DF
Angely Perez
2025-04-22
R Markdown
Problema a analizar: Actividad antimicrobiana sobre las bacterias Streptococcus pyogenes, Proteus mirabilis y Micrococcus luteus.
Including Plots
Cálculo de ANOVA y el Modelo Lineal
## Df Sum Sq Mean Sq F value Pr(>F)
## FactorA 3 1.7449 0.5816 23.586 2.46e-07 ***
## FactorB 2 0.0110 0.0055 0.223 0.801
## FactorA:FactorB 6 0.1457 0.0243 0.984 0.458
## Residuals 24 0.5919 0.0247
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1## Df Sum Sq Mean Sq F value Pr(>F)
## FactorA 3 1.7449 0.5816 23.586 2.46e-07 ***
## FactorB 2 0.0110 0.0055 0.223 0.801
## FactorA:FactorB 6 0.1457 0.0243 0.984 0.458
## Residuals 24 0.5919 0.0247
## ---
## 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
## -0.260000 -0.090833 0.006667 0.089167 0.286667
##
## Coefficients:
## Estimate Std. Error t value Pr(>|t|)
## (Intercept) 1.283333 0.090666 14.154 3.81e-13
## FactorAMalta -0.430000 0.128221 -3.354 0.00264
## FactorAPDB -0.423333 0.128221 -3.302 0.00300
## FactorASabouraud -0.620000 0.128221 -4.835 6.31e-05
## FactorBEscherichia coli -0.210000 0.128221 -1.638 0.11451
## FactorBProteus mirabilis -0.010000 0.128221 -0.078 0.93848
## FactorAMalta:FactorBEscherichia coli 0.220000 0.181333 1.213 0.23684
## FactorAPDB:FactorBEscherichia coli 0.373333 0.181333 2.059 0.05052
## FactorASabouraud:FactorBEscherichia coli 0.120000 0.181333 0.662 0.51442
## FactorAMalta:FactorBProteus mirabilis 0.003333 0.181333 0.018 0.98549
## FactorAPDB:FactorBProteus mirabilis 0.170000 0.181333 0.938 0.35784
## FactorASabouraud:FactorBProteus mirabilis -0.096667 0.181333 -0.533 0.59887
##
## (Intercept) ***
## FactorAMalta **
## FactorAPDB **
## FactorASabouraud ***
## FactorBEscherichia coli
## FactorBProteus mirabilis
## FactorAMalta:FactorBEscherichia coli
## FactorAPDB:FactorBEscherichia coli .
## FactorASabouraud:FactorBEscherichia coli
## FactorAMalta:FactorBProteus mirabilis
## FactorAPDB:FactorBProteus mirabilis
## FactorASabouraud:FactorBProteus mirabilis
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 0.157 on 24 degrees of freedom
## Multiple R-squared: 0.7626, Adjusted R-squared: 0.6538
## F-statistic: 7.01 on 11 and 24 DF, p-value: 3.604e-05sIGNIFICADO DE LA INTERACCIÓN: interacción entre ambos factores representan el hecho de que el efecto de un determinado nivel de un factor sea diferente para cada nivel del otro factor.
