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The phrase "although not statistically significant" is correct and usable in written English.
You can use it when you want to indicate that a result is not statistically significant and this does not necessarily mean that it is insignificant. For example, "Although not statistically significant, the increase in sales from last quarter to this quarter was still noteworthy."
Exact(60)
Although not statistically significant, the difference in the other two categories may be of clinical significance.
Although not statistically significant, the finding raised serious concerns for patient safety.
Although not statistically significant due to only two replications, there was a similar trend for COD.
Although not statistically significant, a tendency of cellular realignment towards the liquid flow direction was demonstrated.
Although not statistically significant, the findings suggest partitions installed in taxicabs may be effective.
Furthermore, although not statistically significant, ethnicity had a strong association with students' perception on research.
Maternal mortality on the other hand appeared to have increased (although not statistically significant).
Adhesions were more likely to be severe in the control group, although not statistically significant.
Results show that most annual series present decreasing trends, although not statistically significant at the 5% level.
Although not statistically significant, there appears to be a trend toward increasing gestational age at delivery with septostomy.
Navigation aid, although not statistically significant, is important because of the subjective responses and the need of cross-referencing.
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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