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 14.11

14.11 Use Table E.

An ANOVA is run to compare four groups. There are eight subjects in each group.

  1. Give the degrees of freedom for the ANOVA statistic.
  2. How large would this statistic need to be to have a -value less than 0.05?
  3. Suppose that we are still interested in comparing the four groups, but we obtain data on 16 subjects per group. How large would the statistic need to be to have a -value less than 0.05?
  4. Explain why the answer to part (c) is smaller than what you found for part (b).

14.11

(a) . (b) Bigger than 2.95. (c) Bigger than 2.76. (d) More observations per group gives a larger DFE, which makes the critical value smaller. Conceptually, more data give more information showing the group differences and giving more evidence the differences we are observing are real and not due to chance. Thus, a larger DFE will give a smaller critical value and smaller -value.