Blocking Ontology

flow "BlockingOntology" v4.0

# ============================================================
# BLOCKING 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/blocking-ontology.html"
  title: "Blocking Ontology"
  domain: "Probability and Statistics"
  category: "Experimental Statistics"
  entity: BLOCKING
  entity_type: EXPERIMENTAL_DESIGN_METHOD

DEFINE_BLOCKING:
  BLOCKING :=
    DESIGN_METHOD(
      GROUP_SIMILAR_EXPERIMENTAL_UNITS,
      CONTROL_NUISANCE_VARIATION,
      RANDOMISE_WITHIN_GROUPS,
      IMPROVE_EFFECT_PRECISION
    )

PURPOSE:
  REDUCE:
    UNEXPLAINED_VARIABILITY
  BY:
    ACCOUNTING_FOR_KNOWN_NUISANCE_SOURCES
  WHILE:
    PRESERVING_VALID_TREATMENT_COMPARISON

CORE_STRUCTURE:
  EXPERIMENTAL_UNITS:
    U := {u_1, u_2, ..., u_n}

  BLOCKS:
    B := {B_1, B_2, ..., B_b}

  TREATMENTS:
    T := {T_1, T_2, ..., T_t}

  BLOCK_ASSIGNMENT:
    EXPERIMENTAL_UNIT
      -> ASSIGNED_TO
      -> BLOCK

  TREATMENT_ASSIGNMENT:
    WITHIN_BLOCK:
      RANDOMISE_TREATMENTS

ENTITIES:
  BLOCK:
    type: GROUP_OF_SIMILAR_EXPERIMENTAL_UNITS

  BLOCKING_FACTOR:
    type: NUISANCE_VARIABLE

  EXPERIMENTAL_UNIT:
    type: UNIT_RECEIVING_TREATMENT

  TREATMENT:
    type: EXPERIMENTAL_CONDITION

  RESPONSE:
    type: MEASURED_OUTCOME

  BLOCK_EFFECT:
    type: SYSTEMATIC_NUISANCE_EFFECT

  TREATMENT_EFFECT:
    type: PRIMARY_EXPERIMENTAL_EFFECT

  WITHIN_BLOCK_VARIATION:
    type: RESIDUAL_VARIATION

  BETWEEN_BLOCK_VARIATION:
    type: STRUCTURED_NUISANCE_VARIATION

RELATIONSHIPS:
  BLOCKING_FACTOR
    -> DEFINES_OR_INFORMS
    -> BLOCKS

  BLOCK
    -> CONTAINS
    -> EXPERIMENTAL_UNITS

  EXPERIMENTAL_UNITS
    -> RECEIVE
    -> TREATMENTS

  TREATMENTS
    -> RANDOMISED_WITHIN
    -> BLOCKS

  BLOCK_EFFECT
    -> EXPLAINS
    -> BETWEEN_BLOCK_VARIATION

  BLOCKING
    -> REDUCES
    -> RESIDUAL_ERROR

  REDUCED_RESIDUAL_ERROR
    -> MAY_IMPROVE
    -> TREATMENT_EFFECT_PRECISION

PRINCIPLE:
  IF:
    EXPERIMENTAL_UNITS_DIFFER
    DUE_TO:
      KNOWN_NUISANCE_FACTOR

  THEN:
    GROUP_UNITS_BY:
      SIMILAR_NUISANCE_FACTOR_VALUES

    RANDOMISE:
      TREATMENTS_WITHIN_BLOCKS

    ANALYSE:
      TREATMENT_EFFECT
      WHILE_ACCOUNTING_FOR:
        BLOCK_EFFECT

RANDOMISED_COMPLETE_BLOCK_DESIGN:
  alias: RCBD

  DEFINE:
    EACH_BLOCK:
      CONTAINS:
        ALL_TREATMENTS
      USUALLY:
        ONCE_OR_EQUALLY_REPLICATED

  model:
    Y_ij :=
      mu
      + tau_i
      + beta_j
      + epsilon_ij

  where:
    mu := OVERALL_MEAN
    tau_i := TREATMENT_EFFECT
    beta_j := BLOCK_EFFECT
    epsilon_ij := RANDOM_ERROR

