Using R for Introductory Statistics : John Verzani

Using R for introductory statistics 256with n=25 for normal, uniform, t, andexponential datacan be constructed with test statistic D. Large values of D support the alternativehypothesis.In R, this test is implemented in the function ks.test(). Its usage follows this pattern:ks.test(x, y=“name”, …)ZThe variable x stores the data. The argument y= is used to set the family name of thedistribution in H 0 . It has a character value of “name” containing the “p” function thatreturns the c.d.f. for the family (e.g., “pnorm” or “pt”). The…argument allows thespecification of the assumed parameter values. These depend on the family name and arespecified as named arguments, as in mean= 1, sd= 1. The parameter values should not beestimated from the data, as this affects the sampling distribution of D.If we have two i.i.d. independent samples X 1 , …, X n and Y 1 , …, Y m , from twocontinuous distributions F X and F Y , then a significance test ofH 0 :F X =F Y , H A :F X ≠F Ycan be constructed with a similar test statistic:In this case, the ks.test() can be used asks.test(x,y)where x and y store the data.We illustrate with some simulated data.> x = rnorm(100,mean=5, sd=2)> ks.test(x,"pnorm",mean=0,sd=2) # "wrong" parametersOne-sample Kolmogorov-Smirnov testdata: xD = 0.7578, p-value = < 2.2e-16alternative hypothesis: two.sided> ks.test(x,"pnorm",mean=5,sd=2) # correct populationparameters...D = 0.1102, p-value = 0.1759...> x = runif(100, min=0, max=5)> ks.test(x,"punif",min=0,max=6) # "wrong" parameters...D = 0.1669, p-value = 0.007588...> ks.test(x,"punif",min=0,max=5) # correct populationparameters...