R help - May 2002 - More on ties with rank()

I am grateful to Prof. Ripley for his explanation. Indeed, rounding explains
it all.

I take the difference between two vectors and call it "z"

method.a <- c(6.3, 6.3, 3.5, 5.1, 5.5, 7.7, 6.3, 2.8, 3.4, 5.7, 5.6, 6.2,
6.6,
                       7.7, 7.4, 5.6, 6.3, 8.4, 5.6, 4.8, 4.3, 4.2, 3.3,
3.8, 5.7, 4.1)

method.b <- c(5.2, 6.6, 2.3, 4.4, 4.1, 6.4, 5.4, 2.3, 3.2, 5.2, 4.9, 6.1,
6.3,
                       7.4, 7.4, 4.9, 5.4, 8.4, 5.1, 4.4, 4.3, 4.1, 2.2,
4.0, 5.8, 4.0)

z <- sort(abs(method.a - method.b))

If I do as suggested, and apply dput(z), the rounding error shows its ugly
head.
> dput(z)
c(0.0999999999999996, 0.0999999999999996, 0.100000000000001,
0.100000000000001, 0.200000000000000, 0.2, 0.3, 0.3, 0.3, 0.399999999999999,
0.5, 0.5, 0.5, 0.699999999999999, 0.699999999999999, 0.699999999999999,
0.9, 0.9, 1.1, 1.1, 1.2, 1.3, 1.4)
>
Now, if I define a new variable rounding off the errors, I get the correct
response.
> k <- round(dput(z),1)
c(0.0999999999999996, 0.0999999999999996, 0.100000000000001,
0.100000000000001, 0.200000000000000, 0.2, 0.3, 0.3, 0.3, 0.399999999999999,
0.5, 0.5, 0.5, 0.699999999999999, 0.699999999999999, 0.699999999999999,
0.9, 0.9, 1.1, 1.1, 1.2, 1.3, 1.4)
> rank(k)
 [1]  2.5  2.5  2.5  2.5  5.5  5.5  8.0  8.0  8.0 10.0 12.0 12.0 12.0 15.0
15.0
[16] 15.0 17.5 17.5 19.5 19.5 21.0 22.0 23.0
>
But it strikes me as odd, that such an innocent calculation could lead to
such a significant miscalculation based on rounding error.

Thanks,
ANDREW



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On Tue, 7 May 2002, arcriswell wrote:
> I am grateful to Prof. Ripley for his explanation. Indeed, rounding
explains
> it all.
>
> I take the difference between two vectors and call it "z"
>
> method.a <- c(6.3, 6.3, 3.5, 5.1, 5.5, 7.7, 6.3, 2.8, 3.4, 5.7, 5.6,
6.2,
> 6.6,
>                        7.7, 7.4, 5.6, 6.3, 8.4, 5.6, 4.8, 4.3, 4.2, 3.3,
> 3.8, 5.7, 4.1)
>
> method.b <- c(5.2, 6.6, 2.3, 4.4, 4.1, 6.4, 5.4, 2.3, 3.2, 5.2, 4.9,
6.1,
> 6.3,
>                        7.4, 7.4, 4.9, 5.4, 8.4, 5.1, 4.4, 4.3, 4.1, 2.2,
> 4.0, 5.8, 4.0)
>
> z <- sort(abs(method.a - method.b))
>
<snip>
>
> But it strikes me as odd, that such an innocent calculation could lead to
> such a significant miscalculation based on rounding error.
>
Not odd at all. Any result that depends on floating point equality is
going to be sensitive.

Floating point numbers are reliably equal only when the same result is
computed by the same arithmetical steps (and sometimes not even then).

If you know your data are really discrete then you should round them
before ranking, if they aren't really discrete you shouldn't expect tied
values to behave consistently

	-thomas

Thomas Lumley			Asst. Professor, Biostatistics
tlumley at u.washington.edu	University of Washington, Seattle

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