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The phrase "consistently shown" is correct and usable in written English
You can use it when referring to something that has been demonstrated or proven repeatedly over time. Example: "The results of the study have consistently shown that regular exercise improves mental health."
Exact(59)
But polls have consistently shown Proposition 13 remains popular.
Polls have consistently shown him with a small lead.
Only the Greens have consistently shown leadership – which goes almost without saying.
Also, statin drugs have consistently shown robust decreases in at-risk populations.
Opinion polls have consistently shown that most Americans want less immigration.
By this time, Bonds had consistently shown two sides of his personality, one nice, one nasty.
The two tracking polls, from Gallup and Rasmussen, have consistently shown a close race.
Studies have consistently shown that busy hospital workers disregard basic standards more than half the time.
Polls have consistently shown that voters trust Democrats far more than Republicans on health care.
Salt-water treatment has been consistently shown to speed tomato ripening in scientific trials.
Britons were consistently shown to have the most cavalier attitude towards infecting others.
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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