Statistics Ontology
type: Ontology
abstract: This module provides terms and relations for representing statistical models and analyses that quantify variation, effects, and quality across experimental, process development, testing, and historical data. It integrates core concepts from STATO within the IOF framework to support design of experiments, regression and variance analysis, response surface methodology, and statistical evaluation used for process characterization, monitoring, and validation.
license: http://opensource.org/licenses/MIT
imports: stato.owl
imports: Core
version IRI: Statistics
copyright: Copyright (c) 2022, 2023, 2024, 2025, 2026 Open Applications Group
maturity: Provisional

covariate variable
type: Class
subclass of: STATO_0000258
example: dissolved oxygen concentration recorded throughout each cell culture run and specified as a covariate when feed strategy is a factor and harvest titer is the dependent variable; actual culture temperature recorded throughout each bioreactor run and specified as a covariate when temperature is not deliberately varied; initial viable cell density specified as a covariate when culture temperature and feed strategy are factors; seed culture age at inoculation recorded for each bioreactor run and specified as a covariate in an analysis of culture growth and productivity
adapted from: http://purl.obolibrary.org/obo/OBCS_0000040
first order logic axiom: CovariateVariable(x) → Variable(x)
is primitive: true
natural language definition: variable representing an observed rather than deliberately assigned characteristic that is specified for accounting for variation in a dependent variable separately from variation associated with the factors under study
primitive rationale: There are insufficient constructs to create a set of necessary and sufficient conditions.
semi formal natural language axiom: if x is a 'covariate variable' then x is a 'variable'

data preparation process
type: Class
subclass of: ComputingProcess
example: removing duplicate records from analytical data; converting measurement results to common units; harmonizing timestamps from equipment and laboratory systems; joining experimental-run metadata with analytical results; imputing missing observations according to a specified method; encoding categorical variables for statistical modeling; applying logarithmic transformations to skewed variables; standardizing variables before multivariate analysis
explanatory note: Data preparation involves applying one or more data transformations to convert raw or heterogeneous data into a consistent, usable form. It typically includes steps such as handling missing values, correcting errors, standardizing formats, or restructuring data for analysis, integration, or reporting.
first order logic axiom: DataPreparationProcess(x) → ComputingProcess(x)
is primitive: true
natural language definition: computing process in which input data are cleaned, organized, or otherwise transformed to make them suitable for subsequent analysis or use
primitive rationale: There are insufficient constructs to create a set of necessary and sufficient conditions.
semi formal natural language axiom: if x is a 'data preparation process' then x is a 'computing process'

explained variance
type: Class
subclass of: STATO_0000039
example: coefficient of determination that represents the variance explained by a linear model; eta-squared that represents the variance explained in an ANOVA analysis
adapted from: https://www.statology.org/explained-variance/
first order logic axiom: ExplainedVariance(x) → Statistic(x)
is primitive: true
natural language definition: statistic representing the portion of the total variance in a dependent variable that is accounted for by one or more variables included in a statistical model
primitive rationale: There are insufficient constructs to create a set of necessary and sufficient conditions.
semi formal natural language axiom: if x is an 'explained variance' then x is a 'statistic'

exploratory data analysis
type: Class
subclass of: PlannedProcess
example: computing summary statistics such as mean, variance, or correlation coefficients; plotting histograms, boxplots, or scatter matrices to visualize data distributions and relationships; identifying missing values or outliers in experimental results before modeling
adapted from: https://www.iso.org/obp/ui/en/#iso:std:iso-iec:22989:ed-1:v1:en:term:3.2.6 and https://www.ibm.com/think/topics/exploratory-data-analysis
explanatory note: Exploratory Data Analysis involves determining and describing features through summary statistics, visualization, and other descriptive techniques. It supports understanding of data structure, relationships, outliers, and quality before applying formal modeling or hypothesis testing.
first order logic axiom: ExploratoryDataAnalysis(x) → PlannedProcess(x)
is primitive: true
natural language definition: planned process used to determine and analyze characteristics of input data in order to identify structure, trends, or irregularities
primitive rationale: There are insufficient constructs to create a set of necessary and sufficient conditions.
semi formal natural language axiom: if x is an 'exploratory data analysis' then x is a 'planned process'

