Hypothesis Specification Type

A Hypothesis Specification Type is a statistical classification type that categorizes statistical hypotheses based on how completely they specify the parameter space of a probability distribution.

• AKA: Hypothesis Type, Statistical Hypothesis Type, Parameter Specification Type.
• Context:
  • It can typically classify a Simple Hypothesis that specifies exact parameter values.
  • It can typically classify a Composite Hypothesis that specifies parameter ranges or sets.
  • It can often determine the test statistic distribution under different hypothesis types.
  • It can often influence the statistical power calculation for hypothesis tests.
  • It can range from being a Point Hypothesis Specification Type to being a Interval Hypothesis Specification Type, depending on its parameter constraint.
  • It can range from being a One-Sided Hypothesis Specification Type to being a Two-Sided Hypothesis Specification Type, depending on its directional constraint.
  • It can range from being a Parametric Hypothesis Specification Type to being a Non-Parametric Hypothesis Specification Type, depending on its distributional assumption.
  • It can range from being a Univariate Hypothesis Specification Type to being a Multivariate Hypothesis Specification Type, depending on its parameter dimensionality.
  • ...
• Example(s):
  • Mean Hypothesis Specifications, such as:
    • A Point Null Hypothesis: μ = 0.
    • A One-Sided Alternative Hypothesis: μ > 0.
    • A Two-Sided Alternative Hypothesis: μ ≠ 0.
  • Variance Hypothesis Specifications, such as:
    • A Simple Variance Hypothesis: σ² = 1.
    • A Composite Variance Hypothesis: σ² > 1.
  • Distribution Hypothesis Specifications, such as:
    • A Normality Hypothesis: data follows N(μ, σ²).
    • A Non-Parametric Hypothesis: F(x) = F₀(x).
  • ...
• Counter-Example(s):
  • A Research Hypothesis, which is conceptual rather than statistical.
  • A Scientific Theory, which is broader than a statistical hypothesis.
  • A Prediction, which doesn't specify parameter values.
• See: Null Hypothesis, Alternative Hypothesis, Simple Hypothesis, Composite Hypothesis, Statistical Hypothesis Testing Task, Parameter Space, Test Statistic, Likelihood Ratio Test, Uniformly Most Powerful Test.

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