t-test A B Diff x^2
1 3550 2450 1100 1210000
2 2000 2400 -400 160000
3 3000 1800 1200 1440000
4 3950 3200 750 562500
5 3800 3250 550 302500
6 3750 2700 1050 1102500
7 3450 2500 950 902500
8 3050 1750 1300 1690000
sum 26550 20050 6500
M=6500/8 812.5 42250000 7370000
SS [7370000-422500/8]/(8-1)= 298392.9 sqrt= 546.2535
t=(M-u)/(s/n^1/2) 4.207016 546.25/n^1/2 193.1298
3318.75 2506.25 812.5

　

SS-Analsis A B C SUM
(X)^2 (X)^2 (X)^2 (X)^2-sum
1 3.3 10.89 4.4 19.36 3.6 12.96 11.3 127.69
1 3.6 12.96 4.4 19.36 4.4 19.36 12.4 153.76
1 4.3 18.49 3.4 11.56 5.1 26.01 12.8 163.84
1 4.1 16.81 4.2 17.64 5 25 13.3 176.89
1 4.2 17.64 4.7 22.09 5.5 30.25 14.4 207.36
1 3.3 10.89 4.2 17.64 4.7 22.09 12.2 148.84
Exi 22.8 519.84 25.3 640.09 28.3 800.89 76.4 5836.96
SUMi/N ni 6 86.64 6 106.6817 6 133.4817 18 324.2756
Mi 3.8 4.216667 4.716667 4.244444
(Xa)^2 87.68 107.65 135.67 331
SUMi/N (Xexi)^2/6 86.64 106.6817 133.4817 326.8033
N=18 k=3 n=17,V=2,V=15
Ma-b-c N-k=15 k-1=2 (min 1 for free degagree
C: (X)^2-sum  /N 324.2756 SSsum 331-324.2756= 6.724444
SS-total  =331-324 6.724444 V-total=18-1=17 17 SSbwt 326.8033-324.2756= 2.527778
SS-btw  =326.8033 -C 2.527778 Vk=k-1=3-1=2 2 SSinr SSsum-SSbwt= 4.196667
SS-inner SSt - SSb 4.196667 Vi=N-Vk=18-3=15 15
MSbtw SSbtw / Vbwt= 2.527778/2 1.263889 MSbwt=SSbwt/Vb.2 1.263889
MSi Ssi/Vi 0.279778 MSinr=SSinr/Vi15 0.279778
F=MSbte/MSinr 4.517474

　

march Contro A B C D Sum
X^2
1 1.4 1.96 4.1 16.81 1.9 3.61 1.8 3.24 2 4 11.2 125.44
2 1.5 2.25 3.6 12.96 1.9 3.61 2.3 5.29 2.3 5.29 11.6 134.56
3 1.5 2.25 4.3 18.49 2.1 4.41 2.3 5.29 2.4 5.76 12.6 158.76
4 1.8 3.24 3.3 10.89 2.4 5.76 2.5 6.25 2.6 6.76 12.6 158.76
5 1.5 2.25 4.2 17.64 1.8 3.24 1.8 3.24 2.6 6.76 11.9 141.61
6 1.5 2.25 3.3 10.89 1.7 2.89 2.4 5.76 2.1 4.41 11 121
Sum 9.2 84.64 22.8 519.84 11.8 139.24 13.1 171.61 14 196 70.9 5026.81
14.2 87.68 23.52 29.07 32.98 840.13
N,k, 6 6 6 6 6 30 167.5603 168.026
M 1.533333 3.8 1.966667 2.183333 2.333333 2.363333      b=6 0.465667
14.2 87.68 23.52 29.07 32.98 187.45 187-167= 19.88967
14.10667 86.64 23.20667 28.60167 32.66667 185.2217 185-167= 17.66133
19.8-17.6 2.228333 1.762667
5 total treatment with 6 group F= 17.7/2.2 7.925804
SSsum: 167.5603 Vsum=N-1=29
SStreat 17.66133 V=k-1=5-1=4
SScontrol 0.465667 V=b-1=6-1=5
SSerr=Sssum-Sstreat-Sscontrl 1.762667 Verr=Vtotal-vtreat-Vcontrl=29-4-5=20
MStrat=Sstreat/Vtreat 4.415333
MScotrl=SScontrl/Vcontrl 0.093133
MSerr=SSerr/Verr 0.088133
F=MScontrl/MSerr 1.056732 V1=5,V2=20, F value, P>0.05)
it is not refuse the Ho, Therefore, combine Sscontrl
Sserr=0.466+1,762=2.228, Verr=5+20=25
Mserr-combin=2.228/25=0.0891
F=Mstreat/Mserr=4.416/0.00891=49.562
V1=4,v2=25 p<0.01, a=0.05, accept H1