outlier detection
type: Class
subclass of: ComputingProcess
example: applying a generalized extreme Studentized deviate test to replicate assay results to identify one or more potential outliers; applying an interquartile-range criterion to supplier-lot impurity results to flag atypical observations; applying robust multivariate-distance criteria to metabolite profiles to identify atypical culture samples; applying an isolation-based anomaly-detection algorithm to historical process data to flag observations for investigation
adapted from: https://www.sciencedirect.com/topics/mathematics/outlier-detection#:~:text=Outlier%20detection%20is%20defined%20as,fraud%20detection%20and%20data%20cleaning.&text=How%20useful%20is%20this%20definition?
explanatory note: 1) This class is intended to cover a broader range of outlier detection approaches than those currently represented in STATO, including both hypothesis-based statistical tests and non-hypothesis or algorithmic methods for identifying outliers. 2) Outlier detection is distinct from evaluation against a material specification, statistical control-chart rules, or an expected process trend. An observation may be flagged as a potential outlier without being out of specification, out of control, or out of trend, and those classifications do not by themselves establish that the observation is an outlier.
first order logic axiom: DataTransformation(x) ∧ ∃y (achievesPlannedObjective(x, y) ∧ OutlierDetectionTestingObjective(y)) → OutlierDetection(x)
is primitive: true
natural language definition: computing process in which input data are evaluated for the presence of outliers according to a detection criterion
primitive rationale: There are insufficient constructs to create a set of necessary and sufficient conditions.
semi formal natural language axiom: if x is a 'data transformation' and x 'achieves planned objective' some 'outlier detection testing objective' then x is an 'outlier detection'

response surface plot
type: Class
subclass of: IAO_0000308
example: three-dimensional surface showing predicted product titer across combinations of culture temperature and pH while feed rate is held fixed; contour plot showing predicted galactosylated-species abundance across coded manganese and zinc concentrations; response surface showing predicted chromatography yield as a function of load density and residence time at a fixed buffer pH
adapted from: https://www.jmp.com/en/statistics-knowledge-portal/design-of-experiments/response-surface-methodology and https://wolfson.huji.ac.il/purification/PDF/Others/GE_DOE_in_Protein_Production_and_Purification_Handbook.pdf
explanatory note: A response surface plot is typically constructed from the predictions of a fitted regression model, most often a second-order (quadratic) polynomial, derived from data obtained in a designed experiment such as a central composite or Box–Behnken design. The figure illustrates how the predicted value of the dependent variable changes as the independent variables vary and may be presented as either a three-dimensional surface or a two-dimensional contour projection. Such plots facilitate the interpretation of main, interaction, and curvature effects and assist in locating regions of optimal or critical response.
first order logic axiom: ResponseSurfacePlot(x) → Figure(x)
is primitive: true
natural language definition: figure that depicts the predicted values of a dependent variable as a continuous surface over two or more independent variables
primitive rationale: There are insufficient constructs to create a set of necessary and sufficient conditions.
semi formal natural language axiom: if x is a 'response surface plot' then x is a 'figure'

contains values for variable
type: ObjectProperty
sub property of: isAbout
domain: InformationContentEntity
range: STATO_0000258
example: time-series dataset used in parameter fitting that holds pH measurements for the covariate variable denoting pH; design matrix providing the coded temperature levels (–1, 1) for twelve experimental runs of the temperature factor variable; regression dataset providing z-score-normalized substrate concentration values for an independent variable; single-run dataset recording the product titer value (measured or predicted) for the dependent variable representing product yield
natural language definition: relation from an information content entity to a variable that holds when the information content entity contains one or more values associated with that variable

quantifies statistical association of
type: ObjectProperty
sub property of: isAbout
domain: STATO_0000610
range: InformationContentEntity
example: a correlation coefficient that quantifies statistical association of a temperature variable and a growth-rate variable; a mutual-information value that quantifies statistical association of a transcriptomic profile and a proteomic profile
natural language definition: relation from a measure of association to an information content entity involved in the statistical relationship quantified by that measure