How to report analysis for means of proportions/chi square significance

[#1]

Hi!

I am examining the career outcomes of four grants (1, 2, 3, and 4) and trying to determine if there are differences in whether a grant recipient would get a subsequent college degree (yes, no). Please see attached pictures

How do I report this?

I could report that the Chi Square is significant, but based on the Analysis of Means for Proportions, am I allowed to say that grant 2 was significantly less likely to get a subsequent degree, whereas recipients of grant 4 were significantly more likely to get a degree? 

If this is inappropriate, is there a different chi square post hoc I can perform to see if there are differences between groups?

  

Thanks so much!

[#2 · Accepted solution]

The hypothesis tests based on chi square assume the null hypothesis of the marginal distribution. The ANOM of proportions assumes the null hypothesis of the average proportion.

Your interpretation of the four grants using the decision limits is correct.