Preface to First Edition - lib

ANALYSIS USING R 61R> cor.test(~ mortality + hardness, data = water)Pearson's product-moment correlationdata: mortality and hardnesst = -6.6555, df = 59, p-value = 1.033e-0895 percent confidence interval:-0.7783208 -0.4826129sample estimates:cor-0.6548486Figure 3.9R output of Pearsons’ correlation coefficient for the water data.R> data("pistonrings", package = "HSAUR2")R> chisq.test(pistonrings)Pearson's Chi-squared testdata: pistonringsX-squared = 11.7223, df = 6, p-value = 0.06846Figure 3.10R output of the chi-squared test for the pistonrings data.depicts the residuals for the piston ring data. The deviations from independenceare largest for C1 and C4 compressors in the centre and south leg.It is tempting to think that the size of these residuals may be judged bycomparison with standard normal percentage points (for example greater than1.96 or less than 1.96 for significance level α = 0.05). Unfortunately it can beshown that the variance of a standardised residual is always less than or equalto one, and in some cases considerably less than one, however, the residualsare asymptotically normal. A more satisfactory ‘residual’ for contingency tabledata is considered in Exercise 3.3.3.3.5 Rearrests of JuvenilesThe data in Table 3.5 are available as table object viaR> data("rearrests", package = "HSAUR2")R> rearrestsJuvenile courtAdult court Rearrest No rearrestRearrest 158 515No rearrest 290 1134and in rearrests the counts in the four cells refer to the matched pairs ofsubjects; for example, in 158 pairs both members of the pair were rearrested.© 2010 by Taylor and Francis Group, LLC