-
Analysis of Variance ANOVA )
-
ANOVA R.A.FisherFisherF F F test
-
One-way analysis of variance FF factor(level)
-
1. 2. homogeneity of variance
t
-
9-1 (/ml)
i
(Yij)
1
23
12
18
16
28
14
6
18.5
5.99
111
2233.0
2
28
31
23
24
28
34
6
28.0
4.15
168
4790.0
3
14
24
17
19
16
22
6
18.7
3.78
112
2162.0
4
8
12
21
19
14
15
6
14.8
4.71
89
1431.0
73
79
79
78
86
85
24
20.0
6.65
480
10616.0
_1062652699.unknown
_1062652964.unknown
_1286080594.unknown
_1062652790.unknown
_1062652436.unknown
Chart1
23281482018.52818.6714.83
123124122018.52818.6714.83
18231721
16241919
28281614
14342215
1234
1234
1234
1234
1234
1234
1234
1234
1234
1
2
3
4
20
A18.5
B28
C18.67
D14.83
m/ml
Sheet1
1232283144820
11223132441218.5
11822331742128
11622431941918.6666666667
12822831641414.8333333333
114234322415
1234
1234
1234
1234
1234
1234
1234
1234
1234
231218162814
283123242834
142417191622
81221191415
2328148
12312412
18231721
16241919
28281614
14342215
Sheet1
2018.52818.6714.83
2018.52818.6714.83
1
2
3
4
20
A18.5
B28
C18.67
D14.83
m/ml
Sheet2
20.7922.2228.5631.93
22.9124.7428.6737.94
27.2121.5325.2839.76SUMMARY
19.3419.6630.3827.94
17.8525.8923.1329.65 115319.6621.310666666711.5389780952
23.7929.123.4734.23 215348.4823.23212.3715028571
22.618.9328.8832.63 315422.0328.135333333316.0325266667
18.5318.6429.6229.13 415492.5632.837333333321.6853495238
23.2326.3924.8239.62
20.1425.4934.6436.15
26.7120.4322.2928.85
19.3622.6929.2224.07SSdfMSFP-valueF crit
17.2229.6725.6329.291205.7963401.93226.0870.0002.769
24.1320.3635.1235.24862.7975615.407
15.8522.7432.3236.132068.59359
Sheet3
20.791
22.911
27.211
19.341
17.851
23.791
22.61
18.531
23.231
20.141
26.711
19.361
17.221
24.131
15.851
22.222
24.742
21.532
19.662
25.892
29.12
18.932
18.642
26.392
25.492
20.432
22.692
29.672
20.362
22.742
28.563
28.673
25.283
30.383
23.133
23.473
28.883
29.623
24.823
34.643
22.293
29.223
25.633
35.123
32.323
31.934
37.944
39.764
27.944
29.654
34.234
32.634
29.134
39.624
36.154
28.854
24.074
29.294
35.244
36.134
-
g
Xi
YYij
1
Y11
Y12
Y1j
n1
S1
2
Y21
Y22
Y2j
n2
S2
i
Yi1
Yi2
Yij
ni
Si
g
Yg1
Yg2
Ygj
ng
Sg
N
_1232778371.unknown
_1286001437.unknown
_1286001549.unknown
_1286001590.unknown
_1286001615.unknown
_1286001700.unknown
_1286001701.unknown
_1286001600.unknown
_1286001577.unknown
_1286001494.unknown
_1286001541.unknown
_1286001464.unknown
_1235479419.unknown
_1286001397.unknown
_1232778451.unknown
_1232777698.unknown
_1232777729.unknown
_1232777741.unknown
_1232777714.unknown
_1232776589.unknown
_1232776602.unknown
_1232776562.unknown
-
9-1 factor
levelg=4A
Di=1,2,3,4ABCD
ni=j=1,2,,6
Yijij
(/ml)
24
1~24
66
-
9-1 Total variationYij between group variation within group
variation )Yij (sum of squares of deviations from meanSS)
-
1. :
-
9-1 (/ml)
i
(Yij)
1
23
12
18
16
28
14
6
18.5
5.99
111
2233.0
2
28
31
23
24
28
34
6
28.0
4.15
168
4790.0
3
14
24
17
19
16
22
6
18.7
3.78
112
2162.0
4
8
12
21
19
14
15
6
14.8
4.71
89
1431.0
73
79
79
78
86
85
24
20.0
6.65
480
10616.0
_1062652699.unknown
_1062652964.unknown
_1286080594.unknown
_1062652790.unknown
