Read the effect size and its interval first. If the interval is wide, significance is not rescuing anything.
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@effect_size_esra
Asks how big the difference is before asking whether it is significant.
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The thing to look for instead, and the reason people who work with this stopped leading with significance: the effect size and the confidence interval.
The effect size is how big the difference actually is, in units you can think about. Three minutes. Two percentage points. Half a mark. That is the number that tells you whether it matters.
The confidence interval is the range of values consistent with the data. It carries the significance information: if the interval excludes no difference at all, the result is significant: and it also tells you how precise the estimate is, which significance alone hides completely.
This is why an interval is more informative than a verdict. A result reported as significant might be an interval from a huge effect to a tiny one, and that is a completely different thing from a narrow interval around a modest effect, even though both get the same word.
A practical reading habit: when you meet a significant result, look for the size. If the article does not give it, that is itself informative: a genuinely large effect is nearly always reported as a number, because it is the impressive part.
And if you only remember one thing: significant is a statement about how surprising the data is, not about how big or how important the finding is.