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

[Benilton Carvalho]

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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