  assumptions:
    - APPROPRIATE_ADDITIVE_MODEL
    - INDEPENDENT_ERRORS_AS_REQUIRED
    - APPROPRIATE_VARIANCE_STRUCTURE

COMPLETE_BLOCK:
  definition:
    BLOCK_CONTAINS_ALL_TREATMENTS

INCOMPLETE_BLOCK:
  definition:
    BLOCK_CONTAINS_SUBSET_OF_TREATMENTS

  use_when:
    BLOCK_CAPACITY:
      LESS_THAN:
        NUMBER_OF_TREATMENTS

BALANCED_INCOMPLETE_BLOCK_DESIGN:
  alias: BIBD

  parameters:
    v := NUMBER_OF_TREATMENTS
    b := NUMBER_OF_BLOCKS
    r := REPLICATIONS_PER_TREATMENT
    k := TREATMENTS_PER_BLOCK
    lambda := PAIRWISE_COOCCURRENCE_COUNT

  relations:
    v * r = b * k
    lambda * (v - 1) = r * (k - 1)

  purpose:
    ACHIEVE_BALANCED_TREATMENT_COMPARISONS
    UNDER:
      INCOMPLETE_BLOCK_CAPACITY

MATCHED_PAIRS:
  DEFINE:
    BLOCK_SIZE := 2
    FOR:
      TWO_TREATMENT_COMPARISON

  process:
    MATCH_SIMILAR_UNITS
      -> FORM_PAIRS
      -> RANDOMISE_TREATMENTS_WITHIN_PAIR

  interpretation:
    PAIR:
      SPECIAL_CASE_OF_BLOCK

STRATIFICATION_RELATION:
  BLOCKING:
    used_in:
      EXPERIMENTAL_DESIGN

  STRATIFICATION:
    often_used_in:
      SAMPLING
      OR:
      RANDOMISATION

  similarity:
    BOTH:
      GROUP_UNITS_BY_RELEVANT_CHARACTERISTICS

  distinction:
    BLOCKING != STRATIFIED_SAMPLING

BLOCK_SELECTION:
  GOOD_BLOCKING_FACTOR:
    PREDICTS:
      RESPONSE_VARIATION

  SHOULD_NOT_BE:
    PRIMARY_TREATMENT_EFFECT_OF_INTEREST

  examples:
    - LOCATION
    - BATCH
    - AGE_GROUP
    - BASELINE_MEASUREMENT
    - DAY
    - MACHINE
    - OPERATOR

  goal:
    HIGH_WITHIN_BLOCK_SIMILARITY
    HIGH_BETWEEN_BLOCK_DIFFERENCE
    FOR:
      NUISANCE_VARIATION

BLOCK_SIZE:
  SMALLER_BLOCKS:
    MAY:
      IMPROVE_HOMOGENEITY

  BUT:
    MAY:
      LIMIT_TREATMENT_COMBINATIONS
      INCREASE_DESIGN_COMPLEXITY

  REQUIRE:
    BALANCE:
      HOMOGENEITY
      TREATMENT_REPRESENTATION
      OPERATIONAL_CONSTRAINTS

RANDOMISATION_WITHIN_BLOCKS:
  FOR_EACH_BLOCK:
    APPLY:
      VALID_RANDOM_ASSIGNMENT_SCHEME

  purpose:
    PREVENT:
      SYSTEMATIC_TREATMENT_ASSIGNMENT
      WITHIN:
        BLOCK

  preserve:
    BLOCK_MEMBERSHIP
    RANDOMISATION_RECORD

ANOVA_DECOMPOSITION:
  TOTAL_VARIATION:
    PARTITION_INTO:
      TREATMENT_VARIATION
      BLOCK_VARIATION
      RESIDUAL_VARIATION

  symbolic:
    SS_TOTAL :=
      SS_TREATMENT
      + SS_BLOCK
      + SS_ERROR
    UNDER:
      APPROPRIATE_BALANCED_ADDITIVE_RCBD_CONTEXT

  treatment_test:
    F_TREATMENT :=
      MS_TREATMENT
      /
      MS_ERROR

  block_test:
    F_BLOCK :=
      MS_BLOCK
      /
      MS_ERROR
    WHEN:
      SUCH_TEST_IS_SCIENTIFICALLY_AND_MODELLING_APPROPRIATE

