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What is the difference between correlation and significance?

Why a correlation of two variables have a r value of .23 is significant while the correlation of another set (different variables) has a r value of .15 is NOT significant in a research study?

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    $\begingroup$ There can be two ways to look at significance. Statistical significance means that the test that correlation is different from 0 is reject a some level of significance (often taken to be 0.05). A significant value could mean that a value statistically significantly different from 0 is considered to be large for the given application (0.60 in some cases 0.90 in some other). $\endgroup$
    – Michael R. Chernick
    Commented Jan 13, 2018 at 1:03
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    $\begingroup$ Also statistical significance depends on both the estimate are the sample size. So an estimate of 0.25 can be statistically significant because the sample size is large enough to detect that it is different from 0 while for a low sample size an estimate of 0.35 can be non-significantly different from 0. $\endgroup$
    – Michael R. Chernick
    Commented Jan 13, 2018 at 1:06

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Answered in comments:

There can be two ways to look at significance. Statistical significance means that the test that correlation is different from 0 is reject a some level of significance (often taken to be 0.05). A significant value could mean that a value statistically significantly different from 0 is considered to be large for the given application (0.60 in some cases 0.90 in some other).

Also statistical significance depends on both the estimate are the sample size. So an estimate of 0.25 can be statistically significant because the sample size is large enough to detect that it is different from 0 while for a low sample size an estimate of 0.35 can be non-significantly different from 0. – Michael R. Chernick

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