# Gender and Medical Condition - Is a Chi-Square Test of Independence the Correct Test to Use?

Data from our local hospital's Emergency Department suggests that there are certain conditions with which females present more often than males. I wish to determine whether the difference in observations is statistically significant.

The following is the gender breakdown for all Emergency Department patients:

Gender         GenderCount
F              70001
M              55466


Which is about a 5:4 ratio, or 1.26 females for each male.

The following is the gender breakdown for Emergeny Deparment patients who present with the studied condition:

Gender        GenderCount
F              8516
M              3836


Which is about an 11:5 ratio, or 2.22 females for each male.

Is the correct test to use a Chi-Square Test of Independence? My current approach is to view the variables this way:

                       Condition Presented
Studied Condition   |     Any Other Condition
male    |                       |
--------|-----------------------|---------------------------
female  |                       |


Next, I would like to repeat the process for an arbitrary number of other conditions. Is there a good way to perform the same test on a set of independent categorical variables, at once? For example, could I perform a Chi-Square Test of Independence on the following matrix:

                                                  Condition Presented
Condition 01       |       Condition 02        |      ...      |       Condition n
male    |                      |                           |               |
--------|----------------------|---------------------------|---------------|--------------------
female  |                      |                           |               |


My data is in a SQL server, and I can use R.

I actually have data for all hospital departments, so should I be starting with that data as population data and treating the Emergency Department set as a sample?

Is a Chi-Square Test of Independence the right approach?

Bonus Question (not required for accepted answer) - If I get a statistically significant result, what measure of association should I use for this kind of data?

• A chisquare test should be OK. If you have other covariables than sex, yuou should try logistic regression. And, as for Association measure, maybe the odds ratio? Commented Apr 6, 2017 at 14:54

This Problem (depending on a research task) could be handled by a chi-squared test.

There a 2 ways to use chisq.test() in R:

• chisq.test(vector) tests against a uniform distribution (you could for example test if the distribution of studied condition & research condition differ from a uniform distribution)
• chisq.test(data.frame(vector1, vector2)) tests if the 2 vectors are from the same distribution. (you could compare female vs male patients based on their condition)

"Next, I would like to repeat the process for an arbitrary number of other conditions. Is there a good way to perform the same test on a set of independent categorical variables, at once? For example, could I perform a Chi-Square Test of Independence on the following matrix:"

the length of the vector (no of condition) is not limited -> yes

I actually have data for all hospital departments, so should I be starting with that data as population data and treating the Emergency Department set as a sample?

You can compare the departments but I cannot answer if it is useful to your research.