_1062652436.unknown
-
2
SS +
-
9-1 (/ml)
i
(Yij)
1
23
12
18
16
28
14
6
18.5
5.99
111
2233.0
2
28
31
23
24
28
34
6
28.0
4.15
168
4790.0
3
14
24
17
19
16
22
6
18.7
3.78
112
2162.0
4
8
12
21
19
14
15
6
14.8
4.71
89
1431.0
73
79
79
78
86
85
24
20.0
6.65
480
10616.0
_1062652699.unknown
_1062652964.unknown
_1286080594.unknown
_1062652790.unknown
_1062652436.unknown
-
3()SS Yij
-
9-1 (/ml)
i
(Yij)
1
23
12
18
16
28
14
6
18.5
5.99
111
2233.0
2
28
31
23
24
28
34
6
28.0
4.15
168
4790.0
3
14
24
17
19
16
22
6
18.7
3.78
112
2162.0
4
8
12
21
19
14
15
6
14.8
4.71
89
1431.0
73
79
79
78
86
85
24
20.0
6.65
480
10616.0
_1062652699.unknown
_1062652964.unknown
_1286080594.unknown
_1062652790.unknown
_1062652436.unknown
-
ANOVA table
SS
MS
F
P
568.33
3
189.44
8.46
0.00079
447.67
20
22.38
1016.00
23
-
= +
SS
SS +
_1061022586.unknown
-
One-Factor ANOVA Partitions of Total VariationVariation Due to
Treatment SSBVariation Due to Random Sampling SSWTotal Variation
SSTCommonly referred to as:Sum of Squares Within, orSum of Squares
Error, orWithin Groups VariationCommonly referred to as:Sum of
Squares Among, orSum of Squares Between, orSum of Squares Model,
orAmong Groups Variation=+
-
(mean squareMS)
(mean squareMS)
:
_1076789538.unknown
_1076789550.unknown
-
F F
H0
F
FlH0F
H0
_1079002900.unknown
_1080389338.unknown
_1105999533.unknown
_1079422929.unknown
_1071777461.unknown
-
F
-
F 5 FP=0.05 P=0.015
n2n11234561161200216225230234405249995403562557645859218.5119.0019.1619.2519.3019.3398.4999.0099.1799.2599.3099.33254.243.392.992.762.602.497.775.574.684.183.853.63
-
F
-
9-2 3(g)
i
(g) (Yij)
4.2
3.3
3.7
4.3
4.1
3.3
6
3.82
0.449
22.9
88.41
4.5
4.4
3.5
4.2
4.6
4.2
6
4.23
0.393
25.4
108.30
5.6
3.6
4.5
5.1
4.9
4.7
6
4.73
0.671
28.4
136.68
14.3
11.3
11.7
13.6
13.6
12.2
18
4.26
0.622
76.7
333.39
_1062652699.unknown
_1062652964.unknown
_1286080594.unknown
_1062652790.unknown
_1062652436.unknown
Chart2
4.24.55.644.263.824.234.73
3.34.43.644.263.824.234.73
3.73.54.54
4.34.25.14
4.14.64.94
3.34.24.74
1
2
3
4.26
3.82
4.23
4.73
g
Sheet1
14.224.535.644.2611111111
13.324.433.643.8166666667
13.723.534.544.2333333333
14.324.235.144.7333333333
14.124.634.94
13.324.234.74
14
34
22
15
Sheet1
4.263.824.234.73
4.263.824.234.73
1
2
3
4.26
3.82
4.23
4.73
g
Sheet2
20.7922.2228.5631.93
22.9124.7428.6737.94
27.2121.5325.2839.76SUMMARY
19.3419.6630.3827.94
17.8525.8923.1329.65 115319.6621.310666666711.5389780952
23.7929.123.4734.23 215348.4823.23212.3715028571
22.618.9328.8832.63 315422.0328.135333333316.0325266667
18.5318.6429.6229.13 415492.5632.837333333321.6853495238
23.2326.3924.8239.62
20.1425.4934.6436.15
26.7120.4322.2928.85
19.3622.6929.2224.07SSdfMSFP-valueF crit
17.2229.6725.6329.291205.7963401.93226.0870.0002.769
24.1320.3635.1235.24862.7975615.407
15.8522.7432.3236.132068.59359
Sheet3
20.791
22.911
27.211
19.341
17.851
23.791
22.61
18.531
23.231
20.141
26.711
19.361
17.221
24.131
15.851
22.222
24.742
21.532
19.662
25.892
29.12
18.932
18.642
26.392
25.492
20.432
22.692
29.672
20.362
22.742
28.563
28.673
25.283
30.383
