Problema 7.17

Se cree que la adhesividad de un pegamento depende de la presión y de la temperatura, al ser aplicado se realiza un experimento con ambos factores fijos.Realice una prueba de NO aditividad.

PRESIÓN TEMPERATURA250 260 270 yi

120 9.60 11.28 9.00 27.88130 9.69 10.10 9.57 29.36140 8.43 11.01 9.03 28.47150 9.98 10.44 9.80 30.22

37.7 42.03 37.4 117.43

SS AT=∑

i=1

aYi2

b− y ..2

ab ¿

(29.88 )2+(29.36 )2+(28.47 )2+(30.22 )2

3=

(117.43)2

(4 ) (3 )

37786133

−13907.4812

=1159.53−1158.95=0.58

SSBT=∑

i=1

aYi2

b− y ..2

ab =

(37.7 )2+ (42.83 )2 +(37.4 )2

4−

(117.93)2

(4 ) (3 )

465.454

−13907.4812

=1163.61−1158.95=4.66

SST=∑i=1

a

∑j=1

b

y2ij−y ..

2

ab=1166.3493−1158.95=7.3493

(9.60 )2+(11.28)2+(9.00 )2+(9.69 )2…−(117.93 )2

12

SSResidual=S ST−SS A−SSB

= 7.394 – 0.58 – 4.66 = 2.159

Suma de cuadrados de la No aditividad

∑i=1

a

∑j=1

b

y2ij−y ..

2

ab=¿

(9.60 ) (29.88 ) (37.7 )+ (11.28 ) (29.88 ) (42.83 )+(9.00 ) (29.88 ) (37.4 )+(9.69 ) (29.36 ) (37.7 )+(10.10 ) (29.36 ) (42.83 )+(9.57 ) (29.36 ) (37.4 )+ (8.43 ) (28.47 ) (37.7 )+(11.01 ) (28.47 ) (42.83 )+(9.03 ) (28.47 ) (37.4 )+ (9.98 ) (30.22 ) (37.7 )+ (10.44 ) (30.22 ) ( 42.83 )+(9.80 ) (30.22 ) (37.4 )=137237.8068

SSN=[∑i=1

a

∑j=1

b

y2ij− y (S SA+S SB+ y ..

2

ab )]abS S AS SB

¿¿

¿¿¿

¿ 3038.203332.4336

=93.674

La suma de cuadrados del error

SS Error=S SResidual−S SN

SS E=2.159−93.676=−91.517

Los datos de la interacción de Fo ( ser aprobado o rechazada)

f o=SSN

ssError /(a−1)(b−1)−1

fo= 93.676−91.517/(4−1)(3−1)−1

fo= 93.676−91.517/(3)(2)−1

fo= 93.676−91.517/5

fo= 93.676−18.3034

=−5.1179

ANOVA

Fuente de variación Suma de cuadrados

Grados de libertad

Media de cuadrados

Fo

Temperatura 0.58 4-1 =3 0.2 -5.1179Presión 4.66 3-1= 2 2.33

No adivitidad 93.6744 1 93.6Error -91.515 (4-1)(3-1)=6 -15.2525Total 7.3922 12

Análisis de datos

Expected Mean Squares SectionSource Term Denominator ExpectedTerm DF Fixed? Term Mean SquareA: Temp 2 Yes S(AB) S+bsAB: Presion 3 Yes S(AB) S+asBS(AB) 6 No SNote: Expected Mean Squares are for the balanced cell-frequency case.

Analysis of Variance TableSource Sum of Mean Prob PowerTerm DF Squares Square F-Ratio Level

(Alpha=0.05)A: Temp 2 4.65765 2.328825 6.49 0.031618* 0.695279B: Presion 3 0.5806917 0.1935639 0.54 0.672704 0.109303S 6 2.153883 0.3589806Total (Adjusted) 11 7.392225Total 12* Term significant at alpha = 0.05