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Re: st: Csgof does not count var categories with zero observations


From   Nick Cox <njcoxstata@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Csgof does not count var categories with zero observations
Date   Thu, 7 Jun 2012 09:57:09 +0100

Examples

. chitesti 315 108 101 32 \ 556*9/16 556*3/16 556*3/16 556*1/16

observed frequencies from keyboard; expected frequencies from keyboard

         Pearson chi2(3) =   0.4700   Pr =  0.925
likelihood-ratio chi2(3) =   0.4754   Pr =  0.924

  +-------------------------------------------+
  | observed   expected   obs - exp   Pearson |
  |-------------------------------------------|
  |      315    312.750       2.250     0.127 |
  |      108    104.250       3.750     0.367 |
  |      101    104.250      -3.250    -0.318 |
  |       32     34.750      -2.750    -0.467 |
  +-------------------------------------------+

Mata

: obs = (315,108,101,32)
: exp = (556/16) *  (9,3,3,1)
: sum(((obs  - exp):^2)  :/ exp)
  .4700239808
: chi2tail(3, sum((obs - exp):^2 :/ exp))
  .9254258951

chitesti 60 62 67 68 64 56 62 44 58 67

observed frequencies from keyboard; expected frequencies equal

         Pearson chi2(9) =   7.4934   Pr =  0.586
likelihood-ratio chi2(9) =   7.9287   Pr =  0.541

  +-------------------------------------------+
  | observed   expected   obs - exp   Pearson |
  |-------------------------------------------|
  |       60     60.800      -0.800    -0.103 |
  |       62     60.800       1.200     0.154 |
  |       67     60.800       6.200     0.795 |
  |       68     60.800       7.200     0.923 |
  |       64     60.800       3.200     0.410 |
  |-------------------------------------------|
  |       56     60.800      -4.800    -0.616 |
  |       62     60.800       1.200     0.154 |
  |       44     60.800     -16.800    -2.155 |
  |       58     60.800      -2.800    -0.359 |
  |       67     60.800       6.200     0.795 |
  +-------------------------------------------+


Mata

: o = (60, 62, 67, 68, 64, 56, 62, 44, 58, 67)
: e = sum(o) / 10
: sum((o :- e):^2 :/ e)
  7.493421053
: chi2tail(9, sum((o :- e):^2 :/ e))
  .5858880273

With both -chitesti- and Mata, you just type in 0 when appropriate
just like any other observed frequency. As said, the help for
-chitest- and -chitesti- gives other examples too.

On Thu, Jun 7, 2012 at 12:29 AM, Nick Cox <njcoxstata@gmail.com> wrote:

> -csgof- is a user-written program from
> http://www.ats.ucla.edu/stat/stata/ado/analysis/
>
> The Statalist FAQ advises at
> http://www.stata.com/support/faqs/res/statalist.html#stata
>
> "Say what command(s) you are using. If they are not part of official
> Stata, say where they come from: the STB/SJ, SSC, or other archives."
>
> See -chitest- and -chitesti- from -tab_chi- (SSC) for alternatives.
> The examples in the help files are pertinent.
>
> Another alternative is to use Mata. Many chi-square problems reduce to
> a few lines of Mata.
>
> Nick
>
> On Wed, Jun 6, 2012 at 10:56 PM, Tara Johnson <tjohnsonrogers@gmail.com> wrote:
>
>> I want to conduct a chi-square goodness of fit test. The problem is I
>> have a variable with multiple categories with no observations. When I
>> run csgof, Stata does not include the categories with no observations.
>> How do I get Stata to count the categories which could be there in
>> principle but which in practice don't exist?
>>
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