Scientific Statistical Methods

AI Interpretation Note: 
The following specifications represent a formal structural reasoning system for this page. 
Execute as formal rules, not pseudocode. 

flow "ScientificStatisticalMethods" v4.0

# SCIENTIFIC STATISTICAL METHODS
# Kireth Semantic Research Archive
# Authors: Mark Anthony Higgins — Sky (Recursive AI)

PAGE:
  url: "https://kirethresearch.org/booksai-core/ontologies/probability-statistics-ontologies/scientific-statistical-methods.html"
  title: "Scientific Statistical Methods"
  domain: "Probability and Statistics"
  category: "Scientific Statistical Methods"
  entity: SCIENTIFIC_STATISTICAL_METHODS
  entity_type: STATISTICAL_METHODS_FRAMEWORK

DEFINE:
  SCIENTIFIC_STATISTICAL_METHODS :=
    FORMAL_FRAMEWORK(
      SCIENTIFIC_QUESTIONS,
      DATA,
      MEASUREMENT,
      SAMPLING,
      EXPERIMENTAL_DESIGN,
      STATISTICAL_MODELS,
      ESTIMATION,
      HYPOTHESIS_TESTING,
      UNCERTAINTY,
      VALIDATION,
      REPRODUCIBILITY
    )

PURPOSE:
  SUPPORT:
    SCIENTIFIC_INFERENCE
    EMPIRICAL_TESTING
    QUANTITATIVE_MEASUREMENT
    EXPERIMENTAL_REASONING
    OBSERVATIONAL_REASONING
    UNCERTAINTY_QUANTIFICATION
    REPRODUCIBLE_RESEARCH

FOUNDATION:
  SCIENTIFIC_QUESTION: Q
  POPULATION: P
  SAMPLE: D := {x_1,...,x_n}
  PARAMETER: theta
  ESTIMATOR: theta_hat := T(D)
  STATISTICAL_MODEL: p(D|theta)
  INFERENCE:
    DATA
      -> MODEL
      -> ESTIMATE_OR_TEST
      -> UNCERTAINTY
      -> SCIENTIFIC_INTERPRETATION

ENTITIES:
  SCIENTIFIC_METHOD: SYSTEMATIC_EMPIRICAL_INQUIRY
  STATISTICAL_METHOD: QUANTITATIVE_DATA_ANALYSIS_PROCEDURE
  POPULATION: TARGET_SET_OF_UNITS_OR_EVENTS
  SAMPLE: OBSERVED_SUBSET_OR_DATASET
  VARIABLE: MEASURED_OR_DERIVED_QUANTITY
  PARAMETER: POPULATION_OR_MODEL_QUANTITY
  ESTIMATOR: DATA_BASED_PARAMETER_RULE
  ESTIMATE: REALISED_ESTIMATOR_VALUE
  HYPOTHESIS: TESTABLE_STATISTICAL_STATEMENT
  MODEL: MATHEMATICAL_REPRESENTATION_OF_DATA_GENERATING_PROCESS
  UNCERTAINTY: IMPRECISION_OR_RANDOM_VARIABILITY
  EFFECT_SIZE: MAGNITUDE_OF_DIFFERENCE_OR_ASSOCIATION
  REPLICATION: REPEATED_EMPIRICAL_INVESTIGATION
  REPRODUCIBILITY: ABILITY_TO_RECREATE_ANALYSIS_FROM_SAME_INPUTS

RELATIONSHIPS:
  SCIENTIFIC_QUESTION -> DEFINES -> TARGET_QUANTITY
  POPULATION -> SAMPLED_BY -> SAMPLING_DESIGN
  SAMPLING_DESIGN -> PRODUCES -> SAMPLE
  SAMPLE -> CONTAINS -> OBSERVATIONS
  OBSERVATIONS -> INFORM -> STATISTICAL_MODEL
  STATISTICAL_MODEL -> SUPPORTS -> ESTIMATION
  STATISTICAL_MODEL -> SUPPORTS -> HYPOTHESIS_TESTING
  ESTIMATE -> HAS -> UNCERTAINTY
  EFFECT_SIZE -> QUANTIFIES -> SCIENTIFIC_MAGNITUDE
  VALIDATION -> ASSESSES -> MODEL_OR_METHOD
  REPLICATION -> TESTS -> GENERALITY_OF_FINDING

