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The phrase "many studies have shown" is grammatically correct and commonly used in written English
It can be used in a variety of contexts, but it is often used to introduce evidence or support for a statement or argument. Example: Many studies have shown that regular exercise can improve mental health and overall well-being.
Exact(60)
Many studies have shown a link between positive mood and generosity.
Many studies have shown that young children do not readily distinguish program content from commercials.
Many studies have shown that high volume tends to mean greater expertise and better care.
Many studies have shown that private health insurance is invariably more expensive to administer.
Many studies have shown that talk therapy and antidepressants lead to significant improvement in most patients.
"Many studies have shown that having animals can have a profound impact on these people".
Many studies have shown that extended television watching can produce a decline in several types of mental ability.
Many studies have shown that investors pour a disproportionate amount of money into funds that lead the rankings.
Many studies have shown high-sensitivity C-reactive protein to be a leading marker for cardiovascular disease.
(Many studies have shown that smokers inhale those cigarettes more deeply).
Many studies have shown foreign-owned factories in Britain to be more productive than indigenous enterprises.
More suggestions(15)
ample studies have shown
Many works have shown
Many studies have indicated
substantial studies have shown
Many studies have pointed
multiple studies have shown
countless studies have shown
Many studies have demonstrated
Many studies have confirmed
Many investigations have shown
diverse studies have shown
abundant studies have shown
extensive studies have shown
Many studies have suggested
innumerable studies have shown
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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