Are Buddhists happier than average? Has anyone ever tried to measure happiness of Buddhist practitioners and compare it in a scientific or analytically way to other religious groups or the population as a whole? If there are studies what were the results and are the measurements reliable or meaningful in any way?

I appreciate that the notion of happiness is an incredibly slippy notion but people do crop up from time to time who talk about happiness as a (sort of) scientific study and try to compare different locations and so forth e.g. this study indicates that Panama is the happiest country on earth. I'm not claiming that this is a great or accurate study but it's just an example of this kind of thing. Also perhaps a better word might be well-being rather than happiness but I'm not sure that does much to tighten the definition.
Bhutan is a Buddhist country famous for its Gross National Happiness metric. So far, poverty is a drag on that metric: Bhutan Happiness Index: Buddhist Country Fails On Its 'Gross National Happiness'

Other economists have thought about happiness and how Buddhism might figure in to it, ref. Happiness and economics: a
Buddhist perspective (too much material to summarize quickly).