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# Anova

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### Anova

1. 1. A B C D 8 12 18 13 10 11 12 9 12 9 16 12 8 14 6 16 7 4 8 15 45 50 60 65 220 correction factor= 220*220/20 2420 Total sum of squares=2678-2420=258 sum of the squares between schools= 50 3 45*45/5+50*50/5+60*60/5+65*65/5=50 Sum of the squres within schools=s-sb=258-50=208 Source of Degree of Mean Variance variation Sum of Squares Freedom Squares Ratio F Inference Within Months S=SS-CF n0-1=19 Not S 16.66 258 13 Between Vr/Ve=3.3 Months Sc=50 k-1=3 Vr=16.66 27 (2,6)=5.14 1.28 Residual Se=S-Sc=208 n0-k=6 Ve=13 samples 1 60 65 71 74 76 82 85 87 samples2 61 66 67 85 78 63 85 86 Diet A 5 6 8 1 12 4 3 9 Diet B 2 3 6 8 1 10 2 8 Batch1 1600 1610 1650 1680 1700 1720 1800 Batch 2 1580 1640 1640 1700 1750 Batch 3 1460 1550 1600 1620 1640 1660 1740 1820 Batch4 1510 1520 1530 1570 1600 1680 A B C D 8 12 18 13 10 11 12 9 12 9 16 12 8 14 6 16
2. 2. 7 4 8 15 Salesman Month A B C D May 50 40 48 39 177 June 46 48 50 45 189 July 39 44 40 39 162 135 132 138 123 528 Source of Degree of Mean Variance variation Sum of Squares Freedom Squares Ratio F Inference Total S=Sij²-CF=216 4*3-1=11 Not S Between Vr/Ve=3.3 Months Sr=91.5 3-1=2 Vr=4.575 27 (2,6)=5.14 Between Salesman Sc=42 4-1=3 Vc=14 Vc/Ve=1.018 (3,6)-4.76 Not S Residual Se=S-Sr-Sc=82.5 6 Ve=13.75 Source of Degree of Mean Variance variation Sum of Squares Freedom Squares Ratio F Inference Total S=Exy-CF rc-1 Vr=4.575 Sig/Not Sr=Sxc²-CF Between r Months r-1 Vc=14 Vr/Ve F(r-1),(r-1)(c-1) Sig/Not Sc=Sxr²-CF Between c Salesman c-1 Vc/Ve F(c-1),(r-1)(c-1) Sig/Not Residual Se=S-Sr-Sc (r-1)(c-1) Ve=Se/(r-1)(c-1) Source of Degree of Mean Variance variation Sum of Squares Freedom Squares Ratio F Inference Total S=Exy-CF n0-1 Sb=Sxc²-CF Between r Months k-1 Vb=Sb/k-1 Vb/Vw F(k-1),(n0-k) Sig/Not Within ClassesSw=S-Sb Sw=S-Sb n0-K Vw=Sw/(n0-k)
3. 3. 88 91 6 10