I have searched for multiple websites, and only found the information regarding how to test the trend in a 2*k table, which was not the exact information I needed. I want to perform a trend test in a r*c table. And I have some ideas but not sure whether they are appropriate or not.

The dependent variable is ordinal one grouped in to 1-, 2-, 3-level. Independent variable is also an ordinal one, categorized into five groups. I want to test:

1) if two variables are not associated with each other? I am planning to perform a chi-square or Kruskal Wallis test to verify this.

2) if proportion (percentage) of each level of dependent variable (within the same level of the dependent variable) is significantly increased or decreased across the five levels of independent variable? I am planning to perform two-sample proportional t-test for the proportions (percentages) between the two adjacent independent variable levels. Also, within each level of independent variable, I will still apply the same test to exam the proportions (percentages) between each dependent variable levels. OR I should re-categorize the dependent variable into a binary one (not ordinal one): 1-level vs not 1-level, then run the t-test across five levels of independent variable; and 2-level vs not 2-level, the runt the same test; and apply the same strategy for the 3-level as well?

For the #2 test purpose, do I need to adjust the p-value and CI after each proportional t-test?

Thank you in advance for your professional insight!