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The phrase "a very insignificant increase" is correct and usable in written English
It can be used to describe a change or growth that is so small that it has little to no impact or importance. Example: "After analyzing the data, we found that there was a very insignificant increase in sales over the last quarter."
Exact(2)
SIDOTI: "But would the world be safer if bin laden were caught?" GOVERNOR ROMNEY: "Yes, but by a small percentage increase — a very insignificant increase in safety by virtue of replacing bin Laden with someone else.
Results of the calculations show that integrating a ZTO buffer layer into a CdTe cell with the intention of modifying the TCO layer (rather than CdS) results in a very insignificant increase in Jsc, since the optical losses in the TCO are mainly due to reflection rather than absorption.
Similar(58)
"It's a very insignificant loss in terms of everything transported into Afghanistan," he said.
It was, well, a loser, struggling to impress a very insignificant new acquaintance with pitiful boasts about his masculinity.
A statistically insignificant increase in mortality was observed in non-ARDS patients with high EVLW (50% versus 17%; P = 0.20).
Pretreatment at 2°C induced a small, insignificant increase in ser-HSP20 phosphorylation without significant effects on force.
The other agricultural sectors are likely to show a slight, but insignificant increase in output level.
which showed a small but insignificant increase in PTH.
A slight but insignificant increase in 16- and 20-week-old mice was observed (Fig. S3b).
Results indicated a small yet insignificant increase in the values of RBC counts and Hb levels of subjects.
Compared to wt, the Δ freB and Δ sidA strains displayed only a mild, statistically insignificant, increase in fluorescence.
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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