Using R for Introductory Statistics : John Verzani

Using R for introductory statistics 258D = 0.2125, p-value = 0.001456alternative hypothesis: two.sided9.3.2 The Shapiro-Wilk test for normalityThe Kolmogorov-Smirnov test for a univariate data set works when the distribution in thenull hypothesis is fully specified prior to our looking at the data. In particular, anyassumptions on the values for the parameters should not depend on the data, as this canchange the sampling distribution. Figure 9.5 shows the sampling distribution of theKolmogorov-Smirnov statistic for Normal(0, 1) data and the sampling distribution of theKolmogorov-Smirnov statistic for the same data when the sample values of and s areused for the parameters of the normal distribution (instead of 0 and 1). The figure wasgenerated with this simulation:> res.1 res.2 = c()> for(i in 1:500) {+ x = rnorm(25)+ res.1[i] = ks.test(x,pnorm)$statistic+ res.2[i] = ks.test(x,pnorm,mean(x),sd(x))$statistic+}> plot(density(res.1),main="K-S sampling distribution”)> lines(density(res.2),lty=2)(To retrieve just the value of the test statistic from the output of ks.test() we takeadvantage of the fact that its return value is a list with one component named statisticcontaining the desired value. This is why the syntax ks. test (…) $statistic is used.)Figure 9.5 The sampling distributionfor the Kolmogorov-Smirnovstatistic when the parameters areestimated (dashed line) and whennot