definition 11.74 Hypotheses and tests

open in the book · parts/02-mathematical-methods/09-probability-statistics.tex:2300 · p. 398

ground object -- no derivation owed

Rests on

depends_on definition 11.53 Statistical model ¶

Supports

depends_on definition 11.75 $p$-value ¶
- depends_on definition 11.92 Significance ¶
  - depends_on proposition 113.19 The trials factors of the 2012 result ¶
  - depends_on proposition 11.93 $Z=\sqrt{q}$ ¶
    - depends_on example 11.107 Degrading a local five sigma ¶
    - depends_on proposition 113.15 Why categorizing helps, and by how much ¶
    - depends_on proposition 113.12 Sensitivity is set by ratio, not by rate ¶
- depends_on definition 11.96 Local, global, trials factor ¶
  - depends_on corollary 11.105 Trials factor at high significance ¶
  - depends_on definition 11.100 Upcrossings ¶
    - depends_on definition A.218 The hypotheses ¶
      - depends_on lemma A.220 At each point, field and derivative are independent Gaussians ¶
      - depends_on theorem A.219 Rice's formula ¶
    - depends_on lemma A.221 Counting identity ¶
    - depends_on theorem A.219 Rice's formula ¶ ↺
    - depends_on theorem 11.101 Davies' bound ¶
      - depends_on corollary 11.105 Trials factor at high significance ¶ ↺
      - depends_on example 11.107 Degrading a local five sigma ¶ ↺
    - depends_on theorem 11.103 Level dependence of the mean upcrossing count ¶
      - depends_on corollary 11.105 Trials factor at high significance ¶ ↺
      - depends_on example 11.107 Degrading a local five sigma ¶ ↺
    - depends_on theorem 11.102 Rice's formula ¶
      - depends_on theorem 11.103 Level dependence of the mean upcrossing count ¶ ↺
  - depends_on proposition 113.19 The trials factors of the 2012 result ¶ ↺
  - depends_on proposition 11.97 The trials factor is at least one ¶
  - depends_on proposition 11.98 Union bound and the naive estimate ¶
    - depends_on example 11.107 Degrading a local five sigma ¶ ↺
- depends_on proposition 11.76 Uniformity ¶
depends_on proposition 11.76 Uniformity ¶ ↺
depends_on theorem 11.78 Neyman–Pearson ¶

Neighborhood

Every logical edge within two steps of this node.

declared and complete
partly declared
a check failed
not graded
declared in the source
inferred from structure

Edges

type	direction	node	provenance	where
`depends_on`	→	Statistical model	declared	parts/02-mathematical-methods/09-probability-statistics.tex:2313
`depends_on`	←	$p$-value	declared	parts/02-mathematical-methods/09-probability-statistics.tex:2327
`depends_on`	←	Uniformity	declared	parts/02-mathematical-methods/09-probability-statistics.tex:2335
`depends_on`	←	Neyman–Pearson	declared	parts/02-mathematical-methods/09-probability-statistics.tex:2429