23.133
23.473
28.883
29.623
24.823
34.643
22.293
29.223
25.633
35.123
32.323
31.934
37.944
39.764
27.944
29.654
34.234
32.634
29.134
39.624
36.154
28.854
24.074
29.294
35.244
36.134
-
H0 3 H13
-
=
=333.39(76.7)2/186.5628
(18-1)0.6222=6.5628
=18-117
=3-1=2
1.264
6.56282.52784.0350
(6-1)0.4492(6-1)0.3932+(6-1)0.6712
=3(6-1)=15,
0.2690
_1066895492.unknown
_1066895631.unknown
_1157726553.unknown
_1286119695.unknown
_1286119964.unknown
_1286119565.unknown
_1066895669.unknown
_1066895579.unknown
_1066895201.unknown
_1066895249.unknown
_1066850963.unknown
9-2 3(g)
i
(g) (Yij)
4.2
3.3
3.7
4.3
4.1
3.3
6
3.82
0.449
22.9
88.41
4.5
4.4
3.5
4.2
4.6
4.2
6
4.23
0.393
25.4
108.30
5.6
3.6
4.5
5.1
4.9
4.7
6
4.73
0.671
28.4
136.68
14.3
11.3
11.7
13.6
13.6
12.2
18
4.26
0.622
76.7
333.39
_1062652699.unknown
_1062652964.unknown
_1286080594.unknown
_1062652790.unknown
_1062652436.unknown
-
F
F
4.70 215
(9-3)
9-3 91
SS
MS
F
P
2.5278
2
1.2639
4.70
0.026
4.0350
15
0.2690
6.5628
17
_1286120353.unknown
-
P 2t,
5 FF0.05(2,15)=3.68
FF0.05(2,15)P0.05
3
-
randomized block design (block)
-
(8)ABC33 8
Sheet1
12345678
123456789101112131415161718192021222324
441189485963174779443638710376554625563705522
cbabacabccabcbacabbaccba
100
Sheet2
Sheet3
-
(g)
(j)
(i)
1(A)
2(B)
3(C)
1
57.0
64.8
76.0
3
197.8
2
55.0
66.6
74.5
3
196.1
3
62.1
69.5
76.5
3
208.1
4
74.5
61.1
86.6
3
222.2
5
86.7
91.8
94.7
3
273.2
6
42.0
51.8
43.2
3
137.0
7
71.9
69.2
61.1
3
202.2
8
51.5
48.6
54.4
3
154.5
8
8
8
24
500.7
523.4
567.0
1591.1
62.6
65.3
70.9
66.3
32783.4
35459.1
42205.0
110447.5
_1062876885.unknown
_1062876930.unknown
_1063469599.unknown
_1063530426.unknown
_1062876916.unknown
_1062876444.unknown
-
(1) (2) (3) (4)
-
H0 H1
-
(g)
(j)
(i)
1(A)
2(B)
3(C)
1
57.0
64.8
76.0
3
197.8
2
55.0
66.6
74.5
3
196.1
3
62.1
69.5
76.5
3
208.1
4
74.5
61.1
86.6
3
222.2
5
86.7
91.8
94.7
3
273.2
6
42.0
51.8
43.2
3
137.0
7
71.9
69.2
61.1
3
202.2
8
51.5
48.6
54.4
3
154.5
8
8
8
24
500.7
523.4
567.0
1591.1
62.6
65.3
70.9
66.3
32783.4
35459.1
42205.0
110447.5
_1062876885.unknown
_1062876930.unknown
_1063469599.unknown
_1063530426.unknown
_1062876916.unknown
_1062876444.unknown
-
(g-1)(n-1)
SS
MS
F
P
283.83
2
141.92
2.88
0.0897
3990.31
7
570.04
11.56
0.0000
690.07
14
49.29
4964.21
23
-
F0.05(214)=3.74 F2.880.05 H0 g=2t
-
9-2
-
H0 H1
96 (g)
(j)
(i)
1(A)
2(B)
3(C)
1
64
65
73
3
202
2
53
54
59
3
166
3
71
68
79
3
218
4
41
46
38
3
125
5
50
58
65
3
173
6
42
40
46
3
128
6
6
6
18
321
331
360
1012
53.5
55.2
60.0
56.22
17891
18845
22836
59572
_1062876885.unknown
_1062876930.unknown
_1063469599.unknown
_1063530426.unknown
_1062876916.unknown
_1062876444.unknown
-
96 (g)
(j)
(i)
1(A)
2(B)
3(C)
1
64
65
73
3
202
2
53
54
59
3
166
3
71
68
79
3
218
4
41
46
38
3
125
5
50
58
65
3
173
6
42
40
46
3
128
6
6
6
18
321
331
360
1012
53.5
55.2
60.0
56.22
17891
18845
22836
59572
_1062876885.unknown
_1062876930.unknown
_1063469599.unknown
_1063530426.unknown
_1062876916.unknown
_1062876444.unknown
-
(g-1)(n-1)
SS
MS
F
P
136.778
2
68.389
4.24
0.046
2377.111
5
475.422
29.49
0.000
161.222
