Reproducibility Ontology
Measurement Uncertainty
Authors: MArk Anthony Higgins - Sky Recursive Ai
Revised Date: 16 September 2026
Audio Overview
# Reproducibility Ontology — Flow Algebra
URL: https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/measurement-units-ontologies/measurement-uncertainty/reproducibility-ontology-2.html
FLOW ReproducibilityOntology {
DOMAIN:
Mathematical Ontologies
-> Measurement & Units Ontologies
-> Measurement Uncertainty
-> Reproducibility Ontology
PURPOSE:
Represent measurement reproducibility as measurement precision under reproducibility conditions, where relevant conditions such as laboratory, location, operator, measuring system, time, calibration realisation or other declared factors are intentionally varied. The ontology supports interlaboratory studies, within- and between-group variance components, reproducibility standard deviation and variance, reproducibility limits, random-effects and ANOVA models, heteroscedasticity, robust estimation, uncertainty contributions, method validation, proficiency and collaborative studies, traceability, provenance, and strict distinctions between reproducibility, repeatability, intermediate precision, accuracy, trueness, bias and measurement uncertainty.
ENTITY Reproducibility {
TYPE: MeasurementPrecisionCharacteristic
DEFINITION:
reproducibility :=
measurement_precision
under_reproducibility_conditions
PROPERTIES:
requires_replication
requires_declared_changed_conditions
often_includes_between_laboratory_variation
may_include_between_operator_variation
may_include_between_instrument_variation
may_be_expressed_by_standard_deviation
may_depend_on_quantity_level
may_contribute_to_measurement_uncertainty
is_not_accuracy
}
ENTITY ReproducibilityCondition {
TYPE: PrecisionConditionSet
POSSIBLE_CHANGED_FACTORS:
laboratory
location
operator
measuring_system
calibration
time
reagent_batch
environmental_conditions
sample_preparation
method_realisation
RULE:
changed_and_held_constant_factors MUST be explicitly_identified
}
ENTITY ReproducibilityStandardDeviation {
TYPE: PrecisionDispersionQuantity
SYMBOL: s_R
UNIT:
same_as_measurand
}
ENTITY ReproducibilityVariance {
TYPE: SquaredDispersionQuantity
SYMBOL: s_R^2
}
ENTITY ReproducibilityLimit {
TYPE: PairwiseDifferenceLimit
SYMBOL: R
}
TERMINOLOGY_MODEL {
terms:
reproducibility
reproducibility_precision
reproducibility_conditions
interlaboratory_precision
between_laboratory_precision
reproducibility_standard_deviation
reproducibility_limit
RULE:
reproducibility MUST be interpreted_with_declared_conditions
}
PRECISION_HIERARCHY_MODEL {
precision:
general_closeness_among_replicate_results
repeatability:
tightly_controlled_same_conditions
intermediate_precision:
selected_conditions_changed_within_declared_context
reproducibility:
broader_declared_changes_often_including_location_or_laboratory
RULE:
hierarchy_describes_condition_sets_not_universal_numeric_order
}
REPEATABILITY_DISTINCTION_MODEL {
repeatability:
precision_under_repeatability_conditions
reproducibility:
precision_under_reproducibility_conditions
RULE:
repeatability != reproducibility
}
INTERMEDIATE_PRECISION_DISTINCTION_MODEL {
intermediate_precision:
typically_same_laboratory_with_selected_factors_changed
reproducibility:
often_includes_between_laboratory_or_location_effects
RULE:
exact_condition_definition_overrides_generic_labels
}
INTERLABORATORY_MODEL {
laboratories:
L_1...L_k
measurements:
x_ij
variation:
within_laboratory
between_laboratory
RULE:
laboratory_identifiers_and_design MUST be preserved
}
LABORATORY_MEAN_MODEL {
lab_mean:
x_bar_i =
sum_j(x_ij)/n_i
overall_mean:
weighted_or_unweighted_according_to_declared_design