PRECISION:
  IF:
    BLOCKING_FACTOR:
      EXPLAINS_SUBSTANTIAL_RESPONSE_VARIATION

  THEN:
    RESIDUAL_VARIANCE:
      MAY_DECREASE

    STANDARD_ERROR_OF_TREATMENT_COMPARISON:
      MAY_DECREASE

    STATISTICAL_POWER:
      MAY_INCREASE

  ELSE:
    BLOCKING:
      MAY_ADD_COMPLEXITY
      WITH_LIMITED_PRECISION_GAIN

BLOCK_TREATMENT_INTERACTION:
  SIMPLE_ADDITIVE_RCBD:
    typically_assumes:
      NO_SEPARATELY_ESTIMABLE_BLOCK_BY_TREATMENT_INTERACTION
    WITHOUT:
      ADDITIONAL_REPLICATION_OR_STRUCTURE

  CAUTION:
    IF_TREATMENT_EFFECT_VARIES_BY_BLOCK:
      ADDITIVE_MODEL:
        MAY_BE_INADEQUATE

  response:
    CONSIDER:
      INTERACTION_MODEL
      RANDOM_EFFECTS_MODEL
      ADDITIONAL_REPLICATION
      ALTERNATIVE_DESIGN

FIXED_VS_RANDOM_BLOCK_EFFECTS:
  FIXED_BLOCKS:
    inference:
      CONDITIONAL_ON:
        SPECIFIC_BLOCKS

  RANDOM_BLOCKS:
    model:
      BLOCK_EFFECT:
        RANDOM_VARIABLE

    supports:
      VARIANCE_COMPONENT_ESTIMATION
      GENERALISATION_ACROSS_BLOCK_POPULATION
      WHEN:
        MODEL_JUSTIFIES

  require:
    BLOCK_EFFECT_INTERPRETATION:
      EXPLICIT

MULTIPLE_BLOCKING_FACTORS:
  possible_designs:
    - LATIN_SQUARE
    - GRAECO_LATIN_SQUARE
    - ROW_COLUMN_DESIGN

  purpose:
    CONTROL:
      MULTIPLE_NUISANCE_DIMENSIONS

LATIN_SQUARE_CONNECTION:
  structure:
    treatments:
      BALANCED_ACROSS:
        ROW_BLOCKS
        COLUMN_BLOCKS

  requirement:
    NUMBER_OF_TREATMENTS:
      MATCHES:
        NUMBER_OF_ROWS
        NUMBER_OF_COLUMNS
    IN:
      STANDARD_LATIN_SQUARE

BLOCKING_VS_COVARIATE_ADJUSTMENT:
  BLOCKING:
    design_stage:
      GROUPS_UNITS_BEFORE_RANDOMISATION

  COVARIATE_ADJUSTMENT:
    analysis_stage:
      MODELS_RESPONSE_USING_COVARIATE

  combination:
    MAY_USE:
      BLOCKING
      + COVARIATE_ADJUSTMENT

  caution:
    POST_HOC_ADJUSTMENT:
      DOES_NOT_RECREATE:
        RANDOMISED_BLOCK_DESIGN

MISSING_DATA:
  IF:
    OBSERVATION_MISSING_WITHIN_BLOCK

  THEN:
    DESIGN:
      MAY_BECOME_UNBALANCED

    analysis:
      USE:
        APPROPRIATE_LINEAR_MODEL
        MIXED_MODEL
        OR:
        OTHER_METHOD_MATCHING_DESIGN

