Diseño Factorial CMI
Vivian Slendy Castañeda
2025-04-21
Diseño Factorial
Problema a analizar: Se busca determinar el efecto de medios diferentes sobre la concentracion minima inhibitoria frente a algunas bacterias patogenas.
## [1] "Medio" "Bacteria" "Replica" "CMI"## tibble [24 × 4] (S3: tbl_df/tbl/data.frame)
## $ Medio : chr [1:24] "Sabouraud" "Sabouraud" "Sabouraud" "Sabouraud" ...
## $ Bacteria: chr [1:24] "Micrococcus luteus" "Micrococcus luteus" "Proteus mirabilis" "Proteus mirabilis" ...
## $ Replica : num [1:24] 2 1 2 1 2 1 2 1 2 1 ...
## $ CMI : num [1:24] 0.55 0.65 0.5 0.54 0.46 0.51 1.36 0.99 1.35 1.24 ...Diagrama Box Plot
Cálculo ANOVA y modelo lineal
## Df Sum Sq Mean Sq F value Pr(>F)
## FactorA 3 1.6341 0.5447 32.32 4.98e-06 ***
## FactorB 2 0.0101 0.0051 0.30 0.746
## FactorA:FactorB 6 0.0789 0.0132 0.78 0.601
## Residuals 12 0.2022 0.0169
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Df Sum Sq Mean Sq F value Pr(>F)
## FactorA 3 1.6341 0.5447 32.32 4.98e-06 ***
## FactorB 2 0.0101 0.0051 0.30 0.746
## FactorA:FactorB 6 0.0789 0.0132 0.78 0.601
## Residuals 12 0.2022 0.0169
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1##
## Call:
## lm(formula = CMI ~ (FactorA + FactorB + FactorA:FactorB))
##
## Residuals:
## Min 1Q Median 3Q Max
## -0.18500 -0.06125 0.00000 0.06125 0.18500
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.1600 0.0918 12.636 2.71e-08
## FactorAMalta -0.2900 0.1298 -2.234 0.045300
## FactorAPDB -0.0550 0.1298 -0.424 0.679314
## FactorASabouraud -0.6750 0.1298 -5.199 0.000222
## FactorBMicrococcus luteus 0.0150 0.1298 0.116 0.909927
## FactorBProteus mirabilis 0.1350 0.1298 1.040 0.318898
## FactorAMalta:FactorBMicrococcus luteus -0.0850 0.1836 -0.463 0.651671
## FactorAPDB:FactorBMicrococcus luteus 0.0650 0.1836 0.354 0.729456
## FactorASabouraud:FactorBMicrococcus luteus 0.1000 0.1836 0.545 0.595959
## FactorAMalta:FactorBProteus mirabilis -0.2350 0.1836 -1.280 0.224747
## FactorAPDB:FactorBProteus mirabilis -0.2600 0.1836 -1.416 0.182166
## FactorASabouraud:FactorBProteus mirabilis -0.1000 0.1836 -0.545 0.595959
##
## (Intercept) ***
## FactorAMalta *
## FactorAPDB
## FactorASabouraud ***
## FactorBMicrococcus luteus
## FactorBProteus mirabilis
## FactorAMalta:FactorBMicrococcus luteus
## FactorAPDB:FactorBMicrococcus luteus
## FactorASabouraud:FactorBMicrococcus luteus
## FactorAMalta:FactorBProteus mirabilis
## FactorAPDB:FactorBProteus mirabilis
## FactorASabouraud:FactorBProteus mirabilis
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.1298 on 12 degrees of freedom
## Multiple R-squared: 0.895, Adjusted R-squared: 0.7987
## F-statistic: 9.294 on 11 and 12 DF, p-value: 0.0002779Gráficas de efectos principales e interacciones
## Warning: package 'phia' was built under R version 4.4.3## Cargando paquete requerido: car## Warning: package 'car' was built under R version 4.4.2## Cargando paquete requerido: carData## Warning: package 'carData' was built under R version 4.4.2
Análisis de la idoneidad del modelo
Normalidad de residuos
