Atmospheric vapor can be measured and the changes can be detected.What is the timescale you want to apply to explore whether it increases or reduces rainfall? During the rain or in a year?
I assume the vapor and the rainfall have strong positive correlation with on a year scale and possible positive correlation during the rain.
One of the issue to understand what is the cause and what is the consequence (chicken and egg). During the rain the vapor concentration is close to the maximum.
all answers above are addressing a particular aspect of the problem and are right to the point. I would simply add that water vapor in itself is just one of the ingredients in leading to rainfall formation. Aerosol is a key factor as well. For example maritime- and continental-type aerosols make a world of difference in precipitating cloud formation. So, the problem quickly goes into the cloud physics realm. Make sure you pay attention to this aspect too.