Fase 3 Trabajo Final

Diseño Experimental

Fase 3

Grupo

30156_55

Estudiante Luz Angela Gil Hernandez 10306!!335

"utor  Diego A# $arin %d&rraga

'ni(ersidad na)ional a*ierta + a distan)ia ,'-AD. Es)uela de )ien)ias *&si)as te)nolog/a e ingenier/a ,E"%. !012

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FASE 3 DISEÑO EXPERIMENTAL FACTORIAL DESIGN

Autor: Luz Angela Gil Hernández Universidad Nacional Abierta y Distancia (UNAD) lagilh@unadvirtualeduco

Resumen !or "edio de este articulo se da a conocer el te"a tratado de la unidad # $Dise%o &actorial $ en la cual se desarrolla 'or "edio de variables &or"ulas entre otros "todos 'ara la co"'rensi*n del te"a a tratar a travs de la realizaci*n de los e+ercicios 'ro'uestos 'ro'uestos en el curso

Abstract ,y "eans o& this article is to -no. the to'ic o& the unit # /&actorial design in .hich .hich develo develo's 's throug through h variab variables les &or"ul &or"ulas as a"ong a"ong other other "ethod "ethods s &or the understanding o& the to'ic to be addressed through the i"'le"entation o& the 'ro'osed e0ercises e0ercises in the course

Palabras claves Cuadro Greco-latino Diseño factorial Diseño de bloque

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Unidad experimental

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Intr!ucc"#n $ 1l dise%o &actorial estudia el in2u+o de una sola variable inde'endiente sobre una variable de'endiente en dos o "ás gru'os e3uivalentes 1l investigador s*lo "ani'ula una variable inde'endiente 3ue co"o "4ni"o debe tener dos valores valores 1s un ti'o de e0'eri"ent e0'eri"ento o dise%ado dise%ado 3ue 'er"ite 'er"ite estudiar los e&ectos e&ectos 3ue 3ue 'ued 'ueden en tene tenerr vari varios os &act &actor ores es sobr sobre e una una res'u es'ues esta ta Al reali ealiza zarr un e0'eri"ento el hecho de variar los niveles de todos los &actores al "is"o tie"'o en lugar de uno a la vez 'er"ite estudiar las interacciones entre los &actores

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A%&n!"ce 3$ Fase 3$ '. Se estudia el efecto de cuatro ingredientes diferentes sobre el tiempo de retardo de un proceso  bioquímico. ara lo cual se se toman cuatro cantinas con lec!e pro"eniente de cuatro cuatro sitios diferentes# diferentes# recolectadas en cuatro días diferentes. Se les agregan los ingredientes independientemente independientemente $ se determina el tiempo de cambio de una de las propiedades características de la lec!e# utili%ando medios electr&nicos. 'os datos obtenidos son(

Prce!enc"a

Días

' ' ( 3 )

C)*+ ,)*/ )+2 D)*3

( , ) * C)** D)*0 )+4

3 )+/ D)01 C)*+ ,)*

) ,)* )+2 D)*0 C)*0

a* 56u7 tipo de diseño experimental siguieron los pro$ectantes8 Rta+ 9l tipo de diseño diseño experimental que siguieron los los pro$ectantes fue un cuadro 'atino# la cual se utili%a un diseño de bloques completos al a%ar. 'os diseños en cuadrados latinos son apropiados cuando es necesario controlar dos fuentes de "ariabilidad. 9n dic!os diseños el n:mero de ni"eles del factor principal tiene que coincidir con el n:mero de ni"eles de las dos "ariables de bloque o factores secundarios $ adem;s !a$ que suponer  que no existe interacci&n entre ninguna pare a una disposici&n en filas $ columnas de > letras latinas# de tal forma que cada letra aparece una sola "e% en cada fila $ en cada columna.  continuaci&n "amos a dar una forma simple de construcci&n de cuadrados latinos. Se parte de una

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'as sucesi"as filas se obtienen mo"iendo la primera letra de la fila anterior a la :ltima posici&n ?construcci&n por permutaci&n cíclica@# el cuadrado así obtenido es un cuadrado latino est;ndar. Un cuadrado latino se denomina est;ndar cuando las letras de la primera fila $ la primera columna est;n ordenadas alfab7ticamente.  parte de los cuadrados latinos así obtenidos existen otros cuadrados latinos diferentes# est;ndares $ no est;ndares. 9n el p7ndice , se muestran algunos cuadrados latinos est;ndares para los &rdenes A# +# *# 0# /# 2 $ 3. 9l procedimiento para construir un diseño en cuadrado latino es el siguiente( 

Se elige aleatoriamente un cuadrado latino de los disponibles.



