GLOBAL KNOWLEDGE ARK

Reference library

Foundations

Explore concepts, laws, equations and methods, with clear explanations of their use and sources. Choose an area of study or find a specific entry.

More filters

Reference entries

Showing 1–30 of 123 reference entries

Mathematics & logic · Physics · MeasurementRatios and rates

Distinguish part-to-part ratios, fractions of a whole and rates with units. Scale quantities together, compare unit rates, and explain when a relationship is proportional. Check zero cases, starting amounts and whether a result fits its context.

DefinitionMathematics & logic · Physics · MeasurementQuantities and units

Describe a quantity as a numerical value with a unit, and distinguish its physical kind from its dimension. Build length, area, volume and rate units, check meaningful combinations, and separate exact unit relations from measurement uncertainty.

DefinitionMathematics & logic · Physics · MeasurementUnit conversions

Convert quantities with exact unit ratios, track cancellation through compound units, and apply the correct powers to area and volume. Distinguish temperature readings from differences, check dimensions and context, and retain measurement uncertainty when reporting.

MethodMathematics & logic · Physics · MeasurementEstimation and uncertainty

Distinguish exact model values, rounded approximations and estimates from measurements. Declare the rounding rule, preserve information through calculations and unit changes, and interpret resolution, precision, accuracy and the stated uncertainty type without turning a report’s digits into guaranteed bounds.

DefinitionMathematics & logic · Physics · MeasurementReading graphs

Read a graph’s quantities, units, ticks and context before judging its visual impression. Calculate differences, reference-based percentages and interval rates from the represented values; distinguish legitimate zoom from distorted spacing; and keep samples, interpolation, missing information, uncertainty and causal explanations separate.

MethodPhysics · MeasurementObservables and measurement

Choose the physical quantity you want to investigate, specify the point, event or location involved, and explain how a reading relates to that quantity.

MethodPhysics · Information · MeasurementScientific records

Build an inspectable physics record, test and revise a bounded cart model, preserve processing history, and plan findable data with appropriate sharing conditions.

MethodPhysics · MeasurementSpeed of light in vacuum

c denotes the speed of light in vacuum. Its numerical value is fixed exactly in SI units.

DefinitionPhysics · MeasurementPlanck constant

h denotes the Planck constant. Its numerical value is fixed exactly in SI units.

DefinitionPhysics · MeasurementCaesium-133 defining frequency

ΔνCs denotes the unperturbed ground-state hyperfine transition frequency of caesium-133. Its numerical value is fixed exactly in SI units.

DefinitionMathematics & logic · MeasurementEuclidean right triangles and the Pythagorean theorem

In a Euclidean right triangle, squared leg lengths sum to the squared hypotenuse length.

Mathematical statementMathematics & logic · MeasurementConfidence interval for a population mean

A confidence level describes repeated-sampling coverage of an interval procedure.

MethodMeasurementSI base units

Seven named base units organize the SI quantity system.

DefinitionMeasurementSI decimal prefixes

Prefix symbols specify decimal scale factors.

DefinitionMeasurementMetrological traceability

Connect a result to a reference through documented calibrations.

DefinitionMeasurement · Mathematics & logicFirst-order uncertainty propagation

Combine input uncertainty through a measurement model.

MethodMeasurement · Physics · Mathematics & logicDimensional consistency

Use dimensions to detect impossible quantity equations.

MethodPhysics · MeasurementElectric current

Current measures charge crossing a chosen surface per unit time.

DefinitionPhysics · MeasurementElementary charge

The elementary charge has an exact SI numerical value.

DefinitionPhysics · MeasurementBoltzmann constant

The Boltzmann constant has an exact SI numerical value.

DefinitionMeasurement · Chemistry · PhysicsAvogadro constant

The mole is linked to a specified number of entities.

DefinitionMeasurement · PhysicsSI defining luminous efficacy

A specified frequency fixes the photometric SI reference.

