Following a previous question I posted about statistical analysis for a table (image included), I conducted a chi-square test - χ2 (6, N = 317) = 28.78, p < .0001.
As these results were for a 4x3 table, I conducted a post hoc test to determine where any relationship existed. However, I've not conducted a post hoc test before so am uncertain as to how to interpret their residuals (image included from R).
Any help would be greatly appreciated.
It isn't straightforward, but essentially the residuals give you an idea of which cells are contributing to the overall chi-square statistic. These cells with have large residuals and be higher or lower than the expected values. The p values tell you whether that departure is statistically significant. While this can be useful it isn't always the case that the overall significance boils down to a few cells - it could be a more subtle pattern (for which one could use a contrast approach - perhaps via a log linear model).
There is also some discussion about how to handle multiple testing and how to compute standardised residuals. See:
https://seriousstats.wordpress.com/2019/09/05/chi-square-and-the-egon-pearson-correction/
It also links to R code to run analyses with corrections for multiple testing.
In your case Not possible to match: CFAs and ISAs are the main contributors (and it looks like your package has some kind of multiple testing correction). Essentially the CFAs are less frequent when Not possible to match and ISAs more frequent with other cells largely as expected.
Thom Baguley Brilliant, thanks for this - very helpful and helps clarify some of what I have read elsewhere online.
Jos Feys Brilliant, thank you very much for those resources. Reading the PDF through now.
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