e j j Ii j) + Zeros
2 2 2 2
=a +a +a +aa P 7 e
( 4-2)
(4- 3)
(4-4)
A2 2 A2 2
aJ3 = {1'1SB(A) -1'1SE- (2:~2: (n , jkf j ;)a'Y)}/~2: (n , jf i j)1 J 1 i J
(4- 5)
A 2 2
ap}/~niC1
(4-6)
c,-.:) *1I*j§9:M!~¥{ft~~ztftJi:
aTM*IIR*j§9:M!~¥{ftz.~'W*~ID~~.~~m~,~tftJi:~~
tE~*~:m~B91ilJ1JLT ' jl; E (1'1S) ~fMAZ{'*.:M;Jm~ 0 j.:J F 5.t/lEtftJi:z ' lka~~ 0 m.tE~*~~~B91ilJV?T ' 133 E (MS) ~fMAz{,*lZ%~~ , jl;tftJi::JJi*~Ulkaf!~ , %~Ji:~ 0 m.-Jilt1l&"iJlffl Snedecor zili:{);J. F 5.t/lEtftJi:z (~-t
.=:) 0 @PI33*~5.t!J!~lZzt!i~tfi5.t7J1Jt\::A E (1'1S):JJfMAzf*lZ' ~w.;{Hr~~2 2
~Z'llBIDJf{jt.zp.:M;Jf*fJ: ' t!i~tjl; E (MS) 0 :t(il~~Ho : (J = 0 , H. : a ~ 0 ,a a
ltUF=E (MSA)/E (MSB) '131331t7}7JIJ~dfA:&dfB(A), ~~t!iHE(MS)
•• ,jl;ffi~~~'llBID,Jf{jl;.zp.~fio~~H.~*B9Ffi'~F5.trel3l33lt:m
tt+~ : George W. Snedecor, "Statistical Methods." Iowa State College,1957, PP. 271-275.
( 23 )
-140-
2 2 .... .zLfffi1.~ilt' ~PtEa%~lii'l*~~iiJgm O"tt~ 0 ' ITffjj\~ O"tt=O"a 0 ~1ltEEtrnx;5t
.A.L.~,~m~§.tr~~*.~L*~'.~*.tr~M••&L••o
~ JtIj~L~ii*
(l) ~iI!!:l1J!rg:.*~tt10~\HiJtU~LM*7UJn:;&4 - 4 , trnJ(:5t~~tzfi5~t
it' ~{iIH*fi5~t14t*' ~rf3'~~ff1r~*i¥J~:£ 0 ~. Searle LlJf5E ' ~!m~it••~'Eft~S~M.~A•• @+ml °EE~.nJ(:ID~~tzL*~'.
~~~~••L~~,m~~~*~~i¥J:£~'~~~F.~~*ft:1. tE 5 %i¥J~~*~~ , fi~L5tIlM•••m0 0
2. tE 1%LIl~*~~' l$jn1tll*L5tllflb.jl..;~•• 0
3. tE 1%i¥J~1¥*~~' 1:J:f'tmftM••&LM.Ai'f•• 0
~~~~L%~'~~flb~.&.~~M~•• ,m~rpJft.&LM•••~Jn~r:ttmJ~~~.&otEtr.~,m~.*~II*ft5t••~.A•.. ' :Ei1~JlU71'Jl,•• 0
(2) gtm~7JIJITffn, ~:liU:.~A:&Jt.~A ' #~H~·till!lpq5tft.m •~*~~M~.,*~pq~5t~~~~~ft••:l1J!~-.o~:£~ft~~pqfi~L~
"2 11.2 "2 .2
~~*m*:, QPfrliHAnJ(:5t~~l\(j,' <« -~, fli1I 0"{3' "r : 0"" ~~~ 0 JIt-
~m~N•• ,mgtH.~.~~*~~Jn:;&4-3o
rn~4-3*ti~pqL~5t~~~L~~it*~, trti~L~5t~~tz~
m:+gy: S.R. Searle, "Topics in Variance Component Estimation." BiometricsVol. 27 No. I, March 1971, PP.22-25.
(24)
-141-
~4-2 ~M*~~*z~~~~.~~(~~~~~~W~)
I
I I '
~ J! *~ s s ~f_i_~s i ______E~M s) I F 1W!_
I i I I I*ll!1iIr<!J~J! '1.615,5821 5
1323,116
0":+20":+ 116.740"~+ 255.010":i 0.6536*'!-
i i 2 2 2 IJii~rJl~~ 3.391,396
1! 121 282,616'10".-'-20"r+74. 480"{3 15.4279*
, ! 2 2ffm.r.lJ~,~ 14,302,432 782
1
18,289
1
0"• ..;-20"r 1.8676*
p rJl ~ J'J, i 7.834,411 800
1
' 9,793j <*~\ ~ ~ 1127,143,821' 1,599 16,975
. ,
Jt.:M*llm:II1r:N4-1tt: 1.*~z.~~}Jl'!~gg~liAmJWjjiJz.iir~z.~.2(iJjfl1roiHJIt\A0
2. *~~t£a =0. 196'Fmi1- ' *"'~5.Ka = 5 96'Fg~ 0
A 2 i A 2 A 2 A 2
*1: ~ 5.l1j 0"{3 , 0" 0" 0"I r • y
--------- - --- -"..---_.._- _._-- ._( ----- _ .•.. _-------.----._ .._----.--_..
