Statistical test to assess differences between two groups with different trait measures

#1
I have two groups of individuals (A and B), and I would like to test for a difference in reproductive state between these two groups. However, reproductive state cannot be measured the same way for males and females, resulting in two reproductive state metrics (one for males and one for females). Yet, I don't want to test for a difference between A and B for males and females independently, but jointly. How would I do this?

Here a data frame exemplifying the problem:
structure(list(Individual = 1:20, sex = c("male", "male", "male","male", "male", "male", "male", "male", "male", "male", "female","female", "female", "female", "female", "female", "female", "female","female", "female"), type = c("A", "A", "A", "A", "A", "B", "B","B", "B", "B", "A", "A", "A", "A", "A", "B", "B", "B", "B", "B"), male.reproductive.state = c(12L, 10L, 14L, 18L, 12L, 17L,19L, 16L, 19L, 20L, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA),female.reproductive.state = c(NA, NA, NA, NA, NA, NA, NA,NA, NA, NA, 2L, 4L, 3L, 2L, 3L, 4L, 6L, 7L, 4L, 5L)), class = "data.frame", row.names = c(NA,-20L))
 

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hlsmith

Less is more. Stay pure. Stay poor.
#3
This is an interesting question. Could we liken it to saying we are going to evaluate overweight in people, so we have a scale weight and others have a percent body fat. So the two outcomes are on completely different scales that it would be inappropriate to merge them together or try to compare them?
 
#4
This is an interesting question. Could we liken it to saying we are going to evaluate overweight in people, so we have a scale weight and others have a percent body fat. So the two outcomes are on completely different scales that it would be inappropriate to merge them together or try to compare them?
I was thinking along similar lines... How about normalizing each variable and then combine it? Not sure this would be ok to do? – Otherwise, would it be possible to run one test for males between type A and B only (for male reproductive state), and one for females, and then combine the test statistics (P-values)?
 

hlsmith

Less is more. Stay pure. Stay poor.
#6
Yes, if they are on different scales running two models would be best. Not sure why you think you need to pool the genders. It would be perfectly fine to report out each model results independently.
 
#7
Yes, if they are on different scales running two models would be best. Not sure why you think you need to pool the genders. It would be perfectly fine to report out each model results independently.
I can rund two independent models. But I still want to have combined statistics (e.g., a P-value for the difference). The problem with the real data is that each test (for each sex) is, on its own, underpowered.