ANALISIS DE VARIANZA DESBALANCEADO
Geraldine Barbosa
2023-05-26
ANALISIS DE VARIANZA DESBALANCEADO
###MODELO DISEÑO DESBALANCEADO \[H_0 = \mu_{C0} = \mu_{C1} = \mu_{C2} \]
set.seed(123)
porc_germ = c(
rnorm(40, 60, 6),
rnorm(40, 70, 7),
rnorm(40, 80, 8))
acido = gl(3, 40, 120, c('C0', 'C1', 'C2'))
datos = data.frame(acido, porc_germ)
head(datos)## acido porc_germ
## 1 C0 56.63715
## 2 C0 58.61894
## 3 C0 69.35225
## 4 C0 60.42305
## 5 C0 60.77573
## 6 C0 70.29039table(datos$acido)##
## C0 C1 C2
## 40 40 40datos_des = datos[-c(50, 111, 120), ]
table(datos_des$acido)##
## C0 C1 C2
## 40 39 38### Analisis de varianza balanceado.
mod1= aov(porc_germ ~ acido, datos)
summary(mod1)## Df Sum Sq Mean Sq F value Pr(>F)
## acido 2 7835 3918 98.15 <2e-16 ***
## Residuals 117 4670 40
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1- Rechaza la hipotesis nula, la concentración de acido influye en el porcentaje de germinación
boxplot(datos$porc_germ ~ datos$acido)
- Una pequeña concentración de acido mejora la germinación.
### Analisis de varianza balanceado (con los datos desbalanceados)
mod2 = aov(porc_germ ~ acido, datos_des)
summary(mod2)## Df Sum Sq Mean Sq F value Pr(>F)
## acido 2 7898 3949 98.39 <2e-16 ***
## Residuals 114 4576 40
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1- los diseños desbalanciados reuiqeren tratamiento especial (aov: no esta diseñado para modelos desvalanceados)
mod3 = lm(porc_germ ~ acido, datos_des)
library(car)## Warning: package 'car' was built under R version 4.2.3## Loading required package: carData## Warning: package 'carData' was built under R version 4.2.3mod3_res = Anova(mod3, type ='II')
mod3_res## Anova Table (Type II tests)
##
## Response: porc_germ
## Sum Sq Df F value Pr(>F)
## acido 7898.3 2 98.392 < 2.2e-16 ***
## Residuals 4575.6 114
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1- En un diseño de n solo factor, el balanceo y desbalanceo funciona bien - si le agrego bloques o mas factores no se puede usa aov, es mejor usar la libreria car
### Diseño agregando bloqueo
set.seed(123)
porc_germ = c(
rnorm(40, 60, 6),
rnorm(40, 70, 7),
rnorm(40, 80, 8))
bloq = gl(3, 40, 120, c('B0','B1','B2'))
acido = gl(4, 10, 120, c('C0','C1','C2','C3'))
datos = data.frame(acido, bloq, porc_germ)
datos_des = datos[-c(50, 111, 120), ]
datos_des## acido bloq porc_germ
## 1 C0 B0 56.63715
## 2 C0 B0 58.61894
## 3 C0 B0 69.35225
## 4 C0 B0 60.42305
## 5 C0 B0 60.77573
## 6 C0 B0 70.29039
## 7 C0 B0 62.76550
## 8 C0 B0 52.40963
## 9 C0 B0 55.87888
## 10 C0 B0 57.32603
## 11 C1 B0 67.34449
## 12 C1 B0 62.15888
## 13 C1 B0 62.40463
## 14 C1 B0 60.66410
## 15 C1 B0 56.66495
## 16 C1 B0 70.72148
## 17 C1 B0 62.98710
## 18 C1 B0 48.20030
## 19 C1 B0 64.20814
## 20 C1 B0 57.16325
## 21 C2 B0 53.59306
## 22 C2 B0 58.69215
## 23 C2 B0 53.84397
## 24 C2 B0 55.62665
## 25 C2 B0 56.24976
## 26 C2 B0 49.87984
## 27 C2 B0 65.02672
## 28 C2 B0 60.92024
## 29 C2 B0 53.17118
## 30 C2 B0 67.52289
## 31 C3 B0 62.55879
## 32 C3 B0 58.22957
## 33 C3 B0 65.37075
## 34 C3 B0 65.26880
## 35 C3 B0 64.92949
## 36 C3 B0 64.13184
## 37 C3 B0 63.32351
## 38 C3 B0 59.62853
## 39 C3 B0 58.16422
## 40 C3 B0 57.71717
## 41 C0 B1 65.13705
## 42 C0 B1 68.54458
## 43 C0 B1 61.14223
## 44 C0 B1 85.18269
## 45 C0 B1 78.45573
## 46 C0 B1 62.13824
## 47 C0 B1 67.17981
## 48 C0 B1 66.73341
## 49 C0 B1 75.45976
## 51 C1 B1 71.77323
## 52 C1 B1 69.80017
## 53 C1 B1 69.69991
## 54 C1 B1 79.58022
## 55 C1 B1 68.41960
## 56 C1 B1 80.61529
## 57 C1 B1 59.15873
## 58 C1 B1 74.09230
## 59 C1 B1 70.86698
## 60 C1 B1 71.51159
## 