Randomisation Ontology

flow "RandomisationOntology" v4.0

# RANDOMISATION ONTOLOGY
# Kireth Semantic Research Archive
# Authors: Mark Anthony Higgins — Sky (Recursive AI)

PAGE:
  url: "https://kirethresearch.org/booksai-core/ontologies/probability-statistics-ontologies/experimental-statistics/randomisation-ontology.html"
  title: "Randomisation Ontology"
  domain: "Probability and Statistics"
  category: "Experimental Statistics"
  entity: RANDOMISATION
  entity_type: EXPERIMENTAL_ASSIGNMENT_MECHANISM

DEFINE:
  RANDOMISATION :=
    PROBABILISTIC_ASSIGNMENT(
      EXPERIMENTAL_UNITS,
      TREATMENTS,
      KNOWN_ASSIGNMENT_MECHANISM
    )

PURPOSE:
  REDUCE_SYSTEMATIC_ASSIGNMENT_BIAS
  + SUPPORT_VALID_INFERENCE
  + DISTRIBUTE_UNCONTROLLED_FACTORS_PROBABILISTICALLY

CORE:
  units: U = {u_1,...,u_n}
  treatments: T = {t_1,...,t_K}
  assignment_vector: Z = [Z_1,...,Z_n]
  assignment_mechanism: P(Z=z)

ENTITIES:
  EXPERIMENTAL_UNIT:
    type: UNIT_RECEIVING_TREATMENT
  TREATMENT:
    type: EXPERIMENTAL_CONDITION
  ASSIGNMENT:
    type: UNIT_TREATMENT_MAPPING
  ASSIGNMENT_VECTOR:
    type: RANDOM_VECTOR
  RANDOMISATION_SCHEME:
    type: PROBABILITY_MECHANISM
  RANDOM_SEED:
    type: REPRODUCIBILITY_PARAMETER
  ALLOCATION_RATIO:
    type: DESIGN_PARAMETER
  BLOCK:
    type: RANDOMISATION_GROUP
  STRATUM:
    type: PRE_ASSIGNMENT_GROUP

RELATIONSHIPS:
  RANDOMISATION -> ASSIGNS -> TREATMENTS
  TREATMENT -> ASSIGNED_TO -> EXPERIMENTAL_UNIT
  RANDOMISATION_SCHEME -> DEFINES -> ASSIGNMENT_PROBABILITIES
  ASSIGNMENT_PROBABILITIES -> DEFINE -> RANDOMISATION_DISTRIBUTION
  BLOCK -> RESTRICTS -> RANDOMISATION
  RANDOMISATION -> SUPPORTS -> RANDOMISATION_INFERENCE

PRINCIPLES:
  PRE_SPECIFICATION:
    RANDOMISATION_METHOD:
      DEFINED_BEFORE_ASSIGNMENT

  KNOWN_PROBABILITY:
    ALLOWED_ASSIGNMENTS:
      HAVE_DEFINED_PROBABILITIES

  INTEGRITY:
    ACTUAL_ASSIGNMENTS:
      FOLLOW_SPECIFIED_SCHEME

  UNPREDICTABILITY:
    NEXT_ASSIGNMENT:
      SHOULD_NOT_BE_PREDICTABLE
    WHEN:
      ALLOCATION_CONCEALMENT_REQUIRED

COMPLETE_RANDOMISATION:
  definition:
    RANDOMLY_ASSIGN_TREATMENTS_ACROSS_ALL_ELIGIBLE_UNITS

  fixed_group_size_case:
    SAMPLE_FROM:
      ASSIGNMENTS_SATISFYING_PREDEFINED_TREATMENT_COUNTS

