R help - Nov 2011 - understanding all.equal() output: "Mean relative difference"

Dear all
How should one parse all.equal() output? I'm specifically referring to
the 'mean relative difference' messages. For
example,
> all.equal(pi, 355/113)
[1] "Mean relative difference: 8.491368e-08"

But I'm not sure how to understand these messages. When they're close
to 0 (or 1xe-16), then it's intuitive. But when they're
big,
> all.equal(1, 4)
[1] "Mean relative difference: 3"
> all.equal(2, 4)
[1] "Mean relative difference: 1"
> all.equal(3, 4)
[1] "Mean relative difference: 0.3333333"

the messages start making much less sense. I tried Wikipedia [1], but
the description is cryptic, as is the help page. Also, Fox and
Weisberg (2011) don't explain this particular message.

Regards
Liviu

[1] http://en.wikipedia.org/wiki/Mean_difference#Relative_mean_difference


-- 
Do you know how to read?
http://www.alienetworks.com/srtest.cfm
http://goodies.xfce.org/projects/applications/xfce4-dict#speed-reader
Do you know how to write?
http://garbl.home.comcast.net/~garbl/stylemanual/e.htm#e-mail

On 11-11-24 7:44 AM, Liviu Andronic wrote:
> Dear all
> How should one parse all.equal() output? I'm specifically referring to
> the 'mean relative difference' messages. For example,
>> all.equal(pi, 355/113)
> [1] "Mean relative difference: 8.491368e-08"
>
> But I'm not sure how to understand these messages. When they're
close
> to 0 (or 1xe-16), then it's intuitive. But when they're big,
>> all.equal(1, 4)
> [1] "Mean relative difference: 3"
>> all.equal(2, 4)
> [1] "Mean relative difference: 1"
>> all.equal(3, 4)
> [1] "Mean relative difference: 0.3333333"
In the first case, the difference is 3, and 3/1 = 3.

In the second case, the difference is 2, and 2/2 = 1.

In the third case, the difference is 1, and 1/3 = 0.3333333.

It's the difference relative to the first number.

It says "mean" because the two arguments could both be vectors, in
which
case it would calculate a vector of differences first.  You'll have to 
look at all.equal.numeric to see the exact way those are combined, but 
its something like mean(abs(x-y))/mean(abs(x))

Duncan Murdoch
>
> the messages start making much less sense. I tried Wikipedia [1], but
> the description is cryptic, as is the help page. Also, Fox and
> Weisberg (2011) don't explain this particular message.
>
> Regards
> Liviu
>
> [1] http://en.wikipedia.org/wiki/Mean_difference#Relative_mean_difference
>
>

The help page says that large differences are returned as relative difference. A
look at the code shows that all.equal.numeric, the version used for a numeric
first argument, uses the 'target', that is, the first parametter, as the
scaling factor. Thus

c(1,4) has a difference of 3, scaled by 1, giving 3
c(2,4) has a difference of 2, scaled by 2, giving 1

... and so on.

The other potentially useful part of the help page is the bit right at the
beginning than says
"Don't use 'all.equal' directly in 'if'
expressions-either use 'isTRUE(all.equal(....))' or 'identical'
if
appropriate."

which usually avoids the need to parse the result at all. 


> -----Original Message-----
> From: r-help-bounces at r-project.org 
> [mailto:r-help-bounces at r-project.org] On Behalf Of Liviu Andronic
> Sent: 24 November 2011 12:45
> To: r-help at r-project.org Help
> Subject: [R] understanding all.equal() output: "Mean relative 
> difference"
> 
> Dear all
> How should one parse all.equal() output? I'm specifically 
> referring to the 'mean relative difference' messages. For example,
> > all.equal(pi, 355/113)
> [1] "Mean relative difference: 8.491368e-08"
> 
> But I'm not sure how to understand these messages. When 
> they're close to 0 (or 1xe-16), then it's intuitive. But when 
> they're big,
> > all.equal(1, 4)
> [1] "Mean relative difference: 3"
> > all.equal(2, 4)
> [1] "Mean relative difference: 1"
> > all.equal(3, 4)
> [1] "Mean relative difference: 0.3333333"
> 
> the messages start making much less sense. I tried Wikipedia 
> [1], but the description is cryptic, as is the help page. 
> Also, Fox and Weisberg (2011) don't explain this particular message.
> 
> Regards
> Liviu
> 
> [1] 
> http://en.wikipedia.org/wiki/Mean_difference#Relative_mean_difference
> 
> 
> --
> Do you know how to read?
> http://www.alienetworks.com/srtest.cfm
> http://goodies.xfce.org/projects/applications/xfce4-dict#speed-reader
> Do you know how to write?
> http://garbl.home.comcast.net/~garbl/stylemanual/e.htm#e-mail
> 
> ______________________________________________
> R-help at r-project.org mailing list
> https://stat.ethz.ch/mailman/listinfo/r-help
> PLEASE do read the posting guide 
> http://www.R-project.org/posting-guide.html
> and provide commented, minimal, self-contained, reproducible code.
> *******************************************************************
This email and any attachments are confidential. Any use...{{dropped:8}}