setwd("C:/Users/nazan/Desktop/ANLY510/Weekly Lab datafiles-20180511")
library(readxl)
WeeklyLab4Data <- read_excel("WeeklyLab4Data.xlsx")
View(WeeklyLab4Data)
data=WeeklyLab4Data
data
## # A tibble: 54 x 5
## RunningTemperature StorageTemperature Formulation Machine LifeinHours
## <chr> <chr> <chr> <chr> <dbl>
## 1 high high F1 M1 25
## 2 high high F1 M3 16
## 3 high high F1 M2 20
## 4 low high F1 M2 27
## 5 low high F1 M3 24
## 6 low high F1 M1 26
## 7 med high F1 M2 26
## 8 med high F1 M3 26
## 9 med high F1 M1 20
## 10 high low F1 M2 24
## # ... with 44 more rows
plot(density(data$LifeinHours)) ###Take a look at data and see how it is distributed
It looks data is distributed normally but lets check it by running agostino test
library(moments)
agostino.test(data$LifeinHours) ###P-value is larger than alpha==> fail to reject null hypothesis.(no sign of skew)
##
## D'Agostino skewness test
##
## data: data$LifeinHours
## skew = 0.49196, z = 1.57380, p-value = 0.1155
## alternative hypothesis: data have a skewness
Take a look at variables to see if they are defined correctly(To check equality of variances across factors we need them as factor)
library(dplyr)
##
## Attaching package: 'dplyr'
## The following objects are masked from 'package:stats':
##
## filter, lag
## The following objects are masked from 'package:base':
##
## intersect, setdiff, setequal, union
glimpse(data)
## Observations: 54
## Variables: 5
## $ RunningTemperature <chr> "high", "high", "high", "low", "low", "low"...
## $ StorageTemperature <chr> "high", "high", "high", "high", "high", "hi...
## $ Formulation <chr> "F1", "F1", "F1", "F1", "F1", "F1", "F1", "...
## $ Machine <chr> "M1", "M3", "M2", "M2", "M3", "M1", "M2", "...
## $ LifeinHours <dbl> 25, 16, 20, 27, 24, 26, 26, 26, 20, 24, 24,...
Checking variances(Chaeck if they are equal across factors(The test has the null hypothesis that the variances are equal and the alterntive hypothesis that they are not equal,P-values are larger than alpha==>Fail to reject null hypothesis==>Variances are equal))
bartlett.test(data$LifeinHours~data$RunningTemperature)
##
## Bartlett test of homogeneity of variances
##
## data: data$LifeinHours by data$RunningTemperature
## Bartlett's K-squared = 5.3959, df = 2, p-value = 0.06734
bartlett.test(data$LifeinHours~data$StorageTemperature)
##
## Bartlett test of homogeneity of variances
##
## data: data$LifeinHours by data$StorageTemperature
## Bartlett's K-squared = 3.9424, df = 2, p-value = 0.1393
bartlett.test(data$LifeinHours~data$Formulation)
##
## Bartlett test of homogeneity of variances
##
## data: data$LifeinHours by data$Formulation
## Bartlett's K-squared = 0.7178, df = 1, p-value = 0.3969
bartlett.test(data$LifeinHours~data$Machine)
##
## Bartlett test of homogeneity of variances
##
## data: data$LifeinHours by data$Machine
## Bartlett's K-squared = 0.57663, df = 2, p-value = 0.7495
Looks everythings are what we want==>Run ANOVA(including machines as a blocking factor)
model=aov(LifeinHours~Machine+Formulation*StorageTemperature*RunningTemperature,data=data)
model
## Call:
## aov(formula = LifeinHours ~ Machine + Formulation * StorageTemperature *
## RunningTemperature, data = data)
##
## Terms:
## Machine Formulation StorageTemperature RunningTemperature
## Sum of Squares 64.0370 362.9630 585.4815 770.2593
## Deg. of Freedom 2 1 2 2
## Formulation:StorageTemperature
## Sum of Squares 4.5926
## Deg. of Freedom 2
## Formulation:RunningTemperature
## Sum of Squares 7.1481
## Deg. of Freedom 2
## StorageTemperature:RunningTemperature
## Sum of Squares 201.6296
## Deg. of Freedom 4
## Formulation:StorageTemperature:RunningTemperature
## Sum of Squares 0.9630
## Deg. of Freedom 4
## Residuals
## Sum of Squares 474.6296
## Deg. of Freedom 34
##
## Residual standard error: 3.736268
## Estimated effects may be unbalanced
summary(model) ###It seems all main effects are significant and also interaction of StorageTemperature:RunningTemperature(For the formulas main effect we get the means)