61 C2 B1 72.65748
## 62 C2 B1 66.48374
## 63 C2 B1 67.66755
## 64 C2 B1 62.86997
## 65 C2 B1 62.49746
## 66 C2 B1 72.12470
## 67 C2 B1 73.13747
## 68 C2 B1 70.37103
## 69 C2 B1 76.45587
## 70 C2 B1 84.35059
## 71 C3 B1 66.56278
## 72 C3 B1 53.83582
## 73 C3 B1 77.04017
## 74 C3 B1 65.03559
## 75 C3 B1 65.18394
## 76 C3 B1 77.17900
## 77 C3 B1 68.00659
## 78 C3 B1 61.45498
## 79 C3 B1 71.26912
## 80 C3 B1 69.02776
## 81 C0 B2 80.04611
## 82 C0 B2 83.08224
## 83 C0 B2 77.03472
## 84 C0 B2 85.15501
## 85 C0 B2 78.23611
## 86 C0 B2 82.65426
## 87 C0 B2 88.77471
## 88 C0 B2 83.48145
## 89 C0 B2 77.39255
## 90 C0 B2 89.19046
## 91 C1 B2 87.94803
## 92 C1 B2 84.38718
## 93 C1 B2 81.90985
## 94 C1 B2 74.97675
## 95 C1 B2 90.88522
## 96 C1 B2 75.19792
## 97 C1 B2 97.49866
## 98 C1 B2 92.26089
## 99 C1 B2 78.11440
## 100 C1 B2 71.78863
## 101 C2 B2 74.31675
## 102 C2 B2 82.05507
## 103 C2 B2 78.02646
## 104 C2 B2 77.21966
## 105 C2 B2 72.38705
## 106 C2 B2 79.63978
## 107 C2 B2 73.72076
## 108 C2 B2 66.65646
## 109 C2 B2 76.95819
## 110 C2 B2 87.35197
## 112 C3 B2 84.86371
## 113 C3 B2 67.05694
## 114 C3 B2 79.55550
## 115 C3 B2 84.15526
## 116 C3 B2 82.40923
## 117 C3 B2 80.84541
## 118 C3 B2 74.87435
## 119 C3 B2 73.20237table(datos_des$bloq, datos_des$acido)##
## C0 C1 C2 C3
## B0 10 10 10 10
## B1 9 10 10 10
## B2 10 10 10 8mod1 = aov(porc_germ ~ bloq * acido,
datos_des)
summary(mod1)## Df Sum Sq Mean Sq F value Pr(>F)
## bloq 2 7898 3949 102.076 <2e-16 ***
## acido 3 248 83 2.133 0.100
## bloq:acido 6 266 44 1.145 0.342
## Residuals 105 4062 39
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1- Ya que es de dos factores se usa este método:
mod2 = lm(porc_germ ~ bloq * acido,
datos_des)
mod2_res = Anova(mod2, type='II')
mod2_res## Anova Table (Type II tests)
##
## Response: porc_germ
## Sum Sq Df F value Pr(>F)
## bloq 7850.6 2 101.4603 <2e-16 ***
## acido 247.6 3 2.1333 0.1004
## bloq:acido 265.7 6 1.1447 0.3418
## Residuals 4062.3 105
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1Ajustando desbalance con diferente orden:
mod3 = lm(porc_germ ~ bloq + acido + bloq:acido, datos_des)
Anova(mod3, type = 'II')## Anova Table (Type II tests)
##
## Response: porc_germ
## Sum Sq Df F value Pr(>F)
## bloq 7850.6 2 101.4603 <2e-16 ***
## acido 247.6 3 2.1333 0.1004
## bloq:acido 265.7 6 1.1447 0.3418
## Residuals 4062.3 105
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1mod3 = lm(porc_germ ~ acido + bloq + bloq:acido, datos_des)
Anova(mod3, type = 'II')## Anova Table (Type II tests)
##
## Response: porc_germ
## Sum Sq Df F value Pr(>F)
## acido 247.6 3 2.1333 0.1004
## bloq 7850.6 2 101.4603 <2e-16 ***
## acido:bloq 265.7 6 1.1447 0.3418
## Residuals 4062.3 105
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1mod3 = lm(porc_germ ~ bloq:acido + bloq + acido , datos_des)
Anova(mod3, type = 'II')## Anova Table (Type II tests)
##
## Response: porc_germ
## Sum Sq Df F value Pr(>F)
## bloq 7850.6 2 101.4603 <2e-16 ***
## acido 247.6 3 2.1333 0.1004
## bloq:acido 265.7 6 1.1447 0.3418
## Residuals 4062.3 105
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1mod3 = lm(porc_germ ~ bloq:acido + acido + bloq , datos_des)
Anova(mod3, type = 'II')## Anova Table (Type II tests)
##
## Response: porc_germ
## Sum Sq Df F value Pr(>F)
## acido 247.6 3 2.1333 0.1004
## bloq 7850.6 2 101.4603 <2e-16 ***
## bloq:acido 265.7 6 1.1447 0.3418
## Residuals 4062.3 105
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1- Type II: evita difrencias en los datos, normalmente se usa I para balanceado y III para desbalanceado.
