我的数据如下所示：
Location=c("lcn","lcn","lcn","etb","lcs","bbs","lcn","lcs","bbs","lcn","lcs","bbs","lcs","lcs","lcn",
"bbs","etb","bbs","etb","etb","lcs","lcn","lcn","bbs","bbs","etb","bbs","etb","bbs","bbs",
"lcs","lcs","lcs","lcs","lcs","lcn","lcs","etb","lcn","lcn","etb","etb","etb","etb","lcn",
"bbs","bbs","lcs","etb","lcs","bbs","bbs","lcs","bbs","lcs","lcn","lcn","lcn","etb","lcn",
"lcs","bbs","etb","etb","etb","bbs","etb","bbs","etb","etb","bbs","lcs")
Treatment=c(rep("control",each=21),rep("foam",each=20),rep("hail",each=17),rep("teda",each=14))
Growth=c( 0.24, -0.05, 0.19, 1.02, 0.84, 0.11, 0.13, 0.08, -0.18, -0.06,
0.38, 1.04, 0.55, -1.71, 0.24, 0.05, 0.49, -0.41, 0.70, 0.30,
1.03, 0.14, 0.73, 0.56, 0.56, 0.98, 0.53, 0.27, 0.32, 0.95,
0.10, 0.55, 1.18, 0.49, 0.58, 0.36, 0.18, 0.30, 1.71, 0.65,
0.69, 0.68, 0.66, 1.24, 0.47 , 1.28, 0.60, 1.01, 0.76, 1.35,
1.02, 0.75, 0.40, 0.37, 0.46, 0.47, 0.25, 0.61, 0.63, 0.86,
0.92, 0.09, 1.66, 0.88, 0.68, 1.02, 1.17, 1.18, 1.71, 1.01,
0.42, 0.56)
Mang=data.frame(Location,Treatment,Growth)
我想使用双向Anova来了解更改Location和Treatment对Growth的影响。我想问两个问题：
（1）如果某些级别的预测变量无法通过正态性测试（如下所示），我还可以使用Anova吗？
> shapiro.test(subset(Mang,Location=="lcn")[,3])$p.value
[1] 0.01317841
> shapiro.test(subset(Mang,Treatment=="control")[,3])$p.value
[1] 0.008312405
（2）为什么在Anova中改变预测变量的顺序时结果会有所不同？
> test1=aov(Growth~Location+Treatment,data=Mang)
> summary(test1)
Df Sum Sq Mean Sq F value Pr(>F)
Location 3 1.713 0.5710 2.708 0.05235 .
Treatment 3 3.495 1.1650 5.524 0.00193 **
Residuals 65 13.707 0.2109
---
Signif. codes: 0 ?**?0.001 ?*?0.01 ??0.05 ??0.1 ??1
> test2=aov(Growth~Treatment+Location,data=Mang)
> summary(test2)
Df Sum Sq Mean Sq F value Pr(>F)
Treatment 3 4.402 1.4673 6.958 0.000393 ***
Location 3 0.806 0.2687 1.274 0.290658
Residuals 65 13.707 0.2109
---
Signif. codes: 0 ?**?0.001 ?*?0.01 ??0.05 ??0.1 ??1