สถิติ แนวข้อสอบ

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<p>4 : (two-way classification) 1. (nuisancefactor)(response) 59(randomization)(analysisof covariance) (blocking) (CRD) (homogeoneous) plot (cited) 60 1 2 2. a a a 1 1 2 3 . . . bTr4Tr2Tr1. . . Tra Tr1Tr5Tr4. . . Tr4Tr3Tr1Tr6. . .Tr2 TraTr3Tr2. . .Tr14.1 6113 A,B,C 5 33 A, B, C 1, 2, 3 1 5 11 4 33276 70997 79936 56865 05859 90106 3159501547 85590 91610 78188 63553 40961 4823503427 49626 69445 18663 72695 52180 2084712234 90511 33703 90322551(3,2,1), 2(3, 1, 2) , 3 (3, 2, 1) , 4 (2, 1, 3) 5 (1, 3, 2) 4.2 1 C B A 2 C A B 3 C B A 4 B A C 5 A C B 4.2 5 3 6226 446 1 3 2 4 4.3 6A,B,C,D,E,F1,2,3,4,5,61 4 4 1(3, 2, 6, 5, 1, 4)(C, B, F, E, A, D) 2(5, 1, 6, 3, 4, 2)(E, A, F, C, D, B) 3(3, 5, 4, 2, 6, 1)(C, E, D, B, F, A) 4(6, 3, 2, 5, 1, 4)(F, C, B, E, A, D) 63 1C B F C E D 3E A D B F A 2E A F F C B 4C D B E A D4.3 . 4 6 32 2 4.3 . 1 C B F E A D 2 E A F C D B 3 C E D B F A 4 F C B E A D 4.3. 4 6 643. 3.1 ab 1 4.1 1 2 . . . b 1 y11y12. . . y1b 2 y21y22. . . y2b a ya1ya2. . . yab3.2 yij = + ti+ |j+ ciji=1, 2, , aj = 1, 2, , b65 tii |jjcij =a1 ii= 0=b1 jj = 03.3 .{ti},{|j} = = ca1 ib1 j2ij= | t = =a1 ib1 j2ij) - - - (yj i(normal equations): -2 | t ) - - - (yj i ij j i=0ti:-2 | t ) - - - (yj i ij j=0|j:-2 | t ) - - - (yj i ij i=0 G = N+bEi ti+aEj|j= NTi= b+bti+Ej|j= b(+ti)i=1a Bj= a+Ei ti+a|j= a(+|j)j=1b ^ ^ ^^^^ ^^^^ ^^^^^ ^^^ ^^ ^^^^66G = = =a1 ib1 jijy Ti= =b1 jijy i Bj= =a1 iijyj =NGti=bTi-NG|j=aBj-NG3.4 (residualsumofsquares)SSE , {ti} , {|j} = =a1 ib1 j2ije == =+a1 ib1 j2j i ij) y y - y - (yiy= Ti/ b,jy =Bj/ a y =G / N = =a1 ib1 j2j i ij)} y - (y - ) y - (y - ) y - {(ycross-product + +i j i j2j2i2ij) y - y ( a ) y - y (b ) y - (y (total sum of squares) : SST (treatment sum of squares) : SSTr^^^^ ^^67(Block sum of squares) : SSB SSTr=i2i) y - y ( b= NG - bT2 2iiSSB=j2j) y - y ( a= NG - aB2j2jSB = j2jaB STr =i2ibT, CT = NG2 ,S =i j2ijy 4.2 Source ofd.f. Sum of SquareMean Square Variation (b - 1)SSB= SB- CT= j2jB /a - G2/ NSSB/ (b - 1)(a - 1)SSTr= STr- CT=i2iT /b - G2/ NSSTr/ (a - 1) (a 1)(b 1) SSE= SSE/ (a - 1)(b - 1)Totalab-1SST= S - CT= i j2ijy -G2/ N 683.5 H0:1=2==a H1: i=j1(i=j) i ==b1 j b1( + ti+ |j)= + ti H0:t1=t2==ta=0 H1: ti=013.6 E(MSTr)= o2+1 - aba1 i2i= E(MSB) = o2+1 - bab1 j2j= E(MSE) = o23.7 1) F0 = ETrMSMSF(a-1),(a-1)(b-1)H0 