I'm examining a series of 2 x 5 cross-tabs / contingency tables. I have taken the approach of: (1) determining whether the chi-square statistic (test of independence) is significant (i.e., p < .05), indicating presence of an association in the table; then (2) examining adjusted standardised residuals (i.e., > 1.96) in these tables to see which cells are driving that association.

I've noticed that for cross-tabs where the chi-square statistic is not significant, it can still have adjusted standardised residuals > 1.96. I realise these are two separate statistics (although perhaps not the implications of this), but should I interpret adjusted standardised residuals greater than 1.96 in the absence of a significant chi-square statistic? Are they best discounted, or can they still be interpreted as meaningful?

Many thanks in advance.

  • $\begingroup$ Although this is not a straight answer to your question, it explains what are adjusted and standardized residuals. $\endgroup$ – ttnphns Jul 27 '17 at 7:19
  • $\begingroup$ Chi-sq statistic (and hence test) is comprised of standardized, not adjusted standardized residuals $\endgroup$ – ttnphns Jul 27 '17 at 7:25
  • $\begingroup$ The chi-sq test is of H0 that residuals (raw) in all cells are zero in the population. Therefore it doesn't matter how you standardize the residuals afterwards, 0 residual will transform to 0 residual. However, whereas st. residuals (squared) are what the chi-sq statistic is made of, adj. st. residuals are specially corrected, they are "overnormalized", so to speak, to relate the "strength" of the association in the cell. $\endgroup$ – ttnphns Jul 27 '17 at 7:51
  • $\begingroup$ (cont.) I believe that if the omnibus chi-sq test is nonsignificant (and assumptions well hold) but an adj. st. residual is large in magnitude it is the falsely exagerrated value - by chance, like in multiple comparisons testing without corrections. Don't interpret it. $\endgroup$ – ttnphns Jul 27 '17 at 7:51

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