El diseño del experimento se modeló como factorial completo. Por lo tanto, se realizaron 24 (622) experimentos en total para 6 fluidos de corte, con diferentes ambiente, 2 cargas diferentes y 2 velocidades de deslizamiento diferentes. En el ámbito del estudio, se analizaron 4 variables de salida diferentes como la pérdida de peso, el coeficiente de fricción, la rugosidad de la superficie y el cambio de temperatura. El modelo lineal de análisis de la varianza (ANOVA) y los valores de R-Squared (R-Sq) se utilizaron para medir la significación de de los resultados del experimento. Elija 1 de las 4 varianles de salida para desarrollar el análisis.

df<-read.csv("https://raw.githubusercontent.com/gidasan08/DExperimental/main/Examen%20Final.csv")
df
##             WE Ld SS   TD
## 1          Dry  1 -1 1.50
## 2          Dry -1 -1 1.60
## 3          Dry  1  1 1.30
## 4          Dry -1  1 1.40
## 5   Pure Water  1 -1 0.25
## 6   Pure Water -1 -1 0.28
## 7   Pure Water  1  1 0.34
## 8   Pure Water -1  1 0.39
## 9           EG  1 -1 0.43
## 10          EG -1 -1 0.38
## 11          EG  1  1 0.35
## 12          EG -1  1 0.40
## 13 EG +4% AgNP  1 -1 0.45
## 14 EG +4% AgNP -1 -1 0.40
## 15 EG +4% AgNP  1  1 0.42
## 16 EG +4% AgNP -1  1 0.56
## 17 EG +8% AgNP  1 -1 0.77
## 18 EG +8% AgNP -1 -1 0.47
## 19 EG +8% AgNP  1  1 0.66
## 20 EG +8% AgNP -1  1 0.75
## 21  EG+12%AgNP  1 -1 0.82
## 22  EG+12%AgNP -1 -1 0.87
## 23  EG+12%AgNP  1  1 0.70
## 24  EG+12%AgNP -1  1 0.80
df$WE=factor(df$WE)
df$Ld=factor(df$Ld)
df$SS=factor(df$SS)
df$TD=as.numeric(df$TD)
df
##             WE Ld SS   TD
## 1          Dry  1 -1 1.50
## 2          Dry -1 -1 1.60
## 3          Dry  1  1 1.30
## 4          Dry -1  1 1.40
## 5   Pure Water  1 -1 0.25
## 6   Pure Water -1 -1 0.28
## 7   Pure Water  1  1 0.34
## 8   Pure Water -1  1 0.39
## 9           EG  1 -1 0.43
## 10          EG -1 -1 0.38
## 11          EG  1  1 0.35
## 12          EG -1  1 0.40
## 13 EG +4% AgNP  1 -1 0.45
## 14 EG +4% AgNP -1 -1 0.40
## 15 EG +4% AgNP  1  1 0.42
## 16 EG +4% AgNP -1  1 0.56
## 17 EG +8% AgNP  1 -1 0.77
## 18 EG +8% AgNP -1 -1 0.47
## 19 EG +8% AgNP  1  1 0.66
## 20 EG +8% AgNP -1  1 0.75
## 21  EG+12%AgNP  1 -1 0.82
## 22  EG+12%AgNP -1 -1 0.87
## 23  EG+12%AgNP  1  1 0.70
## 24  EG+12%AgNP -1  1 0.80
summary(df)
##            WE     Ld      SS           TD        
##  Dry        :4   -1:12   -1:12   Min.   :0.2500  
##  EG         :4   1 :12   1 :12   1st Qu.:0.3975  
##  EG +4% AgNP:4                   Median :0.5150  
##  EG +8% AgNP:4                   Mean   :0.6787  
##  EG+12%AgNP :4                   3rd Qu.:0.8050  
##  Pure Water :4                   Max.   :1.6000
str(df)
## 'data.frame':    24 obs. of  4 variables:
##  $ WE: Factor w/ 6 levels "Dry","EG","EG +4% AgNP",..: 1 1 1 1 6 6 6 6 2 2 ...
##  $ Ld: Factor w/ 2 levels "-1","1": 2 1 2 1 2 1 2 1 2 1 ...
##  $ SS: Factor w/ 2 levels "-1","1": 1 1 2 2 1 1 2 2 1 1 ...
##  $ TD: num  1.5 1.6 1.3 1.4 0.25 0.28 0.34 0.39 0.43 0.38 ...
modelo<-lm(TD~WE+Ld+SS+WE*Ld+WE*SS+Ld*SS,data=df)

