I found that it is possible to look at adjusted residuals and treat them as a z-score and then use a two-tailed test to find a p-value. The problem is how do you calculate adjusted residuals on what I realise is a 1xr table (as it is a goodness of fit test)?
In addition if anyone is interested in seeing what I was doing in regards to my pairwise and more details on my issues then please look at a forum question here.
I also have tables of habitat use vs. availability. Some of the values are small but only two groups have a mean value below 5. I use a $\chi^2$ as I did not know how to do a Fisher's on such a large table (9 or 5 habitats). The issue is, I then did pairwise comparisons for each habitat combo to add the p-values to come up with which habitats were contributing to the significant result. Should I somehow have used Fisher's for these 2x2 tests?
I have not found a way to do these pairwise for chi-squared so I set up an Excel file to do it and then compared each p-value (smallest first) with Holm's Bonferroni p-values i.e.
0.05/8 etc., for each in turn. Does this sound feasible rather than delving into Fisher's within the test? The results found did look valid and ironically the habitat type with
E=2 was not significant.
In addition, if I am doing the Holm's correction by hand (i.e., comparing each with the respective p-value) should the real p-value be shown in the results, or should you show a p-value that has been multiplied by the respective correction so that they can all look as if they are being compared to
For example, my fifth smallest of 9 p values is
0.02. According to Holm's I should compare this to
0.01 so it is not significant. If I need to report the p-values, should this one, for example, be shown as
0.10, i.e., it has been multiplied by the 5? Or should I show the original
0.02 and then have a reference such as "significant using Holm's correction?