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From |
"Nick Cox" <n.j.cox@durham.ac.uk> |

To |
<statalist@hsphsun2.harvard.edu> |

Subject |
st: RE: chitesti -- warning -- expected |

Date |
Wed, 10 Mar 2004 23:02:02 -0000 |

Good question. -chitesti- and its sibling -chitest- are in a package -tab_chi- on SSC. The latest public versions of -chitesti- and -chitest- are 2.0.0, both from July 2003. The immediate command -chitesti- in fact calls -chitest- (with a secret handshake indicating keyboard input). What happens internally is that the observed and expected frequencies are put in -float- variables. This is not adequate for your problem to hold all the digits you want to hold. I make the expected frequencies 406694.3598 and 29766.6402 which add to 436441 exactly by virtue of 0.9318 + 0.0682 equalling 1. However, putting them in a -float- and then getting the total yields 436461.015625. Of course everything is done in binary and we are just seeing the decimal representation here. Here is that difference in hexadecimal: . di %21x 436461.015625 +1.aa3b410000000X+012 . di %21x 436461 +1.aa3b400000000X+012 So near, and yet so far! Now -chitest- squawks if the sum of observed and the sum of expected differ by more than 0.01 and the difference here of 0.015625 qualifies. The absolute difference criterion of 0.01 was just plucked out of the air when -chitest- was first written several years ago. For numbers as big as yours a relative difference criterion would presumably make more sense. Why then is -chitest- telling you both that numbers are the same and that they are different? "Same" comes from the display statement, here equivalent to . di %8.0g 436461.015625 436461 That format in turn was based on getting integers to show as such as far as at all possible, without irritating extra ".00000" or whatever. The format here loses the small details, however. "Different" comes from the numbers held in memory, which differ by 0.015625. I just rewrote -chitest- and -chitesti- to use doubles throughout. The results are better: . chitesti 314795 121666 \ 0.9318*436461 0.0682*436461 observed frequencies from keyboard; expected frequencies from keyboard Pearson chi2(1) = 3.0e+05 Pr = 0.000 likelihood-ratio chi2(1) = 1.8e+05 Pr = 0.000 +-----------------------------------------------+ | observed expected obs - exp Pearson | |-----------------------------------------------| | 314795 406694.360 -91899.360 -144.105 | | 121666 29766.640 91899.360 532.657 | +-----------------------------------------------+ In short, this is a salutary lesson in precision. The program author should perhaps read e.g. http://www.stata.com/support/faqs/data/mod.html The defence, if there is one, is that the author grew up in a small house in a small country and still thinks that using -double- where -float- apparently will do fine is profligate use of space. Incidentally, the chi-square test shows a P-value indistinguishable from 0. Nick n.j.cox@durham.ac.uk > -----Original Message----- > From: owner-statalist@hsphsun2.harvard.edu > [mailto:owner-statalist@hsphsun2.harvard.edu]On Behalf Of > Benoit Dulong > Sent: 10 March 2004 21:53 > To: statalist > Subject: st: chitesti -- warning -- expected > > > The command > chitesti 314795 121666 \ 0.9318*436461 0.0682*436461 > produced > > Chi-square test: > observed frequencies from keyboard > expected frequencies from keyboard > > Warning: totals of observed and expected differ > total > observed 436461 > expected 436461 > > Pearson chi2(1) = 304489.6035 Pr = 0.000 > likelihood-ratio chi2(1) = 181321.5938 Pr = 0.000 > > residuals > observed expected classic Pearson > 1. 314795 406694.375 -91899.375 -144.105 > 2. 121666 29766.641 91899.359 532.657 > > ------------------------------------------------------ > > QUESTION-1. > I do not understand the warning because > observed and expected do NOT differ ? > > QUESTION-2 > Expected (1) should be 436461*0.9318 = 406694.3598, > not 406694.375 ? * * For searches and help try: * http://www.stata.com/support/faqs/res/findit.html * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

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