fit.aov<-aov(modelo)
summary(fit.aov)
##             Df Sum Sq Mean Sq F value   Pr(>F)    
## WE           5  3.495  0.6991 130.241 2.73e-05 ***
## Ld           1  0.004  0.0040   0.746   0.4272    
## SS           1  0.001  0.0009   0.175   0.6933    
## WE:Ld        5  0.026  0.0053   0.979   0.5091    
## WE:SS        5  0.070  0.0141   2.625   0.1566    
## Ld:SS        1  0.023  0.0234   4.367   0.0909 .  
## Residuals    5  0.027  0.0054                     
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Prueba de Normalidad

qqnorm(fit.aov$residuals)
qqline(fit.aov$residuals)

shapiro.test(modelo$residuals)
## 
##  Shapiro-Wilk normality test
## 
## data:  modelo$residuals
## W = 0.96222, p-value = 0.4847

Prueba de TukeyHSD

tk<-TukeyHSD(fit.aov)
tk
##   Tukey multiple comparisons of means
##     95% family-wise confidence level
## 
## Fit: aov(formula = modelo)
## 
## $WE
##                            diff         lwr         upr     p adj
## EG-Dry                  -1.0600 -1.28099495 -0.83900505 0.0000349
## EG +4% AgNP-Dry         -0.9925 -1.21349495 -0.77150505 0.0000464
## EG +8% AgNP-Dry         -0.7875 -1.00849495 -0.56650505 0.0001551
## EG+12%AgNP-Dry          -0.6525 -0.87349495 -0.43150505 0.0003994
## Pure Water-Dry          -1.1350 -1.35599495 -0.91400505 0.0000272
## EG +4% AgNP-EG           0.0675 -0.15349495  0.28849495 0.7752844
## EG +8% AgNP-EG           0.2725  0.05150505  0.49349495 0.0216714
## EG+12%AgNP-EG            0.4075  0.18650505  0.62849495 0.0036926
## Pure Water-EG           -0.0750 -0.29599495  0.14599495 0.7056141
## EG +8% AgNP-EG +4% AgNP  0.2050 -0.01599495  0.42599495 0.0661887
## EG+12%AgNP-EG +4% AgNP   0.3400  0.11900505  0.56099495 0.0083643
## Pure Water-EG +4% AgNP  -0.1425 -0.36349495  0.07849495 0.2143856
## EG+12%AgNP-EG +8% AgNP   0.1350 -0.08599495  0.35599495 0.2479159
## Pure Water-EG +8% AgNP  -0.3475 -0.56849495 -0.12650505 0.0075917
## Pure Water-EG+12%AgNP   -0.4825 -0.70349495 -0.26150505 0.0016837
## 
## $Ld
##             diff        lwr       upr    p adj
## 1--1 -0.02583333 -0.1027184 0.0510517 0.427226
## 
## $SS
##         diff         lwr        upr     p adj
## 1--1 -0.0125 -0.08938503 0.06438503 0.6933427
## 
## $`WE:Ld`
##                                 diff           lwr         upr     p adj
## EG:-1-Dry:-1                  -1.110 -1.4893900233 -0.73060998 0.0003888
## EG +4% AgNP:-1-Dry:-1         -1.020 -1.3993900233 -0.64060998 0.0005859
## EG +8% AgNP:-1-Dry:-1         -0.890 -1.2693900233 -0.51060998 0.0011057
## EG+12%AgNP:-1-Dry:-1          -0.665 -1.0443900233 -0.28560998 0.0043528
## Pure Water:-1-Dry:-1          -1.165 -1.5443900233 -0.78560998 0.0003026
## Dry:1-Dry:-1                  -0.100 -0.4793900233  0.27939002 0.9304241
## EG:1-Dry:-1                   -1.110 -1.4893900233 -0.73060998 0.0003888
## EG +4% AgNP:1-Dry:-1          -1.065 -1.4443900233 -0.68560998 0.0004769
## EG +8% AgNP:1-Dry:-1          -0.785 -1.1643900233 -0.40560998 0.0019980
## EG+12%AgNP:1-Dry:-1           -0.740 -1.1193900233 -0.36060998 0.0026406
## Pure Water:1-Dry:-1           -1.205 -1.5843900233 -0.82560998 0.0002516
## EG +4% AgNP:-1-EG:-1           0.090 -0.2893900233  0.46939002 0.9602927
## EG +8% AgNP:-1-EG:-1           0.220 -0.1593900233  0.59939002 0.3114256
## EG+12%AgNP:-1-EG:-1            0.445  0.0656099767  0.82439002 0.0259973
## Pure Water:-1-EG:-1           -0.055 -0.4343900233  0.32439002 0.9987101
## Dry:1-EG:-1                    1.010  0.6306099767  1.38939002 0.0006137
## EG:1-EG:-1                     0.000 -0.3793900233  0.37939002 1.0000000
## EG +4% AgNP:1-EG:-1            0.045 -0.3343900233  0.42439002 0.9997682
## EG +8% AgNP:1-EG:-1            0.325 -0.0543900233  0.70439002 0.0903312
## EG+12%AgNP:1-EG:-1             0.370 -0.0093900233  0.74939002 0.0551990
## Pure Water:1-EG:-1            -0.095 -0.4743900233  0.28439002 0.9466193
## EG +8% AgNP:-1-EG +4% AgNP:-1  0.130 -0.2493900233  0.50939002 0.7876046
## EG+12%AgNP:-1-EG +4% AgNP:-1   0.355 -0.0243900233  0.73439002 0.0648291
## Pure Water:-1-EG +4% AgNP:-1  -0.145 -0.5243900233  0.23439002 0.6983750
## Dry:1-EG +4% AgNP:-1           0.920  0.5406099767  1.29939002 0.0009473
## EG:1-EG +4% AgNP:-1           -0.090 -0.4693900233  0.28939002 0.9602927
## EG +4% AgNP:1-EG +4% AgNP:-1  -0.045 -0.4243900233  0.33439002 0.9997682
## EG +8% AgNP:1-EG +4% AgNP:-1   0.235 -0.1443900233  0.61439002 0.2603141
## EG+12%AgNP:1-EG +4% AgNP:-1    0.280 -0.0993900233  0.65939002 0.1520088
## Pure Water:1-EG +4% AgNP:-1   -0.185 -0.5643900233  0.19439002 0.4669102
## EG+12%AgNP:-1-EG +8% AgNP:-1   0.225 -0.1543900233  0.60439002 0.2934142
## Pure Water:-1-EG +8% AgNP:-1  -0.275 -0.6543900233  0.10439002 0.1612818
## Dry:1-EG +8% AgNP:-1           0.790  0.4106099767  1.16939002 0.0019389
## EG:1-EG +8% AgNP:-1           -0.220 -0.5993900233  0.15939002 0.3114256
## EG +4% AgNP:1-EG +8% AgNP:-1  -0.175 -0.5543900233  0.20439002 0.5206639
## EG +8% AgNP:1-EG +8% AgNP:-1   0.105 -0.2743900233  0.48439002 0.9117513
## EG+12%AgNP:1-EG +8% AgNP:-1    0.150 -0.2293900233  0.52939002 0.6679275
## Pure Water:1-EG +8% AgNP:-1   -0.315 -0.6943900233  0.06439002 0.1011831
## Pure Water:-1-EG+12%AgNP:-1   -0.500 -0.8793900233 -0.12060998 0.0157559
## Dry:1-EG+12%AgNP:-1            0.565  0.1856099767  0.94439002 0.0091636
## EG:1-EG+12%AgNP:-1            -0.445 -0.8243900233 -0.06560998 0.0259973
## EG +4% AgNP:1-EG+12%AgNP:-1   -0.400 -0.7793900233 -0.02060998 0.0404320
## EG +8% AgNP:1-EG+12%AgNP:-1   -0.120 -0.4993900233  0.25939002 0.8424311
## EG+12%AgNP:1-EG+12%AgNP:-1    -0.075 -0.4543900233  0.30439002 0.9870551
## Pure Water:1-EG+12%AgNP:-1    -0.540 -0.9193900233 -0.16060998 0.0112203
## Dry:1-Pure Water:-1            1.065  0.6856099767  1.44439002 0.0004769
## EG:1-Pure Water:-1             0.055 -0.3243900233  0.43439002 0.9987101
## EG +4% AgNP:1-Pure Water:-1    0.100 -0.2793900233  0.47939002 0.9304241
## EG +8% AgNP:1-Pure Water:-1    0.380  0.0006099767  0.75939002 0.0496821
## EG+12%AgNP:1-Pure Water:-1     0.425  0.0456099767  0.80439002 0.0315188
## Pure Water:1-Pure Water:-1    -0.040 -0.4193900233  0.33939002 0.9999207
## EG:1-Dry:1                    -1.010 -1.3893900233 -0.63060998 0.0006137
## EG +4% AgNP:1-Dry:1           -0.965 -1.3443900233 -0.58560998 0.0007589
## EG +8% AgNP:1-Dry:1           -0.685 -1.0643900233 -0.30560998 0.0037927
## EG+12%AgNP:1-Dry:1            -0.640 -1.0193900233 -0.26060998 0.0051961
## Pure Water:1-Dry:1            -1.105 -1.4843900233 -0.72560998 0.0003977
## EG +4% AgNP:1-EG:1             0.045 -0.3343900233  0.42439002 0.9997682
## EG +8% AgNP:1-EG:1             0.325 -0.0543900233  0.70439002 0.0903312
## EG+12%AgNP:1-EG:1              0.370 -0.0093900233  0.74939002 0.0551990
## Pure Water:1-EG:1             -0.095 -0.4743900233  0.28439002 0.9466193
## EG +8% AgNP:1-EG +4% AgNP:1    0.280 -0.0993900233  0.65939002 0.1520088
## EG+12%AgNP:1-EG +4% AgNP:1     0.325 -0.0543900233  0.70439002 0.0903312
## Pure Water:1-EG +4% AgNP:1    -0.140 -0.5193900233  0.23939002 0.7286527
## EG+12%AgNP:1-EG +8% AgNP:1     0.045 -0.3343900233  0.42439002 0.9997682
## Pure Water:1-EG +8% AgNP:1    -0.420 -0.7993900233 -0.04060998 0.0331038
## Pure Water:1-EG+12%AgNP:1     -0.465 -0.8443900233 -0.08560998 0.0215658
## 
## $`WE:SS`
##                                 diff          lwr          upr     p adj
## EG:-1-Dry:-1                  -1.145 -1.524390023 -0.765609977 0.0003316
## EG +4% AgNP:-1-Dry:-1         -1.125 -1.504390023 -0.745609977 0.0003632
## EG +8% AgNP:-1-Dry:-1         -0.930 -1.309390023 -0.550609977 0.0009009
## EG+12%AgNP:-1-Dry:-1          -0.705 -1.084390023 -0.325609977 