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How do you decide which hypothesis test to run — paired...
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See plansAll three test a null hypothesis against your data and report a p-value: the probability of seeing a result at least as extreme as what you observed, if the null hypothesis were actually true. A small p-value (conventionally ≤0.05) means your data would be surprising under the null, so you reject it; it is not the probability that the null hypothesis is true, and it says nothing about effect size — with enough samples, even a trivial difference becomes “significant.”
Which test to use depends on what you’re comparing. A paired t-test compares the means of two related samples measured on the same units (before/after, or two models evaluated on the same test examples) and asks whether their mean difference is zero — use this over an unpaired test whenever the two measurements aren’t independent, because pairing removes per-unit variance and gives you more power. An F-test compares variances, or more commonly in ML compares the fit of two nested models (does adding these extra coefficients explain significantly more variance than chance) — this is how you’d formally justify keeping extra features rather than eyeballing R-squared. A chi-squared test checks whether an observed categorical distribution matches an expected one, or whether two categorical variables are independent — the natural tool for A/B test conversion counts or feature-independence checks. Getting this wrong, say running an unpaired t-test on paired data, inflates your variance estimate and makes you miss real effects.