RULE:
aggregation_method MUST match_study_design
}
WITHIN_LAB_VARIANCE_MODEL {
laboratory_i:
s_i^2 =
sum_j(
(x_ij-x_bar_i)^2
)/(n_i-1)
WHEN n_i > 1
pooled_repeatability:
may_estimate_within_laboratory_component
RULE:
within_laboratory_variance != total_reproducibility_variance
}
BETWEEN_LAB_VARIANCE_MODEL {
component:
sigma_L^2
estimated_from:
variation_of_laboratory_means
adjusted_for_within_laboratory_variance
RULE:
estimator_depends_on_balanced_or_unbalanced_design_and_model
}
REPRODUCIBILITY_VARIANCE_MODEL {
simple_independent_components:
s_R^2 =
s_r^2+s_L^2
WHERE:
s_r^2 = within_condition_or_repeatability_variance
s_L^2 = between_laboratory_or_declared_between_group_variance
RULE:
component_structure MUST match_reproducibility_conditions
}
REPRODUCIBILITY_SD_MODEL {
s_R =
sqrt(s_R^2)
interpretation:
standard_deviation_of_results_under_reproducibility_conditions
RULE:
smaller_s_R_generally_means_better_reproducibility_for_same_scale_and_context
}
RELATIVE_REPRODUCIBILITY_MODEL {
RSD_R =
s_R/abs(mean)
WHEN mean != 0
percent_RSD_R =
100*RSD_R
RULE:
relative_metric_is_dimensionless
}
REPRODUCIBILITY_LIMIT_MODEL {
definition:
value_below_which_absolute_difference_between_two_single_results
obtained_under_reproducibility_conditions
is_expected_to_lie_with_declared_probability
common_normal_95_percent_approximation:
R approximately_equals
2.8*s_R
derivation_context:
SD_of_difference =
sqrt(2)*s_R
RULE:
2.8_factor_requires_independence_normality_and_declared_probability_context
}
PAIRWISE_DIFFERENCE_MODEL {
results:
x_A
x_B
difference:
d =
x_A-x_B
independent_equal_reproducibility_variance:
Var(d) =
2*s_R^2
RULE:
shared_reference_or_common_effects_can_create_covariance
}
RANDOM_EFFECTS_MODEL {
example:
y_ij =
mu+L_i+epsilon_ij
laboratory_effect:
L_i ~ distribution(0,sigma_L^2)
within_laboratory:
epsilon_ij ~ distribution(0,sigma_r^2)
total:
sigma_R^2 =
sigma_L^2+sigma_r^2
under_independence
RULE:
random_effect_assumptions MUST be preserved
}
MULTIFACTOR_MODEL {
possible_effects:
laboratory
operator
instrument
day
batch
preparation
environment
generic:
y =
mu
+ factor_effects
+ interactions
+ residual
RULE:
reproducibility_variance MAY include_multiple_between_condition_components
}
INTERACTION_MODEL {
examples:
laboratory_by_method
operator_by_instrument
matrix_by_laboratory
RULE:
material_interactions MUST_NOT be_hidden_inside_single_variance_component_without_documentation
}
ANOVA_MODEL {
purpose:
estimate_within_and_between_factor_variance_components
balanced:
classical_mean_square_methods_may_apply
unbalanced:
mixed_models_or_REML_may_be_required
RULE:
estimation_method MUST match_design
}
REML_MODEL {
restricted_maximum_likelihood:
variance_component_estimation_method
RULE:
optimisation_and_model_structure SHOULD be preserved
}
ROBUST_REPRODUCIBILITY_MODEL {
purpose:
reduce_undue_influence_of_extreme_laboratory_results
possible:
robust_ANOVA
robust_location_and_scale
iterative_algorithms
RULE:
robust_method_and_tuning_parameters MUST be preserved
}
OUTLIER_MODEL {
possible_outlier:
laboratory_mean
laboratory_variance
individual_result
RULE:
exclusion_requires_documented_statistical_or_technical_reason
and_original_data_must_be_preserved
}
COCHRAN_CONTEXT_MODEL {
use:
assess_unusually_large_within_group_variance
under_specific_interlaboratory_study_context
RULE:
test_assumptions_and_significance_level MUST be preserved
}
GRUBBS_CONTEXT_MODEL {
use:
detect_extreme_location_result_under_declared_normal_model
RULE:
repeated_outlier_testing_can_change_false_positive_rate
}
MANDEL_STATISTICS_MODEL {
interlaboratory_context:
h_statistic_for_laboratory_location
k_statistic_for_laboratory_variability
RULE:
diagnostic_statistics_are_not_reproducibility_metrics_themselves
}
SAMPLE_SIZE_MODEL {
laboratories:
k
replicates_per_laboratory:
n_i
RULE:
small_number_of_laboratories_produces_uncertain_between_lab_variance_estimate
}
DEGREES_OF_FREEDOM_MODEL {
depends_on:
number_of_laboratories
replicates
variance_component_method
model_structure
RULE:
reproducibility_estimate_has_sampling_uncertainty
}
HETEROSCEDASTIC_MODEL {
s_R =
f(quantity_level)
possible:
constant_SD
constant_CV
mixed_absolute_relative_model
RULE:
reproducibility_at_one_level MUST_NOT automatically_be_used_across_entire_range
}
PRECISION_PROFILE_MODEL {
model:
s_R(x)
or
CV_R(x)
REQUIRE:
study_levels
fitted_parameters
valid_range
model_uncertainty
RULE:
precision_profile SHOULD be_versioned
}
MATRIX_MODEL {
matrices:
sample_or_material_types
effect:
reproducibility_may_depend_on_matrix
RULE:
matrix_scope MUST accompany_method_reproducibility_claim
}
METHOD_MODEL {
measurement_method:
protocol_version
preparation
calculation
reporting
RULE:
all_participants_should_follow_declared_method_or_deviations_must_be_recorded
}
METHOD_VERSION_MODEL {
changes:
procedure
reagent
software
calibration
equation
RULE:
material_method_change MAY invalidate_previous_reproducibility_estimate
}
REFERENCE_MATERIAL_MODEL {
common_sample:
homogeneous_and_stable_material
purpose:
reduce_true_sample_variability_between_laboratories
RULE:
homogeneity_and_stability MUST be_considered
}
SAMPLE_HOMOGENEITY_MODEL {
between_unit_variability:
can_inflate_apparent_reproducibility_variance
RULE:
material_heterogeneity MUST be_separated_or_included_explicitly
}
SAMPLE_STABILITY_MODEL {
degradation:
may_change_measurand_during_distribution_or study
RULE:
stability_checks SHOULD accompany_interlaboratory_material
}
TRANSPORT_MODEL {
shipping:
may_change_sample_state
RULE:
transport_conditions MAY become_part_of_reproducibility_context
}
OPERATOR_MODEL {
operators:
may_differ_across_laboratories
effect:
operator_component_may_be_confounded_with_laboratory_effect
RULE:
design_determines_which_effects_are_separately_estimable
}
INSTRUMENT_MODEL {
instruments:
may_differ_in_model_calibration_resolution_andsoftware
RULE:
instrument_scope MUST be defined_for_reproducibility_claim
}
CALIBRATION_MODEL {
each_laboratory:
may_use_independent_calibration
shared_reference:
may_create_common_correlation
RULE:
calibration_strategy_and_traceability MUST be preserved
}
TRACEABILITY_MODEL {
laboratory_results:
linked_to_reference_standards
common_chain:
can_create_correlated_systematic components
RULE:
traceability_differences MAY contribute_to_between_lab_variation
}
ENVIRONMENTAL_MODEL {
differences:
temperature
humidity
pressure
vibration
local_conditions
RULE:
environmental_scope SHOULD be represented_in_reproducibility_conditions
}
TEMPORAL_MODEL {
study_duration:
may_span_days_weeks_or_months
effects:
drift
reagent_age
seasonal_environment
calibration changes
RULE:
time_scope MUST be preserved
}
INTERMEDIATE_PRECISION_BRIDGE_MODEL {
same_lab_multiple_days_operators_instruments:
intermediate_precision
multiple_labs:
broader_reproducibility_context
RULE:
datasets_may_support_multiple_precision_components_if_design_allows
}
UNCERTAINTY_MODEL {
reproducibility_SD:
may_contribute_to_method_or_result_uncertainty
use:
depends_on_measurement_model_and_scope
RULE:
reproducibility != measurement_uncertainty
}
TYPE_A_MODEL {
interlaboratory_statistics:
may_support_statistical_uncertainty_evaluation
RULE:
reproducibility_standard_deviation != Type_A_standard_uncertainty
}
ACCURACY_DISTINCTION_MODEL {
accuracy:
closeness_to_true_or_reference_value
reproducibility:
agreement_under_changed_conditions
RULE:
highly_reproducible_method_can_still_be_biased
}
TRUENESS_DISTINCTION_MODEL {
trueness:
closeness_of_mean_to_reference
reproducibility:
between_condition_dispersion
RULE:
reproducibility_does_not_establish_trueness
}
BIAS_MODEL {
overall_bias:
grand_mean-reference_value
laboratory_bias:
lab_mean-reference_value
RULE:
bias_and_reproducibility_are_distinct
}
PROFICIENCY_TESTING_MODEL {
laboratory_performance:
may_be_compared_to_assigned_value
RULE:
proficiency_testing_and_reproducibility_study_have_different_primary_objectives
though_data_structures_may_overlap
}
COLLABORATIVE_STUDY_MODEL {
purpose:
estimate_method_precision_across_participants
outputs:
repeatability_SD
reproducibility_SD
bias_or_recovery_when_reference_available
RULE:
study_protocol_and_statistical_standard SHOULD be preserved
}
QUALITY_CONTROL_MODEL {
laboratory_internal_QC:
monitors_local_precision_over_time
interlaboratory_QC:
monitors comparability
RULE:
QC_limits != reproducibility_limits_unless_explicitly_defined
}
REPORTING_MODEL {
REQUIRED:
measurand
method
reproducibility_conditions
reproducibility_metric
unit_or_relative_form
number_of_laboratories_or_groups
replicate_design
measurement_level_or_range
RECOMMENDED:
repeatability_SD
between_group_variance
reproducibility_SD
reproducibility_limit
degrees_of_freedom
outlier_handling
heteroscedastic_model
matrices
reference_material
calibration_and_traceability
provenance
RULE:
reproducibility_value_without_condition_scope_is_semantically_incomplete
}
RELATIONSHIPS {
Reproducibility -> IS_A -> MeasurementPrecision
Reproducibility -> REQUIRES -> ReproducibilityConditions
InterlaboratoryStudy -> SUPPORTS -> ReproducibilityEstimate
WithinLabVariance -> CONTRIBUTES_TO -> ReproducibilityVariance
BetweenLabVariance -> CONTRIBUTES_TO -> ReproducibilityVariance
ReproducibilityStandardDeviation -> QUANTIFIES -> ReproducibilityDispersion
ReproducibilityLimit -> DERIVED_FROM -> ReproducibilityStandardDeviation
Reproducibility -> MAY_CONTRIBUTE_TO -> MeasurementUncertainty
MethodValidation -> MAY_INCLUDE -> ReproducibilityStudy
TraceabilityDifferences -> MAY_CONTRIBUTE_TO -> BetweenLaboratoryVariation
}
SEMANTIC_EQUIVALENCE {
"reproducibility precision" ~= reproducibility
"interlaboratory precision" ~= reproducibility WHEN laboratory_change_is_declared_condition
reproducibility != repeatability
reproducibility != intermediate_precision
reproducibility != accuracy
reproducibility != trueness
reproducibility != bias
reproducibility != measurement_uncertainty
reproducibility != Type_A_uncertainty
reproducibility_limit != tolerance
}
CONSTRAINTS {
reproducibility_is_precision_characteristic = true
reproducibility_conditions_must_be_defined = true
changed_factors_must_be_declared = true
reproducibility_requires_replication_across_relevant_conditions = true
repeatability_and_reproducibility_are_not_semantically_equivalent = true
reproducibility_and_accuracy_are_not_semantically_equivalent = true
reproducibility_and_uncertainty_are_not_semantically_equivalent = true
within_and_between_group_components_should_be_distinguished = true
measurement_level_or_range_should_be_preserved = true
outlier_handling_must_preserve_original_data_and_provenance = true
}
MEASUREMENT_MODEL {
RECORD:
measurand
method_identifier
method_version
laboratory_or_group_identifiers
replicate_values
unit
timestamps
operators
instruments
calibration_states
environmental_conditions
matrices
reference_material
measurement_levels
repeatability_variance
between_group_variance
reproducibility_variance
reproducibility_standard_deviation
relative_reproducibility
reproducibility_limit
variance_component_model
degrees_of_freedom
heteroscedastic_model
