7/17/2019 2008-05

1/21

CURSO DEESTADSTICASociedad Espaola Sociedad Espaola de Bioqumica Clnica y Patologa Molecular (SEQC),

Calle Padilla 268, despacho 68, 08025-Barcelona, http://www.seqc.es

Gua de estudio. 6.

Estadstica aplicada

(I) La calidad analtica

Conocimientos previos

Contenidos

Bibliografa

Introduccin

7/17/2019 2008-05

2/21

Vol. 2, nm. 5, Pg. 2Curso de estadstica

Objetivos

Contenidos

Bibliografa acerca de la validacin de

http://www.ministeriodesalud.go.cr/protocolos/guiavalidacionmetodosanaliticos.pdfhttp://www.ministeriodesalud.go.cr/protocolos/guiavalidacionmetodosanaliticos.pdfhttp://www.eurachem.org/guides/valid.pdf

7/17/2019 2008-05

3/21

Vol. 2, nm. 5, Pg. 4Curso de estadstica

http://www.clinchem.org/cgi/reprint/54/3/612http://www.clinchem.org/cgi/reprint/44/11/2240http://www.clinchem.org/cgi/reprint/44/11/2240http://www.clinchem.org/cgi/reprint/44/11/2340http://www.clinchem.org/cgi/reprint/44/11/2340http://www.clinchem.org/cgi/reprint/43/11/2039http://www.clinchem.org/cgi/reprint/43/11/2039http://www.clinchem.org/cgi/reprint/30/5/751.pdfhttp://www.clinchem.org/cgi/reprint/30/5/751.pdfhttp://www.clinchem.org/cgi/reprint/46/1/100http://www.multiqc.com/MethodComparison.pdfhttp://www.multiqc.com/MethodComparison.pdfhttp://www.clinchem.org/cgi/reprint/45/2/314http://www.clinchem.org/cgi/reprint/45/6/882http://www.clinchem.org/cgi/reprint/48/6/919

7/17/2019 2008-05

4/21

Vol. 2, nm. 5, Pg. 5Curso de estadstica

7/17/2019 2008-05

5/21

Vol. 2, nm. 5, Pg. 6Curso de estadstica

Nombres propios:

Harold Jeffreys (1891-1989)

The earth: Its origin, history andphysical constitution

Earthquakes andmountains.

Methods of mathematical physics

Mathematics,probability & miscellaneous other science

Theory ofprobability

Grammar ofScience

Statistical methods for research workers

7/17/2019 2008-05

6/21

Vol. 2, nm. 5, Pg. 7Curso de estadstica

Tests de significacin parael coeficiente de correlacin

t

Objetivo

Limitaciones

( ),

Hiptesis

0

1

: 0

: 0

=

( ) ( ) ( ){ }1 1 2 2, , , , , ,

Procedimiento

( ) ( ) ( ){ }1 1 2 2, , , , , ,

7/17/2019 2008-05

7/21

Vol. 2, nm. 5, Pg. 8Curso de estadstica

( )

( ) ( )

1

2 2

1 1

=

= =

=

1

1

=

=

=

=

22

1=

7/17/2019 2008-05

8/21

Vol. 2, nm. 5, Pg. 10Curso de estadstica

n 27 24

r 0, 65 0, 74

Z 1 0, 65

ln 1, 5511 0, 65

+=

1 0, 74ln 1, 901

1 0, 74

+=

1 1

0,29927 3 24 3= + =

1, 551 1, 9011,17

0,299

= =

( )0,05 1,96=

Y X

n GGT edad GGT- media edad-media

(GGT-media) x

(edad-media)

(GGT-

media)2(edad-

media)2

50,4 15 -8,96 -3,52 31,538 80,274 12,390

63,6 24 4,25 5,48 23,277 18,043 30,030

66,6 12 7,28 -6,52 -47,477 53,024 42,510

64,6 22 5,22 3,48 18,181 27,294 12,110

52,7 17 -6,63 -1,52 10,082 43,998 2,310

61,3 21 1,93 2,48 4,788 3,727 6,150

49,2 19 -10,13 0,48 -4,861 102,549 0,230

68,7 13 9,37 -5,52 -51,715 87,772 30,470

52,1 15 -7,23 -3,52 25,464 52,331 12,390

58,8 13 -0,57 -5,52 3,163 0,328 30,47063,8 16 4,45 -2,52 -11,210 19,790 6,350

58,8 9 -0,54 -9,52 5,161 0,294 90,630

60,3 21 0,94 2,48 2,335 0,886 6,150

53,2 25 -6,15 6,48 -39,865 37,847 41,990

54,8 19 -4,51 0,48 -2,163 20,300 0,230

66,5 22 7,15 3,48 24,896 51,181 12,110

53,2 15 -6,12 -3,52 21,543 37,457 12,390

56,8 14 -2,51 -4,52 11,341 6,296 20,430

57,0 13 -2,28 -5,52 12,571 5,187 30,470

69,3 25 9,95 6,48 64,453 98,931 41,990

56,5 26 -2,83 7,48 -21,182 8,019 55,950

63,8 21 4,50 2,48 11,170 20,286 6,150

54,2 25 -5,09 6,48 -32,988 25,916 41,990

74,2 14 14,86 -4,52 -67,159 220,764 20,430

53,0 27 -6,35 8,48 -53,850 40,326 71,910

-2 23

suma 1483,2 463 -62,5058 1062,8188 638,2400

media 59,3 18,5

-0,076

-0,365

crtica 1,714

7/17/2019 2008-05

9/21

7/17/2019 2008-05

10/21

7/17/2019 2008-05

11/21

Vol. 2, nm. 5, Pg. 11Curso de estadstica

Problemas

1 2 3 4

56 221 259 110 646

= + + +

+ + + =

2 2 2 2 2

1 2 3 4

2 2 2 2

2

9 8 6 7 230

15,166

= + + +

+ + + =

= =

2

11 0,80

12,236

0,20

=

= =

( )( )( )( )