## Df Sum Sq Mean Sq
## Machine 2 64.0 32.0
## Formulation 1 363.0 363.0
## StorageTemperature 2 585.5 292.7
## RunningTemperature 2 770.3 385.1
## Formulation:StorageTemperature 2 4.6 2.3
## Formulation:RunningTemperature 2 7.1 3.6
## StorageTemperature:RunningTemperature 4 201.6 50.4
## Formulation:StorageTemperature:RunningTemperature 4 1.0 0.2
## Residuals 34 474.6 14.0
## F value Pr(>F)
## Machine 2.294 0.1163
## Formulation 26.001 1.28e-05 ***
## StorageTemperature 20.970 1.17e-06 ***
## RunningTemperature 27.589 7.60e-08 ***
## Formulation:StorageTemperature 0.164 0.8490
## Formulation:RunningTemperature 0.256 0.7756
## StorageTemperature:RunningTemperature 3.611 0.0148 *
## Formulation:StorageTemperature:RunningTemperature 0.017 0.9994
## Residuals
## ---
## Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
tapply(data$LifeinHours, data$Formulation, mean) ###F2 is largers that means lasts longer.
## F1 F2
## 27.48148 32.66667
look at the effects of running and storage temperature.(Doing Tukey test to look at the temperature effects)
TukeyHSD(model, c("StorageTemperature", "RunningTemperature")) ###Low temperature leads to long life hour in both cases.
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = LifeinHours ~ Machine + Formulation * StorageTemperature * RunningTemperature, data = data)
##
## $StorageTemperature
## diff lwr upr p adj
## low-high 8.000000 4.948172 11.05182766 0.0000007
## med-high 4.888889 1.837061 7.94071654 0.0011388
## med-low -3.111111 -6.162939 -0.05928346 0.0449486
##
## $RunningTemperature
## diff lwr upr p adj
## low-high 9.111111 6.059283 12.162939 0.0000001
## med-high 5.944444 2.892617 8.996272 0.0000981
## med-low -3.166667 -6.218494 -0.114839 0.0406306
To see the interactions
library(lsmeans)
## The 'lsmeans' package is being deprecated.
## Users are encouraged to switch to 'emmeans'.
## See help('transition') for more information, including how
## to convert 'lsmeans' objects and scripts to work with 'emmeans'.
lsmip(model, StorageTemperature~RunningTemperature) ###NOTE: Results may be misleading due to involvement in interactions(Levels of running temerature and storage temperature are not in order)
## NOTE: Results may be misleading due to involvement in interactions
Defining order for levels of the factors
data$RunningTemperature=factor(data$RunningTemperature, levels = c("high","med","low"))
data$RunningTemperature
## [1] high high high low low low med med med high high high low low
## [15] low med med med high high high low low low med med med high
## [29] high high low low low med med med high high high low low low
## [43] med med med high high high low low low med med med
## Levels: high med low
data$StorageTemperature=factor(data$StorageTemperature, levels = c("high","med","low"))
data$StorageTemperature
## [1] high high high high high high high high high low low low low low
## [15] low low low low med med med med med med med med med high
## [29] high high high high high high high high low low low low low low
## [43] low low low med med med med med med med med med
## Levels: high med low
lsmip(model,StorageTemperature~RunningTemperature) ###There is two interactions.One from High to med and secondonr from med to low(running temperature for med and low storage temperatures)
## NOTE: Results may be misleading due to involvement in interactions
TukeyHSD(model, "StorageTemperature:RunningTemperature") ###Confirmation of Low Temperature is better