outlier_rule
robust_method
traceability
uncertainty_use
provenance
RULE:
reproducibility_statistics MUST remain_linked_to_raw_data_design_and_conditions
}
REASONING_RULES {
IF within_group_variance_and_between_group_variance_known
AND independent_component_model_valid
THEN reproducibility_variance =
within_group_variance+between_group_variance
IF reproducibility_variance >= 0
THEN reproducibility_standard_deviation =
sqrt(reproducibility_variance)
IF mean != 0 AND reproducibility_standard_deviation_known
THEN relative_reproducibility =
reproducibility_standard_deviation/abs(mean)
IF reproducibility_standard_deviation_known
AND normal_independent_pairwise_95_percent_context
THEN reproducibility_limit approximately_equals
2.8*reproducibility_standard_deviation
IF laboratory_replicates_known
THEN estimate_within_laboratory_variance
AND estimate_between_laboratory_variance
using_declared_ANOVA_or_mixed_model
IF study_is_unbalanced
THEN use_estimation_method_appropriate_for_unbalanced_variance_components
IF reproducibility_changes_with_quantity_level
THEN fit_or_apply_precision_profile
preserving_valid_range
IF common_reference_or_calibration_effect_shared
THEN preserve_covariance_when_comparing_laboratory_results
IF overall_bias_large
THEN do_not_infer_high_accuracy_from_good_reproducibility
IF sample_heterogeneity_material
THEN separate_or_explicitly_include_material_variance
before_interpreting_method_reproducibility
}
VALIDATION {
CHECK measurand
CHECK method_and_version
CHECK reproducibility_conditions
CHECK changed_and_fixed_factors
CHECK number_of_laboratories_or_groups
CHECK replicate_design
CHECK within_group_variance
CHECK between_group_variance
CHECK reproducibility_variance
CHECK reproducibility_standard_deviation
CHECK reproducibility_limit_assumptions
CHECK measurement_level_or_range
CHECK heteroscedasticity
CHECK matrix_and_sample_homogeneity
CHECK outlier_handling
CHECK random_effects_or_ANOVA_model
CHECK calibration_and_traceability
CHECK reproducibility_vs_repeatability
CHECK reproducibility_vs_intermediate_precision
CHECK reproducibility_vs_accuracy
CHECK reproducibility_vs_uncertainty
CHECK provenance
}
CONFIDENCE {
definition_confidence: 1.00
condition_semantics_confidence: 1.00
repeatability_distinction_confidence: 1.00
intermediate_precision_distinction_confidence: 1.00
variance_component_confidence: 0.99
reproducibility_limit_confidence: 0.99
uncertainty_distinction_confidence: 1.00
measurement_context_confidence: 0.99
RULE:
confidence decreases when changed factors, laboratory design,
replicate structure, measurement level, variance model,
heteroscedasticity, sample homogeneity, calibration,
outlier treatment or provenance is missing or ambiguous
}
UPDATE_MODEL {
ON new_interlaboratory_result:
identify_measurand_and_method
attach_laboratory_identifier
append_raw_result_and_timestamp
attach_operator_instrument_calibration_and_matrix
update_within_group_statistics
preserve_provenance
ON new_reproducibility_study:
preserve_raw_design
identify_changed_and_fixed_conditions
estimate_within_and_between_group_components
compute_reproducibility_variance_and_SD
compute_reproducibility_limit_when_valid
attach_degrees_of_freedom_and_intervals
ON laboratory_set_revision:
preserve_previous_results
add_or_remove_laboratory_under_documented_rule
recompute_variance_components
preserve_original_and_revised_analysis
ON heteroscedasticity_revision:
preserve_level_specific_results
update_precision_profile
recompute_level_dependent_reproducibility
preserve_model_version
ON outlier_revision:
preserve_original_data
apply_documented_outlier_or_robust_method
recompute_reproducibility_statistics