0.0033156
## Pure Water:-1-Dry:-1          -1.285 -1.664390023 -0.905609977 0.0001732
## Dry:1-Dry:-1                  -0.200 -0.579390023  0.179390023 0.3938693
## EG:1-Dry:-1                   -1.175 -1.554390023 -0.795609977 0.0002890
## EG +4% AgNP:1-Dry:-1          -1.060 -1.439390023 -0.680609977 0.0004879
## EG +8% AgNP:1-Dry:-1          -0.845 -1.224390023 -0.465609977 0.0014107
## EG+12%AgNP:1-Dry:-1           -0.800 -1.179390023 -0.420609977 0.0018268
## Pure Water:1-Dry:-1           -1.185 -1.564390023 -0.805609977 0.0002760
## EG +4% AgNP:-1-EG:-1           0.020 -0.359390023  0.399390023 0.9999999
## EG +8% AgNP:-1-EG:-1           0.215 -0.164390023  0.594390023 0.3304539
## EG+12%AgNP:-1-EG:-1            0.440  0.060609977  0.819390023 0.0272648
## Pure Water:-1-EG:-1           -0.140 -0.519390023  0.239390023 0.7286527
## Dry:1-EG:-1                    0.945  0.565609977  1.324390023 0.0008364
## EG:1-EG:-1                    -0.030 -0.409390023  0.349390023 0.9999951
## EG +4% AgNP:1-EG:-1            0.085 -0.294390023  0.464390023 0.9714877
## EG +8% AgNP:1-EG:-1            0.300 -0.079390023  0.679390023 0.1202524
## EG+12%AgNP:1-EG:-1             0.345 -0.034390023  0.724390023 0.0723021
## Pure Water:1-EG:-1            -0.040 -0.419390023  0.339390023 0.9999207
## EG +8% AgNP:-1-EG +4% AgNP:-1  0.195 -0.184390023  0.574390023 0.4171562
## EG+12%AgNP:-1-EG +4% AgNP:-1   0.420  0.040609977  0.799390023 0.0331038
## Pure Water:-1-EG +4% AgNP:-1  -0.160 -0.539390023  0.219390023 0.6074680
## Dry:1-EG +4% AgNP:-1           0.925  0.545609977  1.304390023 0.0009238
## EG:1-EG +4% AgNP:-1           -0.050 -0.429390023  0.329390023 0.9994181
## EG +4% AgNP:1-EG +4% AgNP:-1   0.065 -0.314390023  0.444390023 0.9952653
## EG +8% AgNP:1-EG +4% AgNP:-1   0.280 -0.099390023  0.659390023 0.1520088
## EG+12%AgNP:1-EG +4% AgNP:-1    0.325 -0.054390023  0.704390023 0.0903312
## Pure Water:1-EG +4% AgNP:-1   -0.060 -0.439390023  0.319390023 0.9974199
## EG+12%AgNP:-1-EG +8% AgNP:-1   0.225 -0.154390023  0.604390023 0.2934142
## Pure Water:-1-EG +8% AgNP:-1  -0.355 -0.734390023  0.024390023 0.0648291
## Dry:1-EG +8% AgNP:-1           0.730  0.350609977  1.109390023 0.0028153
## EG:1-EG +8% AgNP:-1           -0.245 -0.624390023  0.134390023 0.2308673
## EG +4% AgNP:1-EG +8% AgNP:-1  -0.130 -0.509390023  0.249390023 0.7876046
## EG +8% AgNP:1-EG +8% AgNP:-1   0.085 -0.294390023  0.464390023 0.9714877
## EG+12%AgNP:1-EG +8% AgNP:-1    0.130 -0.249390023  0.509390023 0.7876046
## Pure Water:1-EG +8% AgNP:-1   -0.255 -0.634390023  0.124390023 