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I would greatly appreciate an easy-to-understand answer. To my understanding, if the adjusted residual is +/- 1.96 or more (or less if negative), then something is going on. What exactly does the adjusted residual tell me, and if possible please explain with an example. I am using SPSS.

According to the explanation in SPSS (from https://www.ibm.com/support/pages/interpreting-adjusted-residuals-crosstabs-cell-statistics), they state the following: "As noted by Agresti, the standardized residuals (called Pearson residuals in Agresti) that are also provided as cell statistics in Crosstabs, are also asymptotically normally distributed with a mean of 0 under the null hypothesis of independence."

But what exactly does it mean that something is going on if the adjusted residuals are greater than 1.96 or less than -1.96?

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  • $\begingroup$ Which specific definition of residuals are these? Presumably this is coming from some particular stats program; they should define these 'adjusted residual' values in the help or documentation somewhere, or at least offer a reference. $\endgroup$
    – Glen_b
    Commented Aug 16, 2022 at 22:35
  • $\begingroup$ @Glen_b I am using SPSS but I do not understand what is meant in the documentation when they explain the adjusted residuals $\endgroup$
    – ineedhelp
    Commented Aug 17, 2022 at 0:06
  • $\begingroup$ Not being able to see what you can see could make that difficult for many people to help. There's multiple ways that one might 'adjust residuals', so this phrase might mean any of several possible things. $\endgroup$
    – Glen_b
    Commented Aug 17, 2022 at 0:10
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    $\begingroup$ From your link; they're what Agresti calls "Standardized Pearson Residuals". This will help; you could quote the line that explains this from the help and the reference immediately under it: "Agresti, A. (2002). Categorical Data Analysis (2nd Ed.). New York: Wiley. (the definition is on page 81.)" in your question. I think this will increase the number of people able to answer the question. $\endgroup$
    – Glen_b
    Commented Aug 17, 2022 at 2:14
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    $\begingroup$ See stats.stackexchange.com/a/178068/3277 $\endgroup$
    – ttnphns
    Commented May 13, 2023 at 7:29

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CROSSTABS provides three kinds of residuals. For the adjusted residuals, Adjusted standardized. The residual for a cell (observed minus expected value) divided by an estimate of its standard error. The resulting standardized residual is expressed in standard deviation units above or below the mean.

The Algorithms Manual, available via Help > Documentation in PDF format, has the specific formulas for each type.

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  • $\begingroup$ thanks for your comment but what what I was asking which still confuses me is what the adjusted residuals means in SPSS crosstabs when using it for a chi-square that is larger than 2 x 2 $\endgroup$
    – ineedhelp
    Commented Aug 31, 2022 at 3:41

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