DefinitionChemistry · MeasurementMole and amount of substance

The mole counts specified entities using the exact Avogadro constant.

DefinitionMeasurementCalibration

Relate indications to standards, then infer measurement results.

DefinitionMeasurementType A and Type B uncertainty evaluation

The classification describes how a component is evaluated.

MethodMeasurementExpanded uncertainty and coverage

A coverage factor scales standard uncertainty to a reported interval.

MethodMeasurement · Mathematics & logicCovariance in uncertainty models

Shared input variation belongs in the joint uncertainty description.

MethodMeasurementMeasurement models

Specify how input quantities determine the measurand.

MethodMeasurement · InformationMonte Carlo uncertainty propagation

Sample the joint input model to approximate the output distribution.

MethodMeasurementRepeatability and reproducibility

Precision depends on which measurement conditions are held or changed.

Definition
MethodSource checked

Confidence interval for a population mean

Mathematics & logicMeasurement

A confidence level describes repeated-sampling coverage of an interval procedure.

Key knowledge

A confidence interval procedure with coverage 1−α contains the fixed target parameter in that fraction of repeated samples under its assumptions. For independent observations from one normal population with unknown variance, a two-sided t interval estimates the population mean.

Values and equations

x̄ ± t₁₋α/₂,ₙ₋₁ s/√n

x̄
Sample mean
s
Sample standard deviation with denominator n−1
n
Sample size
α
One minus the confidence level
t₁₋α/₂,ₙ₋₁
Student t quantile at cumulative probability 1−α/2 and n−1 degrees of freedom

Conditions and scope

  • The displayed t interval assumes independent, identically distributed normal observations, n≥2, positive finite population variance and 0<α<1.
  • Coverage applies to the procedure under its model; it is not a posterior probability that the fixed mean lies in an already computed interval.
  • Dependence, selection bias or a different population distribution require further assessment.
Sources · 3

References

Sources retain their recorded scope. A source link alone does not establish verification of every statement.

  1. e-Handbook of Statistical Methods, 1.3.5.2: Confidence limits for the meanUS National Institute of Standards and TechnologyReference guideitl.nist.govRead source
  2. Introductory Statistics 2e, 8.2: Student t interval for a population meanOpenStaxTextbook chapteropenstax.orgRead source
  3. Discrete Mathematics; Probability and Statistical Methods · COR 4.1Audrija Choudhury and Arun Sarkar, University of Kalyani DODLTeaching resource · PDFdodl.klyuniv.ac.inRead source

Evidence and review

Frequentist coverage interpretation, t-interval formula and normal-sampling assumptions.

2026-10-10 · Compared NIST's coverage statement and formula with the textbook's sampling assumptions; no dataset-specific inference is made.

Foundational review

2026-10-10 · Fresh primary-source inspection of the complete compact record, including every statement, equation, quantity and material condition, followed by independent AI editorial review. This check does not certify all linked lessons or every passage of every cited publication.

Sources from other places

Scope or convention differs

A sampling-based confidence construction and the normal-mean t interval with sample variance divided by n minus one.

The source uses an upper-tail t subscript; the repository equivalent quantile notation is clearer. Adjacent formula errors are excluded.

Related reference entries

Explore relationships within this area of study and its connections to other areas.

Showing 1–1 of 1 relationships

Scientific relationships · 1 / 1

The relationship type describes the connection. Its linked statements, sources and conditions define the scope.

  1. Uses definition
    Relationship sources · 1

    Linked statements

    • If Z∼N(0,1) and U∼χ²ν are independent, Z/√(U/ν) has tν law. For iid N(μ,σ²) data, T=√n(X̄−μ)/S follows t_(n−1), where S²=Σ(Xᵢ−X̄)²/(n−1); t quantiles give exact normal-mean confidence intervals and tests.
Entry detailsPermanent link to this entry ↗
Record identity
math-statistical-estimation
Revision
core.1
Structured reference record
Essential core · first collection