Question 14.77

14.77 The effect of an outlier.

Refer to the weight-loss study described in Exercise 14.59 (page 754).

loss

  1. Suppose that when entering the data into the computer, you accidentlly entered the first observation as 53 pounds rather than 5.3 pounds. Run the ANOVA with this incorrect observation, and record the statistic, the estimate of the within-group variance , and the estimated treatment means.
  2. Alternatively, suppose that when entering the data into the computer, you accidentally entered Observation #101 as 79.4 pounds rather than 19.4 pounds. Run the ANOVA with this incorrect observation, and record the same information requested in part (a).
  3. Compare the results of each of these two cases with the results obtained with the correct data set. What happens to the within-group variance ? Do the estimated treatment means move closer or further apart? What effect do these changes have on the test?
  4. What do these two cases illustrate about the effects of an outlier in an ANOVA? Write a one-paragraph summary.
  5. Explain why a table of means and standard deviations for each of the three treatments would help you to detect an incorrect observation.

14.77

(a) The results are nearly identical as before: .

Loss
Level of
Group		 Mean Std Dev
Ctrl 35 0.3543 14.6621
Grp 34 −10.7853 11.1392
Indiv 35 −3.7086 9.0784

(b) The results are not as significant: .

Loss
Level of
Group		 Mean Std Dev
Ctrl 35 −1.0086 11.5007
Grp 34 −9.0206 18.4317
Indiv 35 −3.7086 9.0784

(c) With the first outlier, the means got farther apart, suggesting more significance, but the estimated variance went from 112.81 to 140.65, suggesting a worse fit, which resulted in a very similar and -value. With the second outlier, the means got closer together, suggesting less significance, and the estimated variance went from 112.81 to 183.27, also suggesting a much worse fit, which resulted in a -value much less significant than originally and almost not significant. In both cases, the estimate variance got much worse, so generally outliers should make it harder to so see significance. But as shown in the first example, if the outlier pulls the means farther apart, this may not be true. (d) We can see the incorrect observation because the standard deviation for the group with the outlier becomes much larger than the standard deviations for the other groups.