Gráficas de efectos principales e interacciones
## Warning: package 'car' was built under R version 4.3.3## Loading required package: carData## Warning: package 'carData' was built under R version 4.3.3
Supuestos del Diseño Experimental
- Normalidad
##
## Shapiro-Wilk normality test
##
## data: rstandard(Modelo)
## W = 0.97266, p-value = 0.5025- Prueba de homocedasticidad o igualdad de varianzas
## Non-constant Variance Score Test
## Variance formula: ~ fitted.values
## Chisquare = 0.9555026, Df = 1, p = 0.32832- Revisión grafica de supuestos
- cálculo del efecto (ANOVA)
## eta.sq eta.sq.part
## FactorA 0.699803153 0.7467201
## FactorB 0.004418198 0.0182733
## FactorA:FactorB 0.058412457 0.1974871Pruebas aposteriori(Comparaciones multiples de medias)
library(agricolae)## Warning: package 'agricolae' was built under R version 4.3.3TukeyHSD(ANOVA)## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = Modelo)
##
## $FactorA
## diff lwr upr p adj
## Malta-Czapeck -0.3555556 -0.55977175 -0.15133936 0.0003753
## PDB-Czapeck -0.2422222 -0.44643842 -0.03800603 0.0158940
## Sabouraud-Czapeck -0.6122222 -0.81643842 -0.40800603 0.0000001
## PDB-Malta 0.1133333 -0.09088286 0.31754953 0.4355178
## Sabouraud-Malta -0.2566667 -0.46088286 -0.05245047 0.0100596
## Sabouraud-PDB -0.3700000 -0.57421619 -0.16578381 0.0002303
##
## $FactorB
## diff lwr upr p adj
## Escherichia coli-Bacillus cereus -0.031666667 -0.1917696 0.1284362 0.8748627
## Proteus mirabilis-Bacillus cereus 0.009166667 -0.1509362 0.1692696 0.9887978
## Proteus mirabilis-Escherichia coli 0.040833333 -0.1192696 0.2009362 0.8013981
##
## $`FactorA:FactorB`
## diff lwr
## Malta:Bacillus cereus-Czapeck:Bacillus cereus -0.430000000 -0.89231902
## PDB:Bacillus cereus-Czapeck:Bacillus cereus -0.423333333 -0.88565235
## Sabouraud:Bacillus cereus-Czapeck:Bacillus cereus -0.620000000 -1.08231902
## Czapeck:Escherichia coli-Czapeck:Bacillus cereus -0.210000000 -0.67231902
## Malta:Escherichia coli-Czapeck:Bacillus cereus -0.420000000 -0.88231902
## PDB:Escherichia coli-Czapeck:Bacillus cereus -0.260000000 -0.72231902
## Sabouraud:Escherichia coli-Czapeck:Bacillus cereus -0.710000000 -1.17231902
## Czapeck:Proteus mirabilis-Czapeck:Bacillus cereus -0.010000000 -0.47231902
## Malta:Proteus mirabilis-Czapeck:Bacillus cereus -0.436666667 -0.89898568
## PDB:Proteus mirabilis-Czapeck:Bacillus cereus -0.263333333 -0.72565235
## Sabouraud:Proteus mirabilis-Czapeck:Bacillus cereus -0.726666667 -1.18898568
## PDB:Bacillus cereus-Malta:Bacillus cereus 0.006666667 -0.45565235
## Sabouraud:Bacillus cereus-Malta:Bacillus cereus -0.190000000 -0.65231902
## Czapeck:Escherichia coli-Malta:Bacillus cereus 0.220000000 -0.24231902
## Malta:Escherichia coli-Malta:Bacillus cereus 0.010000000 -0.45231902
## PDB:Escherichia coli-Malta:Bacillus cereus 0.170000000 -0.29231902
## Sabouraud:Escherichia coli-Malta:Bacillus cereus -0.280000000 -0.74231902
## Czapeck:Proteus mirabilis-Malta:Bacillus cereus 0.420000000 -0.04231902
## Malta:Proteus mirabilis-Malta:Bacillus cereus -0.006666667 -0.46898568
## PDB:Proteus mirabilis-Malta:Bacillus cereus 0.166666667 -0.29565235
## Sabouraud:Proteus mirabilis-Malta:Bacillus cereus -0.296666667 -0.75898568
## Sabouraud:Bacillus cereus-PDB:Bacillus cereus -0.196666667 -0.65898568
## Czapeck:Escherichia coli-PDB:Bacillus cereus 0.213333333 -0.24898568
## Malta:Escherichia coli-PDB:Bacillus cereus 0.003333333 -0.45898568
## PDB:Escherichia coli-PDB:Bacillus cereus 0.163333333 -0.29898568
## Sabouraud:Escherichia coli-PDB:Bacillus cereus -0.286666667 -0.74898568
## Czapeck:Proteus mirabilis-PDB:Bacillus cereus 0.413333333 -0.04898568
## Malta:Proteus mirabilis-PDB:Bacillus cereus -0.013333333 -0.47565235
## PDB:Proteus mirabilis-PDB:Bacillus cereus 0.160000000 -0.30231902
## Sabouraud:Proteus mirabilis-PDB:Bacillus cereus -0.303333333 -0.76565235
## Czapeck:Escherichia coli-Sabouraud:Bacillus cereus 0.410000000 -0.05231902
## Malta:Escherichia coli-Sabouraud:Bacillus cereus 0.200000000 -0.26231902
## PDB:Escherichia coli-Sabouraud:Bacillus cereus 0.360000000 -0.10231902
## Sabouraud:Escherichia coli-Sabouraud:Bacillus cereus -0.090000000 -0.55231902
## Czapeck:Proteus mirabilis-Sabouraud:Bacillus cereus 0.610000000 0.14768098
## Malta:Proteus mirabilis-Sabouraud:Bacillus cereus 0.183333333 -0.27898568
## PDB:Proteus mirabilis-Sabouraud:Bacillus cereus 0.356666667 -0.10565235
## Sabouraud:Proteus mirabilis-Sabouraud:Bacillus cereus -0.106666667 -0.56898568
## Malta:Escherichia coli-Czapeck:Escherichia coli -0.210000000 -0.67231902
## PDB:Escherichia coli-Czapeck:Escherichia coli -0.050000000 -0.51231902
## Sabouraud:Escherichia coli-Czapeck:Escherichia coli -0.500000000 -0.96231902
## Czapeck:Proteus mirabilis-Czapeck:Escherichia coli 0.200000000 -0.26231902
## Malta:Proteus mirabilis-Czapeck:Escherichia coli -0.226666667 -0.68898568
## PDB:Proteus mirabilis-Czapeck:Escherichia coli -0.053333333 -0.51565235
## Sabouraud:Proteus mirabilis-Czapeck:Escherichia coli -0.516666667 -0.97898568
## PDB:Escherichia coli-Malta:Escherichia coli 0.160000000 -0.30231902
## Sabouraud:Escherichia coli-Malta:Escherichia coli -0.290000000 -0.75231902
## Czapeck:Proteus mirabilis-Malta:Escherichia coli 0.410000000 -0.05231902
## Malta:Proteus mirabilis-Malta:Escherichia coli -0.016666667 -0.47898568
## PDB:Proteus mirabilis-Malta:Escherichia coli 0.156666667 -0.30565235
## Sabouraud:Proteus mirabilis-Malta:Escherichia coli -0.306666667 -0.76898568
## Sabouraud:Escherichia coli-PDB:Escherichia coli -0.450000000 -0.91231902
## Czapeck:Proteus mirabilis-PDB:Escherichia coli 0.250000000 -0.21231902
## Malta:Proteus mirabilis-PDB:Escherichia coli -0.176666667 -0.63898568
## PDB:Proteus mirabilis-PDB:Escherichia coli -0.003333333 -0.46565235
## Sabouraud:Proteus mirabilis-PDB:Escherichia coli -0.466666667 -0.92898568
## Czapeck:Proteus mirabilis-Sabouraud:Escherichia coli 0.700000000 0.23768098
## Malta:Proteus mirabilis-Sabouraud:Escherichia coli 0.273333333 -0.18898568
## PDB:Proteus mirabilis-Sabouraud:Escherichia coli 0.446666667 -0.01565235
## Sabouraud:Proteus mirabilis-Sabouraud:Escherichia coli -0.016666667 -0.47898568
## Malta:Proteus mirabilis-Czapeck:Proteus mirabilis -0.426666667 -0.88898568
## PDB:Proteus mirabilis-Czapeck:Proteus mirabilis -0.253333333 -0.71565235
## Sabouraud:Proteus mirabilis-Czapeck:Proteus mirabilis -0.716666667 -1.17898568
## PDB:Proteus mirabilis-Malta:Proteus mirabilis 0.173333333 -0.28898568
## Sabouraud:Proteus mirabilis-Malta:Proteus mirabilis -0.290000000 -0.75231902