10
16.122
2675.111
17
- F0.05(210)=4.10 F4.24>F0.05(2, 10)P
-
P139141
Sheet1
646573
535459
716879SUMMARY
414638 1320267.333333333324.3333333333
505865 2316655.333333333310.3333333333
424046 3321872.666666666732.3333333333
321331360 4312541.666666666716.3333333333
5317357.666666666756.3333333333
6312842.66666666679.3333333333
1632153.5143.5
2633155.1666666667116.9666666667
3636060247.2
SSdfMSFP-valueF crit
ABCD2377.11111111115475.422222222229.4886285320.0000111763.3258345293
BADC136.7777777778268.38888888894.24190213650.04634930164.1028210152
CDAB161.22222222221016.1222222222
DCBA
2675.111111111117
Sheet2
Sheet3
-
H0H1 gmultiple comparisonpost hoc
-
t t 4 t6 0.05 10.056
-
SNKq Dunnett LSDt
TUKEY DUNCAN SCHEFFE WALLER BON
-
SNKqSNKStudent-Newman-Keulsq
=
_1077026404.unknown
_1080398009.unknown
_1165253555.unknown
_1165254019.unknown
_1077026445.unknown
_1077026341.unknown
-
9-4 9-1
1.
2.q
3.817
4.233
4.733
1
2
3
3. aq(9)P
9-12 q
1
2
a
(3)
q
(4)
(5)
P
6)
1 , 2
0.416
2
1.97
3.01
1 , 3
0.916
3
4.33
3.67
2 , 3
0.500
2
2.36
3.01
EMBED Equation.3
EMBED Equation.3
_1106083925.unknown
_1106084452.unknown
_1106085393.unknown
_1286165577.unknown
_1286165769.unknown
_1106085839.unknown
_1106084807.unknown
_1106084443.unknown
_1106084447.unknown
_1106084439.unknown
_1106083748.unknown
_1106083904.unknown
_1012033927.unknown
-
Dunnett
=
i
_1077024697.unknown
_1165253555.unknown
_1165253671.unknown
_1286166270.unknown
_1077024721.unknown
_1077024613.unknown
-
9-5 9-2
1.
2.
MS
,
,
3
10.2P
9-13 2
1
2
(3)
(4)
(5)
P
6)
,
1.667
2
0.719
2.57
,
6.500
2
2.804
2.57
_1106089100.unknown
_1286166648.unknown
_1286167260.unknown
_1286167335.unknown
_1286167607.unknown
_1286167832.unknown
_1286167261.unknown
_1286166817.unknown
_1286166908.unknown
_1286166663.unknown
_1286166615.unknown
_1286166631.unknown
_1106089106.unknown
_1106089074.unknown
_1106089078.unknown
_1021124699.unknown
-
LSDtLeast significant differencet
LSD-t =
=
ij
_1077026404.unknown
_1080395620.unknown
_1165253555.unknown
_1165254019.unknown
_1165253163.unknown
_1077026445.unknown
_1077023182.unknown
-
9-6 9-3, ABCDABCD
LSD-t
EMBED Equation.3 ,
=
=
t( 4 )P
9-14 2
1
2
(3)
(4)
(5)
P
6)
A, B
2.75
5.404
0.509
2.447
C, D
22.75
5.404
4.210
2.447
_1286168489.unknown
_1286168631.unknown
_1286168856.unknown
_1286168992.unknown
_1286169182.unknown
_1286168941.unknown
_1286168855.unknown
_1286168537.unknown
_1286168582.unknown
_1286168514.unknown
_1106087483.unknown
_1106087498.unknown
_1106087547.unknown
_1106087491.unknown
_1106087433.unknown
_1106087478.unknown
_1106087396.unknown
-
H0H1
g
N
g-1
P
H0
_1106093254.unknown
_1286170091.unknown
_1286170138.unknown
_1286170216.unknown
_1286169911.unknown
_1106093252.unknown
_1106093253.unknown
_1106093132.unknown
-
9-7 9-1
-
2. Levene
leveneLEVENE
1
2
2
_1077535219.unknown
_1079444598.unknown
-
14
-
http://statdtedm.6to23.com
-
Factorial design ANOVA
-
1mg22
-
222
-
3ABCSRScm3ABC222
-
4ACTHAB32
-
2factor2level2repeat,
-
main effectsInteractionABABC
-
23545
-
4-622
-
4-6ANOVA()
-
SS
-
Ti Ai Bi
