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The phrase "a specific significance" is correct and usable in written English.
It can be used when discussing the particular meaning or importance of something in a given context.
Example: "In this study, we aim to explore a specific significance of cultural symbols in modern society."
Alternatives: "a particular meaning" or "a distinct importance".
Exact(11)
If there were significant differences among the groups, a specific significance test was performed using Tukey's multiple comparison test at the 0.05 probability level.
"Composite sounds may gain a specific significance again".
It might be a day that has a specific significance to a particular person – the date they moved to the city or the date someone else moved away – and comes at the same time for everyone.
The singer repeated the line three times, accompanying himself on the guitar with the weirdest music I had ever heard.' Virtually everything Handy tells us has a specific significance.
In these contexts, the term "probable" (probabilis) took on a specific significance.
For a specific significance level α (defined as the probability of rejecting the hypothesis if it is true), there is a corresponding acceptance region Ω such that we declare the null hypothesis to be valid if an observed value of the test statistic Tobs ∈ Ω and reject the null hypothesis if Tobs Ɇ Ω.
Similar(48)
Since neither "messiah" nor "son of God" automatically conveys a specific meaning, the significance of these terms must be determined by studying how each author uses them.
Instead of building this environment around dates of specific significance, a process was developed to detect dates with high informational value for the stock under examination.
P. bivia and P. disiens may be of specific significance in a relationship between vaginal and gingival infections.
Further, it was possible to estimate a specific threshold significance level that can be used as an indicator for reliable parameterizations with respect to process design.
For this physical model, it is well known that there is a specific physical significance about the intersection points between the Julia set J ( T n λ ) and the positive real axis R + when λ is a positive integer.
More suggestions(16)
a specific relevance
a specific weight
a specific scope
a specific emphasis
a unique significance
a specific value
a specific salience
a specific importance
a specific significant
a selected significance
a specific important
a concrete significance
a specified significance
a particular significance
a specific profile
a specific purpose
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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