r - TukeyHSD adjusted P value is 0.0000000 -


i performed factorial anova, followed tukeyhsd post-test. of adjusted p values tukeyhsd output 0.0000000. can these p values zero? or rounding situation, , true p value might 1e-17, rounded 0.0000000.

are there options tukeyhsd() function in r give output p-values contain exponents?

here snippet of output:

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

edit: see warning below 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)

the printed p-value zero:

(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

but looking @ (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 ##

you can extract value yourself:

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

or noted in comments, print(tt,digits=15) work ...

warning

i decided dig little deeper , noticed in digging through code of tukeyhsd.aov() relies on ptukey(), in "examples" section warns "the precision may not more 8 digits". in particular, once t-statistic above 30, p-value maxes out (mins out?) @ 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")

enter image description here

the bottom line can't distinguish among p-values small @ all. may need rethink strategy ...


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