> data(trees, package="datasets")

> summary (trees)
     Girth           Height       Volume     
 Min.   : 8.30   Min.   :63   Min.   :10.20  
 1st Qu.:11.05   1st Qu.:72   1st Qu.:19.40  
 Median :12.90   Median :76   Median :24.20  
 Mean   :13.25   Mean   :76   Mean   :30.17  
 3rd Qu.:15.25   3rd Qu.:80   3rd Qu.:37.30  
 Max.   :20.60   Max.   :87   Max.   :77.00  

> attach (trees)

> cor.test (Volume, Height, method = "spearman")

	Spearman's rank correlation rho

data:  Volume and Height
S = 2089.6, p-value = 0.0006484
alternative hypothesis: true rho is not equal to 0
sample estimates:
      rho 
0.5787101 


> cor.test (Volume, Height, method = "kendall")

	Kendall's rank correlation tau

data:  Volume and Height
z = 3.4971, p-value = 0.0004704
alternative hypothesis: true tau is not equal to 0
sample estimates:
      tau 
0.4496306 


> data(ToothGrowth, package="datasets")


> wilcox.test(len ~ supp, alternative="two.sided", data=ToothGrowth)

	Wilcoxon rank sum test with continuity correction

data:  len by supp
W = 575.5, p-value = 0.06449
alternative hypothesis: true location shift is not equal to 0


> data(Burt, package="carData")

> summary (Burt)
     IQbio           IQfoster        class   
 Min.   : 63.00   Min.   : 68.0   high  : 7  
 1st Qu.: 84.50   1st Qu.: 83.5   low   :14  
 Median : 94.00   Median : 94.0   medium: 6  
 Mean   : 95.11   Mean   : 95.3              
 3rd Qu.:107.50   3rd Qu.:104.5              
 Max.   :132.00   Max.   :131.0              


> attach (Burt)

> wilcox.test (IQbio, IQfoster, paired=TRUE)  

	Wilcoxon signed rank test with continuity correction

data:  IQbio and IQfoster
V = 152, p-value = 0.7877
alternative hypothesis: true location shift is not equal to 0


> summary (ToothGrowth)
      len        supp         dose      
 Min.   : 4.20   OJ:30   Min.   :0.500  
 1st Qu.:13.07   VC:30   1st Qu.:0.500  
 Median :19.25           Median :1.000  
 Mean   :18.81           Mean   :1.167  
 3rd Qu.:25.27           3rd Qu.:2.000  
 Max.   :33.90           Max.   :2.000  

> ToothGrowth <- within(ToothGrowth, {
+   dose <- as.factor(dose)
+ })

> kruskal.test (len ~ dose, ToothGrowth)

	Kruskal-Wallis rank sum test

data:  len by dose
Kruskal-Wallis chi-squared = 40.669, df = 2, p-value = 0.000000001475

> library(dunn.test, pos=18)
> attach (ToothGrowth)

> dunn.test (len, dose)
  Kruskal-Wallis rank sum test

data: len and dose
Kruskal-Wallis chi-squared = 40.6689, df = 2, p-value = 0


                           Comparison of len by dose                           
                                (No adjustment)                                
Col Mean-|
Row Mean |        0.5          1
---------+----------------------
       1 |  -3.554911
         |    0.0002*
         |
       2 |  -6.362611  -2.807700
         |    0.0000*    0.0025*

alpha = 0.05
Reject Ho if p <= alpha/2

> ####Friedman test

> summary (CO2)
     Plant             Type         Treatment       conc          uptake     
 Qn1    : 7   Quebec     :42   nonchilled:42   Min.   :  95   Min.   : 7.70  
 Qn2    : 7   Mississippi:42   chilled   :42   1st Qu.: 175   1st Qu.:17.90  
 Qn3    : 7                                    Median : 350   Median :28.30  
 Qc1    : 7                                    Mean   : 435   Mean   :27.21  
 Qc3    : 7                                    3rd Qu.: 675   3rd Qu.:37.12  
 Qc2    : 7                                    Max.   :1000   Max.   :45.50  
 (Other):42                                                                  
                                                             



> CO2 <- within(CO2, {conc <- as.factor(conc)})

> summary (CO2)
     Plant             Type         Treatment    conc        uptake     
 Qn1    : 7   Quebec     :42   nonchilled:42   95  :12   Min.   : 7.70  
 Qn2    : 7   Mississippi:42   chilled   :42   175 :12   1st Qu.:17.90  
 Qn3    : 7                                    250 :12   Median :28.30  
 Qc1    : 7                                    350 :12   Mean   :27.21  
 Qc3    : 7                                    500 :12   3rd Qu.:37.12  
 Qc2    : 7                                    675 :12   Max.   :45.50  
 (Other):42                                    1000:12                  

> CO2 <- within(CO2, {conc <- as.factor(conc)})

> attach (CO2)



> friedman.test (uptake ~ conc|Plant)

	Friedman rank sum test

data:  uptake and conc and Plant
Friedman chi-squared = 59.677, df = 6, p-value = 5.236e-11

#######################SCRIPT####################################


############## RANK CORRELATIONS
data(trees, package="datasets")
summary (trees)
attach (trees)
cor.test (Volume, Height, method = "spearman")
cor.test (Volume, Height, method = "kendall")

#################TWO SAMPLES COMPARISON
data(ToothGrowth, package="datasets")

wilcox.test(len ~ supp, alternative="two.sided", data=ToothGrowth)
data(Burt, package="carData")
summary (Burt)
attach (Burt)
wilcox.test (IQbio, IQfoster, paired=TRUE)

## nonparametric ANOVA
summary (ToothGrowth)

ToothGrowth <- within(ToothGrowth, {
  dose <- as.factor(dose)
})
kruskal.test (len ~ dose, ToothGrowth) 
library(dunn.test, pos=18)
attach (ToothGrowth)
dunn.test (len, dose)

####Friedman test
summary (CO2)
CO2 <- within(CO2, {conc <- as.factor(conc)})
attach (CO2)
friedman.test (uptake ~ conc|Plant)