Fo,a-1,(a-1)(b-1)H0F0&gt; Fo,a-1,(a-1)(b-1)692) H0:|j=0 H1:|j=0 1 F0 = EBMSMS F(b-1),(a-1)(b-1) H0 Fo,b-1,(a-1)(b-1) H0F0&gt; Fo; b-1 , (a - 1)(b - 1)3.8 A,B,C,D,E 5 A,B,C,D,Ems 4.3 (ms) 1 2 3 4 5 A 213 127 155 246 200 941 B 178 143 147 210 192 870 C254 151 174 266 222 1067 D 103 108 122 144 161 638 E 177 199 212 168 182 938 925 728 810 1034 957 445470 CT= NG2 = 2544542 = 793524.64SSTotal = 839414.00-CT = 45889.36SSTr= 51(9412+ + 9382)-CT= 813551.60-793524.64= 20026.96SSB = 51(9252+ + 9572)-CT= 805342.80 -793524.64 = 11818.16 4.4 Source of variationd.f. Sum of squares Mean square F0 ()4 11818.16 2954.54 3.37* ()4 20026.96 5006.74 5.70** 16 14044.24877.765Total24 45889.3671 F .01 H0 1 F .05 (P-value)F s2</p> <p> {cij} n 5 3 3 15 A E 1 4.5 5 A E : B 20 C 28 A 33D 18 A 30 E 26A 28 E 23 B 28C 29 D 16 C 30E 20 B 26 D 1972 4.6 AE () 1 2 3A 28 30 33 91 30.3B 20 26 28 74 24.7C 29 28 30 87 29.0D 18 16 19 53 17.7E 20 23 26 69 23.0115123136374 5 F-test 3 4.7 Source of variation Degree ofSum ofMean squareFfreedomsquare 2 45 22.5 4 307 76.8 22.6 X (Error)8 27 3.4Total 14 379 1. F H0:ti=0,H1:ti=01.1 - corrected term = 153742 73- SSTotal = 282+202+...+262-CT = 9704-9325 = 379 - SS=CT -5136 5123 51152 2 2+ += 45 - SS=CT -369...374 3912 2 2+ + += 307- SS = SSTotal -SS-SS= 379-45-307= 271.2 Mean square = ss / df 1.3 F0 = MSEMS=3.476.8= 22.6 48 1.4 F0 F.05; 4, 8 = 3.84 F.01; 4,8=7.01 F H0 5 .012. 5 Least Significant Different2.1 2 se =|.|</p> <p>\|+31 313.4 = 1.5 742.2 lsd lsd =set.025,8= 15 2.3 = 3.45 2.3 AC BE D 3.9 Haber(1946) 1)1 ..2) 15 ..3) 1 ..4) 15 .. 1927 1930, 1931, 19321933 75 4.8 Total 1 ..15 .. 1 ..15 .. 1 1930 230 212 183 148 7731931 324 415 320 2461,3051932 512 584 456 3041,8561933 399 386 255 1441,1841,4651,597 1,214 842 5,118=y.1.2 1930 216 190 186 126 7181931 317 296 295 201 1,1091932 448 471 387 289 1,5951933 361 280 187 839111,3421,237 1,055699 4,333= 2y3 1930 219 151 177 1076541931 357 278 298 192 1,1251932 496 399 427 271 1,5931933 344 254 239 90927 1,4161,082 1,141 660 4,299= 3y4 1930 200 150 209 168 7271931 362 336 328 226 1,2521932 540 485 462 312 1,7991933 381 279 244 168 1,0721,483 1,250 1,243 874 4,850= 4y iy 5,706 5,166 4,653 3,075 18,600= y763.9.1 yijk = +ti+|j+cij +d(ij)k yijkkj i ti i |j j cij d(ij)k3.9.2 4.9 Sovdfa - 1b - 1Experimental Error(a - 1)(b - 1) Sampling Errorab(n - 1) TotalN - 1CT =Ny2 SST= CT - yi j k2ijk; df=N - 1SSTr= CT - ybn1i2i ; df=a - 1 77SSBlock= CT - yan1j2j ; df = b - 1 SSc= CT - SS - SS - yn1Block Tri j2ij; df=(a - 1)(b - 1) SSd= i j2ijj j k2ijkCT - yn1- y; df=ab(n - 1) 4.10 iaFjbRknR E(MS) ti0 b n1 - a bn n2i2 2dt+ o + oc|ja 1 n2 2dn|o + ocij0 1 n2 2dnco + od(ij)k1 1 12do3.9.3 H0:ti=0H1:ti=0 F=MSEMSTr H0:|j =0H1:|j =0 F=MSdMSB783.9.4 - 2so</p> <p>2d= MSS- 2 22d n+MSE 2 </p> <p>2c =nMSd - MSE3.9.5 iyS =bnMSE3.9.6 C.V.= yMSE C.V.(Sampling Error) = yMSd100% C.V.15%3.9.7 1) CT =Ny2 79=64(18600)2= 5405625SSTotal= CT - yi j k2ijk= (2302+3242+...+1682)-CT =SSTr= CT - ybn1i2i = CT - ) 3075 4653 5166 (57064 4 12 2 2 2+ + += 241376.625SS= j2jCT - yan1= CT - ) 4850 4299 4333 (51184 4 12 2 2 2+ + += 30169.625SSE= CT - SS - SS - yn1 Tri j2ij= CT - ) 874 ... 1342 (1465412 2 2+ + += 21860.750SSSampling error= i j2iji j k2ijkCT - yn1- y= 585386.0 80 4.11 Sov df Sum of SquareMean SquareF0 3 241376.625 80458.875 33.125 3 30169.625 10056.542 4.140Experimental error 9 21860.750 2428.972 .199Sampling error48585386.0 12195.542Total63 4 5706, 5166, 46533075 SS 3 linear, quadraticcubic 4 (-3, -1, +1, +3) (2ic )n 12.14.2 1 .. 15 119 SSlinear,quadraticcubicregression 2 81 4.12 1 ..15 .. 1 .. 15 ..1 695* 691 352 46 1,7842 566 445 95 -41 1,0653 514 430 315 28 1,2874 721 536 239 86 1,582 2,496 2,102 1,001 119 5,718 4.13Sov Degrees of Freedom Sum of SquaresMean Square 3 3,776 (3) 43,633 14,544**Linear 1 42,354Quadratic 1 744Cubic 1 536Error 9 2,236 248* 695=3(399) + 512 - 324 - 3(230),from table 12.14.1 SS 3 4.14 Sov Degrees of Freedom Sum of SquaresMean Square 3 30,170 (3) (241,377)Linear 1 220,815**Quadratic 1 16,835*Cubic1 3,727Error 9 2,42982 quadratic 4. 4.1 least significant differences 2 H0 1 leastsignificantdifferences(lsd)H0:i=j i=jH1: i =j(standard error) / r s 22 2 / r s 22 t t = / r s 2y - y2j it to/2 (df error)to oj iy - y / r s 2 t2/2y - yj i&gt; / r s 2 t2/2o1 1 83 least significant differences least significant differences 1. r2s2=5877.765 2 </p> <p>= 18.7382. least significant differences (lsd) o=.05tdferror =16 o/2 H0: i= j H1: i=ji=j t.025,16=2.120lsd lsd = to/2r2s2= (2.120)(18.738) = 39.723. A 188.2B 174.0C 213.4D 127.6E 187.684 A B 14.2A C 25.2A D 60.6*A E 0.6B C 39.4B D 46.4*B E 13.6C D 85.8*C E 25.8D E 60.0*4. lsdlsdij D 4.2 (duncans multiple range test) least significantdifferences 5%.05 