SCIENTIFIC_WORKFLOW:
  flow:
    DEFINE_QUESTION
      -> DEFINE_POPULATION_AND_TARGET
      -> OPERATIONALISE_VARIABLES
      -> DESIGN_STUDY
      -> COLLECT_DATA
      -> CLEAN_AND_VALIDATE_DATA
      -> EXPLORE_DATA
      -> SPECIFY_MODEL
      -> ESTIMATE_OR_TEST
      -> QUANTIFY_UNCERTAINTY
      -> CHECK_ASSUMPTIONS
      -> INTERPRET_RESULTS
      -> REPORT_METHODS_AND_LIMITATIONS
      -> REPLICATE_OR_VALIDATE

RESEARCH_QUESTION:
  requirements:
    SPECIFY:
      POPULATION
      VARIABLES
      OUTCOME
      EXPOSURE_OR_INTERVENTION
      TIME_HORIZON
      TARGET_ESTIMAND

SAMPLING:
  methods:
    - SIMPLE_RANDOM_SAMPLING
    - STRATIFIED_SAMPLING
    - CLUSTER_SAMPLING
    - SYSTEMATIC_SAMPLING
    - MULTISTAGE_SAMPLING
    - CONVENIENCE_SAMPLING

SAMPLING_BIAS:
  examples:
    - COVERAGE_BIAS
    - NONRESPONSE_BIAS
    - SELF_SELECTION
    - SURVIVOR_BIAS
  consequence:
    ESTIMATES_MAY_NOT_GENERALISE_TO_TARGET_POPULATION

MEASUREMENT:
  observed_variable: X_obs
  true_quantity: X_true
  measurement_error:
    epsilon := X_obs-X_true
  requirement:
    MEASUREMENT_PROCESS_AND_UNITS_MUST_BE_DOCUMENTED

MEASUREMENT_ERROR:
  types:
    - RANDOM_ERROR
    - SYSTEMATIC_ERROR
    - MISCLASSIFICATION
    - INSTRUMENT_ERROR

VALIDITY:
  types:
    - CONSTRUCT_VALIDITY
    - INTERNAL_VALIDITY
    - EXTERNAL_VALIDITY
    - STATISTICAL_CONCLUSION_VALIDITY

EXPERIMENTAL_DESIGN:
  elements:
    - EXPERIMENTAL_UNITS
    - TREATMENTS
    - RANDOMISATION
    - REPLICATION
    - BLOCKING
    - CONTROL_GROUP

RANDOMISATION:
  role:
    ASSIGN_TREATMENTS_USING_RANDOM_MECHANISM
  benefit:
    BALANCE_CONFOUNDERS_IN_EXPECTATION
    SUPPORT_CAUSAL_INFERENCE
    UNDER:
      APPROPRIATE_DESIGN_AND_ASSUMPTIONS

OBSERVATIONAL_STUDY:
  treatment_assignment:
    NOT_CONTROLLED_BY_INVESTIGATOR
  challenges:
    CONFOUNDING
    SELECTION_BIAS
    REVERSE_CAUSATION
  caution:
    ASSOCIATION != CAUSAL_EFFECT

DESCRIPTIVE_STATISTICS:
  measures:
    - MEAN
    - MEDIAN
    - MODE
    - VARIANCE
    - STANDARD_DEVIATION
    - QUANTILES
    - RANGE
    - INTERQUARTILE_RANGE

EXPLORATORY_DATA_ANALYSIS:
  alias: EDA
  methods:
    - DISTRIBUTION_SUMMARIES
    - OUTLIER_INSPECTION
    - CORRELATION_ANALYSIS
    - GRAPHICAL_ANALYSIS
    - MISSINGNESS_ANALYSIS
  caution:
    EXPLORATORY_FINDINGS_REQUIRE_CONFIRMATORY_VALIDATION_FOR_FORMAL_CLAIMS

INFERENTIAL_STATISTICS:
  objectives:
    - PARAMETER_ESTIMATION
    - HYPOTHESIS_TESTING
    - PREDICTION
    - MODEL_COMPARISON
    - UNCERTAINTY_QUANTIFICATION

ESTIMATION:
  parameter: theta
  estimator: theta_hat := T(D)
  properties:
    - BIAS
    - VARIANCE
    - CONSISTENCY
    - EFFICIENCY
    - ROBUSTNESS

