• Data are non-normal and cannot be transformed
• From a sample that is too small for thecentral limit theorem to lead to normalityof averages
• From a distribution not covered byparametric methods
• From an unknown distribution
• Nominal or ordinal

• A sign test is used to decide whether a binomial distributionhas the equalchance of success and failure.
• Probability of success -- It is theprobability of success of the newproduct.
• H0 : Two products are equally popular
• H1 : Customers preferring one productmore than the other product
• R Function : test(x=, n=)
• x -- Number of Success
• N -- Number of trials

• An equivalent test for two pairedt, z test
• H0 : Two means are equal.
• H1 : Difference of the mean isnot equal.
• R Function : test(x,y, paired =)
• x , y -- numeric variable
• paired -- logical value for thepaired test

• An equivalent test for two unpaired t,z test in R.
• H0 : Two means are equal.
• H1 : Difference of the mean isnot equal.
• R Function : test(x~y)
• x -- numeric
• y -- factor

• Chi - Squared is a non- parametric test
• H0 : Two Variables are independent.
• H1 : Two Variables are relative.
• R Function :test(tab)
• tab -- contingency table betweentwo variables

• An equivalent test for variance test
• H0 : Two variance are equal.
• H1 : Two variance are not equal.
• R Package : car
• R Function : leveneTest(x~z)
• x -- numeric
• z - factor

• An equivalent test for one way ANOVA
• H0: Means of different groups are same
• H1: Atleast one sample mean is notequal to others
• R Function : test(x~y)
• x -- factor
• y -- numeric

#Non – Parametric Hypothesis testing
#Input

x<-c(1090,500,9,16,29,37,41,59,735,923)
y<-c(800,276,65,9,466,37,955,749,3787,577)
z<-c(0,1,1,0,0,0,1,1,0,0)

#Checking Normality
#Anderson Darling test
library(“nortest”)
ad.test(x)
ad.test(y)

#Shapiro test
shapiro.test(x)
shapiro.test(y)

#One Sample sign test
binom.test(x=10,n=18)

#Wilcoxon signed rank test
#Equivalent test for two dependent samples t, z test
wilcox.test(x,y,paired = T)

#Wilcoxon rank sum test or Mann- Whitney test
#Equivalent test for two independent samples t, z test
wilcox.test(y,x)

#If x is numeric and z is binary factor
wilcox.test(x~z)

#Chi- Squared test
#Contingency table
tab<-table(x,y)
print(tab)
chisq.test(tab)

#Levene’s test
#Equivalent test for f test
library(“car”)
z<-as.factor(z)
leveneTest(x~z)

#Kruskal- Wallis test
#Equivalent test for one way ANOVA
kruskal.test(mtcars$am~mtcars$mpg)