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The phrase "show significant differences" is correct and usable in written English.
You can use it when you want to express that something is different in a meaningful way. For example, "The results of the experiments showed significant differences between two groups."
Exact(60)
Different letters show significant differences (p < 0.05).
Different letters show significant differences at the 1% level based on Tukey's test.
However, figures show significant differences in the electrification rate between different groups.
Different letters in the same column show significant differences based on a Tukey's test (p ≤ 0.001).
Results show significant differences among control and experimental group.
Most other bank characteristics do not show significant differences.
Both trabecular parameters show significant differences between pairs of sites.
T1 and T2 did not show significant differences concerning to the control.
The results, reported in Fig. 1, do not show significant differences in the distributions.
The uni- and multivariate patient-related analyses did not show significant differences.
For the unemployment dataset, none of the methods show significant differences.
More suggestions(15)
show noteworthy differences
show substantial differences
show major differences
show vast differences
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show large differences
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show significant advantages
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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