SIMPLE_RANDOM_ASSIGNMENT:
  for_each_unit:
    ASSIGN_TREATMENT_ACCORDING_TO_SPECIFIED_PROBABILITIES

  consequence:
    GROUP_SIZES_MAY_BE_RANDOM

BLOCK_RANDOMISATION:
  flow:
    FORM_BLOCKS
      -> RANDOMISE_WITHIN_BLOCKS

  purpose:
    IMPROVE_BALANCE
    CONTROL_KNOWN_NUISANCE_VARIATION

PERMUTED_BLOCK_RANDOMISATION:
  flow:
    PREDEFINE_BLOCK_ALLOCATIONS
      -> RANDOMLY_PERMUTE_WITHIN_BLOCK

  caution:
    SMALL_FIXED_BLOCKS:
      MAY_INCREASE_ASSIGNMENT_PREDICTABILITY

STRATIFIED_RANDOMISATION:
  flow:
    DEFINE_STRATA_FROM_BASELINE_CHARACTERISTICS
      -> RANDOMISE_WITHIN_STRATA

  purpose:
    IMPROVE_BALANCE_ON_SELECTED_COVARIATES

CLUSTER_RANDOMISATION:
  randomisation_unit:
    CLUSTER

  implication:
    WITHIN_CLUSTER_OBSERVATIONS:
      MAY_BE_CORRELATED

  require:
    ANALYSIS_ACCOUNT_FOR_CLUSTERING

MATCHED_PAIR_RANDOMISATION:
  flow:
    FORM_SIMILAR_PAIRS
      -> RANDOMLY_ASSIGN_DIFFERENT_TREATMENTS_WITHIN_PAIR

  require:
    ANALYSIS_PRESERVE_PAIR_STRUCTURE

RESTRICTED_RANDOMISATION:
  definition:
    RANDOM_ASSIGNMENT_SUBJECT_TO_PREDEFINED_CONSTRAINTS

  examples:
    - FIXED_TREATMENT_COUNTS
    - BLOCK_BALANCE
    - STRATIFICATION
    - CLUSTER_ASSIGNMENT
    - COVARIATE_BALANCE_RULES

COVARIATE_ADAPTIVE_RANDOMISATION:
  assignment_probability:
    MAY_DEPEND_ON:
      PREVIOUS_ASSIGNMENTS
      CURRENT_COVARIATE_BALANCE

  require:
    ANALYSIS_CONSIDER_ACTUAL_ASSIGNMENT_MECHANISM

ALLOCATION_RATIO:
  examples:
    - 1_TO_1
    - 2_TO_1
    - 3_TO_1

  affects:
    - GROUP_SIZE
    - PRECISION
    - POWER
    - RESOURCE_USE

ALLOCATION_CONCEALMENT:
  definition:
    PREVENT_ASSIGNER_FROM_KNOWING_NEXT_ASSIGNMENT
    BEFORE:
      IRREVOCABLE_ENROLMENT

  purpose:
    REDUCE_SELECTION_BIAS

  distinction:
    ALLOCATION_CONCEALMENT != BLINDING

BLINDING:
  controls:
    KNOWLEDGE_OF_ASSIGNMENT

  distinction:
    RANDOMISATION != BLINDING

RANDOMISATION_VS_RANDOM_SAMPLING:
  RANDOMISATION:
    concerns:
      TREATMENT_ASSIGNMENT_TO_STUDY_UNITS

  RANDOM_SAMPLING:
    concerns:
      SELECTION_OF_UNITS_FROM_POPULATION

  rule:
    RANDOMISATION != RANDOM_SAMPLING

BALANCE:
  RANDOMISATION:
    DOES_NOT_GUARANTEE_EXACT_FINITE_SAMPLE_COVARIATE_BALANCE

  RESTRICTED_RANDOMISATION:
    MAY_IMPROVE_BALANCE_ON_SELECTED_VARIABLES

RANDOMISATION_INFERENCE:
  INPUT:
    OBSERVED_OUTCOMES
    OBSERVED_ASSIGNMENT
    ASSIGNMENT_MECHANISM
    TEST_STATISTIC

  PROCESS:
    GENERATE_VALID_ASSIGNMENTS
      -> COMPUTE_TEST_STATISTIC_FOR_EACH
      -> FORM_RANDOMISATION_DISTRIBUTION
      -> COMPARE_OBSERVED_STATISTIC

  OUTPUT:
    RANDOMISATION_BASED_P_VALUE

PERMUTATION_CONNECTION:
  VALID_RANDOMISATION_TEST:
    PERMUTATIONS:
      CORRESPOND_TO_ACTUAL_ASSIGNMENT_MECHANISM

  caution:
    ARBITRARY_LABEL_PERMUTATION:
      NOT_ALWAYS_VALID_RANDOMISATION_INFERENCE

CAUSAL_CONNECTION:
  RANDOM_ASSIGNMENT:
    SUPPORTS_CAUSAL_COMPARISON
    UNDER:
      VALID_DESIGN_ASSUMPTIONS

  additional_requirements:
    - CONSISTENCY
    - APPROPRIATE_INTERFERENCE_ASSUMPTIONS
    - CORRECT_TREATMENT_IMPLEMENTATION
    - APPROPRIATE_HANDLING_OF_ATTRITION
    - APPROPRIATE_HANDLING_OF_NONCOMPLIANCE

