> rm(list=ls())
> # set.seed(101)
> rnorm2 <- function(n,mean,sd){ mean+sd*scale(rnorm(n)) }
> ss <- function(x) {
+ sum((x-mean(x))^2)
+ }
>
> n.o <- 30
> n.p <- 30
> o <- rnorm(n.o, 100, 10)
> p <- rnorm(n.p, 105, 10)
> t.test(o,p, var.equal=T)
Two Sample t-test
data: o and p
t = -3.3581, df = 58, p-value = 0.001391
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-14.78163 -3.74076
sample estimates:
mean of x mean of y
97.31987 106.58106
> comb <- list(o = o, p = p)
> op <- stack(comb)
> head(op)
values ind
1 83.05641 o
2 108.25078 o
3 90.81559 o
4 99.74236 o
5 82.61865 o
6 85.64129 o
> colnames(op)[1] <- "values"
> colnames(op)[2] <- "group"
> op$group <- factor(op$group)
> head(op)
values group
1 83.05641 o
2 108.25078 o
3 90.81559 o
4 99.74236 o
5 82.61865 o
6 85.64129 o
> boxplot(op$values~op$group)
>
>
> plot(op$values~op$group)
> boxplot(op$values~op$group, main="values by group",
+ yaxt="n", xlab="value", horizontal=TRUE,
+ col=terrain.colors(2))
> abline(v=mean(op$values), col="red", lwd=3)
> legend("topleft", inset=.05, title="group",
+ c("o","p"), fill=terrain.colors(2), horiz=TRUE)
>
> m.tot <- mean(op$values) > m.o <- mean(o) > m.p <- mean(p) > > min.x <- min(op$values) > max.x <- max(op$values) > br <- seq(floor(min.x), ceiling(max.x), by = 1) >
> hist(o, breaks=br,
+ col=rgb(1,1,1,.5))
> abline(v=m.o, col="red", lwd=3)
> hist(p, add=T, breaks=br,
+ col=rgb(.5,1,1,.5))
> abline(v=m.p, col="blue", lwd=3)
> abline(v=m.tot, col='black', lwd=3)
>
> ss.tot <- ss(op$values)
> df.tot <- length(op$values)-1
> ss.tot/df.tot
[1] 133.9582
> var(op$values)
[1] 133.9582
> ss.tot
[1] 7903.533
>
> ss.o <- ss(o)
> ss.p <- ss(p)
> df.o <- length(o)-1
> df.p <- length(p)-1
>
> m.tot
[1] 101.9505
> m.o
[1] 97.31987
> m.p
[1] 106.5811
> ss.o
[1] 3647.085
> ss.p
[1] 2969.903
>
> ss.bet <- length(o)*(m.tot-m.o)^2+length(p)*(m.tot-m.p)^2
> ss.tot
[1] 7903.533
> ss.bet
[1] 1286.546
> ss.wit <- ss.o+ss.p
> ss.wit
[1] 6616.987
> ss.bet+ss.wit
[1] 7903.533
> ss.tot
[1] 7903.533
>
> df.tot <- length(op$values)-1
> df.bet <- nlevels(op$group) - 1
> df.wit <- (length(o)-1)+(length(p)-1)
> df.tot
[1] 59
> df.bet
[1] 1
> df.wit
[1] 58
>
> ms.tot <- ss.tot / df.tot
> ms.bet <- ss.bet / df.bet
> ms.wit <- ss.wit / df.wit
>
> f.cal <- ms.bet / ms.wit
> f.cal
[1] 11.27699
> p.val <- pf(f.cal, df1=df.bet, df2=df.wit, lower.tail = F)
> p.val
[1] 0.001390984
> summary(aov(op$values~op$group))
Df Sum Sq Mean Sq F value Pr(>F)
op$group 1 1287 1286.5 11.28 0.00139 **
Residuals 58 6617 114.1
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
> t.test(o,p, var.equal = T)
Two Sample t-test
data: o and p
t = -3.3581, df = 58, p-value = 0.001391
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-14.78163 -3.74076
sample estimates:
mean of x mean of y
97.31987 106.58106
>
> diff <- m.o - m.p
> ssp <- (ss.o + ss.p) / (df.o + df.p)
> se <- sqrt(ssp/n.o+ssp/n.p)
> t.cal <- diff/se
> t.cal
[1] -3.358122
> p.t.cal <- pt(abs(t.cal), df=df.o+df.p, lower.tail = F)*2
> p.t.cal
[1] 0.001390984
> t.cal^2
[1] 11.27699
> f.cal
[1] 11.27699
>
> df.bet
[1] 1
> df.wit
[1] 58
> f.cal
[1] 11.27699
>
>