# R-alpha: confidence interval of t.test

Friedrich Leisch Friedrich.Leisch@ci.tuwien.ac.at
Thu, 3 Jul 1997 18:42:55 +0200

```Sorry if this has been discussed here before, but anyway:

The are differences between the confidence intervals of the t.test as
done by R and Splus:

*** R

R> x<-rnorm(1000)+1
R> t.text(x)
Error: couldn't find function "t.text"
R> t.test(x)

One Sample t-test

data:  x
t = 31.4062, df = 999, p-value = 0
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
0.917027 1.039261
sample estimates:
mean of x
0.978144

R> t.test(x, mu=1)

One Sample t-test

data:  x
t = -0.7017, df = 999, p-value = 0.483
alternative hypothesis: true mean is not equal to 1
95 percent confidence interval:
-0.08297297  0.03926111                      <<<<<<<<<<<<<<<<<<<<<<<<<<<<<
sample estimates:
mean of x
0.978144

*** Splus

> x<-rnorm(1000)+1
> t.test(x)

One-sample t-Test

data:  x
t = 28.6918, df = 999, p-value = 0
alternative hypothesis: true mean is not equal to 0
95 percent confidence interval:
0.8975418 1.0293277
sample estimates:
mean of x
0.9634347

> t.test(x, mu=1)

One-sample t-Test

data:  x
t = -1.0889, df = 999, p-value = 0.2764
alternative hypothesis: true mean is not equal to 1
95 percent confidence interval:
0.8975418 1.0293277                    <<<<<<<<<<<<<<<<<<<<<<<<<<<<<
sample estimates:
mean of x
0.9634347

*******************

As you can See R's confidence intervals are centered around the
deviation from the null, whereas those of Splus are centered around
the observed value ... the later seems the more intuitive thing to me.

So is this a bug or feature of R (in my eyes it's a bug)?

Best,
Fritz
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```