Statistical Significance
Statistical significance says how incompatible the data are with a null model at a chosen threshold. It does not say how large or how important an effect is.
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P-Value (probability value)
A p-value is a probability about data given a model. Reading it as a probability about the hypothesis inverts the conditional.
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Statistically Significant
“Unlikely due to chance” is the one reading a p-value cannot support. What it measures is incompatibility with a model, assumptions included.
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Comparing Models: Uncertainty and Significance
Assess the size and uncertainty of a model difference, then consider whether the changed decisions have practical value.