A P i i Accuracy versus Precision:

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Accuracy versus Precision:

the target analogy

Certitud, certeza o exactitud vs. Precisión

,

nitidez o repetitividad

Jorge Márquez - Instrumentación & Señales

- UNAM 2012

1

Precise but inaccurate measurement

small statistical uncertainity average value

Imprecise but accurate measurement

large statistical uncertainity

Individual observations outlier systematic error statistical error outlier true value

Jorge Márquez - Instrumentación & Señales

- UNAM 2012

2

Accuracy versus precision:

the target analogy

Certitud, certeza o exactitud vs. precisión (nitidez, repetibilidad)

target = true value

(a) (b)

Data points with (a) low precision and (b) high precision

(a) Has some average “accuracy” but (b) has low accuracy

Dispersion vs. Concentration

Jorge Márquez - Instrumentación & Señales - UNAM 2012 3

(a) (b)

Data points with (a) low accuracy and (b) high accuracy.

(both (a) and (b) have average high precision)

Jorge Márquez - Instrumentación & Señales - UNAM 2012 4

(a) Very low accuracy and very low precision

(b) Very high accuracy and “very high” precision with

two

outliers (datos intrusos)

Jorge Márquez - Instrumentación & Señales - UNAM 2012 5

(a) “Anisotropic” precision and “medium” average accuracy

(b) Low accuracy (best shot at “8”), but precision is ill-defined

(two populations of “high precision”???)

Jorge Márquez - Instrumentación & Señales - UNAM 2012 6

Imprecise, vague

:

Somebody threw something somewhere before the fire.

Highly precise, detailed

(but some irrelevant details)

:

A caucasic teenager, black-jet haired and dressed in fuchsia, threw a 35 cm burning log in the east border of the forest of Winsburg, 15 minutes before the fire was discovered by Mr. Henry Potter Jr.

¿Is it accurate?

Relatively precise but innacurate

(false and inconsistent):

Benganim Frankylinn invented the chiles rellenos in

Mars 1971, during the 296 anniversary of the Mexican battle of the 6 of may against the Germans in 1784.

Jorge Márquez - Instrumentación & Señales - UNAM 2012 7

A scientific abstract should contain useful and precise information such as:

Abstract

:

We measured the endocardial convective heat transfer coefficient, h, at 22 locations in the cardiac chambers of 15 pigs in vivo. A thin film Pt catheter tip sensor in a Wheatstone-bridge circuit, similar to a hot wire/film anemometer, measured h. Using fluoroscopy, we could precisely locate the steerable catheter sensor tip and sensor orientation in pigs

cardiac chambers.

With flows, h varies from 2500 to 9500 W/m2·K. With zero flow, h is approximately 2400 W/m2·K. These values of h can be used for the FEM modeling of radiofrequency cardiac catheter ablation.

Compare that with an abstract that contains little, imprecise information:

Abstract

:

This paper describes how to measure the convective heat transfer coefficient in pigs. It describes how to make the probe, how to calibrate it, precautions to take when making measurements in the pig.

It also describes the circuit and equations that assist in interpreting the results. It gives references for further study.

Jorge Márquez - Instrumentación & Señales

- UNAM 2012

8

x

1

N

N

n

1

x n

x

 1

N

– 1

N

n

1

(

x n

2

Accuracy and precision in terms of a distribution of observations

(not necessarily a Gaussian); the final measure is the mean

x

of

N

observations.

With regard to

accuracy

we can distinguish:

The difference between the

mean

of the measurements and the

reference value

the

bias

. Establishing and correcting for bias is necessary for

calibration

.

,

The combined effect of bias and

precision

(=spread, ~2

sigma

in a Gaussian).

Jorge Márquez - Instrumentación & Señales - UNAM 2012 9

Precision is often stratified into:

Repeatability

— the variation arising when all efforts are made to keep conditions constant by using the same instrument and operator, and repeating during a short time period; and,

Reproducibility

— the variation arising using the same measurement process among different instruments and operators, and over longer time periods

Precision is given as a

standard deviation

Jorge Márquez - Instrumentación & Señales - UNAM 2012 10

Jorge Márquez - Instrumentación & Señales

11

Accuracy Determination

Accuracy

(Exactitud)

Trueness

(Veracidad)

Precision

(Precisión)

Bias

(Sesgo)

Reproducibility

(Reproducibilidad)

Repeatability

(Repetibilidad)

ISO 5725 Standard (

Norma)

2008

Jorge Márquez - Instrumentación & Señales

- UNAM 2012

12

Random Error

err rand

=

x i

x

Absolute Error

err abs

=

x i

x true

Accuracy

+

Systematic Error

err sys

=

x

x true

Precision

Evaluated by the standard deviation

{

x i

}

Trueness

ISO 5725-6 Quality Control

Jorge Márquez - Instrumentación & Señales

- UNAM 2012

13

Up to date (2013), no accurate definition of accuracy

… and no precise definition of precision…

since noise (dispersion) may increase precision

(as the significant number of digits

resolution)

!

…and accuracy (as in an average)

Jorge Márquez - Instrumentación & Señales

- UNAM 2012

14

*Higher Precision …

with noise

Signal

+

0

noise

=

0

X X X X X X X X X

+

sub-resolution noise

<

1

X X X

X

X

X

n

measurements

+

supra-resolution noise

≈ 1

X

X

X

X

X X X

X

X

X

+

high

0

-mean noise

>>

1

X

X

X

X

X

X X X

X

X

X

X

X

X

*Beyond Nyquist …

with grid noise

Sub-sampling noise

X

X

X

X

X

X

feature size

:

X

X

i

samples

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

X

Super-resolution

X

X

X

X

X

X

X

X

X

feature size

:

Superresolución Morfológica por Nanoposicionamiento en Imágenes de Microscopia Optica

Jorge Márquez y Naser Qureshi

Objetivo:

Aumentar resolución de imágenes de microscopia mediante adquisiciones con diferencias de posición sub-pixel (precisión

0.5 nm. Aplicaciones Biomédicas en 2014: análisis de conexiones de micronúcleos celulares en estudios en citotoxicología y restauración/estudio de la textura de preparaciones inmunohistocitológicas.

N

adquisiciones con variaciones subpixel

Restauración a resolución

Jorge Márquez - Instrumentación

& Señales - UNAM 2012

 factor

N

17

X

+

supra-resolution noise

≈ 1

X

X

X

X

X X X

X

X

X



Under some conditions a high dispersion gives

“better precision” of an average than a low dispersion.

+

sub-resolution noise

<

1

X

X X X

X

X

Better than this !

Jorge Márquez - Instrumentación & Señales

- UNAM 2012

18

Output Output

Input

(a)

Input

(b)

(a) The one-point calibration may miss nonlinearity.

(b) The two-point calibration may also miss nonlinearity.

Jorge Márquez - Instrumentación & Señales - UNAM 2012 20

1

N n

N

1

x n

N

1

–1

n

N

1

x n x

2

Dark blue is less than one standard deviation from the mean. For the normal distribution, this accounts for about 68% of the set, while two standard deviations from the mean (medium and dark blue) account for about 95%, and three standard deviations (light, medium, and dark blue) account for about 99.7%

Jorge Márquez - Instrumentación & Señales - UNAM 2012 21

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