The statistical significance of the overall residuals (expected - observed counts) in a contingency table can be tested through chi-square.
However, is a way to test whether a residual in a particular cell in a contingency table is significant and possibly estimate a confidence range?
E.g. if in a particular cell the expected counts are 100 and the observed counts are 120, we have a residual of 20 which is 20% of the expected value. Can we tell whether this difference is statistically significant? Assuming that the data represented a sample could we extrapolate the residual of the particular cell to the Population?