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# Chi Sq residual graph output in contingency tables By Sue | Dec 04, 2017 11:04PM CET

Hello
There is a 3D graphical output listed as 'residuals' and a table of 'residuals' and 'adjusted residuals' in the contingency table analysis function, but there is no explanation of how these tables are calculated. It doesn't' look like the residuals of observed and expected observations, so what are these tables calculating? I can't find any documentation on this in Help and it's not covered in your tutorial. By Sébastien | Dec 05, 2017 10:06AM CET | XLSTAT Agent

Hi there,

Residuals = (observed – expected) / sqrt(expected)
Adjusted residuals = (observed – expected) / sqrt[ expected*(1 – ( rowtotal / N ) )*(1 – ( coltotal / N ) )]
rowtotal being the sum of frequencies of the corresponding row and coltotal the sum of frequencies of the corresponding column.
Roughly, when residuals are > 2 or < – 2, then the observed frequency is significantly different from the theoretical one for alpha = 5%

Jean Paul

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Down By Sébastien | Dec 05, 2017 10:06AM CET | XLSTAT Agent

Hi there,

Residuals = (observed – expected) / sqrt(expected)
Adjusted residuals = (observed – expected) / sqrt[ expected*(1 – ( rowtotal / N ) )*(1 – ( coltotal / N ) )]
rowtotal being the sum of frequencies of the corresponding row and coltotal the sum of frequencies of the corresponding column.
Roughly, when residuals are > 2 or < – 2, then the observed frequency is significantly different from the theoretical one for alpha = 5%

Jean Paul

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