##
## Shapiro-Wilk normality test
##
## data: rstandard(Modelo)
## W = 0.9893, p-value = 0.9944Prueba de homocedasticidad o igualdad de varianzas
## Non-constant Variance Score Test
## Variance formula: ~ fitted.values
## Chisquare = 1.927121, Df = 1, p = 0.16507Revisión gráfica de supuestos
Cálculo del efecto (ANOVA)
## Warning: package 'lsr' was built under R version 4.4.3## eta.sq eta.sq.part
## FactorA 0.848715091 0.88986379
## FactorB 0.005250003 0.04760036
## FactorA:FactorB 0.040991571 0.28069707Pruebas aposteriori(Comparaciones multiples de medias)
Prueba de Tukey
## Warning: package 'agricolae' was built under R version 4.4.2## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = Modelo)
##
## $FactorA
## diff lwr upr p adj
## Malta-Czapeck -0.3966667 -0.61919676 -0.17413657 0.0009459
## PDB-Czapeck -0.1200000 -0.34253009 0.10253009 0.4139981
## Sabouraud-Czapeck -0.6750000 -0.89753009 -0.45246991 0.0000057
## PDB-Malta 0.2766667 0.05413657 0.49919676 0.0141597
## Sabouraud-Malta -0.2783333 -0.50086343 -0.05580324 0.0136191
## Sabouraud-PDB -0.5550000 -0.77753009 -0.33246991 0.0000424
##
## $FactorB
## diff lwr upr p adj
## Micrococcus luteus-Escherichia coli 0.03500 -0.1381758 0.2081758 0.8537854
## Proteus mirabilis-Escherichia coli -0.01375 -0.1869258 0.1594258 0.9756175
## Proteus mirabilis-Micrococcus luteus -0.04875 -0.2219258 0.1244258 0.7387556
##
## $`FactorA:FactorB`
## diff lwr
## Malta:Escherichia coli-Czapeck:Escherichia coli -0.290 -0.8054198
## PDB:Escherichia coli-Czapeck:Escherichia coli -0.055 -0.5704198
## Sabouraud:Escherichia coli-Czapeck:Escherichia coli -0.675 -1.1904198
## Czapeck:Micrococcus luteus-Czapeck:Escherichia coli 0.015 -0.5004198
## Malta:Micrococcus luteus-Czapeck:Escherichia coli -0.360 -0.8754198
## PDB:Micrococcus luteus-Czapeck:Escherichia coli 0.025 -0.4904198
## Sabouraud:Micrococcus luteus-Czapeck:Escherichia coli -0.560 -1.0754198
## Czapeck:Proteus mirabilis-Czapeck:Escherichia coli 0.135 -0.3804198
## Malta:Proteus mirabilis-Czapeck:Escherichia coli -0.390 -0.9054198
## PDB:Proteus mirabilis-Czapeck:Escherichia coli -0.180 -0.6954198
## Sabouraud:Proteus mirabilis-Czapeck:Escherichia coli -0.640 -1.1554198
## PDB:Escherichia coli-Malta:Escherichia coli 0.235 -0.2804198
## Sabouraud:Escherichia coli-Malta:Escherichia coli -0.385 -0.9004198
## Czapeck:Micrococcus luteus-Malta:Escherichia coli 0.305 -0.2104198
## Malta:Micrococcus luteus-Malta:Escherichia coli -0.070 -0.5854198
## PDB:Micrococcus luteus-Malta:Escherichia coli 0.315 -0.2004198
## Sabouraud:Micrococcus luteus-Malta:Escherichia coli -0.270 -0.7854198
## Czapeck:Proteus mirabilis-Malta:Escherichia coli 0.425 -0.0904198
## Malta:Proteus mirabilis-Malta:Escherichia coli -0.100 -0.6154198
## PDB:Proteus mirabilis-Malta:Escherichia coli 0.110 -0.4054198
## Sabouraud:Proteus mirabilis-Malta:Escherichia coli -0.350 -0.8654198
## Sabouraud:Escherichia coli-PDB:Escherichia coli -0.620 -1.1354198
## Czapeck:Micrococcus luteus-PDB:Escherichia coli 0.070 -0.4454198
## Malta:Micrococcus luteus-PDB:Escherichia coli -0.305 -0.8204198
## PDB:Micrococcus luteus-PDB:Escherichia coli 0.080 -0.4354198
## Sabouraud:Micrococcus luteus-PDB:Escherichia coli -0.505 -1.0204198
## Czapeck:Proteus mirabilis-PDB:Escherichia coli 0.190 -0.3254198
