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An insignificant difference doesn't mean that you've proven no difference; it just means that you haven't proved that there is one.
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The safety analysis regarding to the drug related clinical and laboratory adverse events both proved no difference between the compared treatment arms.
An ANOVA on laterality quotients proved no sex difference in the degree of lateral preference between men (0.81, SE = 0.03) and women (0.79, SE = 0.03).
As this exhibition should prove, Delaunay saw no difference between her painting and what she called her "decorative work".
Predictably, the right wing's all-caps brigade jumped on the occasion: the incident proved there was no difference between Democrats and socialists, and dammit, they were right all along to warn us about Obama's socialist ways.
However, our hypothesis that elderly have an increased incidence of sepsis, bacteremia, pneumonia, cellulitis, and burn wound infection was not proved; there was no difference between adults and elderly.
He is a man who has proven the difference between being lucky and being good.
54– 58, 58 There are no proven clinically meaningful differences between the agents in terms of efficacy.
As it is statistically impossible to demonstrate equivalence (prove the H0 of no difference), Blackwelder 29 proposed a one-sided significance test to reject the null hypothesis by a clinically acceptable amount.
This study had proven that there was no difference in adverse event occurrence between the studied drugs during PSA.
It was not the most scientific approach, and it proved to make absolutely no difference as the Mets mustered just three hits in a 5-1 loss.
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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