  preserve:
    ORIGINAL_BLOCK_STRUCTURE

CONFOUNDING:
  risk:
    IF:
      TREATMENT_ASSIGNMENT
      IS_NOT_RANDOMISED_WITHIN_BLOCK

  THEN:
    TREATMENT:
      MAY_BE_CONFOUNDED_WITH:
        BLOCK_OR_ORDER_EFFECT

  rule:
    BLOCKING_ALONE:
      DOES_NOT_REPLACE:
        RANDOMISATION

DESIGN_EFFICIENCY:
  compare:
    BLOCKED_DESIGN
    WITH:
      COMPLETELY_RANDOMISED_DESIGN

  efficiency_gain:
    DEPENDS_ON:
      BLOCKING_FACTOR_PREDICTIVENESS
      WITHIN_BLOCK_HOMOGENEITY
      DESIGN_BALANCE
      SAMPLE_SIZE

APPLICATIONS:
  BLOCKING
    -> SUPPORTS
    -> AGRICULTURAL_EXPERIMENTS

  BLOCKING
    -> SUPPORTS
    -> CLINICAL_TRIALS

  BLOCKING
    -> SUPPORTS
    -> INDUSTRIAL_EXPERIMENTS

  BLOCKING
    -> SUPPORTS
    -> LABORATORY_EXPERIMENTS

  BLOCKING
    -> SUPPORTS
    -> FIELD_EXPERIMENTS

  BLOCKING
    -> SUPPORTS
    -> A_B_EXPERIMENTS_WITH_STRATA

MODEL_CONNECTIONS:
  BLOCKING
    -> CONNECTS_TO
    -> EXPERIMENTAL_DESIGN

  BLOCKING
    -> CONNECTS_TO
    -> RANDOMISATION

  BLOCKING
    -> CONNECTS_TO
    -> ANOVA

  BLOCKING
    -> CONNECTS_TO
    -> LINEAR_MODELS

  BLOCKING
    -> CONNECTS_TO
    -> MIXED_EFFECTS_MODELS

  BLOCKING
    -> CONNECTS_TO
    -> STATISTICAL_POWER

SEMANTIC_EQUIVALENCE:
  "blocking"
    ~= "grouping experimental units by nuisance-related similarity before treatment comparison"

  "block"
    ~= "group of relatively homogeneous experimental units"

  "randomised complete block design"
    ~= "RCBD"

  "matched pairs"
    ~= "two-unit blocks"
    IN:
      APPROPRIATE_TWO_TREATMENT_CONTEXT

  EXCLUDE_EQUIVALENCE:
    BLOCKING != RANDOMISATION
    BLOCKING != STRATIFIED_SAMPLING
    BLOCK != TREATMENT_GROUP
    REPLICATION != BLOCKING
    BLOCK_EFFECT != TREATMENT_EFFECT
    BLOCKING != COVARIATE_ADJUSTMENT

VALIDATION_RULES:
  RULE_1:
    BLOCKING_FACTOR:
      SHOULD_BE:
        PRE_TREATMENT
        AND:
        RELEVANT_TO_RESPONSE_VARIATION

  RULE_2:
    EXPERIMENTAL_UNITS:
      MUST_HAVE:
        UNIQUE_BLOCK_MEMBERSHIP
      IN:
        STANDARD_NONOVERLAPPING_BLOCK_DESIGN