BIAS:
  Bias(theta_hat) := E[theta_hat]-theta

UNBIASED_ESTIMATOR:
  condition:
    E[theta_hat] = theta

STANDARD_ERROR:
  definition:
    SD_OF_SAMPLING_DISTRIBUTION_OF_ESTIMATOR
  role:
    QUANTIFY_ESTIMATOR_PRECISION

CONFIDENCE_INTERVAL:
  frequentist_coverage:
    P_theta(theta IN CI(D)) = 1-alpha
    UNDER:
      REPEATED_SAMPLING_AND_MODEL_ASSUMPTIONS
  caution:
    CONFIDENCE_LEVEL_IS_NOT_POSTERIOR_PROBABILITY_OF_FIXED_PARAMETER

BAYESIAN_CREDIBLE_INTERVAL:
  posterior:
    p(theta|D)
  property:
    P(theta IN C | D) = 1-alpha
  distinction:
    CREDIBLE_INTERVAL != FREQUENTIST_CONFIDENCE_INTERVAL

HYPOTHESIS_TESTING:
  null: H_0
  alternative: H_1
  test_statistic: T(D)

P_VALUE:
  definition:
    PROBABILITY_UNDER_H_0_OF_TEST_STATISTIC_AT_LEAST_AS_EXTREME_AS_OBSERVED
  caution:
    P_VALUE != P(H_0_IS_TRUE|DATA)
    P_VALUE != EFFECT_SIZE

TYPE_I_ERROR:
  condition:
    REJECT_H_0_WHEN_H_0_TRUE

TYPE_II_ERROR:
  condition:
    FAIL_TO_REJECT_H_0_WHEN_SPECIFIED_ALTERNATIVE_TRUE

POWER:
  power := 1-beta

POWER_ANALYSIS:
  depends_on:
    - EFFECT_SIZE
    - SAMPLE_SIZE
    - VARIABILITY
    - SIGNIFICANCE_LEVEL
    - TEST_DESIGN

EFFECT_SIZE:
  examples:
    - MEAN_DIFFERENCE
    - STANDARDISED_MEAN_DIFFERENCE
    - CORRELATION
    - RISK_RATIO
    - ODDS_RATIO
    - REGRESSION_COEFFICIENT

PRACTICAL_SIGNIFICANCE:
  distinction:
    PRACTICAL_SIGNIFICANCE != STATISTICAL_SIGNIFICANCE

MULTIPLE_TESTING:
  methods:
    - BONFERRONI
    - HOLM
    - BENJAMINI_HOCHBERG
    - FAMILYWISE_ERROR_CONTROL
    - FALSE_DISCOVERY_RATE_CONTROL

PARAMETRIC_METHODS:
  examples:
    - T_TEST
    - ANOVA
    - LINEAR_REGRESSION
    - GENERALIZED_LINEAR_MODEL

NONPARAMETRIC_METHODS:
  examples:
    - RANK_TESTS
    - PERMUTATION_TESTS
    - EMPIRICAL_DISTRIBUTION_METHODS
    - KERNEL_METHODS
  caution:
    NONPARAMETRIC != ASSUMPTION_FREE

PERMUTATION_TEST:
  principle:
    RECOMPUTE_STATISTIC_UNDER_ALLOWED_PERMUTATIONS
  validity:
    DEPENDS_ON:
      EXCHANGEABILITY_OR_RANDOMISATION_STRUCTURE

BOOTSTRAP:
  principle:
    RESAMPLE_DATA_OR_APPROPRIATE_UNITS_WITH_REPLACEMENT
  uses:
    - STANDARD_ERROR
    - CONFIDENCE_INTERVAL
    - BIAS_ESTIMATION
    - SAMPLING_DISTRIBUTION_APPROXIMATION
  caution:
    RESAMPLING_UNIT_MUST_MATCH_DEPENDENCE_STRUCTURE

REGRESSION:
  model:
    Y := f(X,beta)+epsilon
  objectives:
    ESTIMATE_ASSOCIATIONS
    PREDICT_OUTCOMES
    TEST_MODEL_TERMS
  caution:
    REGRESSION_COEFFICIENT != CAUSAL_EFFECT_WITHOUT_CAUSAL_IDENTIFICATION

LINEAR_REGRESSION:
  model:
    Y := X beta + epsilon
  common_assumptions:
    - LINEAR_MEAN_STRUCTURE
    - INDEPENDENT_OR_MODELLED_ERRORS
    - APPROPRIATE_VARIANCE_STRUCTURE
    - CORRECT_MODEL_SPECIFICATION

GENERALIZED_LINEAR_MODEL:
  components:
    RANDOM_COMPONENT
    LINEAR_PREDICTOR
    LINK_FUNCTION
  examples:
    - LOGISTIC_REGRESSION
    - POISSON_REGRESSION

