TukeyHSD 调整后的 P 值为 0.0000000 [英] TukeyHSD adjusted P value is 0.0000000

问题描述

我刚刚执行了阶乘方差分析，然后是 TukeyHSD 后测试.我从 TukeyHSD 输出中调整的一些 P 值是 0.0000000.这些 P 值真的可以为零吗?或者这是四舍五入的情况，我的真实 P 值可能类似于 1e-17，四舍五入为 0.0000000.

I just performed a factorial ANOVA, followed by the TukeyHSD post-test. Some of my adjusted P values from the TukeyHSD output are 0.0000000. Can these P values really be zero? Or is this a rounding situation, and my true P value might be something like 1e-17, that is rounded to 0.0000000.

R 中的 TukeyHSD() 函数是否有任何选项可以提供包含指数的输出 P 值?

Are there any options for the TukeyHSD() function in R that will give output P-values that contain exponents?

这是我的输出片段:

TukeyHSD(fit)

  Tukey multiple comparisons of means
    95% family-wise confidence level

Fit: aov(formula = lum ~ cells * treatment)

$`cells:treatment`
                    diff         lwr          upr     p adj
NULL:a-KR:a     -266.5833333 -337.887800 -195.2788663 0.0000000
WT:a-KR:a       -196.3333333 -267.637800 -125.0288663 0.0000000
KR:ar-KR:a        83.4166667   12.112200  154.7211337 0.0053485
NULL:ar-KR:a    -283.5000000 -354.804467 -212.1955330 0.0000000
WT:ar-KR:a      -196.7500000 -268.054467 -125.4455330 0.0000000
KR:e-KR:a       -219.0833333 -290.387800 -147.7788663 0.0000000
NULL:e-KR:a     -185.0833333 -256.387800 -113.7788663 0.0000000
WT:e-KR:a        -96.1666667 -167.471134  -24.8621996 0.0003216

推荐答案

EDIT:请参阅下面关于 Tukey p 值分辨率的警告！！

EDIT: see warning below about resolution of Tukey p-values!!

dd <- data.frame(y=c(1:10,1001:1010),f=rep(c("A","B"),each=10))
fit <- aov(y~f,data=dd)

打印的 p 值为零:

(tt <- TukeyHSD(fit))
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = y ~ f, data = dd)
## 
## $f
##     diff      lwr      upr p adj
## B-A 1000 997.1553 1002.845     0

但是查看 str() 的(缩写)输出显示那里有更多信息:

But looking at the (abbreviated) output of str() shows there's more information there:

str(tt)

## List of 1
##  $ f: num [1, 1:4] 1.00e+03 9.97e+02 1.00e+03 2.62e-14
##   ..- attr(*, "dimnames")=List of 2
## 

您可以自己提取值:

tt$f[,"p adj"]
## [1] 2.620126e-14

或者如评论中所述，print(tt,digits=15) 将起作用......

Or as noted in the comments, print(tt,digits=15) will work ...

警告

我决定深入挖掘，并在挖掘 TukeyHSD.aov() 的代码时注意到它依赖于 ptukey()，在它的示例"部分警告精度可能不超过约 8 位数字".特别是，一旦 t 统计量超过 30 左右，p 值就会在 2.62e-14 ...

I decided to dig a little deeper and noticed in digging through the code of TukeyHSD.aov() that it relies on ptukey(), which in its "Examples" section warns that "the precision may not be more than about 8 digits". In particular, once the t-statistic is above about 30, the p-value maxes out (mins out?) at 2.62e-14 ...

zval <- 10^seq(1,6,length=100)
pval <- ptukey(zval,2,18,lower.
par(las=1,bty="l")
plot(zval,pval,log="xy",type="l")

最重要的是，您根本无法区分这么小的 p 值.您可能需要重新考虑您的策略......

The bottom line is that you can't distinguish among p-values this small at all. You may need to rethink your strategy ...

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