## Sabouraud:Proteus mirabilis-PDB:Proteus mirabilis -0.463333333 -0.92565235
## upr p adj
## Malta:Bacillus cereus-Czapeck:Bacillus cereus 0.032319018 0.0849093
## PDB:Bacillus cereus-Czapeck:Bacillus cereus 0.038985684 0.0943637
## Sabouraud:Bacillus cereus-Czapeck:Bacillus cereus -0.157680982 0.0029180
## Czapeck:Escherichia coli-Czapeck:Bacillus cereus 0.252319018 0.8781269
## Malta:Escherichia coli-Czapeck:Bacillus cereus 0.042319018 0.0994270
## PDB:Escherichia coli-Czapeck:Bacillus cereus 0.202319018 0.6723591
## Sabouraud:Escherichia coli-Czapeck:Bacillus cereus -0.247680982 0.0005370
## Czapeck:Proteus mirabilis-Czapeck:Bacillus cereus 0.452319018 1.0000000
## Malta:Proteus mirabilis-Czapeck:Bacillus cereus 0.025652351 0.0763004
## PDB:Proteus mirabilis-Czapeck:Bacillus cereus 0.198985684 0.6562943
## Sabouraud:Proteus mirabilis-Czapeck:Bacillus cereus -0.264347649 0.0003926
## PDB:Bacillus cereus-Malta:Bacillus cereus 0.468985684 1.0000000
## Sabouraud:Bacillus cereus-Malta:Bacillus cereus 0.272319018 0.9317728
## Czapeck:Escherichia coli-Malta:Bacillus cereus 0.682319018 0.8442995
## Malta:Escherichia coli-Malta:Bacillus cereus 0.472319018 1.0000000
## PDB:Escherichia coli-Malta:Bacillus cereus 0.632319018 0.9669498
## Sabouraud:Escherichia coli-Malta:Bacillus cereus 0.182319018 0.5747115
## Czapeck:Proteus mirabilis-Malta:Bacillus cereus 0.882319018 0.0994270
## Malta:Proteus mirabilis-Malta:Bacillus cereus 0.455652351 1.0000000
## PDB:Proteus mirabilis-Malta:Bacillus cereus 0.628985684 0.9711906
## Sabouraud:Proteus mirabilis-Malta:Bacillus cereus 0.165652351 0.4937349
## Sabouraud:Bacillus cereus-PDB:Bacillus cereus 0.265652351 0.9160061
## Czapeck:Escherichia coli-PDB:Bacillus cereus 0.675652351 0.8673519
## Malta:Escherichia coli-PDB:Bacillus cereus 0.465652351 1.0000000
## PDB:Escherichia coli-PDB:Bacillus cereus 0.625652351 0.9750182
## Sabouraud:Escherichia coli-PDB:Bacillus cereus 0.175652351 0.5420532
## Czapeck:Proteus mirabilis-PDB:Bacillus cereus 0.875652351 0.1102637
## Malta:Proteus mirabilis-PDB:Bacillus cereus 0.448985684 1.0000000
## PDB:Proteus mirabilis-PDB:Bacillus cereus 0.622319018 0.9784549
## Sabouraud:Proteus mirabilis-PDB:Bacillus cereus 0.158985684 0.4622548
## Czapeck:Escherichia coli-Sabouraud:Bacillus cereus 0.872319018 0.1160525
## Malta:Escherichia coli-Sabouraud:Bacillus cereus 0.662319018 0.9073294
## PDB:Escherichia coli-Sabouraud:Bacillus cereus 0.822319018 0.2375416
## Sabouraud:Escherichia coli-Sabouraud:Bacillus cereus 0.372319018 0.9998447
## Czapeck:Proteus mirabilis-Sabouraud:Bacillus cereus 1.072319018 0.0035183
## Malta:Proteus mirabilis-Sabouraud:Bacillus cereus 0.645652351 0.9454597
## PDB:Proteus mirabilis-Sabouraud:Bacillus cereus 0.818985684 0.2482019
## Sabouraud:Proteus mirabilis-Sabouraud:Bacillus cereus 0.355652351 0.9992393
## Malta:Escherichia coli-Czapeck:Escherichia coli 0.252319018 0.8781269
## PDB:Escherichia coli-Czapeck:Escherichia coli 0.412319018 0.9999996
## Sabouraud:Escherichia coli-Czapeck:Escherichia coli -0.037680982 0.0261530
## Czapeck:Proteus mirabilis-Czapeck:Escherichia coli 0.662319018 0.9073294
## Malta:Proteus mirabilis-Czapeck:Escherichia coli 0.235652351 0.8193436
## PDB:Proteus mirabilis-Czapeck:Escherichia coli 0.408985684 