How to determine significant associations in a mosaic plot? I have a common question on how to explain significant association between categorical variables in mosaic plot.
For example,in this plot,based on Pearson residuals, can we say that $[2.0, 5.1]$ and $[-3,  -2.0]$ residuals values mean there is a statistically significant association in $40+$ age,with memory and moderate attitude? And how to consider Pearson residual value , we use $[2.0, 5.1]$ value or $[4.0,5.1]$ or $[-2.0 ,-3.0]$ also?

 A: This is best interpreted using some specific language.  Within the 40+ age group (in the plot, labeled "40-") there is a significant association between the variables memory and attitude.  We cite associations between variables, not between values or categories within them (such as "moderate" or "no").  
A more specific statement one could make is that, for those 40+ but not for other age groups, "yes" on memory is disproportionately paired with "moderate" on attitude.
We could also say there is an interaction between age and memory as they relate to attitude, or between age and attitude as they relate to memory.  Only rarely would one put a variable like age at the end of such a sentence, since age is ordinarily a candidate to be a predictor or cause, not an effect. 
All of the above is based on the plot's characterization of each cell using, via a color, a range of Pearson residuals.  The plot does not give us sufficient information to further specify the values of each residual.  Nor does any individual residual value determine significance in this context.  The mosaic plot, being based on a Chi-square test, does not address significance except by yielding a single, overall, "omnibus" p-value.  
