This seems like something that should be true, but I think I remember seeing a Mythbusters episode where they decided it didn’t make a difference. That show was more about entertainment than science, so I wondered if there was a more rigorous study done? I’ve definitely seen splashes of water(?) come out from flushes so that alone seems to argue for closing lids.
I remember watching a video where they added some liquid visible with UV to the water and flushed, there were droplets everywhere including the tester’s face.
It’s not a study but it’s enough to make me close the lid, especially when my toothbrush is in the same room.
Yes, toothbrushes live uncomfortably close to the loo in my house too.
A friend gave me some light banter about closing the lid = under my wife’s thumb but it’s absolutely about me attempting to keep the toilet business contained to the toilet!
I’m pretty sure it was mythbusters