I i11 :ft ~ 5,214.121 3,179.71: 8,499.63 16,893
I I11,229.81'fIT ¥r &; 1,818.75 8,726.95 21,777
I,"
~ q:t &; 2,866.77 1 3,051.03 8,577.33 14,495I I
~ m &; 3,290.42 6,730.32 9.665.30 19,686,I1
il'Ii 14t r& 4,715,55, 937.98 12,823.45 18,477P"
I
* ~ r& 4,745.961
3,951.72, 5,759.68, 14,457,
Pft~fI!lff~2¥~pzfI!lff~$BI§:£ ' ~J:j:J:£:W<mt::k~mi\1ljj!UiOO;:f.6~12m~ , J1tIj\~m~'17tioo;:, m:£{i~O.29m 0 RJJ!*ftJttlllff¥tlitlllffmJf~2¥tE*mr,grR'
~~mFRJ 0 tE~nfl!lfflR¥ ' ~~7tJ,;,!fEl: 0 Jit?l- ' Jtil!i*ti~~~m{r.JI*zn\(;~~:W<ttzj@ltt(j::k/j\, t)'!I~tti~5,2141.Ul::k' jljtjilmr,g4,715J5*' Wt)'~'17ti&.: 1,818~mt/j\, RJJ!t).~m{r.t'iJ3tfF~~II~~ztlllff~*J;J.§~ttir,gJ1t
i\1lj , i\1ljiiUiQ[*z ' ~¥rtiQ[1iUl/j\ 0 *tir,gzn\(;7HI!:W<~~ta~*ti* ' tE1%®lf~7.K~r ' A~M~®:£:W<' ~P.~:m-ti~, tJ,~m{r.t'iJ3tf'F~7t1iztl?;
$~A~*'AJ;J.M~m~-fI!lff¥&#~A~~ <tt+n) 0
( 25 )
-142-
~ .~fi*~.~~@W,~.~&~••&~Q9~R~.~M*~~*4-4 0
:&4-4 1§-fJil It!1r.JW*V\]~Jf 1§- f&fiX:/t:JHff~~ 1ti~ r"Z.*B*I "2 "2 i "2 "2
JFr )jlj U U, U trI '" e Y
--------'l\1l -iii 419.81 2,912.61 8,685.51 11.988
J'l( ~lt 298.48 3,482.48 9.293.91 13,074
~Il H - 30.91 6.027.82 11.379.61 17.377
'2~~4-4~~'~.*~~••&Z~9~~MUp~ae~~*'~~
~ft~M.UrpJ~•••~.,~~.rMmJ ,wRrpj~~•••~ilI-mJlV'Jm rMmJ ~=ffr' ~~~~q:t~2. 7ffr, ii/J\:j!f~M)jq:t.1.9ffr' •pr,,'z~9§!!Jrrm§ , ~••~ : _t1>Nit*>:$m' Ji~•••m:~ 0.5 fff 0
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.~'~~~W.~~.~o~*)j~t1m~Q9~R~~U.t1ii*'.*
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A
nrn
-143-
m;lt; illl,Jj~ Z lf1 ,L.\jl nJ3~ JflIl~ra' :&j@!lit¥~~Pz F",' EfJ M~;jt1U~ff(jj >f¥a 0 s:~.I¥J~.~~~~~lf1¥* ••~m.>f~W~m~.o~~.-~~.~~P~~'~~~.>f*'~~~~~~~~*~'*M~~¥&z~~~*~~~~~
JE 0 ~~f1Ujlfl£r' Jiif*z nh:& rnhzJHit~IiFf~~lIilJlj~~*EfJt'jJfl£ffi~ 0 jl&*?X:fl!:~>f~lI~~~*EfJM'~hn t.HHn 0
rn~=.~~z~*,.~m.ilJlj~z~*~~~~m~~~~'W~~M
J:j:r~~ M hMM.!J! (P. S. U) ,w:-t1.!J!lf1~~NhMp (S. S. N) , 4-5t}]IJ~Jt
fl~z¥&~.nal±l rnh1~t1!!1.:& nhlllp • ~~~~-MlJttt:· Jfl~~*~~ :
(~Wh~Yh) 2
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• • 2
rn~~z~5t.~.5tfi·~~~*.~~z~.~~ '~~M~~~
',,~I :m rtf : 1l£ ~ I ~ ff
• @1 ~~~~:~~I-~~::_~_:~-;; I ~:·l ~: ~; I~: I;:• jt @1' 3,5441 8.165;11,709' 5.52{4,77~:~~~29+--~:~;~ll~5~411;2~~*i 11 @1 8,51411,16119,675 5,799,9,30015,099 12,23713,44825,685
, I ! I I 1 1 I• lfl @1: 2,409 5,440' 7,849 4,057 8,77412,381 2,558,10.76813,326
II 1 I I !