## Malta:Proteus mirabilis-PDB:Escherichia coli -0.335 -0.8504198
## PDB:Proteus mirabilis-PDB:Escherichia coli -0.125 -0.6404198
## Sabouraud:Proteus mirabilis-PDB:Escherichia coli -0.585 -1.1004198
## Czapeck:Micrococcus luteus-Sabouraud:Escherichia coli 0.690 0.1745802
## Malta:Micrococcus luteus-Sabouraud:Escherichia coli 0.315 -0.2004198
## PDB:Micrococcus luteus-Sabouraud:Escherichia coli 0.700 0.1845802
## Sabouraud:Micrococcus luteus-Sabouraud:Escherichia coli 0.115 -0.4004198
## Czapeck:Proteus mirabilis-Sabouraud:Escherichia coli 0.810 0.2945802
## Malta:Proteus mirabilis-Sabouraud:Escherichia coli 0.285 -0.2304198
## PDB:Proteus mirabilis-Sabouraud:Escherichia coli 0.495 -0.0204198
## Sabouraud:Proteus mirabilis-Sabouraud:Escherichia coli 0.035 -0.4804198
## Malta:Micrococcus luteus-Czapeck:Micrococcus luteus -0.375 -0.8904198
## PDB:Micrococcus luteus-Czapeck:Micrococcus luteus 0.010 -0.5054198
## Sabouraud:Micrococcus luteus-Czapeck:Micrococcus luteus -0.575 -1.0904198
## Czapeck:Proteus mirabilis-Czapeck:Micrococcus luteus 0.120 -0.3954198
## Malta:Proteus mirabilis-Czapeck:Micrococcus luteus -0.405 -0.9204198
## PDB:Proteus mirabilis-Czapeck:Micrococcus luteus -0.195 -0.7104198
## Sabouraud:Proteus mirabilis-Czapeck:Micrococcus luteus -0.655 -1.1704198
## PDB:Micrococcus luteus-Malta:Micrococcus luteus 0.385 -0.1304198
## Sabouraud:Micrococcus luteus-Malta:Micrococcus luteus -0.200 -0.7154198
## Czapeck:Proteus mirabilis-Malta:Micrococcus luteus 0.495 -0.0204198
## Malta:Proteus mirabilis-Malta:Micrococcus luteus -0.030 -0.5454198
## PDB:Proteus mirabilis-Malta:Micrococcus luteus 0.180 -0.3354198
## Sabouraud:Proteus mirabilis-Malta:Micrococcus luteus -0.280 -0.7954198
## Sabouraud:Micrococcus luteus-PDB:Micrococcus luteus -0.585 -1.1004198
## Czapeck:Proteus mirabilis-PDB:Micrococcus luteus 0.110 -0.4054198
## Malta:Proteus mirabilis-PDB:Micrococcus luteus -0.415 -0.9304198
## PDB:Proteus mirabilis-PDB:Micrococcus luteus -0.205 -0.7204198
## Sabouraud:Proteus mirabilis-PDB:Micrococcus luteus -0.665 -1.1804198
## Czapeck:Proteus mirabilis-Sabouraud:Micrococcus luteus 0.695 0.1795802
## Malta:Proteus mirabilis-Sabouraud:Micrococcus luteus 0.170 -0.3454198
## PDB:Proteus mirabilis-Sabouraud:Micrococcus luteus 0.380 -0.1354198
## Sabouraud:Proteus mirabilis-Sabouraud:Micrococcus luteus -0.080 -0.5954198
## Malta:Proteus mirabilis-Czapeck:Proteus mirabilis -0.525 -1.0404198
## PDB:Proteus mirabilis-Czapeck:Proteus mirabilis -0.315 -0.8304198
## Sabouraud:Proteus mirabilis-Czapeck:Proteus mirabilis -0.775 -1.2904198
## PDB:Proteus mirabilis-Malta:Proteus mirabilis 0.210 -0.3054198
## Sabouraud:Proteus mirabilis-Malta:Proteus mirabilis -0.250 -0.7654198
## Sabouraud:Proteus mirabilis-PDB:Proteus mirabilis -0.460 -0.9754198
## upr p adj
## Malta:Escherichia coli-Czapeck:Escherichia coli 0.225419797 0.5572178
## PDB:Escherichia coli-Czapeck:Escherichia coli 0.460419797 0.9999982
## Sabouraud:Escherichia coli-Czapeck:Escherichia coli -0.159580203 0.0072547
## Czapeck:Micrococcus luteus-Czapeck:Escherichia coli 0.530419797 1.0000000
## Malta:Micrococcus luteus-Czapeck:Escherichia coli 0.155419797 0.2965710
