Experimental Design Ontology

flow "ExperimentalDesignOntology" v4.0

# EXPERIMENTAL DESIGN 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/experimental-design-ontology.html"
  title: "Experimental Design Ontology"
  domain: "Probability and Statistics"
  category: "Experimental Statistics"
  entity: EXPERIMENTAL_DESIGN
  entity_type: STATISTICAL_DESIGN_FRAMEWORK

DEFINE:
  EXPERIMENTAL_DESIGN :=
    STRUCTURED_PLAN(
      EXPERIMENTAL_UNITS,
      FACTORS,
      TREATMENTS,
      RANDOMISATION,
      REPLICATION,
      BLOCKING,
      RESPONSE_MEASUREMENT
    )

PURPOSE:
  DESIGN_EXPERIMENTS
  TO:
    ESTIMATE_EFFECTS
    CONTROL_NUISANCE_VARIATION
    QUANTIFY_UNCERTAINTY
    SUPPORT_VALID_INFERENCE

ENTITIES:
  EXPERIMENT:
    type: STRUCTURED_EMPIRICAL_STUDY
  EXPERIMENTAL_UNIT:
    type: UNIT_RECEIVING_TREATMENT
  FACTOR:
    type: EXPERIMENTAL_VARIABLE
  FACTOR_LEVEL:
    type: FACTOR_SETTING
  TREATMENT:
    type: EXPERIMENTAL_CONDITION
  CONTROL:
    type: REFERENCE_CONDITION
  RESPONSE_VARIABLE:
    type: OUTCOME_MEASURE
  BLOCK:
    type: HOMOGENEOUS_UNIT_GROUP
  REPLICATE:
    type: INDEPENDENT_EXPERIMENTAL_REPETITION
  RANDOMISATION:
    type: PROBABILISTIC_ASSIGNMENT_MECHANISM
  DESIGN_MATRIX:
    type: MATRIX
  NUISANCE_FACTOR:
    type: NON_PRIMARY_VARIATION_SOURCE

RELATIONSHIPS:
  EXPERIMENT -> CONTAINS -> EXPERIMENTAL_UNITS
  FACTOR -> HAS -> FACTOR_LEVELS
  FACTOR_LEVEL_COMBINATION -> DEFINES -> TREATMENT
  TREATMENT -> ASSIGNED_TO -> EXPERIMENTAL_UNIT
  EXPERIMENTAL_UNIT -> PRODUCES -> RESPONSE
  RANDOMISATION -> DETERMINES -> TREATMENT_ASSIGNMENT
  BLOCKING -> CONTROLS -> NUISANCE_VARIATION
  REPLICATION -> SUPPORTS -> ERROR_ESTIMATION
  DESIGN_MATRIX -> REPRESENTS -> EXPERIMENTAL_STRUCTURE

CORE_PRINCIPLES:
  RANDOMISATION:
    purpose:
      REDUCE_SYSTEMATIC_ASSIGNMENT_BIAS
      SUPPORT_PROBABILITY_BASED_INFERENCE

  REPLICATION:
    purpose:
      ESTIMATE_EXPERIMENTAL_VARIATION
      INCREASE_PRECISION

  BLOCKING:
    purpose:
      CONTROL_KNOWN_NUISANCE_VARIATION
      REDUCE_RESIDUAL_VARIANCE

  CONTROL:
    purpose:
      PROVIDE_REFERENCE_FOR_TREATMENT_COMPARISON

EXPERIMENTAL_UNIT:
  definition:
    SMALLEST_UNIT_INDEPENDENTLY_ASSIGNED_TO_TREATMENT

  distinguish_from:
    - OBSERVATION
    - SUBSAMPLE
    - REPEATED_MEASUREMENT

  rule:
    ANALYSIS_MUST_RESPECT_ASSIGNMENT_LEVEL

DESIGN_FLOW:
  RESEARCH_QUESTION
    -> DEFINE_HYPOTHESES
    -> DEFINE_EXPERIMENTAL_UNITS
    -> DEFINE_FACTORS_AND_LEVELS
    -> DEFINE_TREATMENTS
    -> SELECT_DESIGN
    -> PLAN_RANDOMISATION
    -> PLAN_REPLICATION
    -> DEFINE_RESPONSE_MEASUREMENT
    -> EXECUTE_EXPERIMENT
    -> ANALYSE_DATA
    -> INTERPRET_RESULTS