8%.08 2 t-test Duncanmultiplerangetest o=.05.01 85o=.05DBEAC o=.01DBEAC a b b b baabb b b o=.05D B, E, A, C o=.01 D, B B, E, A, C s 5y = 1280 4y = 1358 2y = 1540 3y = 1639 1y = 1754 8y = 1861 7y = 1966 6y = 2101 2. iyS=bMSE =556173.16 =105.994 3. (The least signifieant ranges) R2= r.05(2, 28) iyS = 2.89 (105.994) =306.31 R3= r.05(3, 28) iyS = 3.04 (105.994) = 322.21 86R4= r.05(4, 28) iyS = 3.12 (105.994) = 330.69R5= r.05(5, 28) iyS = 3.20 (105.994) = 339.17R6= r.05(6, 28) iyS = 3.25 (105.994) = 344.47 R7= r.05(7, 28) iyS = 3.26 (105.994) = 345.53 R8= r.05(8, 28) iyS = 3.32 (105.994) = 351.89 4. 65:2101-1280 =821 &gt; 351.89 (R8) 64:2101-1358 = 743 &gt; 345.53 (R7) 62:2101-1540 = 561 &gt; 344.47 (R6) 63:2101-1639 = 462 &gt; 339.17 (R5) 61:2101-1754= 347 &gt; 330.69 (R4) 68:2101-1891 = 240 &lt; 322.21 (R3) 67:2101-1966= 105 &lt; 306.31 (R2) 75:1966-1280 = 716 &gt; 345.53 (R7) 74:1966-1358 = 638 &gt; 344.47 (R6) 72:1966-1540 = 456 &gt; 339.17 (R5) 73:1996-1639 = 357 &gt; 330.69 (R4) 71:1966-1754 = 242 &lt; 322.21 (R3) 78:1966-1861 = 135 &lt; 306.31 (R2) 85:1966-1280 = 581 &gt; 344.47 (R6) 84:1861-1358 = 503 &gt; 339.17 (R5) 82:1861-1540 = 321 &lt; 330.69 (R4) 83:1861-1639 = 222 &lt; 322.21 (R3) 81:1861-1754 = 107 &lt; 306.31 (R2) 15:1754-1280 = 474 &gt; 339.17 (R5) 14:1754-1358= 396 &gt; 330.69 (R4) 12:1754-1540 = 214 &lt; 322.21 (R3) 8713:1754-1639 = 115 &lt; 306.31 (R2) 35:1639-1280 = 359 &gt; 330.69 (R4) 34:1639-1358 = 281 &lt; 322.21 (R3) 32:1639-1540 = 99 &lt; 306.31 (R2) 25:1540-1280 = 260 &lt; 322.21 (R3) 24:1540-1358 = 182 &lt; 306.31 (R2) 45:1358-1280 = 78 &lt; 306.31 (R2) 5. 5y 4y 2y 3y 1y 8y 7y 6y6. : = 4 = 5: = 3 = 41 = 2 = 31 = 7 = 86 = 7 = 8 6 2, 4 5 .05 7 4 5 .05 8 4 5 .05 885. (Contransts) 5.1 (contrasts) r 3 A,B,CA 2 2 1ABC 2BC 1= ) y y (21- yC B A+C B Ay - y - y 2 2TA- TB - TC (2, -1, -1)(1, 21- ,21- ) s2 var) y21- y21- y (C B A = 4r 4r r2 2 2 + += 2r32 2r /3s2 2r /3s) y - y (21- y2C B A89tdferrorH0 :A=21(B+C)5.2 (SSTr)1 F (1,dferror) mutuallyorthogonal failedtoemergeout of 100 planted in each plot 4.15failures out of 100 planted soybean seeds 1 2 3 4 5 8 1012 13 11 54 10.8Arasan2 6 7 11 5 31 6.2Spergon4 10 9 8 10 41 8.2Semesan, Jr. 3 5 9 10 6 33 6.6Fermate9 7 5 5 3 29 5.8 26 38 42 47 3518890 correction term CT =251882= 1,413.76SSTotal = 82+22+...+32-CT = 220.24SSTr=529 ... 31 542 2 2+ + +-CT = 83.84SS=535 ... 