0.9999992
## Sabouraud:Proteus mirabilis-Czapeck:Escherichia coli -0.054347649 0.0194733
## PDB:Escherichia coli-Malta:Escherichia coli 0.622319018 0.9784549
## Sabouraud:Escherichia coli-Malta:Escherichia coli 0.172319018 0.5258321
## Czapeck:Proteus mirabilis-Malta:Escherichia coli 0.872319018 0.1160525
## Malta:Proteus mirabilis-Malta:Escherichia coli 0.445652351 1.0000000
## PDB:Proteus mirabilis-Malta:Escherichia coli 0.618985684 0.9815239
## Sabouraud:Proteus mirabilis-Malta:Escherichia coli 0.155652351 0.4467999
## Sabouraud:Escherichia coli-PDB:Escherichia coli 0.012319018 0.0613823
## Czapeck:Proteus mirabilis-PDB:Escherichia coli 0.712319018 0.7194870
## Malta:Proteus mirabilis-PDB:Escherichia coli 0.285652351 0.9571464
## PDB:Proteus mirabilis-PDB:Escherichia coli 0.458985684 1.0000000
## Sabouraud:Proteus mirabilis-PDB:Escherichia coli -0.004347649 0.0464683
## Czapeck:Proteus mirabilis-Sabouraud:Escherichia coli 1.162319018 0.0006481
## Malta:Proteus mirabilis-Sabouraud:Escherichia coli 0.735652351 0.6074733
## PDB:Proteus mirabilis-Sabouraud:Escherichia coli 0.908985684 0.0648424
## Sabouraud:Proteus mirabilis-Sabouraud:Escherichia coli 0.445652351 1.0000000
## Malta:Proteus mirabilis-Czapeck:Proteus mirabilis 0.035652351 0.0895270
## PDB:Proteus mirabilis-Czapeck:Proteus mirabilis 0.208985684 0.7039868
## Sabouraud:Proteus mirabilis-Czapeck:Proteus mirabilis -0.254347649 0.0004737
## PDB:Proteus mirabilis-Malta:Proteus mirabilis 0.635652351 0.9622749
## Sabouraud:Proteus mirabilis-Malta:Proteus mirabilis 0.172319018 0.5258321
## Sabouraud:Proteus mirabilis-PDB:Proteus mirabilis -0.001014316 0.0491547plot(TukeyHSD(ANOVA))
#Prueba de Tukey
outHSD<-HSD.test(ANOVA, "FactorA",console=TRUE)##
## Study: ANOVA ~ "FactorA"
##
## HSD Test for CMI
##
## Mean Square Error: 0.02466111
##
## FactorA, means
##
## CMI std r se Min Max Q25 Q50 Q75
## Czapeck 1.2100000 0.1835075 9 0.05234619 0.90 1.57 1.14 1.20 1.24
## Malta 0.8544444 0.1342676 9 0.05234619 0.62 1.00 0.79 0.92 0.95
## PDB 0.9677778 0.1716667 9 0.05234619 0.60 1.19 0.89 1.02 1.07
## Sabouraud 0.5977778 0.1113303 9 0.05234619 0.46 0.76 0.51 0.55 0.68
##
## Alpha: 0.05 ; DF Error: 24
## Critical Value of Studentized Range: 3.901262
##
## Minimun Significant Difference: 0.2042162
##
## Treatments with the same letter are not significantly different.
##
## CMI groups
## Czapeck 1.2100000 a
## PDB 0.9677778 b
## Malta 0.8544444 b
## Sabouraud 0.5977778 coutHSD<-HSD.test(ANOVA, "FactorB",console=TRUE)##
## Study: ANOVA ~ "FactorB"
##
## HSD Test for CMI
##
## Mean Square Error: 0.02466111
##
## FactorB, means
##
## CMI std r se Min Max Q25 Q50
## Bacillus cereus 0.9150000 0.2898432 12 0.04533313 0.55 1.57 0.6775 0.945
## Escherichia coli 0.8833333 0.2370398 12 0.04533313 0.46 1.19 0.7800 0.880
## Proteus mirabilis 0.9241667 0.2923714 12 0.04533313 0.50 1.35 0.6275 0.960
## Q75
## Bacillus cereus 1.0350
## Escherichia coli 1.0500
## Proteus mirabilis 1.1325
##
## Alpha: 0.05 ; DF Error: 24
## Critical Value of Studentized Range: 3.531697
##
## Minimun Significant Difference: 0.1601029
##
## Treatments with the same letter are not significantly different.
##
## CMI groups
## Proteus mirabilis 0.9241667 a
## Bacillus cereus 0.9150000 a
## Escherichia coli 0.8833333 a