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The phrase "shows the difference" is correct and commonly used in written English.
It can be used to describe a situation where two things are being compared and the speaker or writer wants to emphasize the contrast between them. Example: The data clearly shows the difference between the two groups, with Group A having significantly higher average scores than Group B.
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P-value 1 shows the difference among different groups.
The following interactive shows the difference that a 10% threshold would make on election results in different countries.
A look back at newspaper articles from the same period 15 years ago shows the difference.
"It shows the difference that we would be making if we were in government now".
"This shows the difference between rich and poor," Mahnoor's mother said.
The first graph shows the difference between budget projections and budget reality.
It shows the difference between how rich men and women and poor men and women acted and thought".
This shows the difference between the leader and the institution, which is more important than the leader".
In this pithy but ingenious example, Dawkins shows the difference between a designed economy and an evolutionary economy.
An example shows the difference.
Basically, it shows the difference between private and public markets.
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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