Simple example of 5 groups of 4 replicates.
>set.seed(5)
>tmp <- rnorm(20)
>gp <- as.factor(rep(1:5,each=4))
>summary(glm(tmp ~ -1 + gp, data=data.frame(tmp, gp)))$coefficients
>Estimate Std. Error t value Pr(>|t|)gp1 -0.1604613084 0.4899868
>-0.3274809061 0.7478301gp2 0.0002487984 0.4899868 0.0005077655 0.9996016gp3
> 0.0695463698 0.4899868 0.1419352018 0.8890200gp4 -0.6121682841 0.4899868
>-1.2493567852 0.2306791gp5 -0.6999545014 0.4899868 -1.4285171713 0.1736348
>m <- data.frame(tmp, gp)
>sapply(gp, function(x) sd(m[m[,"gp"]==x,1])) [1] 1.169284 1.169284 1.169284
>1.169284 1.142974 1.142974 1.142974 1.142974 [9] 0.862423 0.862423 0.862423
>0.862423 0.535740 0.535740 0.535740 0.535740[17] 1.047538 1.047538 1.047538
>1.047538
Why doesn't the standard deviation of each group correlates with the Pr e.g.,
gp = 4 has the smallest sd of 0.535740, but its Pr is not the lowest (i.e.,
only 0.23 vs 0.1736 of gp = 5).
Another example with new tmp1
>tmp1
[1] 9.577969 9.310792 9.666767 9.610164 10.181692 10.155899 10.025943 [8]
9.971243 10.177766 9.265793 9.415818 10.099874 10.238829 9.575591[15]
9.560879 9.617891 9.617891 10.158160 10.592377 10.068443
>summary(glm(tmp1 ~ -1 + age, data=data.frame(as.vector(as.matrix(tmp1)),
>age)))$coefficients Estimate Std. Error t value Pr(>|t|)age1
>9.541423 0.1611603 59.20456 3.380085e-19age2 10.083694 0.1611603 62.56935
>1.479781e-19age3 9.739813 0.1611603 60.43557 2.485380e-19age4 9.748297
>0.1611603 60.48821 2.453251e-19age5 10.109218 0.1611603 62.72773 1.424913e-19
m1 <- data.frame(tmp1, gp)
>sapply(age, function(x) sd(m1[m1[,"age"]==x,1])) [1] 0.1580745 0.1580745
>0.1580745 0.1580745 0.1013207 0.1013207 0.1013207 [8] 0.1013207 0.4658736
>0.4658736 0.4658736 0.4658736 0.3279128 0.3279128[15] 0.3279128 0.3279128
>0.3995426 0.3995426 0.3995426 0.3995426
Can I conclude from the Pr of summary that tmp1 are of better "quality" than
tmp, given that its Pr. values are signficantly smaller ?
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