For Exercises 14.1 and 14.2, see pages 717–718; for 14.3 and 14.4, see page 720; for 14.5 and 14.6, see page 722; for 14.7, see page 724; for 14.8 and 14.9, see page 726; for 14.10 to 14.13, see pages 728–728; for 14.14 and 14.15, see page 731; for 14.16 to 14.19, see page 739; for 14.20 and 14.21, see page 740; for 14.22 and 14.23, see page 741; for 14.24 and 14.25, see page 742; for 14.26 and 14.27, see page 743; for 14.28 and 14.29, see page 744; and for 14.30 and 14.31, see page 748.

Question 14.13

14.13 The effect of between-group variation.

Go to the One-Way ANOVA applet. Set the standard deviation near the middle of its scale and drag the black dots so that the three group means are approximately equal. Note the value of the statistic and its -value. Now increase the variation among the group means: drag the mean of the second group up and the mean of the third group down. Describe the effect on the statistic and its -value. Explain why they change in this way.

14.13

More variation between the groups makes the statistic larger and the -value smaller. This happens because the more variation we have between groups suggests that the differences we are seeing are actually due to actual differences between the groups, not just chance, giving us more evidence of group differences.