38 262 2 2+ + +-CT = 49.84 4.16 Source of variationDegree of FreedomSum of square Mean squareF4 49.84 12.464 83.84 20.96 3.87*Error 16 86.56 5.41Total24 220.24 F F .05 H0 1 1) = 10.8-45.8) 6.6 8.2 (6.2 + + += 10.8-6.7= 4.191 i2i2ncS =541414141(15.412 2 2 22|.|</p> <p>\||.|</p> <p>\||.|</p> <p>\||.|</p> <p>\|+ + + +=41152.326+ =45 52.326 =22.326= 1.16316 95% 4.1(2.120) (1.163) = 4.12.5= (1.6 , 6.6) 2) 4 lsd = n2St2.05 = 2.120 55.41 2 = (2.120) (1.471) = 3.12 8.2-5.8=2.4 SS Ti 92 1) L =i iT c ic = 0, ci 1SS=2i2c /nL 1 n 1 ArasanSpergonSemesan, Jr. Fermate Ti54 31 41 33 29 Ci4 -1 -1 -1 -1 4, -1, -1, -1, -1 1, 41-, 41-, 41-, 41- L = 4(54)-31-41-33-29=82</p> <p>1SS = 2i2c n L =(5)(20)822 =67.27 df=1SS 83.84df=4SS1 16.60df=3SS 4 20134 - 529 33 41 312 2 2 2 2+ + +=16.60 93Source of variation Degree of freedom Sum of squareMean squareF 4 49.84 4 83.84 VS 1 67.24 67.24 12.43** 3 16.60 5.531.02Error 16 86.56 5.41Total24 220.24failurerate .01 4 citrus31)ShamoutiOrange2)Marsh Grapefruit3)ClementineMandarin31)100%2) 50%3) the ratio of leaf area to dry weight Shamouti OrangeMarsh GrapefruitClementine Mandarim 112 90 123 50% 86 73 8980 62 81ANOVA Source of variation Degree of freedomSum of square Mean square F (species)22 942.1 43.2Error421.8Total894Therelativeleaf area 2 1: 2: 50% </p> <p>2i2ic nL 100% 50% Ti325 248 223 Li SS+1 0 -1 1026 1734 a VS +1 -2 +1 52 18 150 ;L1= i iT c= (+1)(325) + (-1)(223) = 102 2 ;L2= i jT c= (+1)(325) + (-2)(248) + (+1)(223) = 52 2 j ic c =0(+1)(+1)+(0)(-2)+(-1)(+1)=0 2 2i21c n L 2j22c nL SS df=1 a mutuallyorthogonal a 1 1SS =(3)(2)1022 =1734 1SS=(3)(6)522 =150.2295 4.17 Source of variation Degree of freedomSum of square Mean square F () 2 ()2 1 1734 1734 79.5 50%VS 1 150150 6.9Error48721.8Total8 4 A B X C X D Y A34, 37, 40, 29, 29 C31, 35, 36, 36, 32 B38, 44, 36, 40, 47 D48, 51, 48, 56, 52 () ()XY ()XX 1) r=5A=169 ,B=205 ,C=170 ,D=255 2) 13TA-(TB+TC+TD) 96 2(TB+TC)-2TD 3TB-TC3) 4.18 A B C D 169 205 170 255 SSC() A VS (B, C, D) 3 -1 -1 -1 -123 12 5 252.15() (B, C) VS D 0 1 1 -2 -135 6 5 607.50() B VS C 0 1 -1 035 2 5 122.50982.15STr=51(1692+2052+1702+2552) = 164511/5 = 32902.20 CT = 7992/20=31920.05SSTr = STr-CT =982.15(SSTr)df 3 =1 ii id c =0 ci, di cd mutually orthogonal 97 4.19 Source ofvariationd.f.Sum ofMeanFOsqluares squareA vs (B, C, D) 1 252.15 252.15 16.75(B, C) vs