Date:         Tue, 10 Nov 1998 08:40:55 +0100
Reply-To:     Andreas Fieger <andreas@STAT.UNI-MUENCHEN.DE>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@UGA.CC.UGA.EDU>
From:         Andreas Fieger <andreas@STAT.UNI-MUENCHEN.DE>
Subject:      Re: Adjusted residuals in crosstabulations
In-Reply-To:  <36476260.E9430EBB@mckenna-group.com>
Content-Type: TEXT/PLAIN; charset=US-ASCII

On Mon, 9 Nov 1998, Nick Vaidya wrote:
 
> Can someone provide me the formula for calculating the adjusted
> residuals in crosstabulations, preferably the one spss uses.
>
> Nick Vaidya
>
 
According to SPSS Statistical Algorithms, 2nd Edition they use:
 
  AR_{ij} = R_{ij} / ( sqrt{ E_{ij} (1 - r_i/W) (1 - c_j/W) } )
 
where
 
  R_{ij} is the residual = f_{ij} - E_{ij}
 
  E_{ij} is the expected count = r_i c_i / W
 
  f_{ij} is the count
 
  r_i is the ith row subtotal = \sum_{j=1}^C f_{ij}
  (C is the number of columns)
 
  c_j is the jth column subtotal = \sum_{i=1}^R f_{ij}
  (R is the number of rows)
 
  W is the grand total = \sum_{j=1}^R r_j = \sum_{i=1}^r c_i
 
HTH,
Andreas
        _ o
      _`\<,
_____( )/( )_____