I don't understand this. Can anyone say this in another way, perhaps a
more mathematical way?

"Why stronger relations between variables are more significant.
Assuming that there is no relation between the respective variables in
the population, the most likely outcome would be also finding no
relation between those variables in the research sample. Thus, the
stronger the relation found in the sample, the less likely it is that
there is no corresponding relation in the population. As you see, the
magnitude and significance of a relation appear to be closely related,
and we could calculate the significance from the magnitude and
vice-versa; however, this is true only if the sample size is kept
constant, because the relation of a given strength could be either
highly significant or not significant at all, depending on the sample
size (see the next paragraph)."
.
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