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RE: st: RE: Kappa query - unequal distribution of scores


From   "Downs, Sara" <Sara.Downs@ahvla.gsi.gov.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: RE: Kappa query - unequal distribution of scores
Date   Tue, 27 Sep 2011 18:17:34 +0100

Hi Nick,

Thanks for the advice which was helpful.

I also found these references that suggest that if the marginal totals are unbalanced the kappa statistic may provide an under or over estimate of association:
Feinstein & Cicchetti (1990) J Clin Epidemiol, vol 43, no 6, 543-549  
Cicchetti & Feinstein (1990) J Clin Epidemiol, vol 43, no 6, 551-558
Sara


-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Nick Cox
Sent: 22 September 2011 11:44
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: RE: Kappa query - unequal distribution of scores

. bootstrap r(kappa), nodots reps(10000): kap rev1 rev2

[...]

Bootstrap results                               Number of obs      =        83
                                                Replications       =     10000

      command:  kap rev1 rev2
        _bs_1:  r(kappa)

------------------------------------------------------------------------------
             |   Observed   Bootstrap                         Normal-based
             |      Coef.   Std. Err.      z    P>|z|     [95% Conf. Interval]
-------------+----------------------------------------------------------
-------------+------
       _bs_1 |    .020649   .0983171     0.21   0.834     -.172049     .213347
------------------------------------------------------------------------------

The s.e. is a bit higher. In this case, as kappa is almost 0, it is pretty much immaterial what s.e. you get.

Nick

On Thu, Sep 22, 2011 at 10:36 AM, Nick Cox <njcoxstata@gmail.com> wrote:
> I'd think about bootstrapping here.

> On Thu, Sep 22, 2011 at 10:06 AM, Downs, Sara 
> <Sara.Downs@ahvla.gsi.gov.uk> wrote:
>> Hi,
>>
>> I am trying to calculate agreement between 2 distributions of scores.
>> There are 3 possible scores: One score predominates and the other 2 
>> are extremely rare :
>>
>>  tab rev1 rev2
>>
>>           |               rev2
>>      rev1 |         0          1          2 |     Total
>> -----------+---------------------------------+----------
>>         0 |         1          6          0 |         7
>>         1 |        13         57          3 |        73
>>         2 |         0          2          1 |         3
>> -----------+---------------------------------+----------
>>     Total |        14         65          4 |        83
>>
>>
>> .         kap rev1 rev2
>>
>>             Expected
>> Agreement   Agreement     Kappa   Std. Err.         Z      Prob>Z
>> -----------------------------------------------------------------
>>  71.08%      70.47%     0.0206     0.0852       0.24      0.4042
>>
>>
>> I understand that the usual kappa statistic is not reliable in this 
>> situation .   Is there any way in STATA that I can adjust for the 
>> high expected frequency. I am using STATA 10.1.
>>
>

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