[R] The equivalence of t.test and the hypothesis testing of one way ANOVA

[Peng Yu]

Has the materials in this paper been integrated to any book?

On Fri, Nov 6, 2009 at 8:48 AM, <JLucke at ria.buffalo.edu> wrote:
>
> There extensions to aov for without assuming equal variances.
>
> Reed, James F., I. & Stark, D. B. (1988), 'Robust alternatives to traditional analyses of variance: Welch $W^*$, James $J_I^*$, James $J_II^*$, and Brown-Forsythe $BF^*$', Computer Methods and Programs in Biomedicine 26, 233--238.
>
>
> I don't   know whether they are implemented in R.
>
>
>
> Peng Yu <pengyu.ut at gmail.com>
> Sent by: r-help-bounces at r-project.org
>
> 11/06/2009 07:59 AM
>
> To
> r-help at stat.math.ethz.ch
> cc
> Subject
> Re: [R] The equivalence of t.test and the hypothesis testing of one        way ANOVA
>
>
>
>
> Is it possible to use aov() to compute the same p-value that is
> generated by t.test() with var.equal=F. An assumption of ANOVA is
> equal variance, I'm wondering how to relax such assumption to allow
> non equal variance?
>
> On Thu, Nov 5, 2009 at 8:31 AM, Benilton Carvalho <bcarvalh at jhsph.edu> wrote:
> > compare
> >
> > t.test(x, y, var.equal=T)
> >
> > with
> >
> > summary(afit)
> >
> > b
> >
> > On Nov 5, 2009, at 12:21 PM, Peng Yu wrote:
> >
> >> I read somewhere that t.test is equivalent to a hypothesis testing for
> >> one way ANOVA. But I'm wondering how they are equivalent. In the
> >> following code, the p-value by t.test() is not the same from the value
> >> in the last command. Could somebody let me know where I am wrong?
> >>
> >>> set.seed(0)
> >>> N1=10
> >>> N2=10
> >>> x=rnorm(N1)
> >>> y=rnorm(N2)
> >>> t.test(x,y)
> >>
> >>       Welch Two Sample t-test
> >>
> >> data:  x and y
> >> t = 1.6491, df = 14.188, p-value = 0.1211
> >> alternative hypothesis: true difference in means is not equal to 0
> >> 95 percent confidence interval:
> >> -0.2156863  1.6584968
> >> sample estimates:
> >> mean of x  mean of y
> >> 0.3589240 -0.3624813
> >>
> >>>
> >>> A = c(rep('x',N1),rep('y',N2))
> >>> Y = c(x,y)
> >>> fr = data.frame(Y=Y,A=as.factor(A))
> >>> afit=aov(Y ~ A,fr)
> >>>
> >>> X=model.matrix(afit)
> >>> B=afit$coefficients
> >>> V=solve(t(X) %*% X)
> >>>
> >>> mse=tail(summary(afit)[[1]]$'Mean Sq',1)
> >>> df=tail(summary(afit)[[1]]$'Df',1)
> >>> t_statisitic=(B/(mse * sqrt(diag(V))))[[2]]
> >>> 2*(1-pt(abs(t_statisitic),df))#the p-value from aov
> >>
> >> [1] 0.1090802
> >>>
> >>
> >> ______________________________________________
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> >
> >
>
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> and provide commented, minimal, self-contained, reproducible code.
>