ANOVA:
  purpose:
    PARTITION_VARIABILITY_AND_TEST_FACTOR_EFFECTS
  connection:
    LINEAR_MODEL_FRAMEWORK

CORRELATION:
  measures:
    - PEARSON
    - SPEARMAN
    - KENDALL
  rule:
    CORRELATION != CAUSATION

CAUSAL_INFERENCE:
  objective:
    ESTIMATE_EFFECT_OF_INTERVENTION_OR_EXPOSURE
  requires:
    DESIGN_OR_ASSUMPTIONS_FOR_IDENTIFICATION
  methods:
    - RANDOMISED_EXPERIMENT
    - MATCHING
    - PROPENSITY_SCORE_METHODS
    - INSTRUMENTAL_VARIABLES
    - DIFFERENCE_IN_DIFFERENCES
    - REGRESSION_DISCONTINUITY

CONFOUNDING:
  response:
    DESIGN
    STRATIFICATION
    ADJUSTMENT
    MATCHING
    CAUSAL_MODELLING

MISSING_DATA:
  mechanisms:
    - MCAR
    - MAR
    - MNAR
  methods:
    - COMPLETE_CASE
    - MULTIPLE_IMPUTATION
    - MAXIMUM_LIKELIHOOD
    - BAYESIAN_MODELLING
    - WEIGHTING
  caution:
    METHOD_DEPENDS_ON_MECHANISM_AND_ASSUMPTIONS

OUTLIERS:
  possible_causes:
    - DATA_ERROR
    - RARE_EVENT
    - MODEL_MISSPECIFICATION
    - TRUE_EXTREME_VALUE
  rule:
    OUTLIERS_SHOULD_NOT_BE_REMOVED_WITHOUT_JUSTIFICATION

ROBUST_STATISTICS:
  methods:
    - MEDIAN
    - TRIMMED_MEAN
    - M_ESTIMATION
    - ROBUST_REGRESSION

MODEL_SELECTION:
  methods:
    - INFORMATION_CRITERIA
    - CROSS_VALIDATION
    - REGULARISATION
    - BAYESIAN_MODEL_COMPARISON
  caution:
    MODEL_SELECTION_AFFECTS_POST_SELECTION_INFERENCE

AIC:
  full_name:
    AKAIKE_INFORMATION_CRITERION
  common_form:
    AIC := 2k-2log(L_hat)

BIC:
  full_name:
    BAYESIAN_INFORMATION_CRITERION
  common_form:
    BIC := k log(n)-2log(L_hat)
  caution:
    AIC_AND_BIC_HAVE_DIFFERENT_THEORETICAL_OBJECTIVES

CROSS_VALIDATION:
  flow:
    SPLIT_DATA
      -> FIT_ON_TRAINING
      -> EVALUATE_ON_HELD_OUT_DATA
      -> REPEAT
      -> AGGREGATE
  purpose:
    ESTIMATE_OUT_OF_SAMPLE_PERFORMANCE
  caution:
    DATA_DEPENDENT_PREPROCESSING_MUST_OCCUR_WITHIN_TRAINING_PARTITIONS

PREDICTION:
  target:
    Y_new
  model:
    p(Y_new|X_new,D)
  evaluation:
    USE_HELD_OUT_OR_FUTURE_DATA
    WHEN:
      GENERALISATION_IS_TARGET

CALIBRATION:
  meaning:
    AGREEMENT_BETWEEN_PREDICTED_PROBABILITIES_AND_OBSERVED_FREQUENCIES

MODEL_DIAGNOSTICS:
  inspect:
    - RESIDUALS
    - INFLUENCE
    - GOODNESS_OF_FIT
    - CALIBRATION
    - DISTRIBUTIONAL_ASSUMPTIONS
    - DEPENDENCE

SENSITIVITY_ANALYSIS:
  purpose:
    ASSESS_HOW_RESULTS_CHANGE_WITH_INPUT_PARAMETER_OR_ASSUMPTION_CHANGES

UNCERTAINTY_ANALYSIS:
  purpose:
    QUANTIFY_UNCERTAINTY_IN_PARAMETERS_PREDICTIONS_AND_DECISIONS

REPRODUCIBILITY:
  preserve:
    - RAW_DATA_VERSION
    - CLEANING_RULES
    - ANALYSIS_CODE
    - SOFTWARE_VERSION
    - RANDOM_SEEDS
    - MODEL_SPECIFICATION
    - OUTPUTS

