R語言實現常用多重比較方法

在單因素方差分析ANOVA中，如果該因素影響比較顯著，那么需要進一步利用多重比較方法比較該因素不同水平的影響，確定不同水平下該因素的影響是否顯著。常見的多重比較方法主要有兩種，LSD法和Tukey HSD法。下面對R語言中，這兩種多重比較方法的實現進行舉例。
前期數據如下，影響因素為group，指標為value：
> head(tarD)
                   value  group      sample   time
A0522W11NC1 0.0002053745 normal A0522W11NC1 11week
A0522W11NC2 0.0031773712 normal A0522W11NC2 11week
A0522W11NC3 0.0060378288 normal A0522W11NC3 11week
A0522W11NC4 0.0017626931 normal A0522W11NC4 11week
A0522W11NC5 0.0018035261 normal A0522W11NC5 11week
A0522W11NC6 0.0036690067 normal A0522W11NC6 11week

> tmp <- aov(value ~ group, tarD)
最小顯著差數檢驗法(LSD法)

> res <- LSD.test(tmp, 'group', p.adj = 'bonferroni')
> print(res$groups)
       trt        means M
1   normal 2.576910e-03 a
2    drug3 7.552555e-04 b
3    drug2 7.269247e-05 b
4 high_fat 6.220610e-05 b
5    drug1 2.954733e-05 b
Tukey氏固定差距檢驗法(Tukey HSD)
> TukeyHSD(tmp)
  Tukey multiple comparisons of means
    95% family-wise confidence level

Fit: aov(formula = value ~ group, data = tarD)

$group
                         diff           lwr          upr     p adj
drug2-drug1      4.314514e-05 -0.0015468705 0.0016331608 0.9999916
drug3-drug1      7.257082e-04 -0.0008643074 0.0023157239 0.6929965
high_fat-drug1   3.265877e-05 -0.0015149488 0.0015802664 0.9999969
normal-drug1     2.547362e-03  0.0009997549 0.0040949700 0.0002613
drug3-drug2      6.825631e-04 -0.0009487586 0.0023138847 0.7563196
high_fat-drug2  -1.048637e-05 -0.0016005020 0.0015795293 1.0000000
normal-drug2     2.504217e-03  0.0009142017 0.0040942330 0.0004945
high_fat-drug3  -6.930494e-04 -0.0022830651 0.0008969662 0.7277757
normal-drug3     1.821654e-03  0.0002316386 0.0034116699 0.0175538
normal-high_fat  2.514704e-03  0.0009670961 0.0040623113 0.0003161
> TukeyHSD(tmp)$group
                         diff           lwr          upr        p adj
drug2-drug1      4.314514e-05 -0.0015468705 0.0016331608 0.9999915820
drug3-drug1      7.257082e-04 -0.0008643074 0.0023157239 0.6929965170
high_fat-drug1   3.265877e-05 -0.0015149488 0.0015802664 0.9999969171
normal-drug1     2.547362e-03  0.0009997549 0.0040949700 0.0002612744
drug3-drug2      6.825631e-04 -0.0009487586 0.0023138847 0.7563195891
high_fat-drug2  -1.048637e-05 -0.0016005020 0.0015795293 0.9999999705
normal-drug2     2.504217e-03  0.0009142017 0.0040942330 0.0004944674
high_fat-drug3  -6.930494e-04 -0.0022830651 0.0008969662 0.7277757202
normal-drug3     1.821654e-03  0.0002316386 0.0034116699 0.0175537862
normal-high_fat  2.514704e-03  0.0009670961 0.0040623113 0.0003161003