0.2047593
## Pure Water:-1-EG+12%AgNP:-1   -0.580 -0.959390023 -0.200609977 0.0081427
## Dry:1-EG+12%AgNP:-1            0.505  0.125609977  0.884390023 0.0150848
## EG:1-EG+12%AgNP:-1            -0.470 -0.849390023 -0.090609977 0.0205993
## EG +4% AgNP:1-EG+12%AgNP:-1   -0.355 -0.734390023  0.024390023 0.0648291
## EG +8% AgNP:1-EG+12%AgNP:-1   -0.140 -0.519390023  0.239390023 0.7286527
## EG+12%AgNP:1-EG+12%AgNP:-1    -0.095 -0.474390023  0.284390023 0.9466193
## Pure Water:1-EG+12%AgNP:-1    -0.480 -0.859390023 -0.100609977 0.0188136
## Dry:1-Pure Water:-1            1.085  0.705609977  1.464390023 0.0004355
## EG:1-Pure Water:-1             0.110 -0.269390023  0.489390023 0.8907252
## EG +4% AgNP:1-Pure Water:-1    0.225 -0.154390023  0.604390023 0.2934142
## EG +8% AgNP:1-Pure Water:-1    0.440  0.060609977  0.819390023 0.0272648
## EG+12%AgNP:1-Pure Water:-1     0.485  0.105609977  0.864390023 0.0179887
## Pure Water:1-Pure Water:-1     0.100 -0.279390023  0.479390023 0.9304241
## EG:1-Dry:1                    -0.975 -1.354390023 -0.595609977 0.0007234
## EG +4% AgNP:1-Dry:1           -0.860 -1.239390023 -0.480609977 0.0012986
## EG +8% AgNP:1-Dry:1           -0.645 -1.024390023 -0.265609977 0.0050130
## EG+12%AgNP:1-Dry:1            -0.600 -0.979390023 -0.220609977 0.0069822
## Pure Water:1-Dry:1            -0.985 -1.364390023 -0.605609977 0.0006899
## EG +4% AgNP:1-EG:1             0.115 -0.264390023  0.494390023 0.8675372
## EG +8% AgNP:1-EG:1             0.330 -0.049390023  0.709390023 0.0853946
## EG+12%AgNP:1-EG:1              0.375 -0.004390023  0.754390023 0.0523579
## Pure Water:1-EG:1             -0.010 -0.389390023  0.369390023 1.0000000
## EG +8% AgNP:1-EG +4% AgNP:1    0.215 -0.164390023  0.594390023 0.3304539
## EG+12%AgNP:1-EG +4% AgNP:1     0.260 -0.119390023  0.639390023 0.1928567
## Pure Water:1-EG +4% AgNP:1    -0.125 -0.504390023  0.254390023 0.8156867
## EG+12%AgNP:1-EG +8% AgNP:1     0.045 -0.334390023  0.424390023 0.9997682
## Pure Water:1-EG +8% AgNP:1    -0.340 -0.719390023  0.039390023 0.0763985
## Pure Water:1-EG+12%AgNP:1     -0.385 -0.764390023 -0.005609977 0.0471610
## 
## $`Ld:SS`
##                   diff        lwr        upr     p adj
## 1:-1--1:-1  0.03666667 -0.1194113 0.19274460 0.8218151
## -1:1--1:-1  0.05000000 -0.1060779 0.20607794 0.6619619
## 1:1--1:-1  -0.03833333 -0.1944113 0.11774460 0.8031286
## -1:1-1:-1   0.01333333 -0.1427446 0.16941127 0.9878870
## 1:1-1:-1   -0.07500000 -0.2310779 0.08107794 0.3816117
## 1:1--1:1   -0.08833333 -0.2444113 0.06774460 0.2732108
plot(tk)