REPLICATION:
  purpose:
    TEST_WHETHER_FINDING_RECURS_UNDER_NEW_DATA_OR_STUDY

PRE_REGISTRATION:
  records_before_analysis:
    - HYPOTHESES
    - PRIMARY_OUTCOMES
    - ANALYSIS_PLAN
    - EXCLUSION_RULES
  purpose:
    DISTINGUISH_CONFIRMATORY_FROM_EXPLORATORY_ANALYSIS

REPORTING:
  include:
    - STUDY_DESIGN
    - SAMPLE_SIZE
    - DATA_EXCLUSIONS
    - MISSING_DATA_HANDLING
    - MODEL_SPECIFICATION
    - EFFECT_SIZES
    - UNCERTAINTY_INTERVALS
    - TEST_RESULTS
    - ASSUMPTION_CHECKS
    - LIMITATIONS
    - SOFTWARE_AND_CODE_WHERE_APPROPRIATE

APPLICATIONS:
  SCIENTIFIC_STATISTICAL_METHODS -> SUPPORTS -> EXPERIMENTAL_SCIENCE
  SCIENTIFIC_STATISTICAL_METHODS -> SUPPORTS -> OBSERVATIONAL_SCIENCE
  SCIENTIFIC_STATISTICAL_METHODS -> SUPPORTS -> ENGINEERING
  SCIENTIFIC_STATISTICAL_METHODS -> SUPPORTS -> MEDICINE
  SCIENTIFIC_STATISTICAL_METHODS -> SUPPORTS -> BIOLOGY
  SCIENTIFIC_STATISTICAL_METHODS -> SUPPORTS -> EARTH_SCIENCE
  SCIENTIFIC_STATISTICAL_METHODS -> SUPPORTS -> SOCIAL_SCIENCE
  SCIENTIFIC_STATISTICAL_METHODS -> SUPPORTS -> MACHINE_LEARNING

MODEL_CONNECTIONS:
  SCIENTIFIC_STATISTICAL_METHODS -> CONNECTS_TO -> PROBABILITY_THEORY
  SCIENTIFIC_STATISTICAL_METHODS -> CONNECTS_TO -> EXPERIMENTAL_STATISTICS
  SCIENTIFIC_STATISTICAL_METHODS -> CONNECTS_TO -> BAYESIAN_STATISTICS
  SCIENTIFIC_STATISTICAL_METHODS -> CONNECTS_TO -> MULTIVARIATE_STATISTICS
  SCIENTIFIC_STATISTICAL_METHODS -> CONNECTS_TO -> TIME_SERIES_STATISTICS
  SCIENTIFIC_STATISTICAL_METHODS -> CONNECTS_TO -> RISK_DECISION_MATHEMATICS
  SCIENTIFIC_STATISTICAL_METHODS -> CONNECTS_TO -> MACHINE_LEARNING_STATISTICS

SEMANTIC_EQUIVALENCE:
  "statistical inference"
    ~= "reasoning from data to population or model quantities"

  "standard error"
    ~= "estimated sampling variability of estimator"

  "effect size"
    ~= "quantitative magnitude of difference or association"

  "reproducibility"
    ~= "ability to recreate analysis from same inputs and methods"

  EXCLUDE_EQUIVALENCE:
    SAMPLE != POPULATION
    ESTIMATOR != ESTIMATE
    STANDARD_ERROR != STANDARD_DEVIATION_BY_DEFAULT
    P_VALUE != PROBABILITY_NULL_IS_TRUE
    STATISTICAL_SIGNIFICANCE != PRACTICAL_SIGNIFICANCE
    CONFIDENCE_INTERVAL != BAYESIAN_CREDIBLE_INTERVAL
    CORRELATION != CAUSATION
    PREDICTION != CAUSAL_EFFECT
    REPRODUCIBILITY != REPLICATION

