##  [Precision](/precision-1) 

 Definition

Degree to which repeated measurements or computations under unchanged conditions yield the same or similar results; commonly associated with low random error or small dispersion of outcomes.

 

 

 

 

 

 





## Principle

Principle

Precision is characterized by the spread (variance, standard deviation) of repeated outcomes around their mean; high precision means low spread regardless of proximity to the true value.

 

 

 

 

 





## Demonstration

Demonstration

Running the same simulation multiple times with the same deterministic code and inputs on a stable platform yields negligible variation in output metrics, indicating high computational precision; in experimental work, repeated instrument readings with narrow scatter show high precision.

 

 

 

 

## Misapplication

Misapplication

Treating high precision as evidence of correctness; a measurement system can be highly precise yet biased, producing repeatable but systematically wrong results if calibration or model bias is neglected.

 

 

 

 

 





## Consequence

Consequence

High precision enables reproducibility, confident statistical estimation of averages and uncertainty reduction by repeated sampling; it allows distinguishing small systematic effects from random noise.

 

 

 

 

## Reversal

Reversal

Imprecision: large scatter among repeated observations that undermines reproducibility and makes it harder to detect systematic trends or validate models without increasing sample size.

 

 

 

 

 





## Boundary

Boundary

Concerns repeatability and dispersion under nominally identical conditions; does not imply closeness to truth (accuracy), and may be affected by uncontrolled changing conditions or hidden systematic influences.

 

 

 

 

 





## Semantic Tension

Semantic Tension

Precision often competes conceptually with accuracy: one can have high precision and low accuracy (consistent bias) or low precision and high accuracy on average; both properties must be considered together.

 

 

 

 

 





## Synthesis

Synthesis

Precision quantifies reproducibility via the spread of repeated results; it is necessary for reliable estimation and detecting systematic effects, but must be paired with accuracy and bias control to yield correct conclusions.