D 1 607.50 607.50 40.37B vs C 1 122.50 122.50 8.14 3 982.15 16 240.80 15.05=s2Total 191222.95 () A B, C, D () D A, C () B C 5.3 1 Var)] y y y (31- y [D C B A+ + =)5 5 5(91 52 2 2 2 + + +=1542= 154(15.05) = 4.013 2 Var)] y y (21- y [C B D+ = )5 5(41 52 2 2 + += 1032=103(15.05) =4.515 3 Var] y - y [C B=52298=52(15.05) =6.020s2df=16 t(16)</p> <p>95%(D-(B+C)/2) 103st )} y y (21- y {216 C B D += 13.52.12 (2.125) = 13.54.50= (9.0 , 18.0) 5.4 O S A, B, C, D ABphysical forms CD . O . S . AB (physical forms ) . CD ( ) . ABCD( ) 6O,S,A,B,C,Dr5 99 4.20 5 O S A B C D 1. O VS (S, A, B, C, D) 5 -1 -1 -1 -1 -1 30r2. S VS (A, B, C, D)0 4 -1 -1 -1 -1 20r3. A VS B 0 0 1 -1 0 0 2r4. C VS D0 0 0 0 1 -1 2r5. (A, B) VS (C, D)0 0 1 1 -1 -1 4r6. 6.1 yij = +ti+|j+cij () (){ti}{|j} {cij} () {ti}{|j} () {cij} N(0,o2) o2</p> <p> () () 1 () 100 () 6.2 (residuals) {cij}fittedvalue(yij) yij = +ti +|jyij-yij cij6.3 5 6 A F ^^ ^ ^^^101 4.21 : A 3.5 C 5.0 F11.5 E 8.5 B 11.0C 2.5 D 8.5 B 9.0 A 8.0 D 12.5E 3.0 A 5.0 C 4.5 C 6.0 F 16.5B 5.0 B 8.5 D11.0 F 13.5 E 9.0F 8.0 E 5.0 E 6.0 B 12.5 C 7.5D 8.0 F 11.5 A 7.0 D 13.0 A 10.530.0 43.549.0 61.5 67.0 A = 34.0, B = 46.0, C = 25.5 ,D = 53.0 , E = 31.5, F = 61.0= 251.0 ; = 30251.0 =8.37 +tA=534.0 = 6.80 ; tA = 6.80-8.37 = -1.57 tB = 0.83, tC = -3.27, tD = 2.23, tE = -2.07, tF = 3.83 +|1=630.0 ^^^^^ ^ ^ ^ ^^ ^102 =5.0 |1= 5.0-8.37= -3.37 |2 = -1.12,|3 = -0.20, |4 = 1.88, |5 = 2.80i= 0( =-0.02 2 ) j = 0 ( =-0.01) yij-yij = yij--ti-|jcij 4.22cij 1 2 3 4 5A 0.07 C 1.02 F -0.50 E 0.32 B -1.00 -0.09C 0.77 D -0.98 B 0.00 A -0.68 D -0.90 -1.79E 0.07 A -0.68 C -0.40 C -0.98 F 1.50 -0.49B -0.83 B 0.42 D 0.60 F -0.58 E -0.10 -0.49F -0.83 E -0.18 E -0.10 B 1.42 C -0.40 -0.09D 0.77 F 0.42 A 0.40 D 0.52 A 0.90 3.010.02 0.020 0.02 0 A 0.01B 0.01 C 0.01^^ ^ ^ ^^^ ^ ^ ^^^103D 0.01E 0.01F 0.01 1=-0.09 , 2=-1.79, 3=-0.49 , 4=-0.49, 5=-0.09 , 6=3.01 6 5 6.4 2 o2{cij} cij yij 1 (transformation) 1 ^^1046.5 {cij}0 2 2 (cij)fittedvalue(yij) 3 3 ^ ^105 5A,B,C, D, E7 A +2 , -3 , 0 , -2 , 4 , 1 , -2 =7 B -5 , -2 , 1 , 0 , -2 , 3 , 5 =10 C -3 , 2 , 0 , 1 , 0 , -2 , 2 =5 D -6 , -4 , 0 , 3 , 2 , 3 , 2 =9 E 2 , 0 , -1 , 1 , -2 , 0 , 0 =4CE o2 6.6 outlieroutlier A 1 , -2 , 4 , 0 , 2 , -5 B-3 , -5 , 0 , 1 , -2 ,9 C -2 , 3 , -1 , 0 , 2 , -2 B 9 1064 1 5 . . . 1. 2 247407...</p>

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