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  • 1.  Rao-Scott chi-square when a cell is = 0

    Posted Wed December 06, 2023 11:30 AM
    We are conducting a study in which we analyze data from a survey whith a complex sampling design. Therefore, to determine if there is an association or independence between categorical variables, we use the Rao-Scott chi-square provided by the complex samples module of SPSS.
     
    As we understand, the Rao-Scott chi-square statistic cannot be calculated when there is a cell with a frequency equal to zero (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4567525/). And we have some contingency tables in which this case occurs and yet SPSS calculates a statistic and its associated p-value.
     
    Would kindly inform us how is it possible for SPSS to calculate it? What adjustments are made to the calculation formula? What assumptions does it make?
    Thanks in advance,


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    Augusto Norte
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  • 2.  RE: Rao-Scott chi-square when a cell is = 0

    Posted Wed December 06, 2023 12:10 PM
    Look at the Algorithms manual for the procedure.  One excerpt:
    "We use the F-based variant of the Rao and Scott's (1984) second-order adjustment"

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    Original Message


  • 3.  RE: Rao-Scott chi-square when a cell is = 0

    Posted Wed December 06, 2023 12:28 PM

    Hi Jon!

    Thankyou very much for your prompt response.

    Where can I find the Algorithms manual?

    Thanks again,

    All the best,

    Augusto.



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    Augusto Norte
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    Original Message


  • 4.  RE: Rao-Scott chi-square when a cell is = 0

    Posted Wed December 06, 2023 12:42 PM
    Help > Documentation in PDF Format.--



    Original Message


  • 5.  RE: Rao-Scott chi-square when a cell is = 0

    Posted Fri April 11, 2025 11:12 AM

     What if in the contingency table when calculated there is a cell whose expected frequency is less than 5 for the 2*2 and 2*3 tables, can we still use the Pearson chi square from the Rao-Scott chi square results? 



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    Love Ara
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    Original Message


  • 6.  RE: Rao-Scott chi-square when a cell is = 0

    Posted Mon April 14, 2025 09:34 AM

    I am not familiar with the Rao-Scott Chi-square.  But I think someone should point out that the various rules of thumb for Pearson Chi-square tests propose minimum expected counts, not observed counts.  

    One common rule of thumb for Pearson's Chi-square says all cells must have expected counts of at least 5.  But IMO, this is not the best rule of thumb.  For 2x2 tables, I recommend this advice from Ian Campbell.  And for tables larger than 2x2, I recommend the advice from Yates, Moore & McCabe (1999, p. 734).  They say that the Chi-square approximation is good enough if "[n]o more than 20% of the expected counts are less than 5 and all individual expected counts are 1 or greater". 



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    Bruce Weaver
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    Original Message


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