Prueba de Varianzas

library(car)
## Loading required package: carData
leveneTest(df$TD~df$WE)
## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value Pr(>F)
## group  5  1.2515 0.3269
##       18
leveneTest(df$TD~df$Ld)
## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value Pr(>F)
## group  1  0.0102 0.9205
##       22
leveneTest(df$TD~df$SS)
## Levene's Test for Homogeneity of Variance (center = median)
##       Df F value Pr(>F)
## group  1  0.1944 0.6636
##       22
library(tidyverse)
## -- Attaching packages --------------------------------------- tidyverse 1.3.1 --
## v ggplot2 3.3.5     v purrr   0.3.4
## v tibble  3.1.4     v dplyr   1.0.7
## v tidyr   1.1.4     v stringr 1.4.0
## v readr   2.0.2     v forcats 0.5.1
## -- Conflicts ------------------------------------------ tidyverse_conflicts() --
## x dplyr::filter() masks stats::filter()
## x dplyr::lag()    masks stats::lag()
## x dplyr::recode() masks car::recode()
## x purrr::some()   masks car::some()
library(ggpubr)
library(rstatix)
## 
## Attaching package: 'rstatix'
## The following object is masked from 'package:stats':
## 
##     filter

Cálculo de Medias por factor por nivel

df %>% group_by(WE) %>% get_summary_stats(TD,type="mean_sd")
## # A tibble: 6 x 5
##   WE          variable     n  mean    sd
##   <fct>       <chr>    <dbl> <dbl> <dbl>
## 1 Dry         TD           4 1.45  0.129
## 2 EG          TD           4 0.39  0.034
## 3 EG +4% AgNP TD           4 0.458 0.071
## 4 EG +8% AgNP TD           4 0.662 0.137
## 5 EG+12%AgNP  TD           4 0.797 0.071
## 6 Pure Water  TD           4 0.315 0.062
df
##             WE Ld SS   TD
## 1          Dry  1 -1 1.50
## 2          Dry -1 -1 1.60
## 3          Dry  1  1 1.30
## 4          Dry -1  1 1.40
## 5   Pure Water  1 -1 0.25
## 6   Pure Water -1 -1 0.28
## 7   Pure Water  1  1 0.34
## 8   Pure Water -1  1 0.39
## 9           EG  1 -1 0.43
## 10          EG -1 -1 0.38
## 11          EG  1  1 0.35
## 12          EG -1  1 0.40
## 13 EG +4% AgNP  1 -1 0.45
## 14 EG +4% AgNP -1 -1 0.40
## 15 EG +4% AgNP  1  1 0.42
## 16 EG +4% AgNP -1  1 0.56
## 17 EG +8% AgNP  1 -1 0.77
## 18 EG +8% AgNP -1 -1 0.47
## 19 EG +8% AgNP  1  1 0.66
## 20 EG +8% AgNP -1  1 0.75
## 21  EG+12%AgNP  1 -1 0.82
## 22  EG+12%AgNP -1 -1 0.87
## 23  EG+12%AgNP  1  1 0.70
## 24  EG+12%AgNP -1  1 0.80
df %>% group_by(Ld) %>% get_summary_stats(TD,type="mean_sd")
## # A tibble: 2 x 5
##   Ld    variable     n  mean    sd
##   <fct> <chr>    <dbl> <dbl> <dbl>
## 1 -1    TD          12 0.692 0.423
## 2 1     TD          12 0.666 0.39
df
##             WE Ld SS   TD
## 1          Dry  1 -1 1.50
## 2          Dry -1 -1 1.60
## 3          Dry  1  1 1.30
## 4          Dry -1  1 1.40
## 5   Pure Water  1 -1 0.25
## 6   Pure Water -1 -1 0.28
## 7   Pure Water  1  1 0.34
## 8   Pure Water -1  1 0.39
## 9           EG  1 -1 0.43
## 10          EG -1 -1 0.38
## 11          EG  1  1 0.35
## 12          EG -1  1 0.40
## 13 EG +4% AgNP  1 -1 0.45
## 14 EG +4% AgNP -1 -1 0.40
## 15 EG +4% AgNP  1  1 0.42
## 16 EG +4% AgNP -1  1 0.56
## 17 EG +8% AgNP  1 -1 0.77
## 18 EG +8% AgNP -1 -1 0.47
## 19 EG +8% AgNP  1  1 0.66
## 20 EG +8% AgNP -1  1 0.75
## 21  EG+12%AgNP  1 -1 0.82
## 22  EG+12%AgNP -1 -1 0.87
## 23  EG+12%AgNP  1  1 0.70
## 24  EG+12%AgNP -1  1 0.80
df %>% group_by(SS) %>% get_summary_stats(TD,type="mean_sd")
## # A tibble: 2 x 5
##   SS    variable     n  mean    sd
##   <fct> <chr>    <dbl> <dbl> <dbl>
## 1 -1    TD          12 0.685 0.453
## 2 1     TD          12 0.672 0.356
df
##             WE Ld SS   TD
## 1          Dry  1 -1 1.50
## 2          Dry -1 -1 1.60
## 3          Dry  1  1 1.30
## 4          Dry -1  1 1.40
## 5   Pure Water  1 -1 0.25
## 6   Pure Water -1 -1 0.28
## 7   Pure Water  1  1 0.34
## 8   Pure Water -1  1 0.39
## 9           EG  1 -1 0.43
## 10          EG -1 -1 0.38
## 11          EG  1  1 0.35
## 12          EG -1  1 0.40
## 13 EG +4% AgNP  1 -1 0.45
## 14 EG +4% AgNP -1 -1 0.40
## 15 EG +4% AgNP  1  1 0.42
## 16 EG +4% AgNP -1  1 0.56
## 17 EG +8% AgNP  1 -1 0.77
## 18 EG +8% AgNP -1 -1 0.47
## 19 EG +8% AgNP  1  1 0.66
## 20 EG +8% AgNP -1  1 0.75
## 21  EG+12%AgNP  1 -1 0.82
## 22  EG+12%AgNP -1 -1 0.87
## 23  EG+12%AgNP  1  1 0.70
## 24  EG+12%AgNP -1  1 0.80