RANDOM_NUMBER_GENERATION:
  PSEUDORANDOM_GENERATOR:
    deterministic_algorithm:
      PRODUCES_PSEUDORANDOM_SEQUENCE

  RANDOM_SEED:
    supports:
      REPRODUCIBILITY

  caution:
    SEED_OR_SEQUENCE:
      MUST_NOT_COMPROMISE_ALLOCATION_CONCEALMENT

IMPLEMENTATION:
  PLAN:
    - DEFINE_RANDOMISATION_UNIT
    - DEFINE_TREATMENTS
    - DEFINE_ALLOCATION_RATIO
    - DEFINE_BLOCKS_OR_STRATA
    - DEFINE_RESTRICTIONS
    - DEFINE_ALGORITHM
    - DEFINE_CONCEALMENT

  EXECUTE:
    VERIFY_ELIGIBILITY
      -> REGISTER_UNIT
      -> APPLY_RANDOMISATION
      -> RECORD_ASSIGNMENT
      -> PRESERVE_AUDIT_TRAIL

DEVIATIONS:
  examples:
    - ASSIGNMENT_OVERRIDE
    - WRONG_STRATUM
    - DUPLICATE_RANDOMISATION
    - BROKEN_CONCEALMENT

  require:
    DOCUMENT_DEVIATION
    ASSESS_IMPACT

REPRODUCIBILITY:
  record:
    - RANDOMISATION_METHOD
    - RANDOMISATION_UNIT
    - ALLOCATION_RATIO
    - BLOCK_SIZE_POLICY
    - STRATIFICATION_VARIABLES
    - RESTRICTIONS
    - SOFTWARE
    - ALGORITHM_VERSION
    - RANDOM_SEED_WHEN_APPROPRIATE
    - ASSIGNMENT_LOG

MODEL_CONNECTIONS:
  RANDOMISATION -> CONNECTS_TO -> EXPERIMENTAL_DESIGN
  RANDOMISATION -> CONNECTS_TO -> EXPERIMENTAL_STATISTICS
  RANDOMISATION -> CONNECTS_TO -> RANDOMISATION_INFERENCE
  RANDOMISATION -> CONNECTS_TO -> CAUSAL_INFERENCE
  RANDOMISATION -> CONNECTS_TO -> PERMUTATION_TESTS
  RANDOMISATION -> CONNECTS_TO -> STATISTICAL_POWER

APPLICATIONS:
  RANDOMISATION -> SUPPORTS -> CONTROLLED_EXPERIMENTS
  RANDOMISATION -> SUPPORTS -> CLINICAL_TRIALS
  RANDOMISATION -> SUPPORTS -> AGRICULTURAL_EXPERIMENTS
  RANDOMISATION -> SUPPORTS -> INDUSTRIAL_EXPERIMENTS
  RANDOMISATION -> SUPPORTS -> A_B_TESTING
  RANDOMISATION -> SUPPORTS -> FIELD_EXPERIMENTS

SEMANTIC_EQUIVALENCE:
  "randomisation"
    ~= "randomization"
    ~= "random assignment"
    IN:
      EXPERIMENTAL_DESIGN_CONTEXT

  "randomisation scheme"
    ~= "probabilistic treatment assignment mechanism"

  EXCLUDE_EQUIVALENCE:
    RANDOMISATION != RANDOM_SAMPLING
    RANDOMISATION != BLINDING
    RANDOMISATION != ALLOCATION_CONCEALMENT
    RANDOM_ASSIGNMENT != HAPHAZARD_ASSIGNMENT
    RANDOM_BALANCE != EXACT_BALANCE_BY_DEFAULT