Ref: ANOVA for unbalance data: Use type II insteas of type III sums of squares. (2003) Lansrud
### Ahora con covariable = DIseño factorial simple en bloques completos generalizados y al azar, desbalanceado y con la tecnica analisis de covaianza.
# FACTORIAL SIMPLE: un solo factor = acido
# BLOSQUES COMPLETOS: 3 bloques =
# GENERALIZADOS: Repeticiones en los bloques
# DESBALANCEADO: No tiene las mismas repeticiones
# ANCOVA = analis de covarianza
set.seed(123)
porc_germ = c(
rnorm(40, 60, 6),
rnorm(40, 70, 7),
rnorm(40, 80, 8))
diam_med = sort(rnorm(120, 12, 1.3))
bloq = gl(3, 40, 120, c('B0','B1','B2'))
acido = gl(4, 10, 120, c('C0','C1','C2','C3'))
datos = data.frame(acido, bloq, porc_germ, diam_med)
datos_des = datos[-sample(120, 5), ]
datos_des## acido bloq porc_germ diam_med
## 1 C0 B0 56.63715 9.330779
## 2 C0 B0 58.61894 9.918003
## 3 C0 B0 69.35225 9.956213
## 4 C0 B0 60.42305 10.030932
## 5 C0 B0 60.77573 10.099718
## 6 C0 B0 70.29039 10.101168
## 7 C0 B0 62.76550 10.122939
## 8 C0 B0 52.40963 10.287879
## 9 C0 B0 55.87888 10.295958
## 10 C0 B0 57.32603 10.326860
## 11 C1 B0 67.34449 10.329870
## 12 C1 B0 62.15888 10.361798
## 13 C1 B0 62.40463 10.373347
## 14 C1 B0 60.66410 10.392845
## 15 C1 B0 56.66495 10.458876
## 17 C1 B0 62.98710 10.617676
## 18 C1 B0 48.20030 10.636070
## 19 C1 B0 64.20814 10.679730
## 20 C1 B0 57.16325 10.689110
## 21 C2 B0 53.59306 10.709741
## 23 C2 B0 53.84397 10.768283
## 24 C2 B0 55.62665 10.836028
## 25 C2 B0 56.24976 10.874833
## 26 C2 B0 49.87984 10.974816
## 27 C2 B0 65.02672 10.984003
## 28 C2 B0 60.92024 11.036263
## 29 C2 B0 53.17118 11.039914
## 30 C2 B0 67.52289 11.060014
## 31 C3 B0 62.55879 11.067616
## 32 C3 B0 58.22957 11.084025
## 33 C3 B0 65.37075 11.152465
## 34 C3 B0 65.26880 11.205484
## 35 C3 B0 64.92949 11.226998
## 36 C3 B0 64.13184 11.253295
## 37 C3 B0 63.32351 11.253834
## 38 C3 B0 59.62853 11.309822
## 39 C3 B0 58.16422 11.329117
## 40 C3 B0 57.71717 11.350920
## 41 C0 B1 65.13705 11.362275
## 42 C0 B1 68.54458 11.371085
## 43 C0 B1 61.14223 11.380879
## 44 C0 B1 85.18269 11.404125
## 45 C0 B1 78.45573 11.426488
## 46 C0 B1 62.13824 11.450754
## 47 C0 B1 67.17981 11.458085
## 48 C0 B1 66.73341 11.461358
## 49 C0 B1 75.45976 11.513045
## 50 C0 B1 69.41642 11.515830
## 51 C1 B1 71.77323 11.527246
## 52 C1 B1 69.80017 11.545454
## 53 C1 B1 69.69991 11.577908
## 54 C1 B1 79.58022 11.635486
## 55 C1 B1 68.41960 11.655311
## 56 C1 B1 80.61529 11.659143
## 57 C1 B1 59.15873 11.667080
## 58 C1 B1 74.09230 11.692837
## 59 C1 B1 70.86698 11.720005
## 60 C1 B1 71.51159 11.743671
## 61 C2 B1 72.65748 11.762197
## 62 C2 B1 66.48374 11.844712
## 63 C2 B1 67.66755 11.882585
## 64 C2 B1 62.86997 11.907299
## 65 C2 B1 62.49746 11.929763
## 66 C2 B1 72.12470 11.955713
## 67 C2 B1 73.13747 12.049125
## 68 C2 B1 70.37103 12.053603
## 70 C2 B1 84.35059 12.084881
## 71 C3 B1 66.56278 12.101349
## 72 C3 B1 53.83582 12.110158
## 