Identificación de outliers

df %>% group_by(WE, Ld, SS) %>% identify_outliers(TD)
## [1] WE         Ld         SS         TD         is.outlier is.extreme
## <0 rows> (or 0-length row.names)

Efectos Principales

par(mfrow=c(2,2))
EfectoWE<-data.frame(df$WE,df$TD)
plot.design(EfectoWE,fun="mean",main="df$WE",ylab="df$TD")
EfectoLd<-data.frame(df$Ld,df$TD)
plot.design(EfectoLd,fun="mean",main="df$Ld",ylab="df$TD")
EfectoSS<-data.frame(df$SS,df$TD)
plot.design(EfectoSS,fun="mean",main="df$SS",ylab="df$TD")
par(mfrow=c(1,1))

Conclusión

Al aplicar en análisis de varianza ANOVA al modelo de regresión lineal, es posible determinar que el el ambiente de degaste (WE), la carga (Ld) y la velocidad de deslizamiento (SS) tienen un efecto significativo sobre la diferencia de temperatura (TD), con un valor de p<0.05 a un intervalo de confianza de 95%. Evaluando el valor de F para cada uno de los factores, los mismos indican que el factor que más influye es el ambiente de desgaste (WE). Las interacciones entre los factores, no presentan efectos significativos. La Prueba de Normalidad de Shapiro, muestra un comportamiento normal de los residuales, con un valor p>0.05 al 95% de confianza. Esto se puede comprobar con el gráfico de residuales. Con la prueba de Tukey de comparación entre las medias de los tratamientos al 95% de confianza y con los valores de p<0.05 en Anova, se puede rechazar la Ho nula sobre igualdad de las medias y se acepta la Ha, donde se dice que alguna de las medias es diferente. Las diferencias entre las medias se muestran en las gráficas de Tukey por factor y por interacción. La Prueba de Levene, con un valor de p>0.05 se acepta la homogeneidad de las varianzas de cada factor. No existe presencia de datos anómalos con 95% de confianza. Al analizar los datos, como los mismos no presentan valores atípicos o sesgos, se presentan los valores de las medianas por nivel y por factor, para comprender la tendencia central de los mismos. Las gráficas de efectos principales muestran los efectos que ejerce cada fáctor por nivel sobre la diferencia de temperatura (TD), se observa que el ambiente de desgaste (WE) contribuye de manera significativa sobre la diferencia de temperatura (TE).

Contraste con los Datos obtenidos por Autor

Al comparar los valores obtenidos para p, F la suma secuencial de cuadrados y grados de libertad de los factores, se obtuvo que, la significancia del factor ambiente de desgaste (WE). Las medias por factor por nivel, tambien muestran igualdad con los valores obtenidos, indicando que las medias con valores mas bajos podrían ser las mejores, si se desea reducir la diferencia de temperatura. Los graficos de efectos no son similares a los del paper en cuanto a forma, pero la información que se obtiene nos permite diferir entre los factores y coincidir que el ambiente de desgaste, es el que proporciona mayor efecto o intercción.