image 12.42 The effect of increased variation within groups. The One-Way ANOVA applet lets you see how the F statistic and the P-value depend on the variability of the data within groups, the sample size, and the differences among the means.

  1. (a) The black dots are at the means of the three groups. Move these up and down until you get a configuration that gives a P-value of about 0.01. What is the value of the F statistic?

  2. (b) Now increase the variation within the groups by sliding the standard deviation bar to the right. Describe what happens to the F statistic and the P-value.

  3. (c) Using between- and within-group variation, explain why the F statistic and P-value change in this way.