# [Rd] Numerical stability in chisq.test

peter dalgaard pdalgd at gmail.com
Thu Dec 28 14:13:10 CET 2017

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> On 28 Dec 2017, at 13:08 , Kurt Hornik <Kurt.Hornik at wu.ac.at> wrote:
>
>>>>>> Jan Motl writes:
>
>> The chisq.test on line 57 contains following code:
>> 	STATISTIC <- sum(sort((x - E)^2/E, decreasing = TRUE))
>
> The preceding 2 lines seem relevant:
>
>            ## Sorting before summing may look strange, but seems to be
>            ## a sensible way to deal with rounding issues (PR#3486):
>            STATISTIC <- sum(sort((x - E) ^ 2 / E, decreasing = TRUE))
>
> -k

My thoughts too. PR 3486 is about simulated tables that theoretically have STATISTIC equal to the one observed, but come out slightly different, messing up the simulated p value. The sort is not actually intended to squeeze the very last bit of accuracy out of the computation, just to make sure that the round-off affects equivalent tables in the same way. "Fixing" the code may therefore unfix PR#3486; at the very least some care is required if this is modified.

-pd

>
>> However, based on book "Accuracy and stability of numerical algorithms" available from:
>> 	http://ftp.demec.ufpr.br/CFD/bibliografia/Higham_2002_Accuracy%20and%20Stability%20of%20Numerical%20Algorithms.pdf
>> Table 4.1 on page 89, it is better to sort the data in increasing order than in decreasing order, when the data are non-negative.
>
>> An example:
>> 	x = matrix(c(rep(1.1, 10000)), 10^16, nrow = 10001, ncol = 1)    # We have a vector with 10000*1.1 and 1*10^16
>> 	c(sum(sort(x, decreasing = TRUE)), sum(sort(x, decreasing = FALSE)))
>> The result:
>> 	10000000000010996 10000000000011000
>> When we sort the data in the increasing order, we get the correct result. If we sort the data in the decreasing order, we get a result that is off by 4.
>
>> Shouldn't the sort be in the increasing order rather than in the decreasing order?
>
>> Best regards,
>> Jan Motl
>
>
>> PS: This post is based on discussion on https://stackoverflow.com/questions/47847295/why-does-chisq-test-sort-data-in-descending-order-before-summation and the response from the post to r-help at r-project.org.
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>
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--
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Office: A 4.23
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com

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