如果不存在交互，什么（有理由）是双向 ANOVA 主效应的有效事后？
示例双向固定效应方差分析：
> aov.example <- aov(Response ~ IV1 * IV2, data=data)
> summary(aov.example)
Df Sum Sq Mean Sq F value Pr(>F)
IV1 1 13.10 13.099 0.7222 0.40547
IV2 4 315.56 78.891 4.3498 0.01081 *
IV1:IV2 4 141.00 35.251 1.9436 0.14240
Residuals 20 362.74 18.137
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
我看到了一些一般选项，但我不确定哪个最合适：
使用双向模型进行多重比较测试的事后
> TukeyHSD(aov.example, which="IV2") Tukey multiple comparisons of means 95% family-wise confidence level Fit: aov(formula = Response ~ IV1 * IV2, data = data) $IV2 diff lwr upr p adj B-A -2.1485711 -9.506162 5.2090200 0.9031415 C-A -2.3382727 -9.695864 5.0193184 0.8733517 D-A 1.4732257 -5.884365 8.8308168 0.9735981 E-A -8.0515205 -15.409112 -0.6939294 0.0277241 C-B -0.1897016 -7.547293 7.1678895 0.9999912 D-B 3.6217968 -3.735794 10.9793879 0.5905067 E-B -5.9029494 -13.260541 1.4546416 0.1559460 D-C 3.8114984 -3.546093 11.1690895 0.5439632 E-C -5.7132478 -13.070839 1.6443432 0.1785266 E-D -9.5247462 -16.882337 -2.1671552 0.0074740使用单向模型进行多重比较测试的事后
> TukeyHSD(aov(Response ~ IV2, data=data)) Tukey multiple comparisons of means 95% family-wise confidence level Fit: aov(formula = Response ~ IV2, data = data) $IV2 diff lwr upr p adj B-A -2.1485711 -9.858179 5.5610365 0.9224401 C-A -2.3382727 -10.047880 5.3713349 0.8976378 D-A 1.4732257 -6.236382 9.1828333 0.9794638 E-A -8.0515205 -15.761128 -0.3419130 0.0375667 C-B -0.1897016 -7.899309 7.5199060 0.9999933 D-B 3.6217968 -4.087811 11.3314044 0.6456949 E-B -5.9029494 -13.612557 1.8066581 0.1951992 D-C 3.8114984 -3.898109 11.5211060 0.6014671 E-C -5.7132478 -13.422855 1.9963597 0.2212053 E-D -9.5247462 -17.234354 -1.8151387 0.0102178总体而言，在此示例中，显着比较没有变化，但使用双向 ANOVA 模型调整后的 p 值较低。哪个最适合事后的双向主效应？
具有其他自变量的子集级别的事后
鉴于对其他自变量没有任何影响，我很确定这是无效的。然而，当 IV1 的一个水平与其他 IV1 水平相比，IV2 水平之间的影响更大时，这不会严重扭曲整体分析吗？换句话说，即使总体上有一个主效应，这种效应在IV1的其他水平上会不会不显着？
> aov.level1 <- aov(Response ~ IV2, data=data[1:15,])
> summary(aov.level1)
Df Sum Sq Mean Sq F value Pr(>F)
IV2 4 334.55 83.639 3.8413 0.03837 *
Residuals 10 217.74 21.774
> aov.level2 <- aov(Response ~ IV2, data=data[16:30,])
> summary(aov.level2)
Df Sum Sq Mean Sq F value Pr(>F)
IV2 4 122.01 30.503 2.1037 0.1551
Residuals 10 145.00 14.500
IV1 的水平 1 具有显着的 IV2 主效应，但水平 2 没有。显着的多重比较也存在差异。我担心的是我使用前两种方法犯了 I 类错误。
> TukeyHSD(aov.level1)
Tukey multiple comparisons of means
95% family-wise confidence level
Fit: aov(formula = Response ~ IV2, data = data[1:15, ])
$IV2
diff lwr upr p adj
B-A -7.86237771 -20.401217 4.67646157 0.3054028
C-A -7.90634218 -20.445181 4.63249709 0.3008150
D-A -0.94962690 -13.488466 11.58921237 0.9989922
E-A -12.55848654 -25.097326 -0.01964727 0.0496014
C-B -0.04396448 -12.582804 12.49487479 1.0000000
D-B 6.91275080 -5.626088 19.45159008 0.4167559
E-B -4.69610883 -17.234948 7.84273044 0.7342625
D-C 6.95671528 -5.582124 19.49555455 0.4111062
E-C -4.65214436 -17.190984 7.88669492 0.7404793
E-D -11.60885964 -24.147699 0.92997964 0.0729541
> TukeyHSD(aov.level2)
Tukey multiple comparisons of means
95% family-wise confidence level
Fit: aov(formula = Response ~ IV2, data = data[16:30, ])
$IV2
diff lwr upr p adj
B-A 3.5652355 -6.667185 13.797656 0.7795224
C-A 3.2297968 -7.002624 13.462218 0.8321507
D-A 3.8960783 -6.336343 14.128499 0.7231230
E-A -3.5445545 -13.776975 6.687866 0.7829174
C-B -0.3354387 -10.567860 9.896982 0.9999634
D-B 0.3308428 -9.901578 10.563264 0.9999654
E-B -7.1097900 -17.342211 3.122631 0.2257310
D-C 0.6662815 -9.566139 10.898702 0.9994435
E-C -6.7743513 -17.006772 3.458070 0.2618999
E-D -7.4406328 -17.673054 2.791788 0.1942037