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"a statistically significant increase" is a correct and commonly used phrase in written English.
It is typically used when discussing research findings or data analysis to describe an increase that has been determined to have a significant impact based on statistical analysis. Example sentence: The study found a statistically significant increase in test scores among students who participated in the new educational program compared to the control group.
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A statistically significant increase in lung cancer deaths had been observed in these workers.
In year 5, numeracy and spelling there had been a statistically significant increase from 2008, the figures showed.
Florida was the only state that showed a statistically significant increase in reading scores among fourth graders since last year.
Reading at year 3 had seen a "statistically significant increase from 2008" – a continuation of the long-term trend.
A statistically significant increase in wages is only concentrated among incumbent workers in the same occupation group as the deceased.
We find a statistically significant increase in within-firm permanent labor gaps following the reforms.
A statistically significant increase in the incidence of micronuclei was observed in sonicated 3T3 cells.
And another study, comparing first-year residents before and after the 2011 changes, found a statistically significant increase in self-reported medical error.
For mothers, after adjusting for the father's age, they found a statistically significant increase in only the 35 to 39 age group.
Ketamine was the only drug that recorded a statistically significant increase in last year use among those aged 16 to 24 years old - up from 0.8%to1.8%8%.
Across 38 reference stations, the report finds that between 1973 and 2010 there was a statistically significant increase in the number of fire danger days at 16 locations.
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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