How to determine differences between each pair of categorical data with 3+ groups

[#1]

Hi!

I feel my question is pretty straight forward. How can I determine differences between each pair of categorical data with 3+ groups?

I have two categorical variables:

1) Type of Grant (Grant 1, Grant 2, Grant 3, & Grant 4)

2) Professorship (Assistant professor, associate professor, full professor)

I can use Fit Y by X and get a significant Chi Square value between the two.... But how can I tell where this differences lies? For example, how do I know if grant 3 is significantly more likely to have associate professors compared to grant 2, or that grant 1 is significantly more likely to have full professors than all of the other grants?

If I make professorship a numerical variable, I can get comparisons and a p value for each pair, is this how it should be done?

Thanks in advance.

[#2 · Accepted solution]

Click the red triangle next to Contingency and select Correspondence Analysis.You only have two variables so it reduces to a one-dimensional plot. You will see the association between levels.

Here is mock data to illustrate.

Screen Shot 2020-06-28 at 8.52.16 AM.png

Here is the initial analysis as you describe.

Screen Shot 2020-06-28 at 8.52.50 AM.png

Here is the addition of the correspondence analysis.

Screen Shot 2020-06-28 at 8.53.04 AM.png

So in this mock up, Assistant is associated with Grants 1 and 2, Associate is associated with Grant 4, and Full is associated with Grant 3.

You can read more about correspondence analysis in Help > JMP Documentation Library > Basic Analysis guide > Contingency Analysis chapter.

Note that there is a richer platform, Analyze > Multivariate Methods > Multiple Correspondence Analysis available. It is described in Help > JMP Documentation Library > Multivariate Methods guide > Multiple Correspondence Analysis chapter