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.