## PDB:Micrococcus luteus-Czapeck:Escherichia coli 0.540419797 1.0000000
## Sabouraud:Micrococcus luteus-Czapeck:Escherichia coli -0.044580203 0.0290518
## Czapeck:Proteus mirabilis-Czapeck:Escherichia coli 0.650419797 0.9924676
## Malta:Proteus mirabilis-Czapeck:Escherichia coli 0.125419797 0.2162997
## PDB:Proteus mirabilis-Czapeck:Escherichia coli 0.335419797 0.9457116
## Sabouraud:Proteus mirabilis-Czapeck:Escherichia coli -0.124580203 0.0110153
## PDB:Escherichia coli-Malta:Escherichia coli 0.750419797 0.7875300
## Sabouraud:Escherichia coli-Malta:Escherichia coli 0.130419797 0.2283052
## Czapeck:Micrococcus luteus-Malta:Escherichia coli 0.820419797 0.4943700
## Malta:Micrococcus luteus-Malta:Escherichia coli 0.445419797 0.9999790
## PDB:Micrococcus luteus-Malta:Escherichia coli 0.830419797 0.4540969
## Sabouraud:Micrococcus luteus-Malta:Escherichia coli 0.245419797 0.6432844
## Czapeck:Proteus mirabilis-Malta:Escherichia coli 0.940419797 0.1463163
## Malta:Proteus mirabilis-Malta:Escherichia coli 0.415419797 0.9993837
## PDB:Proteus mirabilis-Malta:Escherichia coli 0.625419797 0.9985786
## Sabouraud:Proteus mirabilis-Malta:Escherichia coli 0.165419797 0.3278129
## Sabouraud:Escherichia coli-PDB:Escherichia coli -0.104580203 0.0140152
## Czapeck:Micrococcus luteus-PDB:Escherichia coli 0.585419797 0.9999790
## Malta:Micrococcus luteus-PDB:Escherichia coli 0.210419797 0.4943700
## PDB:Micrococcus luteus-PDB:Escherichia coli 0.595419797 0.9999225
## Sabouraud:Micrococcus luteus-PDB:Escherichia coli 0.010419797 0.0567337
## Czapeck:Proteus mirabilis-PDB:Escherichia coli 0.705419797 0.9255978
## Malta:Proteus mirabilis-PDB:Escherichia coli 0.180419797 0.3788431
## PDB:Proteus mirabilis-PDB:Escherichia coli 0.390419797 0.9958837
## Sabouraud:Proteus mirabilis-PDB:Escherichia coli -0.069580203 0.0214246
## Czapeck:Micrococcus luteus-Sabouraud:Escherichia coli 1.205419797 0.0060764
## Malta:Micrococcus luteus-Sabouraud:Escherichia coli 0.830419797 0.4540969
## PDB:Micrococcus luteus-Sabouraud:Escherichia coli 1.215419797 0.0054026
## Sabouraud:Micrococcus luteus-Sabouraud:Escherichia coli 0.630419797 0.9979264
## Czapeck:Proteus mirabilis-Sabouraud:Escherichia coli 1.325419797 0.0015401
## Malta:Proteus mirabilis-Sabouraud:Escherichia coli 0.800419797 0.5786140
## PDB:Proteus mirabilis-Sabouraud:Escherichia coli 1.010419797 0.0640229
## Sabouraud:Proteus mirabilis-Sabouraud:Escherichia coli 0.550419797 1.0000000
## Malta:Micrococcus luteus-Czapeck:Micrococcus luteus 0.140419797 0.2539415
## PDB:Micrococcus luteus-Czapeck:Micrococcus luteus 0.525419797 1.0000000
## Sabouraud:Micrococcus luteus-Czapeck:Micrococcus luteus -0.059580203 0.0241980
## Czapeck:Proteus mirabilis-Czapeck:Micrococcus luteus 0.635419797 0.9970462
## Malta:Proteus mirabilis-Czapeck:Micrococcus luteus 0.110419797 0.1834027
## PDB:Proteus mirabilis-Czapeck:Micrococcus luteus 0.320419797 0.9140213
## Sabouraud:Proteus mirabilis-Czapeck:Micrococcus luteus -0.139580203 0.0092041
## PDB:Micrococcus luteus-Malta:Micrococcus luteus 0.900419797 0.2283052
## Sabouraud:Micrococcus luteus-Malta:Micrococcus luteus 0.315419797 0.9014332
## Czapeck:Proteus