( )( )

Pr , 0,80

Pr 646 2, 236 15,166 , 646 2, 236 15,166 0, 80

Pr 612 , 680 0,80

+

+

7/17/2019 2008-05

12/21

Vol. 2, nm. 5, Pg. 12Curso de estadstica

14,3=

646 14, 3 9237, 8

=

= =

2 2 2

2

230 204, 49 47032, 7

216,87

=

= =

=

( )( )( )( )

( )( )

Pr , 0,80

Pr 9237, 8 2, 236 216, 87 , 9237, 8 2, 236 216, 87 0, 80

Pr 8752, 9 , 9722, 7 0,80

+

+

( )

( )

( ) 0

( ) 1+

=

( )

7/17/2019 2008-05

13/21

Vol. 2, nm. 5, Pg. 13Curso de estadstica

( ) ( ) ( )Pr

= =

( ) ( )lim 0

= =

( ) ( )lim 1+

+ = =

( )

( ) ( ) ( )Pr =

( ) ( ) ( )

=

( )

( ) ( )+

= = E

( ) ( ) ( )( ) ( )( ) ( )( ) ( )( ) = + +E E E E

( ) =E

( )( ) ( )( )=E E

( )=

( ) ( )( ) ( ) ( )

( )

+

+

= = =

=

E E

( )var

( ) ( )( ) ( ) ( )2 2var +

= =

( )

( )

( ) 0 ( )

1

( )( ) ( )( )1

Pr E

7/17/2019 2008-05

14/21

Vol. 2, nm. 5, Pg. 14Curso de estadstica

Demostracin

( )

( )

( )

( )( ) ( ) ( )+

=

( ) ( ) ( )= ( )( ) ( )

( ) ( ) ( ) ( )+

( ) 1+

=

( ) ( )( )Pr=

( )( ) ( ) ( ) ( ) ( ) ( ) ( )( )( )Pr

+

=

(x)

k

(x)

7/17/2019 2008-05

15/21

Vol. 2, nm. 5, Pg. 15Curso de estadstica

( )( ) ( )( )1

Pr E

( )( ) ( )( )Pr 1< E

( ) ( )( ) ( )2 2

= = E

2 2

( )( ) ( )( )22 2 2

2 2Pr 1

<

E

( )( )2E

( )( )2 2 =E

( )( )2

2

2 2 2 2 2

11 1 1

= =

( )( )2 2 2 21

Pr 1 <

( )( ) 21

Pr 1 <

( ) ( )( )

( )

2 2 2

2 2

2 2

Pr Pr

Pr

Pr

< = < < =

< < +=

< < +

2

7/17/2019 2008-05

16/21

Vol. 2, nm. 5, Pg. 16Curso de estadstica

( )2

1100 1

Introduccin a : Regresin en R (1)

lm( ) y glm( )

lm( )

glm( )

glm(formula, family = gaussian, data, weights, subset, na.action, start = NULL,

etastart, mustart, offset, control = glm.control(...), model = TRUE, method ="glm.fit", x = FALSE, y = TRUE, contrasts = NULL, ...)

data data frame

environment(formula), que habitualmente

es el entorno donde se est realizando el procedimiento glm

family

family = binomial

family = poisson

family = gaussian

family = Gamma

family = inverse.gaussian

formula " "

method glm.fit)

model.frame que no realiza realizar ajuste

na.action NA

na.omit ( ) Si se omite este argumento, R toma

el valor options (por defecto, na.fail

NULL (no hacer nada), o na.exclude.

7/17/2019 2008-05

17/21

Vol. 2, nm. 5, Pg. 17Curso de estadstica

subset

...

weights NULL

1. Datos

7/17/2019 2008-05

18/21

Vol. 2, nm. 5, Pg. 18Curso de estadstica

dettach( )

3. Regresin

4. Almacenamiento del resultado

5. Informacin adicional

7/17/2019 2008-05

19/21

Vol. 2, nm. 5, Pg. 19Curso de estadstica

6. Residuales

7/17/2019 2008-05

20/21

Vol. 2, nm. 5, Pg. 20Curso de estadstica

5 10 15 20 25

-10

-5

0

5

10

15

Index

res

-10

-5

0

5

10

15

Histogram of res

res

Frequency

-15 -10 -5 0 5 10 15

0

1

2

3

4

5

6

7

7/17/2019 2008-05

21/21

Vol. 2, nm. 5, Pg. 21Curso de estadstica

7. Valores ajustados

fitted.values() glm( ) glm.lineal

pred

59.25 59.30 59.35 59.40

-10

-5

0

5

10

15

pred

res

8. Consideraciones finales

glm

glm.linear