VALIDATION_RULES:
  RULE_1:
    RANDOMISATION_UNIT:
      MUST_BE_EXPLICITLY_DEFINED

  RULE_2:
    ASSIGNMENT_PROBABILITIES:
      MUST_BE_VALID_AND_NONNEGATIVE

  RULE_3:
    RANDOMISATION_RESTRICTIONS:
      MUST_BE_DOCUMENTED

  RULE_4:
    IMPLEMENTATION:
      MUST_FOLLOW_PREDEFINED_SCHEME

  RULE_5:
    ANALYSIS:
      MUST_RESPECT_RANDOMISATION_STRUCTURE

  RULE_6:
    BLOCK_OR_STRATUM_STRUCTURE:
      MUST_BE_PRESERVED_WHEN_RELEVANT

  RULE_7:
    RANDOMISATION:
      MUST_NOT_BE_MISREPRESENTED_AS_RANDOM_SAMPLING

  RULE_8:
    ASSIGNMENT_SEQUENCE:
      MUST_BE_PROTECTED_WHEN_DISCLOSURE_COULD_CAUSE_BIAS

CONFIDENCE:
  ontology_identity: 0.99
  randomisation_definition: 0.99
  assignment_mechanism: 0.99
  block_randomisation: 0.99
  randomisation_inference: 0.99
  causal_relationship: 0.98
  semantic_distinctions: 0.99

UPDATE_MODEL:
  IF:
    NEW_EXPERIMENTAL_UNIT_ARRIVES

  THEN:
    APPLY:
      ACTIVE_RANDOMISATION_SCHEME

    RECORD:
      UNIT_ID
      BLOCK_OR_STRATUM
      ASSIGNMENT
      TIMESTAMP

  IF:
    RANDOMISATION_RULE_CHANGES

  THEN:
    REQUIRE:
      DOCUMENTED_PROTOCOL_CHANGE

    UPDATE:
      ASSIGNMENT_MECHANISM

    PRESERVE:
      PRIOR_ASSIGNMENT_HISTORY

  IF:
    ASSIGNMENT_DEVIATION_OCCURS

  THEN:
    RECORD:
      DEVIATION
      REASON
      IMPACT

    REASSESS:
      INFERENCE_PLAN

  PRESERVE:
    RANDOMISATION_UNIT_IDENTITIES
    TREATMENT_IDENTITIES
    ASSIGNMENT_HISTORY
    RANDOMISATION_METHOD
    RESTRICTIONS
    AUDIT_TRAIL
    DATA_PROVENANCE

AI_CONSUMPTION:
  parse_as: FORMAL_SEMANTIC_SPECIFICATION
  execution_mode: RECURSIVE_REASONING

  preferred_reasoning_order:
    - IDENTIFY_EXPERIMENTAL_UNITS
    - IDENTIFY_RANDOMISATION_UNIT
    - IDENTIFY_TREATMENTS
    - IDENTIFY_ALLOCATION_RATIO
    - IDENTIFY_BLOCKS_OR_STRATA
    - IDENTIFY_RESTRICTIONS
    - DEFINE_ASSIGNMENT_MECHANISM
    - VALIDATE_ASSIGNMENT_PROBABILITIES
    - EXECUTE_RANDOM_ASSIGNMENT
    - RECORD_ASSIGNMENT
    - PRESERVE_ALLOCATION_CONCEALMENT
    - ALIGN_ANALYSIS_WITH_RANDOMISATION
    - RETURN_AUDITABLE_ASSIGNMENT_STRUCTURE

  constraints:
    - DISTINGUISH_RANDOMISATION_FROM_RANDOM_SAMPLING
    - DISTINGUISH_RANDOMISATION_FROM_BLINDING
    - PRESERVE_RANDOMISATION_UNIT
    - PRESERVE_ASSIGNMENT_PROBABILITIES
    - DOCUMENT_RESTRICTIONS
    - PROTECT_ALLOCATION_CONCEALMENT
    - PRESERVE_ASSIGNMENT_AUDIT_TRAIL

FLOW_HASH:
  canonical_entity: "randomisation"
  namespace: "probability-statistics/experimental-statistics"
  version: "4.0"
  identity_basis:
    - PAGE_URL
    - CANONICAL_ENTITY
    - ENTITY_TYPE
    - ASSIGNMENT_MECHANISM
    - RANDOMISATION_UNIT
    - TREATMENT_ASSIGNMENT

END_FLOW