Se asigna aleatoriamente el orden de las filas $ columnas.



 Se asignan aleatoriamente los tres factores a las filas# columnas $ letras# respecti"amente.

b* Calcule el BV $ pruebe la !ip&tesis correspondiente. Utilice α ) .*. Rta( dentifica el bloque ?factor de bloqueo@ n ) ,loques ?procedencia ) +@ dentifica los tratamientos > ) Tratamientos Tratamientos ?días ) +@  B ) Datos ) n B ) Total Total de datos datos recolectados ?+ x + ) 10@ E' ) grados de libertad ?acorde con la definici&n del m&dulo@ E' totales) B-1 totales)  B-1 ) ?B-1@ ' Totales Totales )10-1) 1*

,L Tratam"ent -  ?n-1@) +-1)A E' ,loque ) ?-1@) +-1) A ,L Ttales Ttales - E' F E', F E' 9rror ?B-1@ ) ?n-1@ F ?-1@ F E 9rror  ,L Errr - ?B-1@ - ?n-1@ - ?-1@ ) 14 EL Errr ) ?10-1@)1* - ?+-1@)A - ?+-1@)A )3

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Tabla Tabla 1. =ecolecci&n de los datos sobre la ganancia de peso de los semo"ientes

Tabla N '+ Gran me!"a$ Prce!enc"a

D.as 1

' ( 3 ) Ttal suma

C ,  D

Ttal suma

4

*+ */ +2 *3 412

, C D 

* ** *0 +4 4A

A  D C ,

+/ 01 *+ * 414

+ ,  D C

* +2 *0 *0 41

41 441 41+ 4/ 2+A

Gran me!"a

/(012/

Tabla N (+ SC ttales$ Prce!enc"a

D.as 1

4

4/)*(54/6*(54)*(754/1*( A

+

842)3*(94):)*;

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Tabla N 3+ SC >l?ues$ Prce!enc"a

D.as 1

4

A

Ttales

Cua!ra!s

41

++1

441

+22+1

41+

+*/30

4/

+42+3

+

'

C

*+

,

*



+/

,

(

,

*/

C

**

D

01



3



+2

D

*0

C

*+

D

)

D

*3



+4

,

*

C

*  + 2 * 0 * 0

SC cua!ra! !el ttal !e la sumatr"a !e ls cua!ra!s !e resulta!s !e ls >l?ues 2+A ST /1.0+3 cua!ra! !el ttal !e la sumatr"a !e ls resulta!s !e ls >l?ues SC >l?ue

1//.22/ ++.+/4

++.+10

/1

Tabla N )+ SCT tratam"ents Prce!enc"a

D.as 1

' ( 3 ) Ttal

4

A

+

C

*+

,

*



+/

,

*

,  D

*/ +2 *3

C D 

** *0 +4 4A

D C ,

01 *+ * 414

 D C

+2 *0 *0

412

41

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Tabla N /+ SCE SC9 SC Total SC Tratamiento SC ,

A21 43 *0

SCE

(=1

Tabla Tabla N 1+ ANO@A Fuentes !e @ar"ac"#n

Gra!s !e l"berta

Suma !e cua!ra!s

Tratam"ent

3

(=

Cua!ra!s Me!"s SC cua!ra9, L"berta! 60=1111111

FC - cua!ra! Me!. 9 cua!ra me!"s Errr 60661/3'/3(

>l?ues

3

/1

'021111111

606'(1'(1'3

Errr

=

(=1

=021111111

6061111111

Ttal

'/

32'

'(0

6062/2'62''

Ft

Ft

/ 

'

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encuentra ninguna diferencia entre los tratamientos  $ ,.  Rta+ Bo se encuentra c1.@ Si su respuesta es afirmati"a# compare la diferencia entre los tratamientos. 5Cu;les tratamientos son diferentes entre sí8

!@ Dibu-/6

) >-/6 A-)2 D-/1 C-/1

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b* Defina la "ariable# los tratamientos# elige una significancia apropiada. 

UBDD 99=M9BT'( 'a unidad experimental fueron los 4* semo"ientes# en los cuales se presenta un incremento en el peso durante el tiempo en que duro el experimento.

 

CTI=9S(



Se e"al:an dos factores los cuales son( los bloques $ los tratamientos.  

T=TM9BTIS( 9n este este caso caso se pres presen enta ta los los trat tratam amie ient ntos os de la letr letraa grie griega gass $ los los tratamientos de las letras latinas.

 

V=,'9S(

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