Which statistical test should be used for comparing frequencies of a categorical variable levels by another categorical variable (figure provided) I would like to show that marital statuses differ between different educational levels. Which statistical test should be used for this purpose?
And how should I write it under my methods?
METHODS: Proportional comparisons were done using test X?
RESULTS: The proportions of marital status levels differed between the educational levels (p-value of test X).


 A: Use a chi-square test.
https://en.wikipedia.org/wiki/Chi-squared_test
The chi-square test compares the "observed" frequencies in each cell with the "expected" frequencies that you would have gotten if there were no relationship whatsoever between the two variables. A significant p value indicates that you can reject the null hypotheses of no relationship at the given significance level, although note that the test does not tell you WHICH categories are significantly different from each other, just that there is a significant difference somewhere in the table.
To report the result of your test you probably want to indicate the value of the chi-Square test itself, the degrees of freedom for the table, which in your case is 12, because the formula is: ​(number of rows-1)*(number of columns-1), and the resulting p value. One warning: Chi-Square tests can be "unstable" (give strange answers) when there are "small" numbers of observations (say <5) in particular cells. You have some cells with only 4 observations in them here, so you might want to first combine widowed and divorced, re-do the table, and run the test again, if you want to be sure.
