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4 Pictures taken with the same camera from the same place, with the same aperture. Taken in low light condition so the differences of noise is visible by eye. With an X-Pro2. Picture are exported to have the same size.

A/ Is taken with the full detector size and a 35mm lens
B/ Is taken with the full detector size but with a 4 time higher shutter speed (so 4 time higher iso) so 4 time less light
C/ Is taken from a 4th (in area) of the detector with a 16mm lens. Detector cropped in post. This mimic a crop factor of 2. Same setting than A
D/ Same crop than C but this time the shutter speed is 4 time lower, so iso 4 time lower : 4 time more light to compensate the crop.

One can see that
- A/ and D/ have comparable image quality
- B/ and C/ have comparable image quality

Image quality comes from the quantity of light gathered for a same render (final print size). A smaller detector (same techno) gather less light for the same picture.
ABCD

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