# [R] Two sample t.test, order of comparions

Helmut Schütz helmut.schuetz at bebac.at
Wed Apr 18 16:17:40 CEST 2007

```Dear Charilaos!

>>
>> Do you know a more elegant way than the clumsy one I have tried?
>>
>>> as.numeric(exp(result\$estimate-result\$estimate))
>>> as.numeric(exp(-result\$conf.int))
>>> as.numeric(exp(-result\$conf.int))
>
> First off, those three could probably be simplified slightly as:
> as.numeric(exp(-diff(result\$estimate)))
> as.numeric(exp(-result\$conf.int))
>
> The simplest solution I think is to specify that resp\$treatment should
> have the levels ordered in the way you like them using this first:
>
> resp\$treatment <- ordered(resp\$treatment,
> levels=rev(levels(resp\$treatment)))
>
> Then the t.test will show things in the order you want them.
I applied relevel() as suggested by Douglas and Dimitri:

> relevel(resp\$treatment, ref = "Reference")
> result <- t.test(logAUC ~ treatment, data = resp, subset = (period ==
1), var.equal = FALSE, conf.level = 0.90)
> result

yielding

Welch Two Sample t-test

data:  logAUC by treatment
t = 1.1123, df = 21.431, p-value = 0.2783
alternative hypothesis: true difference in means is not equal to 0
90 percent confidence interval:
-0.0973465  0.4542311
sample estimates:
mean in group Reference      mean in group Test
3.562273                3.383831

So right now the confidence interval in the log-domain is of the correct
order.

Your first suggestion is working (sign changed due to reversed level)

> as.numeric(exp(diff(result\$estimate)))
>  0.8365723

But still I have to apply

> as.numeric(exp(-result\$conf.int))
 0.634936
> as.numeric(exp(-result\$conf.int))
 1.102242

because
> as.numeric(exp(-result\$conf.int))
 1.102242 0.634936

in order to get the correct CI in the untransformed domain I had to sort
the list:
> sort(as.numeric(exp(-result\$conf.int)))
 0.634936 1.102242

Best regards,
Helmut

--
Ing. Helmut Schütz
BEBAC - Consultancy Services for
Bioequivalence and Bioavailability Studies
Neubaugasse 36/11
1070 Vienna, Austria
tel/fax +43 1 2311746
e-mail  helmut.schuetz at bebac.at
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```