COMPLETELY_RANDOMISED_DESIGN:
  alias: CRD
  structure:
    EXPERIMENTAL_UNITS
      -> RANDOM_ASSIGNMENT
      -> TREATMENTS

  model:
    Y_ij := mu + tau_i + epsilon_ij

RANDOMISED_COMPLETE_BLOCK_DESIGN:
  alias: RCBD
  structure:
    FORM_BLOCKS
      -> RANDOMISE_TREATMENTS_WITHIN_BLOCKS

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

FACTORIAL_DESIGN:
  definition:
    MULTIPLE_FACTORS_STUDIED_SIMULTANEOUSLY

  purpose:
    ESTIMATE:
      MAIN_EFFECTS
      INTERACTIONS

  two_factor_model:
    Y_ijk :=
      mu
      + alpha_i
      + beta_j
      + interaction_ij
      + epsilon_ijk

INTERACTION:
  definition:
    EFFECT_OF_ONE_FACTOR
      DEPENDS_ON
    LEVEL_OF_ANOTHER_FACTOR

FULL_FACTORIAL:
  includes:
    ALL_COMBINATIONS_OF_FACTOR_LEVELS

FRACTIONAL_FACTORIAL:
  includes:
    SELECTED_SUBSET_OF_FULL_FACTORIAL_RUNS

  purpose:
    REDUCE_EXPERIMENTAL_RUNS

  consequence:
    EFFECTS_MAY_BE_ALIASED

  require:
    DOCUMENT_ALIAS_STRUCTURE

LATIN_SQUARE:
  purpose:
    CONTROL_TWO_NUISANCE_DIMENSIONS

  structure:
    EACH_TREATMENT:
      OCCURS_ONCE_PER_ROW
      AND:
      ONCE_PER_COLUMN

SPLIT_PLOT:
  use_when:
    FACTORS_DIFFER_IN_RANDOMISATION_DIFFICULTY

  structure:
    WHOLE_PLOT_FACTOR
      -> RANDOMISE_AT_WHOLE_PLOT_LEVEL

    SUBPLOT_FACTOR
      -> RANDOMISE_WITHIN_WHOLE_PLOTS

  require:
    MODEL_MULTIPLE_ERROR_STRATA

CROSSOVER_DESIGN:
  structure:
    SAME_UNIT
      -> RECEIVES_MULTIPLE_TREATMENTS
      -> ACROSS_PERIODS

  concerns:
    - PERIOD_EFFECT
    - CARRYOVER_EFFECT
    - WITHIN_UNIT_DEPENDENCE

REPEATED_MEASURES:
  structure:
    SAME_UNIT_MEASURED_REPEATEDLY

  implication:
    RESPONSES_NOT_INDEPENDENT_WITHIN_UNIT

  require:
    MODEL_WITHIN_UNIT_CORRELATION

NESTED_DESIGN:
  structure:
    LEVELS_OF_ONE_FACTOR
      NESTED_WITHIN
    LEVELS_OF_ANOTHER_FACTOR

  require:
    PRESERVE_NESTING_IN_MODEL

BALANCED_DESIGN:
  definition:
    EQUAL_OR_STRUCTURALLY_EQUAL_REPLICATION
    ACROSS_RELEVANT_DESIGN_CELLS

  benefits:
    - PRECISION
    - SIMPLER_ESTIMATION
    - POSSIBLE_ORTHOGONALITY

ORTHOGONAL_DESIGN:
  definition:
    EFFECT_ESTIMATORS_OR_DESIGN_COLUMNS
      SEPARABLE_UNDER_MODEL_STRUCTURE

  benefit:
    SIMPLIFIED_EFFECT_ESTIMATION

RANDOMISATION:
  methods:
    - COMPLETE_RANDOMISATION
    - BLOCK_RANDOMISATION
    - STRATIFIED_RANDOMISATION
    - RESTRICTED_RANDOMISATION

  record:
    - ALGORITHM
    - RESTRICTIONS
    - RANDOM_SEED_WHEN_RELEVANT
    - ACTUAL_ASSIGNMENTS

REPLICATION:
  TRUE_REPLICATION:
    INDEPENDENT_EXPERIMENTAL_UNITS
      RECEIVE_TREATMENTS

  PSEUDOREPLICATION:
    DEPENDENT_MEASUREMENTS
      INCORRECTLY_TREATED_AS
    INDEPENDENT_REPLICATES

  rule:
    AVOID_PSEUDOREPLICATION

SAMPLE_SIZE_AND_POWER:
  inputs:
    - MINIMUM_RELEVANT_EFFECT
    - EXPECTED_VARIABILITY
    - DESIRED_POWER
    - SIGNIFICANCE_LEVEL
    - DESIGN_STRUCTURE
    - EXPECTED_ATTRITION