~ m @1' 3,026 7,07510,101'- 2,68118,91116,230 9,025 9,08618,111'ii ! " .
~ tt£ 1£ - 1,27212,38111,209 1,342 7,38118,723 3,200' 1,508 4,708
* ~ 1£ - 48617,420 '6,934 1,155 9111,2461 8.936 '6,224115,160'I I
( 27 )
-144-
*~~~*"M~&~~~~'tt.~~M*~~~.4-6o
~4-6 ~~~*¥~~M•••*M£.~P.~~({t(mrr7tMZ~$)
I itb1'~Ilt!l'r**~ }ill'"
v = 5 v = 8
Sa 2.30
--- -----~----------I------
670 291 419' 182
SS2 5.50
SS3 0.47
Ssl 00
Ss2 0.08
Ss3 0.70
1.16
00
1.31
1.60
1.10
2.26
2.16
4.21
2.34
00
1.01
00
49
44
201
80
84
138
149
125
142
20
306
150
52
155
20
3
62
2,540
42
1
153
50
76
61
69
30
61
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303
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330
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38
89
1,649
31
27
126
50
52
86
93
78
89
12
191
240
33
97
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2
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1,588
27
96
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6
206
25
56
1,007
itt: *@5.JIjM:~IW~4 - 1 0
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(28)
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, ~Jfim1tfjlg{ 670lWMI.JliY 0 1t<lI~7JIJ~Ij. 983lWMI*Z 0 WtJmfi~
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PP.389.
(29)
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( 30 )
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4.~~~ ~rr~~~£~ (W~) ~.~Z~~&~~,mft§~*~.~*'~~~-r1L~:iLJJ 0
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6.~3t. §~!t~*~~~tI~m••~~~~~~'mftr:p~*~.~~m~*,~m~+{:~+=J3o
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10. Donaldp Warick, Charles A. Lininger "The Sample Survey:Theory and practice." McGraw-Hill Books Co. 1975.
11. George W. Snedecor, "Statistical Methods." Iowa State College,
( 31 )
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1957
12. H. C. Fryer, "Concepts and Methods of Experimental Statistics."
~J1Il.~'PJ'§~t, 196913. Henry Scheffe, "The Analysis of Variance." John Wiley & Sons.
Inc., 1959.
14. John Neter. William Wasserman "Applied Linear Statistical
Models." Richard D. Irwin, Inc. 1974.
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"Sample Survey Method and Theory. "Vol. I, II, lJI, John Wiley
& Sons, Inc. 1953.
16. S. R. Searle, "Topics in Variance Component Estimation. "Biome
trics. Vol. 27 No.1, March 1971.
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18. Walter T. Federer, "Experimental Design: Theory and Applica
tion." The Macmilliam Co. 1955.
19. William Edwares Deming, "Some Theory of Sampling." John
Wiley & Sons, Inc. 1950.
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& Sons, Inc. 1977.
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-149-
ON SAMPLING ME fHOD OF FOODCONSUMPTION SURVEY IN TAIWAN
Rong Yih Shyu*
SUMMARY
Food Consumption Survey in Taiwan has been undertaken by Chung
Hsing University annually since 1961. The results obtained serve as
the major source in estimating the aggregate demand for food and as
basic reference for food policies in Taiwan. This paper is aimed at
the evaluation of the existing sampling method of the survey in the
hope that the efficiency of sampling and estimation of survey work
would be improved in the future.
Due to the lack of population data, analysis is based on poststra
tification using the cross-section data collected from the survey in
Feburary 1979.
The important socio-economic factors affecting food consumption
are analysed first by the technique of analysis of variance,
which then served as the criteria for design of stratification. Optimal
sample size for each stratum is thus determined and the sampling
efficiency for various combinations of sampling units is measured.
major findings are summarized as follows:
1. By comparing the coefficent of variation among different sam
pling schemes, it comes out that the coefficient of unstratified
sampling- is larger than that of stratified sampling. The results
imply that the existing stratified sampling method is justified.
2. Significant factors affecting food consumption are in the order
of urbanization, education, occupation, area, income and family
size. Due to the inefficiency of stratifying by area, it is suggested
that the cross of urbanization and occupation will be a suitable
* Instructor, Department of Agricultural Marketing, National Chung-HsingUniversity.
( 33 )
-150-
criteria for the future.
3. Through the testing homogenity of variance, the variances of
average food consumption are heterogenious among strata. If the
sample allocation adopts the rule of the optimal allocaiton, the
efficiency can be increased by 2.38%.
4. The efficiency of the second sampling unit is greater than the
primary sampling unit and the ratio is 220%. It indicates that
each sampled village must include at least 2.2 families.
5. By the rules of optimal allocation, the optimal sample size for
different level of expected precision is calculated. Under the
precision level of 5 and 8, in terms of variances of the sample
means, the minimum required sample size are 2,540 and 1,588
respectively.
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