Should I perform paired t-test or not?

Question

I have the following human population data with me (based on a census) -

Number of women in each educational level (like Illiterate, literate but less than primary, high school, graduate). For the time being call then Educational level $1,2,3$ and so on. And corresponding to each educational level those women were categorized in different age groups (like $20-24$ years, $25-29$ years and so on). And then I have the parity numbers for women in each age group and correspondingly each educational level. So, in short if you pick a random women from the population data, you will have access to the age group and education level to which she belongs and her parity number.

Now, I want to understand the relationship between the mean parities (of women in all age groups) for women in two different educational level. So, I calculate average parities and construct a table with two columns - Women with education level $0$ and women with education level $1$. And I have age groups as my rows.

Now I am thinking of performing a paired t-test for these two columns to asses the relationship between means of these two categories(variables) but I am not sure if this is the appropriate test to perform. As I think these two columns are independent to each other which violates one of the assumptions of paired t-test. I have different sets of women under observation here instead of having same women for these two educational level. But this is simply not possible. Am I right or wrong here? Should I go with this test or should try other test (if yes then please tell me about those tests)?

Also, if anyone can suggest a better question (than testing the mean between these two levels of education) that can be framed from this data, that would also be kind of you.

P.S. - I am not sure if I have explained my data properly but in case of any confusion please let me know.

Answer 1

If you go back to a format with a row for each woman and her educational category, her age and her parity then you can run a regression model with education and age as predictors ad parity as outcome. This will give you an overall test for each explanatory variable and you can subsequently test individual coefficients. If you do this there is no need to categorise age which leads to a mis-specified model. You may of course also want to add non-linear terms of age. Since your outcome is a count it might be better to consider a Poisson regression which would give you an interpretation of percent increase in parity rather than parity itself. It would also avoid impossible predictions like negative parity.