I would like to know what's the difference between the standardized residuals and the adjusted standardized residuals in cross-tabs cell display in SPSS?

The following definitions are the ones that the SPSS gives:

Standardized. The residual divided by an estimate of its standard deviation. Standardized residuals, which are also known as Pearson residuals, have a mean of 0 and a standard deviation of 1. 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.

What I'm searching for actually is the interpretation of these two in a contingency table larger than 2x2 (2x4 to be exact). Which is more helpful for me to use? By using them both I've noticed that they gave my different partial significance levels concerning my cells. Even though the z-test's (compare column proportions) subscript letters indicated a difference between some cells, the standardized residuals didn't support it but the adjusted standardized ones did. How come?

Bonus question: By removing a row from my contingency table that I deemed worthy not to be there, this changed the partial significance of my cells (judging by the z-test) after performing the chi square test. Is it because chi square depends on total cell counts as well? How could a cell that contributed in the significance of a chi square value before, stops to be significant enough when a subcategory of a variable is being removed, but the result is still significant?

  • 1
    $\begingroup$ The residuals stats.stackexchange.com/a/178068/3277 $\endgroup$
    – ttnphns
    May 12 '17 at 9:58
  • 1
    $\begingroup$ z-test of 2 independent proportions is equivalent to 2x2 chi-square test of independence. I.e. if have 4x2 table and are comparing Pr(1,1) with Pr(1,2), that means you are performing chi-square test for table with 2 rows: one is the one above and the second is merged from rows 2-4. Thus, z-test is closer related to the notion of adjusted residuals than to std. residuals. $\endgroup$
    – ttnphns
    May 12 '17 at 10:10

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