  output:
    REQUIRED_SAMPLE_SIZE_OR_REPLICATION

CONFOUNDING:
  definition:
    EFFECTS_CANNOT_BE_SEPARATELY_ESTIMATED

  control_with:
    - RANDOMISATION
    - BLOCKING
    - FACTORIAL_PLANNING
    - ADEQUATE_REPLICATION

DESIGN_MATRIX:
  symbol: X

  rows:
    EXPERIMENTAL_OBSERVATIONS

  columns:
    MODEL_TERMS

  may_encode:
    - INTERCEPT
    - TREATMENT_EFFECTS
    - FACTOR_LEVELS
    - INTERACTIONS
    - BLOCKS
    - COVARIATES

  model:
    Y := X beta + epsilon

ESTIMABILITY:
  depends_on:
    - DESIGN_MATRIX_RANK
    - ALIASING
    - MISSING_CELLS
    - PARAMETERISATION

  require:
    CHECK_DESIGN_MATRIX_RANK

ANALYSIS_ALIGNMENT:
  rule:
    ANALYSIS_MUST_RESPECT_RANDOMISATION_STRUCTURE

  mappings:
    BLOCKED_DESIGN -> INCLUDE_BLOCK_EFFECT
    SPLIT_PLOT -> INCLUDE_ERROR_STRATA
    REPEATED_MEASURES -> MODEL_WITHIN_UNIT_DEPENDENCE
    CLUSTER_RANDOMISATION -> MODEL_CLUSTER_DEPENDENCE

MEASUREMENT_PLAN:
  define:
    - RESPONSE_VARIABLE
    - MEASUREMENT_METHOD
    - TIMING
    - UNIT
    - PRECISION
    - BLINDING_WHEN_RELEVANT

BLINDING:
  possible_types:
    - PARTICIPANT_BLINDING
    - OPERATOR_BLINDING
    - OUTCOME_ASSESSOR_BLINDING
    - ANALYST_BLINDING

  purpose:
    REDUCE_EXPECTATION_RELATED_BIAS

PILOT_EXPERIMENT:
  purpose:
    ESTIMATE:
      FEASIBILITY
      VARIABILITY
      MEASUREMENT_RELIABILITY
      PROCEDURAL_CONSTRAINTS

DESIGN_OPTIMISATION:
  objective:
    MAXIMISE_INFORMATION
    SUBJECT_TO:
      COST
      TIME
      MATERIAL
      ETHICAL
      OPERATIONAL_CONSTRAINTS

  criteria:
    - D_OPTIMALITY
    - A_OPTIMALITY
    - G_OPTIMALITY

REPRODUCIBILITY:
  record:
    - RESEARCH_QUESTION
    - HYPOTHESES
    - EXPERIMENTAL_UNIT_DEFINITION
    - FACTORS_AND_LEVELS
    - TREATMENT_STRUCTURE
    - RANDOMISATION_METHOD
    - BLOCKING_STRUCTURE
    - REPLICATION_PLAN
    - SAMPLE_SIZE_JUSTIFICATION
    - MEASUREMENT_PROTOCOL
    - EXCLUSION_RULES
    - ANALYSIS_PLAN
    - DATA_PROVENANCE

MODEL_CONNECTIONS:
  EXPERIMENTAL_DESIGN -> CONNECTS_TO -> EXPERIMENTAL_STATISTICS
  EXPERIMENTAL_DESIGN -> CONNECTS_TO -> RANDOMISATION
  EXPERIMENTAL_DESIGN -> CONNECTS_TO -> ANOVA
  EXPERIMENTAL_DESIGN -> CONNECTS_TO -> LINEAR_MODELS
  EXPERIMENTAL_DESIGN -> CONNECTS_TO -> STATISTICAL_POWER
  EXPERIMENTAL_DESIGN -> CONNECTS_TO -> CAUSAL_INFERENCE

APPLICATIONS:
  EXPERIMENTAL_DESIGN -> SUPPORTS -> SCIENTIFIC_RESEARCH
  EXPERIMENTAL_DESIGN -> SUPPORTS -> ENGINEERING
  EXPERIMENTAL_DESIGN -> SUPPORTS -> AGRICULTURE
  EXPERIMENTAL_DESIGN -> SUPPORTS -> CLINICAL_RESEARCH
  EXPERIMENTAL_DESIGN -> SUPPORTS -> INDUSTRIAL_OPTIMISATION
  EXPERIMENTAL_DESIGN -> SUPPORTS -> A_B_TESTING

SEMANTIC_EQUIVALENCE:
  "experimental design"
    ~= "design of experiments"
    ~= "DOE"

  "experimental unit"
    ~= "smallest independently treatment-assigned unit"

  "factor"
    ~= "experimental explanatory variable"