mirabilis-Malta:Micrococcus luteus 1.010419797 0.0640229
## Malta:Proteus mirabilis-Malta:Micrococcus luteus 0.485419797 1.0000000
## PDB:Proteus mirabilis-Malta:Micrococcus luteus 0.695419797 0.9457116
## Sabouraud:Proteus mirabilis-Malta:Micrococcus luteus 0.235419797 0.6001351
## Sabouraud:Micrococcus luteus-PDB:Micrococcus luteus -0.069580203 0.0214246
## Czapeck:Proteus mirabilis-PDB:Micrococcus luteus 0.625419797 0.9985786
## Malta:Proteus mirabilis-PDB:Micrococcus luteus 0.100419797 0.1639400
## PDB:Proteus mirabilis-PDB:Micrococcus luteus 0.310419797 0.8878488
## Sabouraud:Proteus mirabilis-PDB:Micrococcus luteus -0.149580203 0.0081696
## Czapeck:Proteus mirabilis-Sabouraud:Micrococcus luteus 1.210419797 0.0057292
## Malta:Proteus mirabilis-Sabouraud:Micrococcus luteus 0.685419797 0.9618775
## PDB:Proteus mirabilis-Sabouraud:Micrococcus luteus 0.895419797 0.2408493
## Sabouraud:Proteus mirabilis-Sabouraud:Micrococcus luteus 0.435419797 0.9999225
## Malta:Proteus mirabilis-Czapeck:Proteus mirabilis -0.009580203 0.0445042
## PDB:Proteus mirabilis-Czapeck:Proteus mirabilis 0.200419797 0.4540969
## Sabouraud:Proteus mirabilis-Czapeck:Proteus mirabilis -0.259580203 0.0022779
## PDB:Proteus mirabilis-Malta:Proteus mirabilis 0.725419797 0.8732938
## Sabouraud:Proteus mirabilis-Malta:Proteus mirabilis 0.265419797 0.7279464
## Sabouraud:Proteus mirabilis-PDB:Proteus mirabilis 0.055419797 0.0973078
##
## Study: ANOVA ~ "FactorA"
##
## HSD Test for CMI
##
## Mean Square Error: 0.01685417
##
## FactorA, means
##
## CMI std r se Min Max Q25 Q50 Q75
## Czapeck 1.2100000 0.13942740 6 0.05300026 0.99 1.36 1.1500 1.210 1.3225
## Malta 0.8133333 0.12110601 6 0.05300026 0.62 0.95 0.7600 0.820 0.9025
## PDB 1.0900000 0.14127986 6 0.05300026 0.89 1.30 1.0325 1.070 1.1600
## Sabouraud 0.5350000 0.06473021 6 0.05300026 0.46 0.65 0.5025 0.525 0.5475
##
## Alpha: 0.05 ; DF Error: 12
## Critical Value of Studentized Range: 4.19866
##
## Minimun Significant Difference: 0.2225301
##
## Treatments with the same letter are not significantly different.
##
## CMI groups
## Czapeck 1.2100000 a
## PDB 1.0900000 a
## Malta 0.8133333 b
## Sabouraud 0.5350000 c##
## Study: ANOVA ~ "FactorB"
##
## HSD Test for CMI
##
## Mean Square Error: 0.01685417
##
## FactorB, means
##
## CMI std r se Min Max Q25 Q50 Q75
## Escherichia coli 0.90500 0.2914496 8 0.04589957 0.46 1.19 0.720 0.985 1.1500
## Micrococcus luteus 0.94000 0.2941817 8 0.04589957 0.55 1.36 0.725 0.920 1.1275
## Proteus mirabilis 0.89125 0.3195728 8 0.04589957 0.50 1.35 0.600 0.905 1.1125
##
## Alpha: 0.05 ; DF Error: 12
## Critical Value of Studentized Range: 3.772929
##
## Minimun Significant Difference: 0.1731758
##
## Treatments with the same letter are not significantly different.
##
## CMI groups
## Micrococcus luteus 0.94000 a
## Escherichia coli 0.90500 a
## Proteus mirabilis 0.89125 aConclusión
Se ha evaluado el efecto de diferentes medios de cultivo y tipos de bacterias en la concentración mínima inhibitoria. El modelo incluye efectos principales e interacción, se evaluaron supuestos y se aplicaron comparaciones múltiples para interpretar diferencias significativas entre niveles.