Using R for Introductory Statistics : John Verzani

Using R for introductory statistics 314Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1‘ ’ 1Residual standard error: 3.45 on 176 degrees of freedomMultiple R-Squared: 0.355, Adjusted R-squared: 0.329F-statistic: 13.8 on 7 and 176 DF, p-value: 3.27e-14The boxplots show many differences. Are they statistically significant? We assume fornow that the data is actually a collection of independent samples (rather than monthlyaverages of varying sizes) and proceed using the TukeyHSD() function.> TukeyHSD(res)Error in TukeyHSD(res) : no applicable method for“TukeyHSD"Oops, the TukeyHSD() function wants aov() to fit the linear model, notlm(). The commands are the same.> res.aov=aov(time ~ airline, data=out)> TukeyHSD(res.aov)Tukey multiple comparisons of means95% family-wise confidence levelFit: aov(formula=time ~ airline, data=out)$airlinediff lwr uprCO-AA 3.83478 0.7093 6.96025DL-AA −2.05217 −5.1776 1.07330…US-TW −2.17826 −5.3037 0.94721US-UA −3.79130 −6.9168 −0.66583> plot(TukeyHSD(res.aov), las=2)The output of TukeyHSD() is best viewed with the plot of the confidence intervals(Figure 11.5). This is created by calling plot() on the output. The argument las=2 turnsthe tick-mark labels perpendicular to the axes.Recall the duality between confidence intervals and tests of hypothesis discussed inChapter 8. For a given confidence level and sample, if the confidence interval excludes apopulation parameter, then the two-sided significance test of the same parameter will berejected. Applying this to the Newark airport example, we see several statisticallysignificant differences at the α=.05 level, the first few being CO-AA and NW-AA (justvisible on the graph shown).11.2.3 Problems11.10 The data set MLB At tend (UsingR) contains attendance data for major leaguebaseball between the years 1969 and 2000. Use 1m () to perform a t-test on attendancefor the two levels of league. Is the difference in mean attendance significant? Compareyour results to those provided by t. test ().