  RULE_3:
    RANDOMISATION:
      MUST_OCCUR:
        WITHIN_BLOCKS
      ACCORDING_TO:
        DESIGN

  RULE_4:
    ANALYSIS:
      MUST_INCLUDE:
        BLOCK_STRUCTURE
      WHEN:
        BLOCKING_WAS_USED

  RULE_5:
    COMPLETE_BLOCK_DESIGN:
      MUST_CONTAIN:
        ALL_REQUIRED_TREATMENTS_PER_BLOCK

  RULE_6:
    INCOMPLETE_BLOCK_DESIGN:
      MUST_DOCUMENT:
        TREATMENT_INCIDENCE_STRUCTURE

  RULE_7:
    BLOCK_TREATMENT_CONFOUNDING:
      MUST_BE_AVOIDED_OR_EXPLICITLY_MODELLED

  RULE_8:
    PSEUDOREPLICATION:
      MUST_NOT_BE_CREATED:
        BY_TREATING_WITHIN_BLOCK_SUBSAMPLES_AS_INDEPENDENT_TREATMENT_REPLICATES

CONFIDENCE:
  ontology_identity: 0.99
  blocking_definition: 0.99
  rcbd_structure: 0.99
  incomplete_block_structure: 0.98
  randomisation_relationship: 0.99
  anova_relationship: 0.99
  precision_relationship: 0.98

UPDATE_MODEL:
  IF:
    NEW_EXPERIMENTAL_UNIT_ARRIVES

  THEN:
    ASSIGN:
      APPROPRIATE_BLOCK
    BASED_ON:
      PREDEFINED_BLOCKING_RULE

    THEN:
      RANDOMISE_TREATMENT_WITHIN_BLOCK
      ACCORDING_TO:
        DESIGN

  IF:
    BLOCK_DEFINITION_CHANGES

  THEN:
    REQUIRE:
      DOCUMENTED_DESIGN_CHANGE

    REASSESS:
      RANDOMISATION
      BALANCE
      ANALYSIS_MODEL

  IF:
    MISSING_OBSERVATION_OCCURS

  THEN:
    PRESERVE:
      BLOCK_MEMBERSHIP

    UPDATE:
      ANALYSIS_METHOD
      IF_REQUIRED

  PRESERVE:
    EXPERIMENTAL_UNIT_IDENTITIES
    BLOCK_IDENTITIES
    BLOCKING_FACTOR_VALUES
    TREATMENT_ASSIGNMENTS
    RANDOMISATION_RECORD
    DATA_PROVENANCE

AI_CONSUMPTION:
  parse_as: FORMAL_SEMANTIC_SPECIFICATION
  execution_mode: RECURSIVE_REASONING

  preferred_reasoning_order:
    - IDENTIFY_EXPERIMENTAL_UNITS
    - IDENTIFY_NUISANCE_VARIATION
    - SELECT_BLOCKING_FACTOR
    - DEFINE_BLOCKS
    - CHECK_WITHIN_BLOCK_HOMOGENEITY
    - SELECT_COMPLETE_OR_INCOMPLETE_BLOCK_STRUCTURE
    - RANDOMISE_TREATMENTS_WITHIN_BLOCKS
    - RECORD_ASSIGNMENTS
    - CONSTRUCT_ANALYSIS_MODEL
    - INCLUDE_BLOCK_EFFECT
    - ESTIMATE_TREATMENT_EFFECT
    - ASSESS_RESIDUAL_VARIATION
    - RETURN_BLOCK_ADJUSTED_INFERENCE

  constraints:
    - PRESERVE_BLOCK_MEMBERSHIP
    - RANDOMISE_WITHIN_BLOCKS
    - DISTINGUISH_BLOCK_EFFECT_FROM_TREATMENT_EFFECT
    - DO_NOT_EQUATE_BLOCKING_WITH_STRATIFIED_SAMPLING
    - ALIGN_ANALYSIS_WITH_BLOCK_STRUCTURE
    - AVOID_PSEUDOREPLICATION
    - PRESERVE_RANDOMISATION_AUDIT_TRAIL

FLOW_HASH:
  canonical_entity: "blocking"
  namespace: "probability-statistics/experimental-statistics"
  version: "4.0"
  identity_basis:
    - PAGE_URL
    - CANONICAL_ENTITY
    - ENTITY_TYPE
    - BLOCK_STRUCTURE
    - NUISANCE_VARIATION_CONTROL
    - WITHIN_BLOCK_RANDOMISATION

END_FLOW