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The phrase "shows the effect" is correct and can be used in written English
It is typically used to describe the outcome or result of something. Example: The experiment clearly shows the effect of sunlight on plant growth.
Exact(60)
Nicholas D. Kristof's column shows the effect of such apathy on a personal level.
"When an ice-shelf of such enormous proportions can break up, that shows the effect that we are having.
Las tierras flacas (1962; The Lean Lands) shows the effect of industrialization on a peasant society.
This shows the effect of subcritical water.
A numerical example shows the effect of the proposed method.
An illustrative example shows the effect ofthe proposed approach.
Figure 2a shows the effect of vertical motion.
Table 2 shows the effect of changing the threshold value.
Figure 6c shows the effect deacetylation with 0.8 M NaOH.
Figure4 shows the effect of contact time on adsorption.
Figure3 shows the effect temperature on the of adsorption.
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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