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The phrase 'experiments have shown that' is correct and usable in written English.
It is often used to introduce a statement backed up by scientific evidence. For example: Experiments have shown that exposure to certain gases can significantly affect the respiratory system.
Exact(58)
But repeated experiments have shown that cuts on trees left undressed heal faster and better than treated ones.
Numerical experiments have shown that (9) does not vary much by adding more sounding points.
Experiments have shown that what we now think is normal is actually overweight and even obese.
Several small experiments have shown that dumping iron into these waters produces large blooms of algae.
Previous experiments have shown that neither dose perceptibly harms bees.
Other experiments have shown that a full night's sleep helps you learn new skills or retain information.
Experiments have shown that the orientation of birds is based on celestial bearings.
Experiments have shown that the system satisfies user requirements.
Experiments have shown that people have a natural taste for cooperation.
Objective: Previous experiments have shown that addition of fragmented fibronectin can induce cartilage chondrolysis.
In addition, some accidents and experiments have shown that parametric resonance also occurs in irregular waves.
More suggestions(15)
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com