  EXCLUDE_EQUIVALENCE:
    EXPERIMENTAL_UNIT != MEASUREMENT_UNIT_BY_DEFAULT
    REPLICATION != REPEATED_MEASUREMENT
    RANDOMISATION != RANDOM_SAMPLING
    RANDOM_ASSIGNMENT != RANDOM_SELECTION
    FULL_FACTORIAL != FRACTIONAL_FACTORIAL

VALIDATION_RULES:
  RULE_1:
    EXPERIMENTAL_UNIT:
      MUST_BE_EXPLICITLY_DEFINED

  RULE_2:
    RANDOMISATION_UNIT:
      MUST_MATCH_ANALYSIS_STRUCTURE

  RULE_3:
    REPLICATION:
      MUST_BE_INDEPENDENT_AT_RELEVANT_LEVEL

  RULE_4:
    BLOCKING:
      MUST_BE_INCLUDED_IN_ANALYSIS_WHEN_USED

  RULE_5:
    INTERACTIONS:
      MUST_BE_CONSIDERED_IN_FACTORIAL_DESIGNS

  RULE_6:
    FRACTIONAL_FACTORIAL:
      MUST_DOCUMENT_ALIAS_STRUCTURE

  RULE_7:
    DESIGN_MATRIX:
      MUST_BE_CHECKED_FOR_RANK_AND_ESTIMABILITY

  RULE_8:
    SAMPLE_SIZE:
      SHOULD_BE_JUSTIFIED_RELATIVE_TO_INFERENTIAL_GOALS

CONFIDENCE:
  ontology_identity: 0.99
  design_definition: 0.99
  randomisation_structure: 0.99
  replication_structure: 0.99
  blocking_structure: 0.99
  factorial_structure: 0.99
  analysis_alignment: 0.99

UPDATE_MODEL:
  IF:
    NEW_EXPERIMENTAL_UNITS_ADDED

  THEN:
    UPDATE:
      SAMPLE_SIZE
      RANDOMISATION_LIST
      DESIGN_MATRIX

    REASSESS:
      BALANCE
      POWER

  IF:
    FACTOR_OR_LEVEL_ADDED

  THEN:
    EXPAND:
      TREATMENT_STRUCTURE
      DESIGN_MATRIX

    REASSESS:
      INTERACTIONS
      REPLICATION
      ALIASING
      POWER

  IF:
    DESIGN_CONSTRAINT_CHANGES

  THEN:
    REOPTIMISE:
      RANDOMISATION
      BLOCKING
      REPLICATION

    REVALIDATE:
      ESTIMABILITY
      ANALYSIS_PLAN

  PRESERVE:
    EXPERIMENTAL_UNIT_IDENTITIES
    TREATMENT_ASSIGNMENTS
    RANDOMISATION_RECORD
    FACTOR_DEFINITIONS
    MEASUREMENT_PROTOCOL
    DATA_PROVENANCE

AI_CONSUMPTION:
  parse_as: FORMAL_SEMANTIC_SPECIFICATION
  execution_mode: RECURSIVE_REASONING

  preferred_reasoning_order:
    - IDENTIFY_RESEARCH_QUESTION
    - IDENTIFY_EXPERIMENTAL_UNITS
    - IDENTIFY_FACTORS_AND_LEVELS
    - IDENTIFY_TREATMENTS
    - IDENTIFY_RESPONSE_VARIABLES
    - IDENTIFY_NUISANCE_FACTORS
    - SELECT_DESIGN_STRUCTURE
    - DEFINE_RANDOMISATION
    - DEFINE_REPLICATION
    - DEFINE_BLOCKING
    - CHECK_ESTIMABILITY
    - PLAN_SAMPLE_SIZE_AND_POWER
    - ALIGN_ANALYSIS_WITH_DESIGN
    - RETURN_EXECUTABLE_EXPERIMENTAL_PLAN

  constraints:
    - PRESERVE_RANDOMISATION_STRUCTURE
    - PRESERVE_EXPERIMENTAL_UNIT_LEVEL
    - DISTINGUISH_REPLICATION_FROM_REPEATED_MEASUREMENT
    - AVOID_PSEUDOREPLICATION
    - EXPOSE_ALIASING_IN_FRACTIONAL_DESIGNS
    - CHECK_DESIGN_MATRIX_RANK
    - PRESERVE_DATA_PROVENANCE

FLOW_HASH:
  canonical_entity: "experimental-design"
  namespace: "probability-statistics/experimental-statistics"
  version: "4.0"
  identity_basis:
    - PAGE_URL
    - CANONICAL_ENTITY
    - ENTITY_TYPE
    - RANDOMISATION
    - REPLICATION
    - BLOCKING
    - TREATMENT_STRUCTURE

END_FLOW