I'm not entirely sure what I am talking about is Simpson's paradox, because an opposite relationship does not appear when you combine two data sets, but merely a different one. Still, I think it is some variation of the paradox.
I present below some data I am working with, made generic as X and Y.
Here are the relationships in question uncombined:
When the two data sets are combined, a strong negative relationship appears between. Clearly, uncombined, there is not a strong negative relationship in both data sets. For my study, it's important that there is not the same strong negative relationship combined as there is uncombined.
What I want to know is there any kosher way to say—or to show statistically—in a publishable paper that a strong negative relationship may only appear when these datasets are combined due to the following: The datapoints for Y in the green set are generally higher than the Y datapoints in the yellow set, and the datapoints for X are generally smaller for green than they are for yellow?
I have asked my statistician working with me on this, and he does not know of any such way, but he advised me to seek out a way to do it, if feasible.
Here are the data for these two sets, color coded:
Y X Color 29.2 3.822954823 orange 45.4 4.446472019 orange 37.8 4.364963504 orange 18.6 4.154740061 orange 36.2 3.449355433 orange 22.2 4.426129426 orange 49.8 3.765931373 orange 28.6 4.552311436 orange 54.4 4.270718232 orange 49.4 4.668501529 orange 18 4.32480195 orange 41.6 3.733698964 orange 59.6 3.371865443 green 52.3 3.404674047 green 76.8 3.20353443 green 41.8 3.198529412 green 64.2 3.352293578 green 34.4 3.559021407 green 69.3 4.107033639 green 62.4 3.363302752 green 45 3.109489051 green 59.2 3.8 green 38.1 3.178023327 green 15.8 4.550671551 green 31.4 3.823887873 green 43.1 3.5 green 72.1 3.613040829 green 61.3 3.386029412 green 59.9 3.549664839 green