　

X^2 not same
Bartett Method A B C
2.3026 value 1 3.8 14.44 5.6 31.36 1.5 2.25
2 9 81 4 16 3.8 14.44
3 2.5 6.25 3 9 5.5 30.25
4 8.2 67.24 8 64 2 4
5 7.1 50.41 3.8 14.44 3 9
6 11 121 4 16 5.1 26.01
7 11.5 132.25 6.4 40.96 3.3 10.89
8 9 81 4.2 17.64 4 16
9 11 121 4 16 2.1 4.41
10 7.9 62.41 7 49 2.7 7.29
81 6561 50 2500 33 1089
sum 656.1 737 250 274.4 108.9 124.54
n=10 SS 8.988889 SS 2.711111 SS 1.737778
lgSS 0.953706 0.433147 0.239994
X^2=2.3026(10-1)(3lg(13.4378/3)-1.6268/[1+(3+1)/(3(3)(1-1)=6.454
n not same A B C
1 0.61 0.3721 0.79 0.6241 0.62 0.3844
2 0.72 0.5184 1.01 1.0201 1.01 1.0201
3 0.72 0.5184 1.24 1.5376 1.18 1.3924
4 1.02 1.0404 1.41 1.9881 1.47 2.1609
5 0.88 0.7744 1.54 2.3716 1.35 1.8225
6 1.36 1.8496 1.75 3.0625 1.52 2.3104
7 1.44 2.0736 1.94 3.7636 1.81 3.2761
8 1.9 3.61 2.54 6.4516 1.86 3.4596
9 1.82 3.3124 3.05 9.3025 2.37 5.6169
10 2.16 4.6656 2.76 7.6176
12.63 159.5169 15.27 233.1729 15.95 254.4025
Sum 15.95169 18.7349 25.9081 30.1217 25.44025 29.0609
n=26 10 2.78321 9 4.2136 10 3.62065
SS 0.309246 SS 0.5267 SS 0.402294
(ni-1)x lgSS -4.58727 -2.22749 -3.5591
1/(ni-1) 0.111111 0.125 0.111111
X^2=2.3026[26lg(10.6064/26)-(-10.3835)]/{1+1/3(3-1)[0.3472-1/26]}=0.567 v=3-1=2 X^2 value
1/400 1/100 sum/2 sum-1/400 1/400 x sum/2
0.0025 0.01 0.00625 0.00375 0.000015625 3.90625E-08 0.000198
 =0.00375/AO44(0.0025)(0.00625)/400]^1/2=  18.97366596
0.0075 0.00002475 0.004975 1.507557
Chi-square test
A+ B- SUM A+/SUM
a check 52 57.17699 19 13.82300885 71 0.732394
b compare 39 33.82301 3 8.17699115 42 0.928571
Sum 91 22 113
Theory 0.80530973  +rate 0.19469   -rate
X2=Sum(A-T)^2/T
1 x^2=(52-57.18)^2/57.18+(19-13.82)^2/13.82+39-33.82)^2/33.82+3-8.18)^2/8.18=6.48
or
2  =[(52*3-19*39)^2*113]/(71*42*19*22)=6.48
correction for continuity:
1: -o.5 upper calc.
2: -n/2 upper calc.
mult row/clm A- B+ Sum  +Rate B+/Sum
a 6 23 29 0.793103
b 30 14 44 0.318182
c 8 3 11 0.272727
sum 44 40 84
rate 0.52380952 0.47619 v=(3-1)(2-1)=2
x^2=84(6*6/29*44+23*23/29*44+30*30/44*44+14*14/44*40+8*8/11*44+3*3/11*40-1)=17.907
march
A+ B- Sum
a+ 11 9 20
b- 1 7 8
sum 12 16 28
x^2=(|11x7-9x1|-28/2)^2x28/20x8x12x16=2.66
(T<1 or n<40, needed the formula for correction for continuity above
X A(Ef) X*A r/X
0 26 0 0 0 0 0
1 51 51 2.49 126.99 2601 330301
2 84 168 1.245 104.58 28224 2951666
3 70 210 0.83 58.1 44100 2562210
4 42 168 0.6225 26.145 28224 737916.5
5 15 75 0.498 7.47 5625 42018.75
6 9 54 0.415 3.735 2916 10891.26
7 3 21 0.355714 1.067142857 441 470.61
sum 28 300 747 558009 328.0871429 112131 6635474
1860.03 1.09362381 373.77 22118.25
n=300 2.49  r