Using R for Introductory Statistics : John Verzani

Significance tests 231Figure 8.5 Densityplots to comparevariances and shapes of the 300 mgdosage (solid) and the 600 mg dosage(dashed)> t.test(x,y,var.equal=TRUE)Two Sample t-testdata: x and yt = −2.034, df = 18, p-value = 0.05696alternative hypothesis: true difference in means is notequal to 0...The p-value is 0.05696 for the two-sided test. This suggests a difference in the meanvalues, but it is not statistically significant at the 0.05 significance level. A look at thereported confidence interval for the difference of the means shows a wide range ofpossible value for µ x −µ y . We conclude that this data is consistent with the assumption ofno mean difference.How would this change if we did not assume equal variances?> t.test(x,y)Welch Two Sample t-testdata: x and yt = −2.034, df = 14.51, p-value = 0.06065alternative hypothesis: true difference in means is notequal to 095 percent confidence interval:−22.3557 0.5557sample estimates:mean of x mean of y289.4 300.3In this example, the same observed value of the test statistic (marked t) is found as in theequal-variance case, as (8.5) and (8.6) yield identical standard errors when the two