/tech/ - Soyence and Technology

Im learning statistics at uni. They tell me a null hypothesis is neutral between groups, and an alternative hypothesis will be bias. For example:
Null hypothesis (H₀) fat and skinny girls give equally good blowjobs.
Alternative hypothesis (H₁) fat girls give better blowjobs than skinny girls.

But say a ton of research has been done, proving fat girls give better blowjobs than skinny girls.

Could the null hypothesis be, fat girls give better blowjobs than skinny girls
And the alternative hypothesis be, skinny girls give better blowjobs than fat girls.

If this is true, it contradicts my uni teachings that all null hypothesis are neutral between groups.

In other words:
Am I right in thinking that by definition most intro stats courses insist
>H₀ is “neutral” (no difference)
>H₁ is “biased” (some directional effect)
yet in practice—once decades of blowjobs research prove fat girls give better blowjobs—could I legitimately swap them around and say
>H₀′: fat girls give better blowjobs than skinny girls
>H₁′: Skinny girls give better blowjobs than fat girls
without violating any formal rules?

If classical nulls must be “zero‐difference,” what happens when prior data are overwhelming? Do we ever choose a non‐zero null to reflect our strong prior belief? Is that simply Bayesian territory, or can it live in the frequentist world too?
nd could my “null hypothesis” actually be a delta‐spike prior at Δ>0 (the fat‐vs‐skinny blowjobs difference), and the alternative a spike at Δ<0? Would this view change the logic of p‐values entirely? How do we interpret evidence when the null is itself “biased”?

also, if I define a field φ_fat(x) = blowjob intensity from a fat girl at point x, and φ_skinny(x) similarly, can I write down a partition functional
Z[J] = ∫ [Dφ] exp(−S[φ] + ∫J·φ)
where S[φ] includes an interaction term λ(φ_fat−φ_skinny)^4?
In that analogy, is the classical null H₀: λ = 0 (free theory; no size‐effect self‐interaction) and the alternative H₁: λ ≠ 0 (interacting theory)? If so, are p‐values akin to calculating two‐point correlation functions ⟨φ_fat(x)φ_skinny(y)⟩ to detect long‐range order or “blowjob correlation” across groups?
Is there a fixed point at Δ = 0 blowjobs difference that’s unstable, flowing under the “size‐bias coupling” toward Δ>0?
Do critical exponents exist for the divergence of variance in measured blowjobs scores as sample size → ∞?
If I rescale lengths x → bx, does the hypothesis test itself exhibit scale invariance at the null fixed point?

Also, in a composite hypothesis scenario, if H₀ is “Δ ≥ δ₀” for some small δ₀ > 0, and H₁ is “Δ < δ₀,” how do I choose δ₀? Do I pick δ₀ based on minimal practical significance (i.e. the smallest blowjobs‐quality difference that matters), or purely by Type I/II error tradeoff? If I drift into equivalence testing or non‐inferiority frameworks, am I already rewriting my null to be “Δ ≤ ε” instead of Δ=0?

Now suppose each blowjobs score is noisy: hpᵢ = μ_group + εᵢ, with εᵢ having covariance Cov(εᵢ,εⱼ)=Cᵢⱼ. Can I incorporate that into my “null model” as a Gaussian free field? If I estimate Cᵢⱼ from pilot data, does that transform the hypothesis‐testing problem into one of model selection between two covariance operators?

And finally, some real head‐scratchers:
Is there a formal contradiction between the requirement that H₀ be “neutral” and the practice—once evidence is overwhelming—of reframing H₀ around an observed effect?
Could I ever do a sequential analysis that shifts the null mid‐stream from neutrality to positivity (fat‐girl‐better) as data accrue?
In the end, is the core lesson “define your hypotheses before you see the data, and stick to them,” or can you more fluidly morph H₀/H₁ once a consensus has emerged in the literature?

Please explain this