Different application you are citing there. We are talking about the roof, not some separation for back seat and boot or other parts of the car. Those can be introduced to reduce vibration or something else, other than noise.

Well. Those examples you cite, they may be cheap, but it serves the application. But not in the case of the roof of the car, when it is cheap but it actually doesn't serve the purpose, it is negligible in terms of soundproofing. Those things you pointed out, they may be necessary items not only for separation but support of the fittings in the car (not necessarily solely for soundproofing). Whereas the roof, you don't need to put anything on it as it is just fine. If you want to put something on the roof, it is better to put something that is effective than something that is not. But in this case, it is a case of cutting-cost, introducing something that will bring minor or negligible effects. Other than the showing of the car manufacturer (or distributor of Renault in Malaysia, either one), cutting-cost to this extent, choosing to use a cheap and ineffective material for soundproofing when you can spend a bit more, likely not more than RM100 to use something that is more efficient and serves the purpose.

By the way, there isn't any need to find out whether there is a difference with or without cardboard, and the need to do a comparison. I can tell you right now that if it's cardboard, in a blind test you will likely not be able to tell the difference in sound when it rains. Maybe in the frequency of 10 times you will get it correct in 5 tries.

I'm surely wasting my time with you. Not that I am an expert and validation isn't required. You can do all the test if you want. But as I have said earlier, the things will turn out as it will be. The most you will get reduction of 1dB or maybe 2 dB via dB meter. You may measure the readings and get a measurement. The sound levels may or may not go down if the cardboard is ineffective in blocking or absorbing the sound. In other words, it may not even go down 1 dB, no difference at all. The tone of the sound of rain drops may change, but the intensity remains.

As I have reiterated, a test can be done. Even if the measurements, (objective) are proven to have some "minor" difference in sound levels, subjectively if you take the blind test you will fail the test if your ears cannot pick up the differences.

Get it?