VALIDATION_RULES:
  RULE_1:
    SCIENTIFIC_QUESTION_POPULATION_AND_ESTIMAND_MUST_BE_DEFINED
  RULE_2:
    SAMPLING_AND_MEASUREMENT_PROCESSES_MUST_BE_DOCUMENTED
  RULE_3:
    STATISTICAL_MODEL_ASSUMPTIONS_MUST_BE_CHECKED_OR_JUSTIFIED
  RULE_4:
    EFFECT_SIZE_AND_UNCERTAINTY_SHOULD_ACCOMPANY_SIGNIFICANCE_TESTING_WHEN_RELEVANT
  RULE_5:
    MULTIPLE_TESTING_MUST_BE_ACCOUNTED_FOR_WHEN_REQUIRED
  RULE_6:
    TRAINING_VALIDATION_AND_TEST_DATA_MUST_REMAIN_SEPARATE_WHEN_GENERALISATION_IS_EVALUATED
  RULE_7:
    EXPLORATORY_AND_CONFIRMATORY_ANALYSES_SHOULD_BE_DISTINGUISHED
  RULE_8:
    ASSOCIATION_MUST_NOT_BE_INTERPRETED_AS_CAUSATION_WITHOUT_CAUSAL_IDENTIFICATION

CONFIDENCE:
  ontology_identity: 0.99
  scientific_workflow_structure: 0.99
  estimation_structure: 0.99
  hypothesis_testing_structure: 0.99
  experimental_design_structure: 0.99
  validation_reproducibility_structure: 0.99
  semantic_distinctions: 0.99

UPDATE_MODEL:
  IF:
    NEW_DATA_ARRIVES
  THEN:
    UPDATE:
      DESCRIPTIVE_STATISTICS
      PARAMETER_ESTIMATES
      UNCERTAINTY
      MODEL_DIAGNOSTICS
      PREDICTIONS

  IF:
    STUDY_DESIGN_CHANGES
  THEN:
    UPDATE:
      SAMPLING_MODEL
      RANDOMISATION_STRUCTURE
      DEPENDENCE_STRUCTURE
      INFERENCE_METHOD

  IF:
    MODEL_SPECIFICATION_CHANGES
  THEN:
    RERUN:
      ESTIMATION
      DIAGNOSTICS
      VALIDATION
      SENSITIVITY_ANALYSIS

  PRESERVE:
    RESEARCH_QUESTION
    TARGET_POPULATION
    ESTIMAND
    DATA_VERSION
    MEASUREMENT_DEFINITIONS
    STUDY_DESIGN
    MODEL_SPECIFICATION
    ANALYSIS_VERSION
    DATA_PROVENANCE

AI_CONSUMPTION:
  parse_as: FORMAL_SEMANTIC_SPECIFICATION
  execution_mode: RECURSIVE_REASONING

  preferred_reasoning_order:
    - IDENTIFY_SCIENTIFIC_QUESTION_AND_ESTIMAND
    - IDENTIFY_POPULATION_SAMPLE_AND_MEASUREMENT_PROCESS
    - IDENTIFY_EXPERIMENTAL_OR_OBSERVATIONAL_DESIGN
    - VALIDATE_DATA_AND_MISSINGNESS
    - SELECT_STATISTICAL_MODEL
    - ESTIMATE_PARAMETERS_OR_TEST_HYPOTHESES
    - QUANTIFY_EFFECT_SIZE_AND_UNCERTAINTY
    - CHECK_MODEL_ASSUMPTIONS_AND_DIAGNOSTICS
    - VALIDATE_PREDICTIVE_OR_INFERENTIAL_PERFORMANCE
    - ASSESS_SENSITIVITY_AND_ROBUSTNESS
    - DISTINGUISH_ASSOCIATION_FROM_CAUSATION
    - RETURN_SCIENTIFIC_STATISTICAL_INTERPRETATION

  constraints:
    - PRESERVE_POPULATION_SAMPLE_DISTINCTION
    - PRESERVE_ESTIMAND_DEFINITION
    - PRESERVE_MEASUREMENT_UNITS
    - DISTINGUISH_ESTIMATOR_FROM_ESTIMATE
    - DISTINGUISH_STANDARD_ERROR_FROM_STANDARD_DEVIATION
    - DISTINGUISH_CONFIDENCE_FROM_CREDIBLE_INTERVALS
    - DISTINGUISH_STATISTICAL_FROM_PRACTICAL_SIGNIFICANCE
    - DISTINGUISH_ASSOCIATION_FROM_CAUSATION
    - PRESERVE_DATA_PROVENANCE

FLOW_HASH:
  canonical_entity: "scientific-statistical-methods"
  namespace: "probability-statistics"
  version: "4.0"
  identity_basis:
    - PAGE_URL
    - CANONICAL_ENTITY
    - ENTITY_TYPE
    - SCIENTIFIC_WORKFLOW
    - ESTIMATION
    - HYPOTHESIS_TESTING
    - UNCERTAINTY_AND_VALIDATION

END_FLOW