73 C3 B1 77.04017 12.122959
## 75 C3 B1 65.18394 12.155019
## 76 C3 B1 77.17900 12.278779
## 77 C3 B1 68.00659 12.278900
## 78 C3 B1 61.45498 12.306003
## 79 C3 B1 71.26912 12.316794
## 80 C3 B1 69.02776 12.387696
## 81 C0 B2 80.04611 12.403625
## 82 C0 B2 83.08224 12.421596
## 83 C0 B2 77.03472 12.431863
## 84 C0 B2 85.15501 12.479654
## 85 C0 B2 78.23611 12.544677
## 86 C0 B2 82.65426 12.567481
## 87 C0 B2 88.77471 12.586955
## 88 C0 B2 83.48145 12.671921
## 89 C0 B2 77.39255 12.706152
## 90 C0 B2 89.19046 12.731886
## 91 C1 B2 87.94803 12.780921
## 92 C1 B2 84.38718 12.803382
## 93 C1 B2 81.90985 12.827541
## 95 C1 B2 90.88522 12.912320
## 96 C1 B2 75.19792 12.919865
## 97 C1 B2 97.49866 12.961932
## 98 C1 B2 92.26089 12.980270
## 99 C1 B2 78.11440 12.999755
## 100 C1 B2 71.78863 13.024061
## 101 C2 B2 74.31675 13.150046
## 102 C2 B2 82.05507 13.270065
## 103 C2 B2 78.02646 13.368525
## 104 C2 B2 77.21966 13.442803
## 105 C2 B2 72.38705 13.442896
## 106 C2 B2 79.63978 13.470738
## 107 C2 B2 73.72076 13.602219
## 108 C2 B2 66.65646 13.642141
## 109 C2 B2 76.95819 13.706137
## 110 C2 B2 87.35197 13.877916
## 111 C3 B2 75.39722 14.146180
## 112 C3 B2 84.86371 14.178406
## 113 C3 B2 67.05694 14.397021
## 114 C3 B2 79.55550 14.481835
## 115 C3 B2 84.15526 14.541882
## 116 C3 B2 82.40923 14.596377
## 117 C3 B2 80.84541 14.730142
## 118 C3 B2 74.87435 14.766987
## 119 C3 B2 73.20237 14.858453
## 120 C3 B2 71.80697 16.213352table(datos_des$bloq, datos_des$acido)##
## C0 C1 C2 C3
## B0 10 9 9 10
## B1 10 10 9 9
## B2 10 9 10 10*Incluimos diametro medio, (si suponemos que no es circular completamente, se deben tomar varias medidas y se realiza un promedio geometrico ó media geometrica - raiz n = numero de medidas - de las medidas multiplicadas)
mod1 = lm(porc_germ ~ diam_med + bloq + acido + bloq:acido, datos_des)
Anova(mod1, type = 'II')## Anova Table (Type II tests)
##
## Response: porc_germ
## Sum Sq Df F value Pr(>F)
## diam_med 6.0 1 0.1574 0.6924
## bloq 1069.4 2 14.0706 4.013e-06 ***
## acido 151.8 3 1.3315 0.2683
## bloq:acido 235.4 6 1.0325 0.4087
## Residuals 3876.1 102
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1set.seed(123)
porc_germ = c(
rnorm(40, 60, 6),
rnorm(40, 70, 7),
rnorm(40, 80, 8)
)
diam_med = sort(rnorm(120, 12, 1.3))
bloq = gl(3, 40, 120, c('B0','B1','B2'))
acido = gl(4, 10, 120, c('C0','C1','C2','C3'))
datos = data.frame(acido, bloq,
porc_germ, diam_med)
datos_des = datos
datos_des[-sample(120, 5), 'porc_germ'] = NA
table(datos_des$bloq, datos_des$acido)##
## C0 C1 C2 C3
## B0 10 10 10 10
## B1 10 10 10 10
## B2 10 10 10 10- Que pasa cuando se corre con NA, en lugar de perder la fila, aparecen los datos faltantes NA … ¿Como trabaja R los faltantes cuando se indican con NA?
tapply(datos_des$porc_germ,
datos_des$acido,
mean, na.rm=TRUE)## C0 C1 C2 C3
## NaN 72.84912 67.57401 65.03559No es capaz de calcular la media, ¿Como se resuelve esto en R?