## Tukey multiple comparisons of means
## 95% family-wise confidence level
##
## Fit: aov(formula = LifeinHours ~ Machine + Formulation * StorageTemperature * RunningTemperature, data = data)
##
## $`StorageTemperature:RunningTemperature`
## diff lwr upr p adj
## low:high-high:high 5.0000000 -2.1378038 12.1378038 0.3600327
## med:high-high:high 2.6666667 -4.4711372 9.8044705 0.9422793
## high:low-high:high 5.8333333 -1.3044705 12.9711372 0.1841865
## low:low-high:high 18.8333333 11.6955295 25.9711372 0.0000000
## med:low-high:high 10.3333333 3.1955295 17.4711372 0.0009592
## high:med-high:high 4.0000000 -3.1378038 11.1378038 0.6475577
## low:med-high:high 10.0000000 2.8621962 17.1378038 0.0014913
## med:med-high:high 11.5000000 4.3621962 18.6378038 0.0001998
## med:high-low:high -2.3333333 -9.4711372 4.8044705 0.9730950
## high:low-low:high 0.8333333 -6.3044705 7.9711372 0.9999817
## low:low-low:high 13.8333333 6.6955295 20.9711372 0.0000083
## med:low-low:high 5.3333333 -1.8044705 12.4711372 0.2803362
## high:med-low:high -1.0000000 -8.1378038 6.1378038 0.9999261
## low:med-low:high 5.0000000 -2.1378038 12.1378038 0.3600327
## med:med-low:high 6.5000000 -0.6378038 13.6378038 0.0977980
## high:low-med:high 3.1666667 -3.9711372 10.3044705 0.8621541
## low:low-med:high 16.1666667 9.0288628 23.3044705 0.0000004
## med:low-med:high 7.6666667 0.5288628 14.8044705 0.0275519
## high:med-med:high 1.3333333 -5.8044705 8.4711372 0.9993722
## low:med-med:high 7.3333333 0.1955295 14.4711372 0.0402654
## med:med-med:high 8.8333333 1.6955295 15.9711372 0.0067147
## low:low-high:low 13.0000000 5.8621962 20.1378038 0.0000259
## med:low-high:low 4.5000000 -2.6378038 11.6378038 0.4986512
## high:med-high:low -1.8333333 -8.9711372 5.3044705 0.9941701
## low:med-high:low 4.1666667 -2.9711372 11.3044705 0.5979620
## med:med-high:low 5.6666667 -1.4711372 12.8044705 0.2130636
## med:low-low:low -8.5000000 -15.6378038 -1.3621962 0.0101667
## high:med-low:low -14.8333333 -21.9711372 -7.6955295 0.0000021
## low:med-low:low -8.8333333 -15.9711372 -1.6955295 0.0067147
## med:med-low:low -7.3333333 -14.4711372 -0.1955295 0.0402654
## high:med-med:low -6.3333333 -13.4711372 0.8044705 0.1153824
## low:med-med:low -0.3333333 -7.4711372 6.8044705 1.0000000
## med:med-med:low 1.1666667 -5.9711372 8.3044705 0.9997649
## low:med-high:med 6.0000000 -1.1378038 13.1378038 0.1583827
## med:med-high:med 7.5000000 0.3621962 14.6378038 0.0333593
## med:med-low:med 1.5000000 -5.6378038 8.6378038 0.9985376
pairwise.t.test(data$LifeinHours,data$StorageTemperature:data$RunningTemperature, p.adj ="none" )
##
## Pairwise comparisons using t tests with pooled SD
##
## data: data$LifeinHours and data$StorageTemperature:data$RunningTemperature
##
## high:high high:med high:low med:high med:med med:low low:high
## high:med 0.13129 - - - - - -
## high:low 0.02997 0.48478 - - - - -
## med:high 0.31100 0.61092 0.23003 - - - -
## med:med 6.2e-05 0.00604 0.03473 0.00145 - - -
## med:low 0.00026 0.01898 0.09064 0.00508 0.65609 - -
## low:high 0.06105 0.70260 0.75029 0.37471 0.01623 0.04629 -
## low:med 0.00038 0.02580 0.11636 0.00716 0.56723 0.89865 0.06105
## low:low 4.5e-09 8.7e-07 9.3e-06 1.5e-07 0.00716 0.00209 3.2e-06
## low:med
## high:med -
## high:low -
## med:high -
## med:med -
## med:low -
## low:high -
## low:med -
## low:low 0.00145
##
## P value adjustment method: none
We can see how much difference is between pvalues by comparing pvalues in Tukey test for model wich we had correction and Pairwise.t,test,without correction.
lower storage and running temperatures do lead to longer running life in general