Frequentist
Unequal sizes break the pooled t-test both ways: 0.0006 one way, 0.2918 the other. Welch holds.
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Posterior Probability
Posterior probability measures a specified event under a prior and likelihood. It differs from a p-value and needs a decision-relevant effect threshold.
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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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Significance Level (α)
α is a tolerance you choose, not a measure of evidence. And the risk it trades against goes up as you push it down.
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Effect Size (δ)
Divide by the standard deviation and you have an effect size. Divide by the standard error and you have a test statistic. They are not the same number.
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Hypothesis Testing
A test rejects or fails to reject — it never confirms. And “fail to reject” covers both no effect and not enough data to tell.
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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.