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## Re: Study about accuracy of statistical software, incl. Octave

 From: Marco Caliari Subject: Re: Study about accuracy of statistical software, incl. Octave Date: Wed, 25 Mar 2009 16:57:42 +0100 (CET) User-agent: Alpine 1.00 (DEB 882 2007-12-20)

```Dear all,

please do not consider the results in the paper reliable. Here is my test
with R 2.5.1

```
```v <- 10000000.2
x <- c(10000000.1,10000000.3)
v <- c(v,rep(x, times = 500))
sqrt(var(v))
```
``` 0.1
```
```options(digits=16)
sqrt(var(v))
```
``` 0.1000000005587935

Octave gives 1.00000000558841e-01, same number of correct digits.
Nevertheless, I think there is space for improving accuracy
of mean, std, var, ...

Best regards,

Marco

On Tue, 24 Mar 2009, John W. Eaton wrote:

```
```On 24-Mar-2009, Marco Caliari wrote:

| > What do you mean by "exact mean" here? I don't think any of the three
| > numbers are exactly representable in IEEE floating-point. It would be
| > better to choose numbers that have an exact representation, such as
| > 1e7 + 0.25, 1e7 + 0.5, 1.7 + 0.75 or such. Otherwise, you can't avoid
| > introducing errors just by writing these numbers.
|
| I agree with you, Jaroslav. On the other hand, in the paper it is
| written that R can compute the standard deviation with 15 correct digits.
| Actually, Octave can compute the mean with 14 correct digits and with 15
| correct digits with the patch I sent. The standard deviation with 8
| correct digits.

Since R is free software, we should be able to do just as well.  Have
you looked at precisely what it does?

jwe

```
```
```