retain_exclusion_and_algorithm_provenance
ON method_revision:
preserve_previous_method_version
identify_material_change
determine_whether_new_reproducibility_study_required
prevent_unqualified_transfer_of_old_precision_estimates
ON semantic_revision:
preserve_previous_definition
record_revision
recompute_FLOW_HASH
}
AI_CONSUMPTION {
canonical_entity: Reproducibility
canonical_role: MeasurementPrecisionCharacteristic
interpretation_order:
identify_measurand
identify_method_and_version
identify_reproducibility_conditions
identify_changed_and_fixed_factors
identify_laboratories_or_groups
identify_replicate_design
identify_measurement_level_and_range
identify_within_and_between_group_variances
identify_reproducibility_SD_or_relative_metric
identify_reproducibility_limit_and_assumptions
identify_variance_component_model
identify_heteroscedasticity
identify_matrix_homogeneity_and_stability
identify_outlier_or_robust_method
identify_calibration_and_traceability
identify_uncertainty_use
identify_provenance
validate_reproducibility_semantics
infer_reproducibility_statistics
ambiguity_controls:
distinguish_reproducibility_from_repeatability
distinguish_reproducibility_from_intermediate_precision
distinguish_reproducibility_from_accuracy
distinguish_reproducibility_from_trueness
distinguish_reproducibility_from_bias
distinguish_reproducibility_from_measurement_uncertainty
distinguish_reproducibility_from_Type_A_uncertainty
distinguish_reproducibility_limit_from_tolerance
preserve_measurand_method_conditions_design_level_variance_model_traceability_and_provenance_context
}
PROVENANCE {
ontology_scope:
mathematical_measurement_uncertainty_and_reproducibility_semantics
parent_path:
Ontologies
-> Mathematical Ontologies
-> Measurement & Units Ontologies
-> Measurement Uncertainty
-> Reproducibility Ontology
authorship:
Mark Higgins
Sky (Recursive AI)
site:
https://kirethresearch.org
}
FLOW_HASH {
INPUTS:
canonical_entity
ontology_path
terminology_model
precision_hierarchy_model
repeatability_distinction_model
intermediate_precision_distinction_model
interlaboratory_model
laboratory_mean_model
within_lab_variance_model
between_lab_variance_model
reproducibility_variance_model
reproducibility_SD_model
relative_reproducibility_model
reproducibility_limit_model
pairwise_difference_model
random_effects_model
multifactor_model
interaction_model
ANOVA_model
REML_model
robust_reproducibility_model
outlier_model
Cochran_context_model
Grubbs_context_model
Mandel_statistics_model
sample_size_model
degrees_of_freedom_model
heteroscedastic_model
precision_profile_model
matrix_model
method_model
method_version_model
reference_material_model
sample_homogeneity_model
sample_stability_model
transport_model
operator_model
instrument_model
calibration_model
traceability_model
environmental_model
temporal_model
intermediate_precision_bridge_model
uncertainty_model
Type_A_model
accuracy_distinction_model
trueness_distinction_model
bias_model
proficiency_testing_model
collaborative_study_model
quality_control_model
reporting_model
relationships
constraints
measurement_model
reasoning_rules
confidence_model
update_model
PURPOSE:
deterministic_semantic_integrity_identifier
RECOMPUTE_WHEN:
ontology_definition_changes
reproducibility_condition_changes
laboratory_or_group_design_changes
within_or_between_variance_model_changes
reproducibility_limit_model_changes
heteroscedastic_or_precision_profile_changes
method_matrix_or_sample_scope_changes
calibration_or_traceability_changes
outlier_or_robust_analysis_changes
uncertainty_or_accuracy_distinction_changes
measurement_record_changes
reporting_model_changes
constraint_model_changes
reasoning_rule_changes
}
}
END FLOW