œƒf[ƒ^“Η‚έ‚±‚έ
> mm <- read.table("Box3_R.tab")@@¦¨ƒf[ƒ^ƒtƒ@ƒCƒ‹FBox3_R.tabCBox3_R.data
> mm
REP V N DATA
1 1 V1 N0 3.852
2 1 V1 N1 4.788
3 1 V1 N2 4.576
4 1 V1 N3 6.034
5 1 V1 N4 5.874
6 1 V2 N0 2.846
7 1 V2 N1 4.956
8 1 V2 N2 5.928
9 1 V2 N3 5.664
10 1 V2 N4 5.458
11 1 V3 N0 4.192
12 1 V3 N1 5.250
13 1 V3 N2 5.822
14 1 V3 N3 5.888
15 1 V3 N4 5.864
16 2 V1 N0 2.606
17 2 V1 N1 4.936
18 2 V1 N2 4.454
19 2 V1 N3 5.276
20 2 V1 N4 5.916
21 2 V2 N0 3.794
22 2 V2 N1 5.128
23 2 V2 N2 5.698
24 2 V2 N3 5.362
25 2 V2 N4 5.546
26 2 V3 N0 3.754
27 2 V3 N1 4.582
28 2 V3 N2 4.848
29 2 V3 N3 5.524
30 2 V3 N4 6.264
31 3 V1 N0 3.144
32 3 V1 N1 4.562
33 3 V1 N2 4.884
34 3 V1 N3 5.906
35 3 V1 N4 5.984
36 3 V2 N0 4.108
37 3 V2 N1 4.150
38 3 V2 N2 5.810
39 3 V2 N3 6.458
40 3 V2 N4 5.786
41 3 V3 N0 3.738
42 3 V3 N1 4.896
43 3 V3 N2 5.678
44 3 V3 N3 6.042
45 3 V3 N4 6.056
46 4 V1 N0 2.894
47 4 V1 N1 4.608
48 4 V1 N2 3.924
49 4 V1 N3 5.652
50 4 V1 N4 5.518
51 4 V2 N0 3.444
52 4 V2 N1 4.990
53 4 V2 N2 4.308
54 4 V2 N3 5.474
55 4 V2 N4 5.932
56 4 V3 N0 3.428
57 4 V3 N1 4.286
58 4 V3 N2 4.932
59 4 V3 N3 4.756
60 4 V3 N4 5.362

> summary(mm)
REP V N DATA
Min. :1.00 V1:20 N0:12 Min. :2.606
1st Qu.:1.75 V2:20 N1:12 1st Qu.:4.303
Median :2.50 V3:20 N2:12 Median :5.059
Mean :2.50 N3:12 Mean :4.957
3rd Qu.:3.25 N4:12 3rd Qu.:5.792
Max. :4.00 Max. :6.458

œˆφŽqŽw’θ
> mm$REP <- factor(mm$REP)
> mm$V <- factor(mm$V)
> mm$N <- factor(mm$N)

œBartlettŒŸ’θ
> bartlett.test(mm$DATA~mm$REP)

Bartlett test for homogeneity of variances

data: mm$DATA by mm$REP
Bartlett's K-squared = 0.1655, df = 3, p-value = 0.983

> bartlett.test(mm$DATA~mm$V)

Bartlett test for homogeneity of variances

data: mm$DATA by mm$V
Bartlett's K-squared = 0.8044, df = 2, p-value = 0.6688

> bartlett.test(mm$DATA~mm$N)

Bartlett test for homogeneity of variances

data: mm$DATA by mm$N
Bartlett's K-squared = 11.0445, df = 4, p-value = 0.02607

œ‚Q—vˆφ—‰ς–@‚Μ•ͺŽU•ͺΝ
> fm <- aov(DATA~REP+V+N+V:N, data=mm)
> summary(fm)
Df Sum Sq Mean Sq F value Pr(>F)
REP 3 2.600 0.867 5.7294 0.002220 **
V 2 1.053 0.526 3.4801 0.039950 *
N 4 41.235 10.309 68.1534 < 2.2e-16 ***
V:N 8 2.291 0.286 1.8931 0.086706 .
Residuals 42 6.353 0.151
---
Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1

‰Ί‹L‚Ν“―ˆκ‚Μ•ͺŽU•ͺΝiV*N = V+N+V:N ‚ΜŠm”Fj
> fm <- aov(DATA~REP+V*N, data=mm)
> summary(fm)
Df Sum Sq Mean Sq F value Pr(>F)
REP 3 2.600 0.867 5.7294 0.002220 **
V 2 1.053 0.526 3.4801 0.039950 *
N 4 41.235 10.309 68.1534 < 2.2e-16 ***
V:N 8 2.291 0.286 1.8931 0.086706 .
Residuals 42 6.353 0.151
---
Signif. codes: 0 `***' 0.001 `**' 0.01 `*' 0.05 `.' 0.1 ` ' 1

œ‘½d”δŠr
> pairwise.t.test(mm$DATA, mm$REP, p.adj="bonferroni")

Pairwise comparisons using t tests with pooled SD

data: mm$DATA and mm$REP

1 2 3
2 1.00 - -
3 1.00 1.00 -
4 0.94 1.00 0.88

P value adjustment method: bonferroni
> pairwise.t.test(mm$DATA, mm$N, p.adj="bonferroni")

Pairwise comparisons using t tests with pooled SD

data: mm$DATA and mm$N

N0 N1 N2 N3
N1 1.6e-07 - - -
N2 3.7e-10 1.00000 - -
N3 5.3e-15 0.00017 0.03075 -
N4 5.8e-16 1.7e-05 0.00420 1.00000

P value adjustment method: bonferroni
> pairwise.t.test(mm$DATA, mm$V, p.adj="bonferroni")

Pairwise comparisons using t tests with pooled SD

data: mm$DATA and mm$V

V1 V2
V2 1 -
V3 1 1

P value adjustment method: bonferroni